design calculations - port of stockton
TRANSCRIPT
June 2020
for Port of Stockton
Fyffe Grade Separation
HDR Project No. 10133899
Fyffe Bridge
TABLE OF CONTENTS:
1 Introduction
1.1 General Information
1.2 General Notes, Plan and Elevation
2 Geometry
2.1 Superstructure Geometry
2.2 Substructure Geometry
2.3 Vertical Clearance
3 Superstructure Design
3.1 Girder Design
3.1.1 Girder Design Calculation
3.1.2 Girder Camber and Deflection
3.2 Deck Design
3.2.1 Stay-in-Place (SIP) Panel with Cast-in-Place (CIP) Deck Design
3.2.2 Deck Overhang Design
4 Substructure Design
4.1 Abutment Pile Loading and Lateral Analysis
4.2 Abutment Footing Design
4.3 Abutment Stem Wall Design
4.4 Abutment Backwall Design
4.5 Abutment Joint Width
4.6 Abutment Seat Width Design
4.7 Wingwall Design
4.8 Bearing Design
5 MSE Wall Design
6 Appendix
6.1 Appendix A Csi Models and Outputs
6.2 Appendix B Lpile Analysis
6.2.1 North Abutment Piles
6.2.2 South Abutment Piles
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
1 Introduction
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
1.1 General Information
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
Project: Port of Stockton Fyffe Grade Separation Computed: CL Date: 3/23/20
Subject: Design Calculations - Materials Checked: JC Date: 4/2/20
Task: Page: of:
Job #: NO:
MATERIALS
Precast Bridge Girder
f'c
wc
(for E) E
Poisson
Ratio
Shear
Modulus
Thermal
Expansion
wc
(weight)
Expected
f'ce
Expected
Ece
ksi kcf ksi ksi 1/ °F kcf ksi ksi
8.0 0.145 5,154 0.20 2,147 6.0E-06 0.155 10.4 5,876
Precast Deck
f'c
wc
(for E) E
Poisson
Ratio
Shear
Modulus
Thermal
Expansion
wc
(weight)
Expected
f'ce
Expected
Ece
ksi kcf ksi ksi 1/ °F kcf ksi ksi
8.0 0.145 5,154 0.20 2,147 6.0E-06 0.155 10.4 5,876
Cast-in-Place Deck
f'c
wc
(for E) E
Poisson
Ratio
Shear
Modulus
Thermal
Expansion
wc
(weight)
Expected
f'ce
Expected
Ece
ksi kcf ksi ksi 1/ °F kcf ksi ksi
5.0 0.145 4,074 0.20 1,698 6.0E-06 0.155 6.5 4,645
Approach Slab
f'c
wc
(for E) E
Poisson
Ratio
Shear
Modulus
Thermal
Expansion
wc
(weight)
Expected
f'ce
Expected
Ece
ksi kcf ksi ksi 1/ °F kcf ksi ksi
4.0 0.145 3,644 0.20 1,518 6.0E-06 0.155 5.2 4,155
Abutment Wall / Wingwal
f'c
wc
(for E) E
Poisson
Ratio
Shear
Modulus
Thermal
Expansion
wc
(weight)
Expected
f'ce
Expected
Ece
ksi kcf ksi ksi 1/ °F kcf ksi ksi
4.0 0.145 3,644 0.20 1,518 6.0E-06 0.155 5.2 4,155
Footing
f'c
wc
(for E) E
Poisson
Ratio
Shear
Modulus
Thermal
Expansion
wc
(weight)
Expected
f'ce
Expected
Ece
ksi kcf ksi ksi 1/ °F kcf ksi ksi
4.0 0.145 3,644 0.20 1,518 6.0E-06 0.155 5.2 4,155
Structural Concrete
Project: Port of Stockton Fyffe Grade Separation Computed: CL Date: 3/23/20
Subject: Design Calculations - Materials Checked: JC Date: 4/2/20
Task: Page: of:
Job #: NO:
Precast Pile
f'c
wc
(for E) E
Poisson
Ratio
Shear
Modulus
Thermal
Expansion
wc
(weight)
Expected
f'ce
Expected
Ece
ksi kcf ksi ksi 1/ °F kcf ksi ksi
5.0 0.145 4,074 0.20 1,698 6.0E-06 0.155 6.5 4,645
ASTM A706 Grade 60
Modulus of Elasticity, Es 29,000 ksi 29,000 ksi
Yield Strength, fy 60.0 ksi 80.0 ksi
Tensile Strength, fu 80.0 ksi 100.0 ksi
Expected Reinf Strength, fye 68.0 ksi 85.0 ksi
Expected Tensile Strength, fue 95.0 ksi 112.0 ksi
εy εye εsu εRsu εsh
#3 0.0021 0.0023 0.1200 0.0900 0.0150
#4 0.0021 0.0023 0.0000 0.0900 0.0150
#5 0.0021 0.0023 0.1200 0.0900 0.0150
#6 0.0021 0.0023 0.1200 0.0900 0.0150
#7 0.0021 0.0023 0.1200 0.0900 0.0150
#8 0.0021 0.0023 0.1200 0.0900 0.0150
#9 0.0021 0.0023 0.1200 0.0900 0.0125
#10 0.0021 0.0023 0.1200 0.0900 0.0115
#11 0.0021 0.0023 0.0900 0.0600 0.0115
#14 0.0021 0.0023 0.0900 0.0600 0.0075
#18 0.0021 0.0023 0.0900 0.0600 0.0050
Reinforcing Steel
Bar
Seismic Design Criteria (SDC 1.7) (Typical Bars)
Grade 60 Grade 80
Project: Port of Stockton Fyffe Grade Separation Computed: CL Date: 3/23/20
Subject: Design Calculations - Materials Checked: JC Date: 4/2/20
Task: Page: of:
Job #: NO:
εy εye εsu εRsu εsh
#3 0.0028 0.0033 0.0950 0.0600 0.0074
#4 0.0028 0.0033 0.0950 0.0600 0.0074
#5 0.0028 0.0033 0.0950 0.0600 0.0074
#6 0.0028 0.0033 0.0950 0.0600 0.0074
#7 0.0028 0.0033 0.0950 0.0600 0.0074
#8 0.0028 0.0033 0.0950 0.0600 0.0074
#9 0.0028 0.0033 0.0950 0.0600 0.0074
#10 0.0028 0.0033 0.0950 0.0600 0.0074
#11 0.0028 0.0033 0.0950 0.0600 0.0074
#14 0.0028 0.0033 0.0950 0.0600 0.0074
#18 0.0028 0.0033 0.0950 0.0600 0.0074
ASTM A416 Grade 270
Modulus of Elasticity, Es 28,500 ksi
Yield Strength, fpy 243.0 ksi
Tensile Strength, fpu 270.0 ksi
Total United Weight of Soil, γtot 110.0 pcf
Internal Angle of Friction, 33.3 degrees
Cohesion 0.0 psf
Active Equivalent Fluid Pressure - Abutment 300.0 psf
Fully developed at - Abutment 0.3 H
Active Equivalent Fluid Pressure - Wingwall 170.0 psf
Fully developed at - Wingwall 0.3 H
Passive Equivalent Fluid Pressure, top 6 ft 300.0 pcf
Passive Equivalent Fluid Pressure, below 6 ft 145.0 pcf
Passive Development below OG Depth 1.0 ft
Total United Weight of Soil, γtot 125.0 pcf
Native Soil
Prestressing Strand
Retained Fill
Bar
Seismic Design Criteria (SDC 2.0) (Grade 80 Bars)
1.2 General Notes, Plan and Elevation
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Design Calculations Checked: CL Date: 6/1/20
Task: Design Loads Page: of:
Job #: NO:
DC DC1 Girder Self Weight 963 plf Each Girder
DC2 Concrete slab + Haunch 9417.44 plf Total
Concrete slab + Haunch 1177.18 plf Each girder
Slab 7789.94 plf
Haunch 1627.5 plf
DC3 Barrier + Raised Median + Chain Railing 1550.00 plf Total
Barrier + Raised Median + Chain Railing 193.75 plf Each Girder
Barrier 600 plf Each Side
Raised Median 300 plf
Railing 25 plf Each Side
DC4 Abutment Diaphragm(3.33ft THK) X2 96 kip 1 side
Abutment Diaphragm(3.33ft THK) 12 kip Each girder
Intermediate Diaphragm (8in THK) X1 32 kip
Intermediate Diaphragm (8in THK) X1 4 kip Each girder (point load @ mid span)
DW DW Waering Surface 2620.80 plf Total
Waering Surface 327.60 plf Each Girder
Wearing surface weight 35 psf
Thickness 2 in
LL + IM 4 Lanes HL-93 Details see "Girder" Tab
Lane load 0.64 klf
BR 25% of axle weight of the design truck 18 kip
5% of the design truck plus the lane load 7 kip
Controlling: 18 kip In Horizonal direction
2 lane load shear force 36 kip Shear force
6ft above the road way 108 k-ft Bending
Multipresence factor should be applied 216 k-ft 2 Lane loaded, multtpresence factor 1.0
2-direction braking force cancels out, so max. 2-lane counted for BR
WL & WS
Wind on superstructure per AASHTO, this bridge satisfies with the condition listed below, so use the values listed directly.
WS, t 50 psf Transverse
WS, l 12 psf Longitudinal
Close to abutment, should not cause
much moment to the girder
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Design Calculations Checked: CL Date: 6/1/20
Task: Design Loads Page: of:
Job #: NO:
Wind Componets on Live load per AASHTO, this bridge satisfies with the condition listed below, so use the values listed directly.
WL, t 100 psf Transverse
WL, l 40 psf Longitudinal
EH & EV Will be developed later for substructure; need more civil info too
CR+SH Short 1-span bridge negligible
CE The curve starts almost at the end of bridge, so maybe negligible
TU&TG Will be calculated; most likely negligible & not incuded in combination
May need for gider seat design
EQ Will be checked again for a complete design; 1 span bridge, not sure how to approch
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Design Calculations Checked: CL Date: 6/1/20
Task: Design Loads Page: of:
Job #: NO:
2 Geometry
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
2.1 Superstructure Geometry
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Design Calculations - Geometry Checked: CL Date: 6/4/20
Task: Page: of:
Job #: NO:
GEOMETRY
Bridge Total Length (BB to EB) ft.
Bridge Deck Width (at Abutment 1) ft.
Bridge Deck Width (at Abutment 2) ft.
Bridge Deck Width (average) ft.
Bridge Girder Length ft.
Bridge Girder Type / Properties
Depth Wtop Wbottom Area Icg yb yt Sb St r
in. in. in. in.2
in.4
in. in. in.3
in.3
in.
55.125 47.25 29.50 925 373,350 28.4 26.7 13,153 13,966 20.0
Bridge Girder Weight lbs/ft.
Number of Girders
Girder Spacing, Centerline to Centerline, Min. ft.
Girder Spacing, Centerline to Centerline, Max. ft.
Girder Spacing, Centerline to Centerline, Average ft.
Deck Edge to the Centerline of Exterior Girder ft.
Deck Precast Panel Width, Max. in.
Deck Precast Panel Thickness in.
Typical Deck Thickness (total) in.
Deck Overhang Thickness in.
Haunch Thickness in.
Barrier Type / Weight Type 836 lbs/ft.
Raised Median Sizes / Weight 3' x 8" lbs/ft.
Chain Link Railing Weight lbs/ft.
Total Number of Lanes
Bridge skew angle degrees
9.70
74.88
10.05
4.00
8.00
8.50
600.0
300.0
25.0
4
31
Superstructure
8
9.35
4.05
82.74
3.50
113.16
113.16
CA BT55
963.0
71.60
78.16
2.2 Substructure Geometry
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
Project: Port of Stockton Fyffe Grade Separation Computed: CL Date: 5/5/20
Subject: Design Calculations - Substructure Geometry Checked: JC Date: 5/6/20
Task: Page: of:
Job #: NO:
GEOMETRY
Abutment Wall Length ft.
Abutment Height, Total ft.
Abutment Stem Wall Thickness in.
Back Wall Height ft.
Back Wall Thickness in.
Centerline of Bearing to Centerline of Footing in.
Centerline of Back Wall to Centerline of Footing in.
Abutment Wall Length ft.
Abutment Height, Total ft.
Abutment Stem Wall Thickness in.
Back Wall Height ft.
Back Wall Thickness in.
Centerline of Bearing to Centerline of Footing in.
Centerline of Back Wall to Centerline of Footing in.
Pile Cap Length ft.
Pile Cap Width ft.
Pile Cap Thickness ft.
Centerline of Stem Wall to Centerline of Pile Cap in.
Soil Cover Depth ft.
Pile Cap Length ft.
Pile Cap Width ft.
Pile Cap Thickness ft.
Centerline of Stem Wall to Centerline of Pile Cap in.
Soil Cover Depth ft.5.00
13.00
3.50
0.00
Pile Cap - Abutment 2
35.00
42.00
7.00
12.00
0.00
-31.00
Pile Cap - Abutment 1
5.00
Wall - Abutment 1
71.60
35.00
42.00
Wall - Abutment 2
7.00
12.00
0.00
-31.00
101.00
95.17
13.00
3.50
0.00
78.16
Project: Port of Stockton Fyffe Grade Separation Computed: CL Date: 5/5/20
Subject: Design Calculations - Substructure Geometry Checked: JC Date: 5/6/20
Task: Page: of:
Job #: NO:
GEOMETRY
Precast Square Concrete Pile Size in.
Total Number of Piles
Number of Rows of Piles
Pile Spacing, Centerline to Centerline (alignment direction) ft.
Pile Spacing, Centerline to Centerline (transverse to alignment) ft.
Edge of Footing to Centerline of Leading Pile (Bridge side) ft.
Edge of Footing to Centerline of Trailing Pile (Embankment side) ft.
Centerline of Stem Wall to Centerline of Leading Pile ft.
Centerline of Stem Wall to Centerline of Trailing Pile ft.
Centerline of Stem Wall to Centerline of Middle Row Pile ft.
Precast Square Concrete Pile Size in.
Total Number of Piles
Number of Rows of Piles
Pile Spacing, Centerline to Centerline (alignment direction) ft.
Pile Spacing, Centerline to Centerline (transverse to alignment) ft.
Edge of Footing to Centerline of Leading Pile (Bridge side) ft.
Edge of Footing to Centerline of Trailing Pile (Embankment side) ft.
Centerline of Stem Wall to Centerline of Leading Pile ft.
Centerline of Stem Wall to Centerline of Trailing Pile ft.
Centerline of Stem Wall to Centerline of Middle Row Pile ft.
Wingwall Width ft.
Wingwall Height ft.
Wingwall Thickness, Top in.
Wingwall Thickness, Bottom in.
Slab Width, Max ft.
Slab Length ft.
Slab Thickness in.
Fill Height ft.
Fill Weight ft.
35.00
5.00
Approach Slab
78.00
30.00
15.00
Retained Fill
15.00
Wingwall
35.00
12.00
12.00
5.00
5.00
5.00
51
3
Piles - Abutment 1
14.0
5.00
5.50
14.0
45
3
1.50
1.50
0.00
Piles - Abutment 2
0.00
1.50
5.00
5.00
5.50
1.50
3 Superstructure Design
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
3.1 Girder Design
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
3.1.1 Girder Design Calculation
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
L, Bridge span length (ft) 113.16
Bridge Width (ft) Upper bound 78.16
Bridge Width (ft) Lower Bound 71.60
Bridge Width (ft) Average 74.88
Number of Lanes 4
m, Multipresent factor for LL 0.65
Nb, Number of Girder 8
S, Max Girder Spacing (ft) 10.05
Bridge Skew Angle (degree) 31
For the bridge girder:
f'ci at transfer (ksi) 6.7 AASHTO 5.4.2.3.1
f'c after 28 days (ksi) 8
E_ci (ksi) for girder @ transfer 4716
During the construction of the bridge, it is required to not interfere with train traffic,
thus, the bridge slab system is precast concrete panel in between girders, stitched with CIP Concrete.
Tendon diameter (in) 0.6
One strand area (in^2) 0.217
Debonding length (from end of beam to where bonding commence), ft
10
Girder Distribution factors for DL, LL moment, LL Shear
Type of deck CIP Concrete, Precast Concrete
Supporting Component Precast Concrete I or Bulb-tee section
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
Common Deck superstructure Table 4.6.2.2.1-1
Typical Cross section K Table 4.6.2.2.1-1
Live Load Distribution Factor for Moment in Interior Beams Table 4.6.2.2.2b-1
Rang of Applicability
S, spacing of beams, ϵ [ 3.5, 16] ft ✔
L, Span Length, ϵ [20,240] ft ✔
Nb, number of beams >=4 ✔
ts, depth of concrete slab ϵ [ 4.5, 12] in ✔
Depth of concrete slab, ts (in) 8.00
kg, longitudinal stiffness factor, ϵ [10^4 , 7x10^6] ✔
kg= n( I + A*eg^2) 1576804.87 4.6.2.2.1-1
n= E_beam / E_deck 1.26491106
f'c_slab (ksi) 6
E_beam (ksi) 5,154
E_slab (ksi) 4,074
A, (non-composite) cross section area of girder (in^2) 925 Caltrans Design Aids, CA BT-55
I, (non-composite) inertia (in^4) 373,350 Caltrans Design Aids, CA BT-55
Yb, CG to bottom of girder (in) 28.4 Caltrans Design Aids, CA BT-55
D, girder height (in) 55.125 Caltrans Design Aids, CA BT-55
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
eg, dist. Btw CL of beam & CL of deck (in) 30.725
b_eff, deck effective width of girder (ft) 9.08
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
Per above table from AASHTO, the LL distribution factor for moment in Interior beams are calculated:
g_int, One design lane loaded: 0.52 lane / girder multiple presence factor included
g_int, Two or more lane loaded: 0.77 lane / girder per C4.6.2.2.2b
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
Per above table from AASHTO, the LL distribution factor for moment in exterior beams are calculated:
de, horizontal distance from CL of ext. web of ext. beam @ deck level, to int. edge of curb of traffic barrier
de (ft) 2.30
e=0.77+de/9.1 1.02
g_ext, one design lane loaded 0.53 lane/girder
g_ext, two or more design lane loaded 0.78 lane/girder
Considering the span length, it is very likley that cross frames & end diaphraagm will be necessary.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
Per AASHTO C4.6.2.2.2d-1, exterior girders have higher load distribution factors due to cross frames
One lane loaded:
NL 1
X_ext, (ft) 35.18
e (ft) 24.03
x_1 (ft) 5.03
x_2 (ft) 15.08
x_3 (ft) 25.13
x_4 (ft) 35.18
R 0.32
Adjust with 1.2 multiple presence factor 0.39
Two Lanes loaded:
NL 2
e1 (ft) 24.03
e2 (ft) 6.5
R 0.50
Adjust with 1.0 multiple presence factor 0.50
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
Three or more Lanes loaded:
NL 3
e1 (ft) 24.03
e2 (ft) 6.5
e3 (ft) 12
R 0.68
Adjust with 0.85 multiple presence factor 0.58
Final design values for moment distribution factors :
Load Case Int. Girder (lane)
One lane 0.52 0.53
NA 0.39
2 lanes loaded NA 0.50
3 lanes loaded NA 0.58
Design Value
Moment
Distribution 0.77 0.78
Max: 0.78
Ext. Girder (lane)
Moment Distribution factor
per Table 4.6.2.2.2 Two or more
lane
0.77
Note that AASHTO 4.6.2.2.2.e for skewed bridge provides reduction factors for live load distribution factors for momen in longitudinal
beams. However, CA amendment ignores reduction. Thus, no reduction applies for moment
Moment D.F. for ext. girder per
C4.6.2.2.2d-1
one lane loaded
0.78
Two values are close enough, use the
maximum value for all to be conservative.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
LL distribution factor for Shear :
Per above table from AASHTO, the LL distribution factor for shear in Interior beams are calculated:
g_int, One design lane loaded: 0.76 lane / girder multiple presence factor included
g_int, Two or more lane loaded: 0.96 lane / girder per C4.6.2.2.2b
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
Per above table from AASHTO, the LL distribution factor for shear in exterior beams are calculated:
de (ft) 2.30
e=0.77+de/9.1 1.02
g_ext, one design lane loaded 0.53 lane/girder use same as ext one-lane for moment
g_ext, two or more design lane loaded 0.98 lane/girder
Notes:
AASHTO 4.6.2.2.3 C-1 provides correction factors for live load distribution factors for support shear of the obtuse girder.
CA Amendment revised AASHTO Table 4.6.2.2.3c-1 with equations provide for exterior girder & first interior girder.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
Design values for shear distribution factors (without skew correction factor)
Load Case Int. Girder (lane)
One lane 0.76 NA
NA
NA 0.53
NA 0.98
Design Value
Shear
Distribution
Factor
0.96 0.98
Max: 0.98
Skew Correction factors for shear:
Ext. Girder (lane)
Shear Distribution factor per
Table 4.6.2.2.3a-1 Two or more
lane
0.96
one lane loaded
Two or more
lane
Shear D.F. for ext. girder per
C4.6.2.2.3b-1Two values are close enough, use the
maximum value for all to be conservative.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
The shear correction factors are applied between the point of support at the obtuse corner and mid-span.
May be decreased linearly to a value of 1.0 at mid-span.
Skew Factor 1.09
Design values for shear distribution factors@ obtuse angle
Load Case Int. Girder (lane)
Design Value Shear D.F. 1.04 1.07 Max: 1.07
Ext. Girder (lane)
Two values are close enough, use the
maximum value for all to be conservative.
1.07
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
Moment Demands Calculations
One lane
0 0.0 0 0 0 0 0 0 0
dv 5.0 260 318 52 10 641 89 568
0.1L 11.3 555 678 112 23 1368 189 1211
0.2L 22.6 987 1206 198 45 2436 336 2152
0.3L 33.9 1295 1583 261 68 3206 440 2825
0.4L 45.3 1480 1809 298 91 3677 503 3228
0.5L 56.6 1541 1884 310 114 3849 524 3363
0.6L 67.9 1480 1809 298 91 3677 503 3228
0.7L 79.2 1295 1583 261 68 3206 440 2825
0.8L 90.5 987 1206 198 45 2436 336 2152
0.9L 101.8 555 678 112 23 1368 189 1211
dv 108.2 260 318 52 10 641 89 568
L 113.2 0 0 0 0 0 0 0
dv Use 0.9h (AASHTO 5.8.2.9) 5.03 ft
LL+IM Use Caltrans Bridge Design Aids attached as following.
Span length Moment (k-ft) End Shear (kip)
110 3229 122.8
120 3652.4 126.7
113.2 3362.8 124.0
Lane Load included from Caltrans Table
2216
1688
M (k-ft) DC1 M (k-ft) DC2 M (k-ft) DC3
M (k-ft)
DC Total
M (k-ft)
DW
For Each Girder
(HL-93) LL+IM -M (k-f)
Min LL Distr.Fact
Length along
girder (ft)
2216
2532
2638
2532
0
0
0
0
0
0
0
0
1688
0
950
0
446
950
M (k-ft)
DC4
0
0
0
446
0
0
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
Moment Capacity Calculations@ Wet Concr. Deck Stage (NonComposite)
Note 1 Note 4 Note 3
0 0.0 8 8 8 6 4 2 2 48.16 8.25 0.68 N.A. @ TF
dv 5.0 8 8 8 6 4 2 2 48.16 8.25 0.68 N.A. @ TF
0.1L 11.3 8 8 8 6 4 2 2 48.16 8.25 0.68 N.A. @ TF
0.2L 22.6 10 10 10 8 4 2 2 48.38 9.98 0.82 N.A. @ TF
0.3L 33.9 10 12 12 8 4 2 2 48.46 10.85 0.89 N.A. @ TF
0.4L 45.3 10 12 12 8 4 2 2 48.46 10.85 0.89 N.A. @ TF
0.5L 56.6 10 12 12 8 4 2 2 48.46 10.85 0.89 N.A. @ TF
0.6L 67.9 10 12 12 8 4 2 2 48.46 10.85 0.89 N.A. @ TF
0.7L 79.2 10 12 12 8 4 2 2 48.46 10.85 0.89 N.A. @ TF
0.8L 90.5 10 10 10 8 4 2 2 48.38 9.98 0.82 N.A. @ TF
0.9L 101.8 8 8 8 6 4 2 2 48.16 8.25 0.68 N.A. @ TF
dv 108.2 8 8 8 6 4 2 2 48.16 8.25 0.68 N.A. @ TF
L 113.2 8 8 8 6 4 2 2 48.16 8.25 0.68 N.A. @ TF
0.6" diameter tendons are used
Reference: AASHTO 2014 LRFD 7th Edition
Note 1: Note 4:
Note 2: Note 5:
Note 3: Note 6:
No.
Tendon at
10.75"
From Bot
No. Tendon
at 12.75"
From Bot
No.
Tendon at
14.75"
From Bot
Calcuated "c" to determine location of section
N.A.
Length
along
girder (ft)
No. Tendon
at 2.75"
From Bot
No.
Tendon at
4.75" from
Bot
No.
Tendon at
6.75"
From Bot
c (in)
Action Type:
Nuetral axis
location
No.
Tendon at
8.75" From
Bot
dp(in) to
Girder top
Aps(in^2)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Wet Concrete Deck Stage
Note 2 Note 5 Note 6 Note 7 Note 8
0 0.0 0.68 0.58 268.9 8848 0.2105 1.00 8848 0 8848 0
dv 5.0 0.68 0.58 268.9 8848 0.2105 1.00 8848 723 8848 0.08
0.1L 11.3 0.68 0.58 268.9 8848 0.2105 1.00 8848 1542 8848 0.17
0.2L 22.6 0.82 0.70 268.7 10736 0.1743 1.00 10736 2741 10736 0.26
0.3L 33.9 0.89 0.76 268.6 11676 0.1605 1.00 11676 3597 11676 0.31
0.4L 45.3 0.89 0.76 268.6 11676 0.1605 1.00 11676 4111 11676 0.35
0.5L 56.6 0.89 0.76 268.6 11676 0.1605 1.00 11676 4282 11676 0.37
0.6L 67.9 0.89 0.76 268.6 11676 0.1605 1.00 11676 4111 11676 0.35
0.7L 79.2 0.89 0.76 268.6 11676 0.1605 1.00 11676 3597 11676 0.31
0.8L 90.5 0.82 0.70 268.7 10736 0.1743 1.00 10736 2741 10736 0.26
0.9L 101.8 0.68 0.58 268.9 8848 0.2105 1.00 8848 1542 8848 0.17
dv 108.2 0.68 0.58 268.9 8848 0.2105 1.00 8848 723 8848 0.08
L 113.2 0.68 0.58 268.9 8848 0.2105 1.00 8848 0 8848 0.00
Note 7: Moment formula chosen depends on girder action type
Beta_1 =0.85 Per AASHTO 5.7.2.2
Value of k =0.28 Per Table C5.7.3.1.1.1
Note 8:
Length
along
girder
(ft)
a (in) f_ps(ksi) Mn(k-ft)Epslon_t
ξ_t
phi
factor φ
φMn(k-
ft)
For Each Girder
Mu (k-ft)
Strength I φMn(k-ft) D/C
Update c (in)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Wet Concrete Deck Stage
Mu=1.25 DC1+1.25DC2
Controlling Combination to design girders:
Strength I 1.25 DC+1.5 DW
0
2000
4000
6000
8000
10000
12000
14000
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Mo
me
nt
(k
-ft)
Length (ft)
Moment Plot along Span Length
Mu (k-ft) Strength I φMn(k-ft)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
0 0.0 0 0 0 0 0 0 0
dv 5.0 260 318 52 10 641 89 1027
0.1L 11.3 555 678 112 23 1368 189 2189
0.2L 22.6 987 1206 198 45 2436 336 3892
0.3L 33.9 1295 1583 261 68 3206 440 5108
0.4L 45.3 1480 1809 298 91 3677 503 5838
0.5L 56.6 1541 1884 310 114 3849 524 6081
0.6L 67.9 1480 1809 298 91 3677 503 5838
0.7L 79.2 1295 1583 261 68 3206 440 5108
0.8L 90.5 987 1206 198 45 2436 336 3892
0.9L 101.8 555 678 112 23 1368 189 2189
dv 108.2 260 318 52 10 641 89 1027
L 113.2 0 0 0 0 0 0 0 0
806
0
1717 0
4579 0
4769 0
4579 0
4006 0
3052 0
0 0
806
Length along
girder (ft)
For Each Girder
(P-15) LL+IM -M (k-f)
M (k-ft) DC1 M (k-ft) DC2 One lane Distr.Fact Min LL M (k-ft) DC3
M (k-ft)
DC4
M (k-ft)
DC Total
M (k-ft)
DW
0
1717 0
3052 0
4006 0
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
Moment Capacity Calculations@ Final Stage Stage
0 0.0 8 8 8 6 4 2 2 8 56.16 8.25 5.50
dv 5.0 8 8 8 6 4 2 2 8 56.16 8.25 5.50
0.1L 11.3 8 8 8 6 4 2 2 8 56.16 8.25 5.50
0.2L 22.6 10 10 10 8 4 2 2 8 56.38 9.98 6.62
0.3L 33.9 10 12 12 8 4 2 2 8 56.46 10.85 7.18
0.4L 45.3 10 12 12 8 4 2 2 8 56.46 10.85 7.18
0.5L 56.6 10 12 12 8 4 2 2 8 56.46 10.85 7.18
0.6L 67.9 10 12 12 8 4 2 2 8 56.46 10.85 7.18
0.7L 79.2 10 12 12 8 4 2 2 8 56.46 10.85 7.18
0.8L 90.5 10 10 10 8 4 2 2 8 56.38 9.98 6.62
0.9L 101.8 8 8 8 6 4 2 2 8 56.16 8.25 5.50
dv 108.2 8 8 8 6 4 2 2 8 56.16 8.25 5.50
L 113.2 8 8 8 6 4 2 2 8 56.16 8.25 5.50
Considering the concrete deck is acting compositely with the CA BT 55 girders.
Also Conservatively igore the precast concrete panel's composite concrete reaction, due to lack of friction btw the panel surface.
c (in) No.
Tendon at
10.75"
From Bot
No. Tendon
at 12.75"
From Bot
No.
Tendon at
14.75"
From Bot
Length
along
girder (ft)
No. Tendon
at 2.75"
From Bot
No.
Tendon at
4.75" from
Bot
No.
Tendon at
6.75"
From Bot
No.
Tendon at
8.75" From
Bot
dp(in) to
Deck top
Aps(in^2)Composite
Deck THK
(in)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Final Stage
0 0.0 N.A. @ Deck 5.50 4.68 262.6 9713 0.0276 1.00 9713
dv 5.0 N.A. @ Deck 5.50 4.68 262.6 9713 0.0276 1.00 9713
0.1L 11.3 N.A. @ Deck 5.50 4.68 262.6 9713 0.0276 1.00 9713
0.2L 22.6 N.A. @ Deck 6.62 5.63 261.1 11634 0.0225 1.00 11634
0.3L 33.9 N.A. @ Deck 7.18 6.10 260.4 12573 0.0206 1.00 12573
0.4L 45.3 N.A. @ Deck 7.18 6.10 260.4 12573 0.0206 1.00 12573
0.5L 56.6 N.A. @ Deck 7.18 6.10 260.4 12573 0.0206 1.00 12573
0.6L 67.9 N.A. @ Deck 7.18 6.10 260.4 12573 0.0206 1.00 12573
0.7L 79.2 N.A. @ Deck 7.18 6.10 260.4 12573 0.0206 1.00 12573
0.8L 90.5 N.A. @ Deck 6.62 5.63 261.1 11634 0.0225 1.00 11634
0.9L 101.8 N.A. @ Deck 5.50 4.68 262.6 9713 0.0276 1.00 9713
dv 108.2 N.A. @ Deck 5.50 4.68 262.6 9713 0.0276 1.00 9713
L 113.2 N.A. @ Deck 5.50 4.68 262.6 9713 0.0276 1.00 9713
Action Type
(Neutral Axis
location)
Update
c (in)
from
deck
top
a (in)
Length
along
girder
(ft)
f_ps(ksi) Mn(k-ft)Epslon_t
ξ_t
phi factor
φ φMn(k-ft)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Final Stage
0 0.0 0 0 9713 0 0.00
dv 5.0 1714 2022 9713 0.18 0.21
0.1L 11.3 3654 4311 9713 0.38 0.44
0.2L 22.6 6503 7670 11634 0.56 0.66
0.3L 33.9 8546 10077 12573 0.68 0.80
0.4L 45.3 9783 11533 12573 0.78 0.92
0.5L 56.6 10214 12037 12573 0.81 0.96
0.6L 67.9 9783 11533 12573 0.78 0.92
0.7L 79.2 8546 10077 12573 0.68 0.80
0.8L 90.5 6503 7670 11634 0.56 0.66
0.9L 101.8 3654 4311 9713 0.38 0.44
dv 108.2 1714 2022 9713 0.18 0.21
L 113.2 0 0 9713 0.00 0.00
Strength I 1.25 DC+1.5 DW+1.75 LL
Strength II 1.25 DC+1.5 DW+1.35 LL-permit
17
Mu (k-ft)
Strength I
Mu (k-ft)
Strength II φMn(k-ft)
For Each Girder
D/C for
Strength I
D/C for
Strength II
Length
along
girder (ft)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
0
2000
4000
6000
8000
10000
12000
14000
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Mo
me
nt
(k
-ft)
Length (ft)
Moment Plot along Span Length
Mu (k-ft) Strength I
φMn(k-ft)
Mu (k-ft) Strength II
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/2020
Subject: Design Calculations Checked: CL Date: 4/14/2020
Task: Girders Stress Page: of:
Job #: NO:
For the stress calc, negative stress is tensile stress; positive stress is compressive stress.
Stress Calculations @ Transfer Stage
Tendons f_pu (ksi) 270
Tendon f_pbt (ksi) 202.5 (AASHTO Table 5.9.3.1)
Tendon E_ps (ksi) 28,500
Girder Concrete E_pc (ksi) 5,154
n'-1 = E_ps/ E_pc -1 4.53
f'c (ksi) 8
f'ci (ksi) 6.7
CA BT 55, Ag (in^2) 925
CA BT 55, w (k/ft) 0.963
CA BT 55, Yt, CG to Top (in) 26.70
CA BT 55, Yb, CG to Bot (in) 28.40
CA BT 55, Ig (in^4) 373,350
Ƴ_h Say H= 70% 1
Ƴ_st 0.65
Δf_pR (ksi) 2.4
Transfer length l_t =60*db (in) 36
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/2020
Subject: Design Calculations Checked: CL Date: 4/14/2020
Task: Girders Stress Page: of:
Job #: NO:
Stress Calculations @ Transfer Stage* debond included
Note 1 Note 2 Note 3 Note 4 Note 5 Note 6
0 0.0 8 8 8 6 4 2 2 8.25 48.16 21.46 0 19 183 ok 378
1.0 8 8 8 6 4 2 2 8.25 48.16 21.46 648 19 183 ok 504
2.0 8 8 8 6 4 2 2 8.25 48.16 21.46 1285 19 184 ok 1009
3.0 8 8 8 6 4 2 2 8.25 48.16 21.46 1910 19 184 ok 1515
dv 5.0 8 8 8 6 4 2 2 8.25 48.16 21.46 3125 18 184 ok 1518
0.1L 11.3 8 8 8 6 4 2 2 8.25 48.16 21.46 6659 17 185 ok 1526
13.0 8 8 8 6 4 2 2 8.25 48.16 21.46 7523 17 185 ok 1528
14.0 10 10 10 8 4 2 2 9.98 48.38 21.68 8021 21 182 ok 1603
15.0 10 10 10 8 4 2 2 9.98 48.38 21.68 8508 21 182 ok 1709
16.0 10 10 10 8 4 2 2 9.98 48.38 21.68 8982 21 182 ok 1816
0.2L 22.6 10 10 10 8 4 2 2 9.98 48.38 21.68 11826 20 183 ok 1824
28.0 10 10 10 8 4 2 2 9.98 48.38 21.68 13778 19 183 ok 1829
29.0 10 12 12 8 4 2 2 10.85 48.46 21.76 14102 21 181 ok 1864
30.0 10 12 12 8 4 2 2 10.85 48.46 21.76 14415 21 182 ok 1917
31.0 10 12 12 8 4 2 2 10.85 48.46 21.76 14716 21 182 ok 1971
0.3L 33.9 10 12 12 8 4 2 2 10.85 48.46 21.76 15538 21 182 ok 1973
0.4L 45.3 10 12 12 8 4 2 2 10.85 48.46 21.76 17757 20 183 ok 1980
0.5L 56.6 10 12 12 8 4 2 2 10.85 48.46 21.76 18497 20 183 ok 1982
0.6L 67.9 10 12 12 8 4 2 2 10.85 48.46 21.76 17757 20 183 ok 1980
0.7L 79.2 10 12 12 8 4 2 2 10.85 48.46 21.76 15538 21 182 ok 1973
82.2 10 12 12 8 4 2 2 10.85 48.46 21.76 14716 21 182 ok 1971
83.2 10 12 12 8 4 2 2 10.85 48.46 21.76 14415 21 182 ok 1917
84.2 10 12 12 8 4 2 2 10.85 48.46 21.76 14102 21 181 ok 1864
85.2 10 10 10 8 4 2 2 9.98 48.38 21.68 13778 19 183 ok 1829
0.8L 90.5 10 10 10 8 4 2 2 9.98 48.38 21.68 11838 20 183 ok 1824
97.2 10 10 10 8 4 2 2 9.98 48.38 21.68 8982 21 182 ok 1816
98.2 10 10 10 8 4 2 2 9.98 48.38 21.68 8508 21 182 ok 1709
99.2 10 10 10 8 4 2 2 9.98 48.38 21.68 8021 21 182 ok 1603
100.2 8 8 8 6 4 2 2 8.25 48.16 21.46 7523 17 185 ok 1528
0.9L 101.8 8 8 8 6 4 2 2 8.25 48.16 21.46 6659 17 185 ok 1526
dv 108.2 8 8 8 6 4 2 2 8.25 48.16 21.46 3125 18 184 ok 1518
110.2 8 8 8 6 4 2 2 8.25 48.16 21.46 1910 19 184 ok 1515
111.2 8 8 8 6 4 2 2 8.25 48.16 21.46 1285 19 184 ok 1009
112.2 8 8 8 6 4 2 2 8.25 48.16 21.46 648 19 183 ok 504
L 113.2 8 8 8 6 4 2 2 8.25 48.16 21.46 0 19 183 ok 378
f_pi
(ksi)
Stress limit
for tendon
0.8fpy
Jakcing
force
@transfer,
Pji (kip)
Length along
girder (ft) No. Tendon
at 2.75"
From Bot
No. Tendon
at 4.75"
from Bot
No.
Tendon at
6.75" From
Bot
No. Tendon
at 10.75"
From Bot
No. Tendon
at 12.75"
From Bot
No. Tendon
at 14.75"
From Bot
Mg (kip-
in) Girder
Self
Weight
Δf_pES
(ksi)No. Tendon
at 8.75"
From Bot
Aps(in^2)
Y_p,
Tendon
CG to Top
of Girder
(in)
e_ti (in)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/2020
Subject: Design Calculations Checked: CL Date: 4/14/2020
Task: Girders Stress Page: of:
Job #: NO:
Note 1: Eccencity equal to value of Y_p minus YtNote 2: Mg is the moment caused by the self weight of the girder+ Concrete deck
Note 4:
Note 3:
Note 5: fpy assumes to be 0.9fpu; Table 5.9.3-1 AASHTO
Note 7: Top fiber concr gider stress=P/A-P*e/(I/Yt)+Mg/(I/Yb) (+ is compression, - is tension)
Note 9:
Note 6: Jakcing force @ transfer taken as f_pi multiplies Aps (Total area of tendons)
Note 8: Bot. fiber concr gider stress=P/A+P*e/(I/Yt)-Mg/(I/Yb) (+ is cpmpression, - is tension )
Note 10:
Girder top bars: #4 Total of 6, 0.2x6=1.2in^2
f_pi is the value of f_pbt minus Δf_pES. Per AASHTO C5.9.5.2.3a, if the transformed
section properties are used, the Δf_pES should not be inlcuded in the prestressing force.
In this case, jacking force is calcuated as f_pbt minus short term elastic shortening loss,
and so the Gorss section properties of the concrete girder are used.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/2020
Subject: Design Calculations Checked: CL Date: 4/14/2020
Task: Girders Stress Page: of:
Job #: NO:
0
500
1000
1500
2000
2500
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Jakcing force @transfer, Pji (kip)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/2020
Subject: Design Calculations Checked: CL Date: 4/14/2020
Task: Girders Stress Page: of:
Job #: NO:
Stress Calculations @ Transfer Stage
Note 7 Note 8 Note 9 Note 10
0 0.0 -0.17 1.02 4.36 -0.62 0.00 0.28 0.24 0.00
1.0 -0.18 1.32 4.36 -0.62 0.00 0.29 0.30 0.00
2.0 -0.37 2.64 4.36 -0.62 0.00 0.59 0.61 0.00
3.0 -0.55 3.97 4.36 -0.62 0.00 0.89 0.91 0.00
dv 5.0 -0.47 3.88 4.36 -0.62 0.00 0.75 0.89 0.00
0.1L 11.3 -0.22 3.64 4.36 -0.62 0.00 0.35 0.83 0.00
13.0 -0.16 3.58 4.36 -0.62 0.00 0.25 0.82 0.00
14.0 -0.18 3.77 4.36 -0.62 0.00 0.29 0.86 0.00
15.0 -0.19 4.02 4.36 -0.62 0.00 0.31 0.92 0.00
16.0 -0.21 4.27 4.36 -0.62 0.00 0.34 0.98 0.00
0.2L 22.6 -0.01 4.08 4.36 -0.62 0.00 0.02 0.94 0.00
28.0 0.13 3.95 4.36 -0.62 0.03 0.00 0.91 0.00
29.0 0.12 4.03 4.36 -0.62 0.03 0.00 0.92 0.00
30.0 0.12 4.15 4.36 -0.62 0.03 0.00 0.95 0.00
31.0 0.12 4.27 4.36 -0.62 0.03 0.00 0.98 0.00
0.3L 33.9 0.17 4.22 4.36 -0.62 0.04 0.00 0.97 0.00
0.4L 45.3 0.33 4.07 4.36 -0.62 0.08 0.00 0.93 0.00
0.5L 56.6 0.38 4.02 4.36 -0.62 0.09 0.00 0.92 0.00
0.6L 67.9 0.33 4.07 4.36 -0.62 0.08 0.00 0.93 0.00
0.7L 79.2 0.17 4.22 4.36 -0.62 0.04 0.00 0.97 0.00
82.2 0.12 4.27 4.36 -0.62 0.03 0.00 0.98 0.00
83.2 0.12 4.15 4.36 -0.62 0.03 0.00 0.95 0.00
84.2 0.12 4.03 4.36 -0.62 0.03 0.00 0.92 0.00
85.2 0.13 3.95 4.36 -0.62 0.03 0.00 0.91 0.00
0.8L 90.5 -0.01 4.08 4.36 -0.62 0.00 0.01 0.94 0.00
97.2 -0.21 4.27 4.36 -0.62 0.00 0.34 0.98 0.00
98.2 -0.19 4.02 4.36 -0.62 0.00 0.31 0.92 0.00
99.2 -0.18 3.77 4.36 -0.62 0.00 0.29 0.86 0.00
100.2 -0.16 3.58 4.36 -0.62 0.00 0.25 0.82 0.00
0.9L 101.8 -0.22 3.64 4.36 -0.62 0.00 0.35 0.83 0.00
dv 108.2 -0.47 3.88 4.36 -0.62 0.00 0.75 0.89 0.00
110.2 -0.55 3.97 4.36 -0.62 0.00 0.89 0.91 0.00
111.2 -0.37 2.64 4.36 -0.62 0.00 0.59 0.61 0.00
112.2 -0.18 1.32 4.36 -0.62 0.00 0.29 0.30 0.00
L 113.2 -0.17 1.02 4.36 -0.62 0.00 0.28 0.24 0.00
Max: 0.09 0.89 0.98 0.00
Length
along
girder (ft)
(comp limit
0.65f'ci)
(Ten limit -
0.24*sqrt(f
'ci) ksi)
f_top
(ksi)f_bot (ksi)
D/C ratio
(comp
limit )
D/C
ratio(Ten
limit )
f_top f_bot
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit )
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/2020
Subject: Design Calculations Checked: CL Date: 4/14/2020
Task: Girders A Stress Page: of:
Job #: NO:
For the stress calc, negative stress is tensile stress; positive stress is compressive stress.
Stress Calculations @ Transfer Stage
Tendons f_pu (ksi) 270
Tendon f_pbt (ksi) 203 (AASHTO Table 5.9.3.1)
Tendon E_ps (ksi) 28500
Girder Concrete E_pc (ksi) 5154
n'-1 = E_ps/ E_pc -1 5
f'c (ksi) 8
f'ci (ksi) 6.7
CA BT 55, Ag (in^2) 925
CA BT 55, w (k/ft) 1
CA BT 55, Yt, CG to Top (in) 27
CA BT 55, Yb, CG to Bot (in) 28
CA BT 55, Ig (in^4) 373350
Ƴ_h Say H= 70% 1
Ƴ_st 0.65
Δf_pR (ksi) 2.4
Transfer length l_t =60*db (in) 36
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/2020
Subject: Design Calculations Checked: CL Date: 4/14/2020
Task: Girders A Stress Page: of:
Job #: NO:
Stress Calculations @ PS + Perm load condition Transformed seciton properties
Note 1 Note 2 Note 3 Note 4 Note 5 Note 6 Note 7 Note 8
0 0.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
1.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
2.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
3.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
dv 5.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
0.1L 11.3 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
13.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
14.0 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
15.0 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
16.0 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
0.2L 22.6 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
28.0 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
29.0 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
30.0 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
31.0 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
0.3L 33.9 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
0.4L 45.3 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
0.5L 56.6 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
0.6L 67.9 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
0.7L 79.2 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
82.2 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
83.2 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
84.2 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
85.2 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
0.8L 90.5 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
97.2 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
98.2 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
99.2 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
100.2 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
0.9L 101.8 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
dv 108.2 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
110.2 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
111.2 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
112.2 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
L 113.2 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
Ʃ Ai*(Y_i-
Y_ttop)^
2
(in^4)
I_final(in
^4)
Transfor
med
S_ttop
(in^3)
Transfor
med
S_tbot
(in^3)
Length
along
girder
(ft) Aps(in^
2)
Y_p,
Tendon CG
to
GirderTop
(in)
Aps*(n'-
1)
(in^2)
Total
Aps*(n-
1)+Ag
(in^2)
ƩAi*Y_i
(in^3)
Transfor
med
Y_ttop
(in)
Transfor
med
Y_tbot
(in)Ig (in^4)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/2020
Subject: Design Calculations Checked: CL Date: 4/14/2020
Task: Girders A Stress Page: of:
Job #: NO:
Note 1: Ignore moment of inertia I from prestrssing tendons, since it is too small compared to that of precast concrete Girder.
Note 2: Summation of tranformed strands area times CG of strands, and area of precast concrete girder times CG of the girder.
Note 3: Values of Note 2 divide by the total area of the transformed section to determine CG of the tranformed section (from top of the section)
Note 4: CG of the tranformed seciton (from bottom of the section)
Note 5:
Note 6: I_final =Ig + values at Note 5
Note 7: Transformed section modulus from top of seciton is I_final divide by Transformed Y_ttop
Note 8: Transformed section modulus from bottom of seciton is I_final divide by Transformed Y_tbot
Summation of tranformed area of strands times squrea of CG differenec between strands and the entire tranformed section, plus such value for
precast concrete girder component.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/2020
Subject: Design Calculations Checked: CL Date: 4/14/2020
Task: Girders A Stress Page: of:
Job #: NO:
Stress Calculations @ PS + Perm load condition * debond included
Note 9 Note 10 Note 11 Note 12 Note 13 Note 14 Note 15 Note 16
0 0.0 21 22 181 372 0 -0.16 0.93 3.60 -0.54 0.00 0.29 0.26 0.00
1.0 21 22 181 496 1440 -0.11 1.14 3.60 -0.54 0.00 0.20 0.32 0.00
2.0 21 22 181 993 2855 -0.21 2.28 3.60 -0.54 0.00 0.40 0.63 0.00
3.0 21 22 181 1489 4244 -0.32 3.42 3.60 -0.54 0.00 0.60 0.95 0.00
dv 5.0 21 22 181 1489 6944 -0.13 3.23 3.60 -0.54 0.00 0.25 0.90 0.00
0.1L 11.3 21 22 181 1489 14799 0.42 2.67 3.60 -0.54 0.12 0.00 0.74 0.00
13.0 21 22 181 1489 16720 0.56 2.54 3.60 -0.54 0.16 0.00 0.71 0.00
14.0 21 24 178 1572 17827 0.59 2.64 3.60 -0.54 0.16 0.00 0.73 0.00
15.0 21 24 178 1675 18907 0.62 2.82 3.60 -0.54 0.17 0.00 0.78 0.00
16.0 21 24 178 1778 19962 0.65 3.00 3.60 -0.54 0.18 0.00 0.83 0.00
0.2L 22.6 21 24 178 1778 26281 1.10 2.56 3.60 -0.54 0.30 0.00 0.71 0.00
28.0 21 24 178 1778 30619 1.40 2.26 3.60 -0.54 0.39 0.00 0.63 0.00
29.0 21 26 177 1817 31340 1.43 2.29 3.60 -0.54 0.40 0.00 0.64 0.00
30.0 21 26 177 1868 32036 1.46 2.37 3.60 -0.54 0.40 0.00 0.66 0.00
31.0 21 26 177 1919 32706 1.48 2.45 3.60 -0.54 0.41 0.00 0.68 0.00
0.3L 33.9 21 26 177 1919 34531 1.61 2.32 3.60 -0.54 0.45 0.00 0.65 0.00
0.4L 45.3 21 26 177 1919 39464 1.96 1.98 3.60 -0.54 0.54 0.00 0.55 0.00
0.5L 56.6 21 26 177 1919 41108 2.07 1.87 3.60 -0.54 0.58 0.00 0.52 0.00
0.6L 67.9 21 26 177 1919 39464 1.96 1.98 3.60 -0.54 0.54 0.00 0.55 0.00
0.7L 79.2 21 26 177 1919 34531 1.61 2.32 3.60 -0.54 0.45 0.00 0.65 0.00
82.2 21 26 177 1919 32706 1.48 2.45 3.60 -0.54 0.41 0.00 0.68 0.00
83.2 21 26 177 1868 32036 1.46 2.37 3.60 -0.54 0.40 0.00 0.66 0.00
84.2 21 26 177 1817 31340 1.43 2.29 3.60 -0.54 0.40 0.00 0.64 0.00
85.2 21 24 178 1778 30619 1.40 2.26 3.60 -0.54 0.39 0.00 0.63 0.00
0.8L 90.5 21 24 178 1778 26309 1.10 2.56 3.60 -0.54 0.31 0.00 0.71 0.00
97.2 21 24 178 1778 19962 0.65 3.00 3.60 -0.54 0.18 0.00 0.83 0.00
98.2 21 24 178 1675 18907 0.62 2.82 3.60 -0.54 0.17 0.00 0.78 0.00
99.2 21 24 178 1572 17827 0.59 2.64 3.60 -0.54 0.16 0.00 0.73 0.00
100.2 21 22 181 1489 16720 0.56 2.54 3.60 -0.54 0.16 0.00 0.71 0.00
0.9L 101.8 21 22 181 1489 14799 0.42 2.67 3.60 -0.54 0.12 0.00 0.74 0.00
dv 108.2 21 22 181 1489 6944 -0.13 3.23 3.60 -0.54 0.00 0.25 0.90 0.00
110.2 21 22 181 1489 4244 -0.32 3.42 3.60 -0.54 0.00 0.60 0.95 0.00
111.2 21 22 181 993 2855 -0.21 2.28 3.60 -0.54 0.00 0.40 0.63 0.00
112.2 21 22 181 496 1440 -0.11 1.14 3.60 -0.54 0.00 0.20 0.32 0.00
L 113.2 21 22 181 372 0 -0.16 0.93 3.60 -0.54 0.00 0.29 0.26 0.00
Max: 0.58 0.60 0.95 0.00
PS+ Perm (DC1+DC2)
Length
along
girder
(ft)
e (in)Δf_pLT
(ksi)
Moment
demands
DC1+DC2
(kip-in)
Compres
sive
Stress
limit (ksi)
Tensile
Stress
limit (ksi)
f_top
D/C ratio
(comp limit)
D/C ratio(Ten
limit)
f_top
(ksi)fpe (ksi) Pf (kiP)
f_bot
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit)
f_Bot
(ksi)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/2020
Subject: Design Calculations Checked: CL Date: 4/14/2020
Task: Girders A Stress Page: of:
Job #: NO:
Note 9: Eccentricity of the seciton is Y_p(in) from girder top subtracted by Transformed Y_ttop
Note 10
Note 11 fpe is stress at transfer minus long term loss Δf_pLT
Note 12 Prestressing force Pf, is fpe times area of the prestressing tendons, Aps.
Note 13
Note 14
Note 15
Note 16:
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/2020
Subject: Design Calculations Checked: CL Date: 4/14/2020
Task: Girders A Stress Page: of:
Job #: NO:
Tendons f_pu (ksi) 270
Tendon f_pbt (ksi) 202.5 (AASHTO Table 5.9.3.1)
CA BT 55, Ag (in^2) 925
CA BT 55, w (k/ft) 0.963
CA BT 55, Yt, CG to Top (in) 26.7
CA BT 55, Yb, CG to Bot (in) 28.4
CA BT 55, Ig (in^4) 373350
Tendon E_ps (ksi) 28,500
Girder Concrete E_pc (ksi) 5,154
n'-1 = E_ps/ E_pc -1 5
Girder f'c (ksi) 8
Girder f'ci (ksi) 6.7
Deck Concrete E_c (ksi) 4,074
Girder Concrete E_pc (ksi) 5,154
n= E_c/E_pc 0.79
CIP Deck f'c (ksi) 5
Deck effective width (ft) 9.08
Depth of concrete slab, ts (in) 8.00
Precast panel thickness (in) 3.50
Tranformed deck area (in^2) 768.74 (based on Ec of 8ksi concrete)
Tranformed effective deck width (in) 96.093 (based on Ec of 8ksi concrete)
Transfer length l_t =60*db (in) 36
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/2020
Subject: Design Calculations Checked: CL Date: 4/14/2020
Task: Girders A Stress Page: of:
Job #: NO:
Stress Calculations @ Service, composite section properties include the Deck Slab
Note 1
0 0 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 372
1 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 496
2 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 993
3 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
dv 5 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
0.1L 11 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
13 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
14 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1572
15 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1675
16 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1778
0.2L 23 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1778
28 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1778
29 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1817
30 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1868
31 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
0.3L 34 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
0.4L 45 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
0.5L 57 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
0.6L 68 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
0.7L 79 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
82 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
83 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1868
84 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1817
85 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1778
0.8L 91 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1778
97 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1778
98 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1675
99 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1572
100 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
0.9L 102 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
dv 108 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
110 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
111 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 993
112 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 496
L 113 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 372
Comp.
Y_tbot
(in)
I_comp
(in^4)
Comp.
S_tg
(in^3)
Comp S_tb
(in^3)I_tg(in^4)
Transformed
Y_ttop (in)
Transfor
med
Y_tbot
(in)
Tranfor
med
A_deck
(in^2)
From PS+Perm stress calc
Length
along
girder (ft)
A_deck+A
ps*(n'-
1)+Ag
(in^2)
Yi to Top
of Deck
ƩAi*Y_i
(in^3)
Comp
Y_ttop
(in)
ToDec
kTope (in)
Δf_pLT
(ksi)
fpe
(ksi)
Pf
(kiP)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/2020
Subject: Design Calculations Checked: CL Date: 4/14/2020
Task: Girders A Stress Page: of:
Job #: NO:
Stress Calculations @ Service, composite section properties include the Deck Slab
* debond included Note 2 Note 3 Note 4
0 0.0 0 0 0 0 -0.16 0.93 4.80 -0.54 0.00 0.29 0.19 0.00
1.0 1440 351 24 1109 -0.08 1.06 4.80 -0.54 0.00 0.15 0.22 0.00
2.0 2855 695 48 2198 -0.16 2.13 4.80 -0.54 0.00 0.31 0.44 0.00
3.0 4244 1034 72 3268 -0.25 3.20 4.80 -0.54 0.00 0.46 0.67 0.00
dv 5.0 6944 1692 120 5347 -0.01 2.86 4.80 -0.54 0.00 0.02 0.60 0.00
0.1L 11.3 14799 3605 272 11395 0.68 1.89 4.80 -0.54 0.14 0.00 0.39 0.00
13.0 16720 4073 313 12874 0.85 1.66 4.80 -0.54 0.18 0.00 0.35 0.00
14.0 17827 4343 337 13726 0.89 1.72 4.80 -0.54 0.19 0.00 0.36 0.00
15.0 18907 4606 361 14558 0.94 1.84 4.80 -0.54 0.20 0.00 0.38 0.00
16.0 19962 4863 385 15370 0.99 1.97 4.80 -0.54 0.21 0.00 0.41 0.00
0.2L 22.6 26281 6402 544 20236 1.55 1.20 4.80 -0.54 0.32 0.00 0.25 0.00
28.0 30619 7459 674 23576 1.93 0.67 4.80 -0.54 0.40 0.00 0.14 0.00
29.0 31340 7635 698 24131 1.97 0.68 4.80 -0.54 0.41 0.00 0.14 0.00
30.0 32036 7804 722 24667 2.01 0.72 4.80 -0.54 0.42 0.00 0.15 0.00
31.0 32706 7967 746 25183 2.04 0.76 4.80 -0.54 0.43 0.00 0.16 0.00
0.3L 33.9 34531 8412 817 26588 2.20 0.54 4.80 -0.54 0.46 0.00 0.11 0.00
0.4L 45.3 39464 9613 1090 30386 2.64 -0.06 4.80 -0.54 0.55 0.00 0.00 0.12
0.5L 56.6 41108 10014 1362 31652 2.79 -0.28 4.80 -0.54 0.58 0.00 0.00 0.51
0.6L 67.9 39464 9613 1090 30386 2.64 -0.06 4.80 -0.54 0.55 0.00 0.00 0.12
0.7L 79.2 34531 8412 817 26588 2.20 0.54 4.80 -0.54 0.46 0.00 0.11 0.00
82.2 32706 7967 746 25183 2.04 0.76 4.80 -0.54 0.43 0.00 0.16 0.00
83.2 32036 7804 722 24667 2.01 0.72 4.80 -0.54 0.42 0.00 0.15 0.00
84.2 31340 7635 698 24131 1.97 0.68 4.80 -0.54 0.41 0.00 0.14 0.00
85.2 30619 7459 674 23576 1.93 0.67 4.80 -0.54 0.40 0.00 0.14 0.00
0.8L 90.5 26309 6409 545 20257 1.55 1.19 4.80 -0.54 0.32 0.00 0.25 0.00
97.2 19962 4863 385 15370 0.99 1.97 4.80 -0.54 0.21 0.00 0.41 0.00
98.2 18907 4606 361 14558 0.94 1.84 4.80 -0.54 0.20 0.00 0.38 0.00
99.2 17827 4343 337 13726 0.89 1.72 4.80 -0.54 0.19 0.00 0.36 0.00
100.2 16720 4073 313 12874 0.85 1.66 4.80 -0.54 0.18 0.00 0.35 0.00
0.9L 101.8 14799 3605 272 11395 0.68 1.89 4.80 -0.54 0.14 0.00 0.39 0.00
dv 108.2 6944 1692 120 5347 -0.01 2.86 4.80 -0.54 0.00 0.02 0.60 0.00
110.2 4244 1034 72 3268 -0.25 3.20 4.80 -0.54 0.00 0.46 0.67 0.00
111.2 2855 695 48 2198 -0.16 2.13 4.80 -0.54 0.00 0.31 0.44 0.00
112.2 1440 351 24 1109 -0.08 1.06 4.80 -0.54 0.00 0.15 0.22 0.00
L 113.2 0 0 0 0 -0.16 0.93 4.80 -0.54 0.00 0.29 0.19 0.00
Max: 0.58 0.46 0.67 0.51
Tensile
Stress
limit (ksi)
D/C ratio
(comp limit)
f_top f_bot
Service I : PS+Perm+LL*(1+IM)
D/C
ratio(Ten
limit)
f_Bot (ksi)Compressive
Stress limit (ksi)
D/C
ratio(Ten
limit)
D/C ratio
(comp limit)
f_top (ksi)
Moment
demands
DC1+DC2
(kip-in)
Moment
demands
DC3+DW (kip-
in)
Moment demands
DC4 (kip-in)
Length
along
girder
(ft)
Moment
demands
LL(1+IM) (kip-
in)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/2020
Subject: Design Calculations Checked: CL Date: 4/14/2020
Task: Girders A Stress Page: of:
Job #: NO:
Note 1:
Note 2
f_bot SIM.
Note 3
Note 4
Check the stress to top of girder, so section modulus of the composite section, is the I_comp / y_tg, and y_tg
is the distance from comp. nuetral axis to the top of the girder.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/2020
Subject: Design Calculations Checked: CL Date: 4/14/2020
Task: Girders A Stress Page: of:
Job #: NO:
0 0.0 0 -0.16 0.93 4.80 -0.54 0.00 0.29 0.19 0.00
1.0 887 -0.08 1.07 4.80 -0.54 0.00 0.16 0.22 0.00
2.0 1759 -0.17 2.15 4.80 -0.54 0.00 0.32 0.45 0.00
3.0 2614 -0.26 3.23 4.80 -0.54 0.00 0.49 0.67 0.00
dv 5.0 4278 -0.03 2.92 4.80 -0.54 0.00 0.06 0.61 0.00
0.1L 11.3 9116 0.64 2.01 4.80 -0.54 0.13 0.00 0.42 0.00
13.0 10299 0.80 1.79 4.80 -0.54 0.17 0.00 0.37 0.00
14.0 10981 0.85 1.85 4.80 -0.54 0.18 0.00 0.39 0.00
15.0 11646 0.90 1.99 4.80 -0.54 0.19 0.00 0.41 0.00
16.0 12296 0.94 2.12 4.80 -0.54 0.20 0.00 0.44 0.00
0.2L 22.6 16189 1.48 1.40 4.80 -0.54 0.31 0.00 0.29 0.00
28.0 18861 1.85 0.90 4.80 -0.54 0.39 0.00 0.19 0.00
29.0 19305 1.89 0.92 4.80 -0.54 0.39 0.00 0.19 0.00
30.0 19733 1.93 0.96 4.80 -0.54 0.40 0.00 0.20 0.00
31.0 20146 1.96 1.01 4.80 -0.54 0.41 0.00 0.21 0.00
0.3L 33.9 21270 2.12 0.80 4.80 -0.54 0.44 0.00 0.17 0.00
0.4L 45.3 24309 2.54 0.24 4.80 -0.54 0.53 0.00 0.05 0.00
0.5L 56.6 25322 2.68 0.04 4.80 -0.54 0.56 0.00 0.01 0.00
0.6L 67.9 24309 2.54 0.24 4.80 -0.54 0.53 0.00 0.05 0.00
0.7L 79.2 21270 2.12 0.80 4.80 -0.54 0.44 0.00 0.17 0.00
82.2 20146 1.96 1.01 4.80 -0.54 0.41 0.00 0.21 0.00
83.2 19733 1.93 0.96 4.80 -0.54 0.40 0.00 0.20 0.00
84.2 19305 1.89 0.92 4.80 -0.54 0.39 0.00 0.19 0.00
85.2 18861 1.85 0.90 4.80 -0.54 0.39 0.00 0.19 0.00
0.8L 90.5 16206 1.48 1.40 4.80 -0.54 0.31 0.00 0.29 0.00
97.2 12296 0.94 2.12 4.80 -0.54 0.20 0.00 0.44 0.00
98.2 11646 0.90 1.99 4.80 -0.54 0.19 0.00 0.41 0.00
99.2 10981 0.85 1.85 4.80 -0.54 0.18 0.00 0.39 0.00
100.2 10299 0.80 1.79 4.80 -0.54 0.17 0.00 0.37 0.00
0.9L 101.8 9116 0.64 2.01 4.80 -0.54 0.13 0.00 0.42 0.00
dv 108.2 4278 -0.03 2.92 4.80 -0.54 0.00 0.06 0.61 0.00
110.2 2614 -0.26 3.23 4.80 -0.54 0.00 0.49 0.67 0.00
111.2 1759 -0.17 2.15 4.80 -0.54 0.00 0.32 0.45 0.00
112.2 887 -0.08 1.07 4.80 -0.54 0.00 0.16 0.22 0.00
L 113.2 0 -0.16 0.93 4.80 -0.54 0.00 0.29 0.19 0.00
Max: 0.56 0.49 0.67 0.00
f_Bot (ksi)
Compressiv
e Stress
limit (ksi)
Tensile
Stress limit
(ksi)
f_top f_bot
D/C ratio
(comp limit)
D/C ratio(Ten
limit)
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit)
Length along
girder (ft)
Moment
demands
0.8*LL(1+IM
) (kip-in)
f_top (ksi)
Service III : PS+Perm+0.8*LL*(1+IM)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/2020
Subject: Design Calculations Checked: CL Date: 4/14/2020
Task: Girders A Stress Page: of:
Job #: NO:
REQUIRED TOP REINFORCEMENT
0 0.0 -0.17 1.02 7.90 31.99 1.07 3
1.0 -0.18 1.32 6.70 28.88 0.96 3
2.0 -0.37 2.64 6.71 58.07 1.94 5
3.0 -0.55 3.97 6.73 87.57 2.92 7
dv 5.0 -0.47 3.88 5.90 64.93 2.16 5
0.1L 11.3 -0.22 3.64 3.10 15.86 0.53 2
13.0 -0.16 3.58 2.30 8.46 0.28 1
14.0 -0.18 3.77 2.49 10.47 0.35 1
15.0 -0.19 4.02 2.53 11.54 0.38 1
16.0 -0.21 4.27 2.57 12.71 0.42 1
0.2L 22.6 -0.01 4.08 0.13 0.03 0.00 1
28.0 0.13 3.95 0.00 0.00 0.00 0
29.0 0.12 4.03 0.00 0.00 0.00 0
30.0 0.12 4.15 0.00 0.00 0.00 0
31.0 0.12 4.27 0.00 0.00 0.00 0
0.3L 33.9 0.17 4.22 0.00 0.00 0.00 0
0.4L 45.3 0.33 4.07 0.00 0.00 0.00 0
0.5L 56.6 0.38 4.02 0.00 0.00 0.00 0
0.6L 67.9 0.33 4.07 0.00 0.00 0.00 0
0.7L 79.2 0.17 4.22 0.00 0.00 0.00 0
82.2 0.12 4.27 0.00 0.00 0.00 0
83.2 0.12 4.15 0.00 0.00 0.00 0
84.2 0.12 4.03 0.00 0.00 0.00 0
85.2 0.13 3.95 0.00 0.00 0.00 0
0.8L 90.5 -0.01 4.08 0.12 0.02 0.00 1
97.2 -0.21 4.27 2.57 12.71 0.42 1
98.2 -0.19 4.02 2.53 11.54 0.38 1
99.2 -0.18 3.77 2.49 10.47 0.35 1
100.2 -0.16 3.58 2.30 8.46 0.28 1
0.9L 101.8 -0.22 3.64 3.10 15.86 0.53 2
dv 108.2 -0.47 3.88 5.90 64.93 2.16 5
110.2 -0.55 3.97 6.73 87.57 2.92 7
111.2 -0.37 2.64 6.71 58.07 1.94 5
112.2 -0.18 1.32 6.70 28.88 0.96 3
L 113.2 -0.17 1.02 7.90 31.99 1.07 3
Length along
girder (ft) f_ci,top (ksi) f_ci,bot (ksi) x (in) T (kip) As (in^2)
# 6 rebars
(in^2)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders B Design Page: of:
Job #: NO:
L, Bridge span length (ft) 112.78
Bridge Width (ft) Upper bound 78.16
Bridge Width (ft) Lower Bound 71.60
Bridge Width (ft) Average 74.88
Number of Lanes 4
m, Multipresent factor for LL 0.65
Nb, Number of Girder 8
S, Max Girder Spacing (ft) 10.05
Bridge Skew Angle (degree) 31
For the bridge girder:
f'ci at transfer (ksi) 6.7 AASHTO 5.4.2.3.1
f'c after 28 days (ksi) 8
E_ci (ksi) for girder @ transfer 4716
During the construction of the bridge, it is required to not interfere with train traffic,
thus, the bridge slab system is precast concrete panel in between girders, stitched with CIP Concrete.
Tendon diameter (in) 0.6
One strand area (in^2) 0.217
Debonding length (from end of beam to where bonding commence), ft
10
Girder Distribution factors for DL, LL moment, LL Shear
Type of deck CIP Concrete, Precast Concrete
Supporting Component Precast Concrete I or Bulb-tee section
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders B Design Page: of:
Job #: NO:
Common Deck superstructure Table 4.6.2.2.1-1
Typical Cross section K Table 4.6.2.2.1-1
Live Load Distribution Factor for Moment in Interior Beams Table 4.6.2.2.2b-1
Rang of Applicability
S, spacing of beams, ϵ [ 3.5, 16] ft ✔
L, Span Length, ϵ [20,240] ft ✔
Nb, number of beams >=4 ✔
ts, depth of concrete slab ϵ [ 4.5, 12] in ✔
Depth of concrete slab, ts (in) 8.00
kg, longitudinal stiffness factor, ϵ [10^4 , 7x10^6] ✔
kg= n( I + A*eg^2) 1576804.87 4.6.2.2.1-1
n= E_beam / E_deck 1.26491106
f'c_slab (ksi) 6
E_beam (ksi) 5,154
E_slab (ksi) 4,074
A, (non-composite) cross section area of girder (in^2) 925 Caltrans Design Aids, CA BT-55
I, (non-composite) inertia (in^4) 373,350 Caltrans Design Aids, CA BT-55
Yb, CG to bottom of girder (in) 28.4 Caltrans Design Aids, CA BT-55
D, girder height (in) 55.125 Caltrans Design Aids, CA BT-55
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders B Design Page: of:
Job #: NO:
eg, dist. Btw CL of beam & CL of deck (in) 30.725
b_eff, deck effective width of girder (ft) 9.08
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders B Design Page: of:
Job #: NO:
Per above table from AASHTO, the LL distribution factor for moment in Interior beams are calculated:
g_int, One design lane loaded: 0.52 lane / girder multiple presence factor included
g_int, Two or more lane loaded: 0.77 lane / girder per C4.6.2.2.2b
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders B Design Page: of:
Job #: NO:
Per above table from AASHTO, the LL distribution factor for moment in exterior beams are calculated:
de, horizontal distance from CL of ext. web of ext. beam @ deck level, to int. edge of curb of traffic barrier
de (ft) 2.30
e=0.77+de/9.1 1.02
g_ext, one design lane loaded 0.53 lane/girder
g_ext, two or more design lane loaded 0.79 lane/girder
Considering the span length, it is very likley that cross frames & end diaphraagm will be necessary.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders B Design Page: of:
Job #: NO:
Per AASHTO C4.6.2.2.2d-1, exterior girders have higher load distribution factors due to cross frames
One lane loaded:
NL 1
X_ext, (ft) 35.18
e (ft) 24.03
x_1 (ft) 5.03
x_2 (ft) 15.08
x_3 (ft) 25.13
x_4 (ft) 35.18
R 0.32
Adjust with 1.2 multiple presence factor 0.39
Two Lanes loaded:
NL 2
e1 (ft) 24.03
e2 (ft) 6.5
R 0.50
Adjust with 1.0 multiple presence factor 0.50
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders B Design Page: of:
Job #: NO:
Three or more Lanes loaded:
NL 3
e1 (ft) 24.03
e2 (ft) 6.5
e3 (ft) 12
R 0.68
Adjust with 0.85 multiple presence factor 0.58
Final design values for moment distribution factors :
Load Case Int. Girder (lane)
One lane 0.52 0.53
NA 0.39
2 lanes loaded NA 0.50
3 lanes loaded NA 0.58
Design Value
Moment
Distribution 0.77 0.79
Max: 0.79
Two values are close enough, use the
maximum value for all to be conservative.
Note that AASHTO 4.6.2.2.2.e for skewed bridge provides reduction factors for live load distribution factors for momen in longitudinal
beams. However, CA amendment ignores reduction. Thus, no reduction applies for moment
Ext. Girder (lane)
Moment Distribution factor
per Table 4.6.2.2.2 Two or more
lane
0.77 0.79
Moment D.F. for ext. girder per
C4.6.2.2.2d-1
one lane loaded
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders B Design Page: of:
Job #: NO:
LL distribution factor for Shear :
Per above table from AASHTO, the LL distribution factor for shear in Interior beams are calculated:
g_int, One design lane loaded: 0.76 lane / girder multiple presence factor included
g_int, Two or more lane loaded: 0.96 lane / girder per C4.6.2.2.2b
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders B Design Page: of:
Job #: NO:
Per above table from AASHTO, the LL distribution factor for shear in exterior beams are calculated:
de (ft) 2.30
e=0.77+de/9.1 1.02
g_ext, one design lane loaded 0.53 lane/girder use same as ext one-lane for moment
g_ext, two or more design lane loaded 0.98 lane/girder
Notes:
AASHTO 4.6.2.2.3 C-1 provides correction factors for live load distribution factors for support shear of the obtuse girder.
CA Amendment revised AASHTO Table 4.6.2.2.3c-1 with equations provide for exterior girder & first interior girder.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders B Design Page: of:
Job #: NO:
Design values for shear distribution factors (without skew correction factor)
Load Case Int. Girder (lane)
One lane 0.76 NA
NA
NA 0.53
NA 0.98
Design Value
Shear
Distribution
Factor
0.96 0.98
Max: 0.98
Skew Correction factors for shear:
Shear D.F. for ext. girder per
C4.6.2.2.3b-1
one lane loaded
Two or more
laneTwo values are close enough, use the
maximum value for all to be conservative.
Ext. Girder (lane)
Shear Distribution factor per
Table 4.6.2.2.3a-1 Two or more
lane
0.96
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders B Design Page: of:
Job #: NO:
The shear correction factors are applied between the point of support at the obtuse corner and mid-span.
May be decreased linearly to a value of 1.0 at mid-span.
Skew Factor 1.09
Design values for shear distribution factors@ obtuse angle
Load Case Int. Girder (lane)
Design Value Shear D.F. 1.04 1.07 Max: 1.07
Two values are close enough, use the
maximum value for all to be conservative.Ext. Girder (lane)
1.07
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders B Design Page: of:
Job #: NO:
Moment Demands Calculations
One lane
0 0.0 0 0 0 0 0 0 0
dv 5.0 259 317 52 10 639 88 567
0.1L 11.3 551 674 111 23 1359 188 1205
0.2L 22.6 980 1198 197 45 2420 333 2141
0.3L 33.8 1286 1572 259 68 3185 438 2811
0.4L 45.1 1470 1797 296 91 3653 500 3212
0.5L 56.4 1531 1872 308 113 3824 521 3346
0.6L 67.7 1470 1797 296 91 3653 500 3212
0.7L 78.9 1286 1572 259 68 3185 438 2811
0.8L 90.2 980 1198 197 45 2420 333 2141
0.9L 101.5 551 674 111 23 1359 188 1205
dv 107.8 259 317 52 10 639 88 567
L 112.8 0 0 0 0 0 0 0
dv Use 0.9h (AASHTO 5.8.2.9) 5.03 ft
LL+IM Use Caltrans Bridge Design Aids attached as following.
Span length Moment (k-ft) End Shear (kip)
110 3229 122.8
120 3652.4 126.7
112.8 3346.8 123.9
Lane Load included from Caltrans Table
0 0
946 0
445 0
2206 0
1681 0
2627 0
2522 0
2206 0
2522 0
1681 0
Min LL
0 0
445 0
946 0
Length along
girder (ft)
For Each Girder
M (k-ft) DC1 M (k-ft) DC2 M (k-ft) DC3
M (k-ft)
DC4
M (k-ft)
DC Total
M (k-ft)
DW
(HL-93) LL+IM -M (k-f)
Distr.Fact
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders B Design Page: of:
Job #: NO:
Moment Capacity Calculations@ Wet Concr. Deck Stage (NonComposite)
Note 1 Note 4 Note 3
0 0.0 8 8 8 6 4 2 2 48.16 8.25 0.68 N.A. @ TF
dv 5.0 8 8 8 6 4 2 2 48.16 8.25 0.68 N.A. @ TF
0.1L 11.3 8 8 8 6 4 2 2 48.16 8.25 0.68 N.A. @ TF
0.2L 22.6 10 10 10 8 4 2 2 48.38 9.98 0.82 N.A. @ TF
0.3L 33.8 10 12 12 8 4 2 2 48.46 10.85 0.89 N.A. @ TF
0.4L 45.1 10 12 12 8 4 2 2 48.46 10.85 0.89 N.A. @ TF
0.5L 56.4 10 12 12 8 4 2 2 48.46 10.85 0.89 N.A. @ TF
0.6L 67.7 10 12 12 8 4 2 2 48.46 10.85 0.89 N.A. @ TF
0.7L 78.9 10 12 12 8 4 2 2 48.46 10.85 0.89 N.A. @ TF
0.8L 90.2 10 10 10 8 4 2 2 48.38 9.98 0.82 N.A. @ TF
0.9L 101.5 8 8 8 6 4 2 2 48.16 8.25 0.68 N.A. @ TF
dv 107.8 8 8 8 6 4 2 2 48.16 8.25 0.68 N.A. @ TF
L 112.8 8 8 8 6 4 2 2 48.16 8.25 0.68 N.A. @ TF
0.6" diameter tendons are used
Reference: AASHTO 2014 LRFD 7th Edition
Note 1: Note 4:
Note 2: Note 5:
Note 3: Note 6:Calcuated "c" to determine location of section
N.A.
No. Tendon
at 12.75"
From Bot
No.
Tendon at
14.75"
From Bot
dp(in) to
Girder top
Aps(in^2) c (in)
Action Type:
Nuetral axis
location
Length
along
girder (ft)
No. Tendon
at 2.75"
From Bot
No.
Tendon at
4.75" from
Bot
No.
Tendon at
6.75"
From Bot
No.
Tendon at
8.75" From
Bot
No.
Tendon at
10.75"
From Bot
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders B Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Wet Concrete Deck Stage
Note 2 Note 5 Note 6 Note 7 Note 8
0 0.0 0.68 0.58 268.9 8848 0.2105 1.00 8848 0 8848 0
dv 5.0 0.68 0.58 268.9 8848 0.2105 1.00 8848 721 8848 0.08
0.1L 11.3 0.68 0.58 268.9 8848 0.2105 1.00 8848 1531 8848 0.17
0.2L 22.6 0.82 0.70 268.7 10736 0.1743 1.00 10736 2722 10736 0.25
0.3L 33.8 0.89 0.76 268.6 11676 0.1605 1.00 11676 3573 11676 0.31
0.4L 45.1 0.89 0.76 268.6 11676 0.1605 1.00 11676 4083 11676 0.35
0.5L 56.4 0.89 0.76 268.6 11676 0.1605 1.00 11676 4253 11676 0.36
0.6L 67.7 0.89 0.76 268.6 11676 0.1605 1.00 11676 4083 11676 0.35
0.7L 78.9 0.89 0.76 268.6 11676 0.1605 1.00 11676 3573 11676 0.31
0.8L 90.2 0.82 0.70 268.7 10736 0.1743 1.00 10736 2722 10736 0.25
0.9L 101.5 0.68 0.58 268.9 8848 0.2105 1.00 8848 1531 8848 0.17
dv 107.8 0.68 0.58 268.9 8848 0.2105 1.00 8848 721 8848 0.08
L 112.8 0.68 0.58 268.9 8848 0.2105 1.00 8848 0 8848 0.00
Note 7: Moment formula chosen depends on girder action type
Beta_1 =0.85 Per AASHTO 5.7.2.2
Value of k =0.28 Per Table C5.7.3.1.1.1
Note 8:
phi
factor φ
φMn(k-
ft)
For Each Girder
Mu (k-ft)
Strength I φMn(k-ft) D/C
Length
along
girder
(ft)
Update c (in) a (in) f_ps(ksi) Mn(k-ft)Epslon_t
ξ_t
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders B Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Wet Concrete Deck Stage
Mu=1.25 DC1+1.25DC2
Controlling Combination to design girders:
Strength I 1.25 DC+1.5 DW
0
2000
4000
6000
8000
10000
12000
14000
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Mo
me
nt
(k
-ft)
Length (ft)
Moment Plot along Span Length
Mu (k-ft) Strength I φMn(k-ft)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders B Design Page: of:
Job #: NO:
0 0.0 0 0 0 0 0 0 0
dv 5.0 259 317 52 10 639 88 1023
0.1L 11.3 551 674 111 23 1359 188 2172
0.2L 22.6 980 1198 197 45 2420 333 3862
0.3L 33.8 1286 1572 259 68 3185 438 5069
0.4L 45.1 1470 1797 296 91 3653 500 5793
0.5L 56.4 1531 1872 308 113 3824 521 6034
0.6L 67.7 1470 1797 296 91 3653 500 5793
0.7L 78.9 1286 1572 259 68 3185 438 5069
0.8L 90.2 980 1198 197 45 2420 333 3862
0.9L 101.5 551 674 111 23 1359 188 2172
dv 107.8 259 317 52 10 639 88 1023
L 112.8 0 0 0 0 0 0 0 0 0
3032 0
1705 0
803 0
4737 0
4547 0
3979 0
3032 0
3979 0
4547 0
Min LL
0 0
803 0
1705 0
Length along
girder (ft)M (k-ft) DC1 M (k-ft) DC2 M (k-ft) DC3
M (k-ft)
DC4
M (k-ft)
DC Total
For Each Girder
M (k-ft)
DW
(P-15) LL+IM -M (k-f)
One lane Distr.Fact
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders B Design Page: of:
Job #: NO:
Moment Capacity Calculations@ Final Stage Stage
0 0.0 8 8 8 6 4 2 2 8 56.16 8.25 5.50
dv 5.0 8 8 8 6 4 2 2 8 56.16 8.25 5.50
0.1L 11.3 8 8 8 6 4 2 2 8 56.16 8.25 5.50
0.2L 22.6 10 10 10 8 4 2 2 8 56.38 9.98 6.62
0.3L 33.8 10 12 12 8 4 2 2 8 56.46 10.85 7.18
0.4L 45.1 10 12 12 8 4 2 2 8 56.46 10.85 7.18
0.5L 56.4 10 12 12 8 4 2 2 8 56.46 10.85 7.18
0.6L 67.7 10 12 12 8 4 2 2 8 56.46 10.85 7.18
0.7L 78.9 10 12 12 8 4 2 2 8 56.46 10.85 7.18
0.8L 90.2 10 10 10 8 4 2 2 8 56.38 9.98 6.62
0.9L 101.5 8 8 8 6 4 2 2 8 56.16 8.25 5.50
dv 107.8 8 8 8 6 4 2 2 8 56.16 8.25 5.50
L 112.8 8 8 8 6 4 2 2 8 56.16 8.25 5.50
Considering the concrete deck is acting compositely with the CA BT 55 girders.
Also Conservatively igore the precast concrete panel's composite concrete reaction, due to lack of friction btw the panel surface.
c (in) No.
Tendon at
10.75"
From Bot
No. Tendon
at 12.75"
From Bot
No.
Tendon at
14.75"
From Bot
Composite
Deck THK
(in)
dp(in) to
Deck top
Aps(in^2)
Length
along
girder (ft)
No. Tendon
at 2.75"
From Bot
No.
Tendon at
4.75" from
Bot
No.
Tendon at
6.75"
From Bot
No.
Tendon at
8.75" From
Bot
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders B Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Final Stage
0 0.0 N.A. @ Deck 5.50 4.68 262.6 9713 0.0276 1.00 9713
dv 5.0 N.A. @ Deck 5.50 4.68 262.6 9713 0.0276 1.00 9713
0.1L 11.3 N.A. @ Deck 5.50 4.68 262.6 9713 0.0276 1.00 9713
0.2L 22.6 N.A. @ Deck 6.62 5.63 261.1 11634 0.0225 1.00 11634
0.3L 33.8 N.A. @ Deck 7.18 6.10 260.4 12573 0.0206 1.00 12573
0.4L 45.1 N.A. @ Deck 7.18 6.10 260.4 12573 0.0206 1.00 12573
0.5L 56.4 N.A. @ Deck 7.18 6.10 260.4 12573 0.0206 1.00 12573
0.6L 67.7 N.A. @ Deck 7.18 6.10 260.4 12573 0.0206 1.00 12573
0.7L 78.9 N.A. @ Deck 7.18 6.10 260.4 12573 0.0206 1.00 12573
0.8L 90.2 N.A. @ Deck 6.62 5.63 261.1 11634 0.0225 1.00 11634
0.9L 101.5 N.A. @ Deck 5.50 4.68 262.6 9713 0.0276 1.00 9713
dv 107.8 N.A. @ Deck 5.50 4.68 262.6 9713 0.0276 1.00 9713
L 112.8 N.A. @ Deck 5.50 4.68 262.6 9713 0.0276 1.00 9713
Mn(k-ft)Epslon_t
ξ_t
phi factor
φ φMn(k-ft)
Length
along
girder
(ft)
Action Type
(Neutral Axis
location)
Update
c (in)
from
deck
top
a (in) f_ps(ksi)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders B Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Final Stage
0 0.0 0 0 9713 0 0.00
dv 5.0 1710 2015 9713 0.18 0.21
0.1L 11.3 3634 4282 9713 0.37 0.44
0.2L 22.6 6467 7618 11634 0.56 0.65
0.3L 33.8 8499 10009 12573 0.68 0.80
0.4L 45.1 9729 11455 12573 0.77 0.91
0.5L 56.4 10158 11956 12573 0.81 0.95
0.6L 67.7 9729 11455 12573 0.77 0.91
0.7L 78.9 8499 10009 12573 0.68 0.80
0.8L 90.2 6467 7618 11634 0.56 0.65
0.9L 101.5 3634 4282 9713 0.37 0.44
dv 107.8 1710 2015 9713 0.18 0.21
L 112.8 0 0 9713 0.00 0.00
Strength I 1.25 DC+1.5 DW+1.75 LL
Strength II 1.25 DC+1.5 DW+1.35 LL-permit
17
Mu (k-ft)
Strength I
Mu (k-ft)
Strength II φMn(k-ft)
D/C for
Strength I
D/C for
Strength II
Length
along
girder (ft)
For Each Girder
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders B Design Page: of:
Job #: NO:
0
2000
4000
6000
8000
10000
12000
14000
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Mo
me
nt
(k
-ft)
Length (ft)
Moment Plot along Span Length
Mu (k-ft) Strength I
φMn(k-ft)
Mu (k-ft) Strength II
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders B Stress Page: of:
Job #: NO:
For the stress calc, negative stress is tensile stress; positive stress is compressive stress.
Stress Calculations @ Transfer Stage
Tendons f_pu (ksi) 270
Tendon f_pbt (ksi) 202.5 (AASHTO Table 5.9.3.1)
Tendon E_ps (ksi) 28,500
Girder Concrete E_pc (ksi) 5,154
n'-1 = E_ps/ E_pc -1 4.53
f'c (ksi) 8
f'ci (ksi) 6.7
CA BT 55, Ag (in^2) 925
CA BT 55, w (k/ft) 0.963
CA BT 55, Yt, CG to Top (in) 26.70
CA BT 55, Yb, CG to Bot (in) 28.40
CA BT 55, Ig (in^4) 373,350
Ƴ_h Say H= 70% 1
Ƴ_st 0.65
Δf_pR (ksi) 2.4
Transfer length l_t =60*db (in) 36
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders B Stress Page: of:
Job #: NO:
Stress Calculations @ Transfer Stage
* debond included
Note 1 Note 2 Note 3 Note 4 Note 5 Note 6
0 0.0 8 8 8 6 4 2 2 8.25 48.16 21.46 0 19 183 ok 378
1.0 8 8 8 6 4 2 2 8.25 48.16 21.46 646 19 183 ok 504
2.0 8 8 8 6 4 2 2 8.25 48.16 21.46 1280 19 184 ok 1009
3.0 8 8 8 6 4 2 2 8.25 48.16 21.46 1903 19 184 ok 1515
dv 5.0 8 8 8 6 4 2 2 8.25 48.16 21.46 3114 18 184 ok 1518
0.1L 11.3 8 8 8 6 4 2 2 8.25 48.16 21.46 6614 17 185 ok 1526
13.0 8 8 8 6 4 2 2 8.25 48.16 21.46 7495 17 185 ok 1528
14.0 10 10 10 8 4 2 2 9.98 48.38 21.68 7991 21 182 ok 1603
15.0 10 10 10 8 4 2 2 9.98 48.38 21.68 8475 21 182 ok 1709
16.0 10 10 10 8 4 2 2 9.98 48.38 21.68 8947 21 182 ok 1816
0.2L 22.6 10 10 10 8 4 2 2 9.98 48.38 21.68 11759 20 183 ok 1824
28.0 10 10 10 8 4 2 2 9.98 48.38 21.68 13716 19 183 ok 1829
29.0 10 12 12 8 4 2 2 10.85 48.46 21.76 14039 21 181 ok 1864
30.0 10 12 12 8 4 2 2 10.85 48.46 21.76 14349 21 182 ok 1917
31.0 10 12 12 8 4 2 2 10.85 48.46 21.76 14648 21 182 ok 1971
0.3L 33.8 10 12 12 8 4 2 2 10.85 48.46 21.76 15434 21 182 ok 1973
0.4L 45.1 10 12 12 8 4 2 2 10.85 48.46 21.76 17639 20 182 ok 1980
0.5L 56.4 10 12 12 8 4 2 2 10.85 48.46 21.76 18373 20 183 ok 1982
0.6L 67.7 10 12 12 8 4 2 2 10.85 48.46 21.76 17639 20 182 ok 1980
0.7L 78.9 10 12 12 8 4 2 2 10.85 48.46 21.76 15434 21 182 ok 1973
81.8 10 12 12 8 4 2 2 10.85 48.46 21.76 14648 21 182 ok 1971
82.8 10 12 12 8 4 2 2 10.85 48.46 21.76 14349 21 182 ok 1917
83.8 10 12 12 8 4 2 2 10.85 48.46 21.76 14039 21 181 ok 1864
84.8 10 10 10 8 4 2 2 9.98 48.38 21.68 13716 19 183 ok 1829
0.8L 90.2 10 10 10 8 4 2 2 9.98 48.38 21.68 11759 20 183 ok 1824
96.8 10 10 10 8 4 2 2 9.98 48.38 21.68 8947 21 182 ok 1816
97.8 10 10 10 8 4 2 2 9.98 48.38 21.68 8475 21 182 ok 1709
98.8 10 10 10 8 4 2 2 9.98 48.38 21.68 7991 21 182 ok 1603
99.8 8 8 8 6 4 2 2 8.25 48.16 21.46 7495 17 185 ok 1528
0.9L 101.5 8 8 8 6 4 2 2 8.25 48.16 21.46 6614 17 185 ok 1526
dv 108.2 8 8 8 6 4 2 2 8.25 48.16 21.46 2888 19 184 ok 1517
109.8 8 8 8 6 4 2 2 8.25 48.16 21.46 1903 19 184 ok 1515
110.8 8 8 8 6 4 2 2 8.25 48.16 21.46 1280 19 184 ok 1009
111.8 8 8 8 6 4 2 2 8.25 48.16 21.46 646 19 183 ok 504
L 112.8 8 8 8 6 4 2 2 8.25 48.16 21.46 0 19 183 ok 378
Δf_pES
(ksi)
f_pi
(ksi)
Stress
limit for
tendon
0.8fpy
Jakcing
force
@transfer,
Pji (kip)
No. Tendon
at 12.75"
From Bot
No. Tendon
at 14.75"
From Bot
Aps(in^2)
Y_p,
Tendon
CG to Top
of Girder
(in)
e_ti (in)
Mg (kip-
in) Girder
Self
Weight
Length along
girder (ft) No. Tendon
at 2.75"
From Bot
No. Tendon
at 4.75"
from Bot
No.
Tendon at
6.75" From
Bot
No. Tendon
at 8.75"
From Bot
No. Tendon
at 10.75"
From Bot
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders B Stress Page: of:
Job #: NO:
Note 1: Eccencity equal to value of Y_p minus YtNote 2: Mg is the moment caused by the self weight of the girder+ Concrete deck
Note 4:
Note 3:
Note 5: fpy assumes to be 0.9fpu; Table 5.9.3-1 AASHTO
Note 7: Top fiber concr gider stress=P/A-P*e/(I/Yt)+Mg/(I/Yb) (+ is compression, - is tension)
Note 9:
Note 6: Jakcing force @ transfer taken as f_pi multiplies Aps (Total area of tendons)
Note 8: Bot. fiber concr gider stress=P/A+P*e/(I/Yt)-Mg/(I/Yb) (+ is cpmpression, - is tension )
Note 10:
Girder top bars: #4 Total of 6, 0.2x6=1.2in^2
f_pi is the value of f_pbt minus Δf_pES. Per AASHTO C5.9.5.2.3a, if the transformed
section properties are used, the Δf_pES should not be inlcuded in the prestressing force.
In this case, jacking force is calcuated as f_pbt minus short term elastic shortening loss,
and so the Gorss section properties of the concrete girder are used.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders B Stress Page: of:
Job #: NO:
0
500
1000
1500
2000
2500
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Jakcing force @transfer, Pji (kip)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders B Stress Page: of:
Job #: NO:
Stress Calculations @ Transfer Stage
Note 7 Note 8 Note 9 Note 10
0 0.0 -0.17 1.02 4.36 -0.62 0.00 0.28 0.24 0.00
1.0 -0.18 1.32 4.36 -0.62 0.00 0.29 0.30 0.00
2.0 -0.37 2.64 4.36 -0.62 0.00 0.59 0.61 0.00
3.0 -0.55 3.97 4.36 -0.62 0.00 0.89 0.91 0.00
dv 5.0 -0.47 3.88 4.36 -0.62 0.00 0.75 0.89 0.00
0.1L 11.3 -0.22 3.64 4.36 -0.62 0.00 0.35 0.84 0.00
13.0 -0.16 3.58 4.36 -0.62 0.00 0.25 0.82 0.00
14.0 -0.18 3.77 4.36 -0.62 0.00 0.29 0.87 0.00
15.0 -0.20 4.02 4.36 -0.62 0.00 0.31 0.92 0.00
16.0 -0.21 4.28 4.36 -0.62 0.00 0.34 0.98 0.00
0.2L 22.6 -0.01 4.08 4.36 -0.62 0.00 0.02 0.94 0.00
28.0 0.12 3.95 4.36 -0.62 0.03 0.00 0.91 0.00
29.0 0.12 4.03 4.36 -0.62 0.03 0.00 0.93 0.00
30.0 0.12 4.15 4.36 -0.62 0.03 0.00 0.95 0.00
31.0 0.11 4.28 4.36 -0.62 0.03 0.00 0.98 0.00
0.3L 33.8 0.17 4.22 4.36 -0.62 0.04 0.00 0.97 0.00
0.4L 45.1 0.32 4.07 4.36 -0.62 0.07 0.00 0.94 0.00
0.5L 56.4 0.37 4.03 4.36 -0.62 0.09 0.00 0.92 0.00
0.6L 67.7 0.32 4.07 4.36 -0.62 0.07 0.00 0.94 0.00
0.7L 78.9 0.17 4.22 4.36 -0.62 0.04 0.00 0.97 0.00
81.8 0.11 4.28 4.36 -0.62 0.03 0.00 0.98 0.00
82.8 0.12 4.15 4.36 -0.62 0.03 0.00 0.95 0.00
83.8 0.12 4.03 4.36 -0.62 0.03 0.00 0.93 0.00
84.8 0.12 3.95 4.36 -0.62 0.03 0.00 0.91 0.00
0.8L 90.2 -0.01 4.08 4.36 -0.62 0.00 0.02 0.94 0.00
96.8 -0.21 4.28 4.36 -0.62 0.00 0.34 0.98 0.00
97.8 -0.20 4.02 4.36 -0.62 0.00 0.31 0.92 0.00
98.8 -0.18 3.77 4.36 -0.62 0.00 0.29 0.87 0.00
99.8 -0.16 3.58 4.36 -0.62 0.00 0.25 0.82 0.00
0.9L 101.5 -0.22 3.64 4.36 -0.62 0.00 0.35 0.84 0.00
dv 108.2 -0.48 3.90 4.36 -0.62 0.00 0.78 0.90 0.00
109.8 -0.55 3.97 4.36 -0.62 0.00 0.89 0.91 0.00
110.8 -0.37 2.64 4.36 -0.62 0.00 0.59 0.61 0.00
111.8 -0.18 1.32 4.36 -0.62 0.00 0.29 0.30 0.00
L 112.8 -0.17 1.02 4.36 -0.62 0.00 0.28 0.24 0.00
Max: 0.09 0.89 0.98 0.00
f_bot (ksi) (comp limit
0.65f'ci)
(Ten limit -
0.24*sqrt(f
'ci) ksi)
f_top f_bot
D/C ratio
(comp
limit )
D/C
ratio(Ten
limit )
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit )
Length
along
girder (ft)
f_top
(ksi)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders B Stress Page: of:
Job #: NO:
For the stress calc, negative stress is tensile stress; positive stress is compressive stress.
Stress Calculations @ Transfer Stage
Tendons f_pu (ksi) 270
Tendon f_pbt (ksi) 203 (AASHTO Table 5.9.3.1)
Tendon E_ps (ksi) 28500
Girder Concrete E_pc (ksi) 5154
n'-1 = E_ps/ E_pc -1 5
f'c (ksi) 8.0
f'ci (ksi) 6.7
CA BT 55, Ag (in^2) 925
CA BT 55, w (k/ft) 1
CA BT 55, Yt, CG to Top (in) 27
CA BT 55, Yb, CG to Bot (in) 28
CA BT 55, Ig (in^4) 373350
Ƴ_h Say H= 70% 1
Ƴ_st 0.65
Δf_pR (ksi) 2.4
Transfer length l_t =60*db (in) 36
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders B Stress Page: of:
Job #: NO:
Stress Calculations @ PS + Perm load condition
Transformed seciton properties
Note 1 Note 2 Note 3 Note 4 Note 5 Note 6 Note 7 Note 8
0 0.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
1.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
2.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
3.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
dv 5.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
0.1L 11.3 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
13.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
14.0 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
15.0 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
16.0 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
0.2L 22.6 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
28.0 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
29.0 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
30.0 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
31.0 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
0.3L 33.8 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
0.4L 45.1 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
0.5L 56.4 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
0.6L 67.7 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
0.7L 78.9 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
81.8 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
82.8 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
83.8 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
84.8 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
0.8L 90.2 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
96.8 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
97.8 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
98.8 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
99.8 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
0.9L 101.5 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
dv 108.2 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
109.8 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
110.8 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
111.8 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
L 112.8 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
Transfor
med
Y_ttop
(in)
Transfor
med
Y_tbot
(in)
Ʃ Ai*(Y_i-
Y_ttop)^
2
(in^4)
I_final(in
^4)
Transfor
med
S_ttop
(in^3)
Transfor
med
S_tbot
(in^3)
Aps(in^
2)
Y_p,
Tendon CG
to
GirderTop
(in)
Aps*(n'-
1)
(in^2)
Total
Aps*(n-
1)+Ag
(in^2) Ig (in^4)
ƩAi*Y_i
(in^3)
Length
along
girder
(ft)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders B Stress Page: of:
Job #: NO:
Note 1: Ignore moment of inertia I from prestrssing tendons, since it is too small compared to that of precast concrete Girder.
Note 2: Summation of tranformed strands area times CG of strands, and area of precast concrete girder times CG of the girder.
Note 3: Values of Note 2 divide by the total area of the transformed section to determine CG of the tranformed section (from top of the section)
Note 4: CG of the tranformed seciton (from bottom of the section)
Note 5:
Note 6: I_final =Ig + values at Note 5
Note 7: Transformed section modulus from top of seciton is I_final divide by Transformed Y_ttop
Note 8: Transformed section modulus from bottom of seciton is I_final divide by Transformed Y_tbot
Summation of tranformed area of strands times squrea of CG differenec between strands and the entire tranformed section, plus such value
for precast concrete girder component.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders B Stress Page: of:
Job #: NO:
Stress Calculations @ PS + Perm load condition
* debond included
Note 9 Note 10 Note 11 Note 12 Note 13 Note 14 Note 15 Note 16
0 0.0 21 22 181 372 0 -0.16 0.93 3.60 -0.54 0.00 0.29 0.26 0.00
1.0 21 22 181 496 1435 -0.11 1.14 3.60 -0.54 0.00 0.20 0.32 0.00
2.0 21 22 181 993 2845 -0.21 2.28 3.60 -0.54 0.00 0.40 0.63 0.00
3.0 21 22 181 1489 4229 -0.32 3.42 3.60 -0.54 0.00 0.60 0.95 0.00
dv 5.0 21 22 181 1489 6920 -0.13 3.23 3.60 -0.54 0.00 0.25 0.90 0.00
0.1L 11.3 21 22 181 1489 14700 0.42 2.68 3.60 -0.54 0.12 0.00 0.74 0.00
13.0 21 22 181 1489 16657 0.55 2.54 3.60 -0.54 0.15 0.00 0.71 0.00
14.0 21 24 178 1572 17758 0.58 2.65 3.60 -0.54 0.16 0.00 0.73 0.00
15.0 21 24 178 1675 18834 0.62 2.83 3.60 -0.54 0.17 0.00 0.78 0.00
16.0 21 24 178 1778 19884 0.65 3.01 3.60 -0.54 0.18 0.00 0.84 0.00
0.2L 22.6 21 24 178 1778 26133 1.09 2.57 3.60 -0.54 0.30 0.00 0.71 0.00
28.0 21 24 178 1778 30483 1.39 2.27 3.60 -0.54 0.39 0.00 0.63 0.00
29.0 21 26 177 1817 31199 1.42 2.30 3.60 -0.54 0.39 0.00 0.64 0.00
30.0 21 26 177 1868 31890 1.45 2.38 3.60 -0.54 0.40 0.00 0.66 0.00
31.0 21 26 177 1919 32555 1.47 2.46 3.60 -0.54 0.41 0.00 0.68 0.00
0.3L 33.8 21 26 177 1919 34300 1.59 2.34 3.60 -0.54 0.44 0.00 0.65 0.00
0.4L 45.1 21 26 177 1919 39200 1.94 2.00 3.60 -0.54 0.54 0.00 0.56 0.00
0.5L 56.4 21 26 177 1919 40833 2.05 1.89 3.60 -0.54 0.57 0.00 0.52 0.00
0.6L 67.7 21 26 177 1919 39200 1.94 2.00 3.60 -0.54 0.54 0.00 0.56 0.00
0.7L 78.9 21 26 177 1919 34300 1.59 2.34 3.60 -0.54 0.44 0.00 0.65 0.00
81.8 21 26 177 1919 32555 1.47 2.46 3.60 -0.54 0.41 0.00 0.68 0.00
82.8 21 26 177 1868 31890 1.45 2.38 3.60 -0.54 0.40 0.00 0.66 0.00
83.8 21 26 177 1817 31199 1.42 2.30 3.60 -0.54 0.39 0.00 0.64 0.00
84.8 21 24 178 1778 30483 1.39 2.27 3.60 -0.54 0.39 0.00 0.63 0.00
0.8L 90.2 21 24 178 1778 26133 1.09 2.57 3.60 -0.54 0.30 0.00 0.71 0.00
96.8 21 24 178 1778 19884 0.65 3.01 3.60 -0.54 0.18 0.00 0.84 0.00
97.8 21 24 178 1675 18834 0.62 2.83 3.60 -0.54 0.17 0.00 0.78 0.00
98.8 21 24 178 1572 17758 0.58 2.65 3.60 -0.54 0.16 0.00 0.73 0.00
99.8 21 22 181 1489 16657 0.55 2.54 3.60 -0.54 0.15 0.00 0.71 0.00
0.9L 101.5 21 22 181 1489 14700 0.42 2.68 3.60 -0.54 0.12 0.00 0.74 0.00
dv 108.2 21 22 181 1489 6418 -0.17 3.27 3.60 -0.54 0.00 0.31 0.91 0.00
109.8 21 22 181 1489 4229 -0.32 3.42 3.60 -0.54 0.00 0.60 0.95 0.00
110.8 21 22 181 993 2845 -0.21 2.28 3.60 -0.54 0.00 0.40 0.63 0.00
111.8 21 22 181 496 1435 -0.11 1.14 3.60 -0.54 0.00 0.20 0.32 0.00
L 112.8 21 22 181 372 0 -0.16 0.93 3.60 -0.54 0.00 0.29 0.26 0.00
Max: 0.57 0.60 0.95 0.00
f_top
(ksi)
f_Bot
(ksi)
Compres
sive
Stress
limit (ksi)
Tensile
Stress
limit (ksi)
f_top f_bot
D/C ratio
(comp limit)
D/C
ratio(Ten
limit)
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit)
Length
along
girder
(ft)
e (in)Δf_pLT
(ksi)fpe (ksi) Pf (kiP)
Moment
demands
DC1+DC2
(kip-in)
PS+ Perm (DC1+DC2)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders B Stress Page: of:
Job #: NO:
Note 9: Eccentricity of the seciton is Y_p(in) from girder top subtracted by Transformed Y_ttop
Note 10
Note 11 fpe is stress at transfer minus long term loss Δf_pLT
Note 12 Prestressing force Pf, is fpe times area of the prestressing tendons, Aps.
Note 13
Note 14
Note 15
Note 16:
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders B Stress Page: of:
Job #: NO:
Tendons f_pu (ksi) 270
Tendon f_pbt (ksi) 202.5 (AASHTO Table 5.9.3.1)
CA BT 55, Ag (in^2) 925
CA BT 55, w (k/ft) 0.963
CA BT 55, Yt, CG to Top (in) 26.7
CA BT 55, Yb, CG to Bot (in) 28.4
CA BT 55, Ig (in^4) 373350
Tendon E_ps (ksi) 28,500
Girder Concrete E_pc (ksi) 5,154
n'-1 = E_ps/ E_pc -1 5
Girder f'c (ksi) 8
Girder f'ci (ksi) 6.7
Deck Concrete E_c (ksi) 4,074
Girder Concrete E_pc (ksi) 5,154
n= E_c/E_pc 0.79
CIP Deck f'c (ksi) 5
Deck effective width (ft) 9.08
Depth of concrete slab, ts (in) 8.00
Precast panel thickness (in) 3.50
Tranformed deck area (in^2) 768.74 (based on Ec of 8ksi concrete)
Tranformed effective deck width (in) 96.093 (based on Ec of 8ksi concrete)
Transfer length l_t =60*db (in) 36
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders B Stress Page: of:
Job #: NO:
Stress Calculations @ Service, composite section properties include the Deck Slab
Note 1
0 0.0 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 372
1.0 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 496
2.0 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 993
3.0 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
dv 5.0 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
0.1L 11.3 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
13.0 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
14.0 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1572
15.0 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1675
16.0 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1778
0.2L 22.6 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1778
28.0 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1778
29.0 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1817
30.0 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1868
31.0 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
0.3L 33.8 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
0.4L 45.1 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
0.5L 56.4 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
0.6L 67.7 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
0.7L 78.9 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
81.8 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
82.8 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1868
83.8 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1817
84.8 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1778
0.8L 90.2 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1778
96.8 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1778
97.8 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1675
98.8 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1572
99.8 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
0.9L 101.5 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
dv 108.2 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
109.8 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
110.8 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 993
111.8 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 496
L 112.8 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 372
e (in)
Δf_pLT
(ksi)
fpe
(ksi) Pf (kiP)
Yi to Top
of Deck
ƩAi*Y_i
(in^3)
Comp
Y_ttop
(in)
ToDeck
Top
Comp.
Y_tbot
(in)
I_comp
(in^4)
Comp.
S_tg
(in^3)
Comp S_tb
(in^3)
Length
along girder
(ft)
I_tg(in^4)Transformed
Y_ttop (in)
Transfor
med
Y_tbot
(in)
Tranfor
med
A_deck
(in^2)
A_deck+A
ps*(n'-
1)+Ag
(in^2)
From PS+Perm stress calc
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders B Stress Page: of:
Job #: NO:
Stress Calculations @ Service, composite section properties include the Deck Slab
* debond included Note 2 Note 3 Note 4
0 0.0 0 0 0 0 -0.16 0.93 4.80 -0.54 0.00 0.29 0.19 0.00
1.0 1435 350 24 1108 -0.08 1.06 4.80 -0.54 0.00 0.15 0.22 0.00
2.0 2845 693 48 2196 -0.17 2.13 4.80 -0.54 0.00 0.31 0.44 0.00
3.0 4229 1030 72 3265 -0.25 3.20 4.80 -0.54 0.00 0.47 0.67 0.00
dv 5.0 6920 1686 120 5342 -0.01 2.87 4.80 -0.54 0.00 0.03 0.60 0.00
0.1L 11.3 14700 3581 272 11347 0.67 1.91 4.80 -0.54 0.14 0.00 0.40 0.00
13.0 16657 4058 313 12858 0.84 1.66 4.80 -0.54 0.18 0.00 0.35 0.00
14.0 17758 4326 337 13708 0.89 1.72 4.80 -0.54 0.19 0.00 0.36 0.00
15.0 18834 4588 361 14539 0.94 1.85 4.80 -0.54 0.20 0.00 0.38 0.00
16.0 19884 4844 385 15350 0.99 1.97 4.80 -0.54 0.21 0.00 0.41 0.00
0.2L 22.6 26133 6366 543 20173 1.54 1.21 4.80 -0.54 0.32 0.00 0.25 0.00
28.0 30483 7426 674 23531 1.92 0.68 4.80 -0.54 0.40 0.00 0.14 0.00
29.0 31199 7600 698 24084 1.96 0.69 4.80 -0.54 0.41 0.00 0.14 0.00
30.0 31890 7768 722 24617 2.00 0.73 4.80 -0.54 0.42 0.00 0.15 0.00
31.0 32555 7930 746 25130 2.03 0.78 4.80 -0.54 0.42 0.00 0.16 0.00
0.3L 33.8 34300 8356 815 26477 2.19 0.56 4.80 -0.54 0.46 0.00 0.12 0.00
0.4L 45.1 39200 9549 1086 30260 2.62 -0.04 4.80 -0.54 0.55 0.00 0.00 0.07
0.5L 56.4 40833 9947 1358 31521 2.76 -0.25 4.80 -0.54 0.58 0.00 0.00 0.46
0.6L 67.7 39200 9549 1086 30260 2.62 -0.04 4.80 -0.54 0.55 0.00 0.00 0.07
0.7L 78.9 34300 8356 815 26477 2.19 0.56 4.80 -0.54 0.46 0.00 0.12 0.00
81.8 32555 7930 746 25130 2.03 0.78 4.80 -0.54 0.42 0.00 0.16 0.00
82.8 31890 7768 722 24617 2.00 0.73 4.80 -0.54 0.42 0.00 0.15 0.00
83.8 31199 7600 698 24084 1.96 0.69 4.80 -0.54 0.41 0.00 0.14 0.00
84.8 30483 7426 674 23531 1.92 0.68 4.80 -0.54 0.40 0.00 0.14 0.00
0.8L 90.2 26133 6366 543 20173 1.54 1.21 4.80 -0.54 0.32 0.00 0.25 0.00
96.8 19884 4844 385 15350 0.99 1.97 4.80 -0.54 0.21 0.00 0.41 0.00
97.8 18834 4588 361 14539 0.94 1.85 4.80 -0.54 0.20 0.00 0.38 0.00
98.8 17758 4326 337 13708 0.89 1.72 4.80 -0.54 0.19 0.00 0.36 0.00
99.8 16657 4058 313 12858 0.84 1.66 4.80 -0.54 0.18 0.00 0.35 0.00
0.9L 101.5 14700 3581 272 11347 0.67 1.91 4.80 -0.54 0.14 0.00 0.40 0.00
dv 108.2 6418 1564 111 4955 -0.06 2.93 4.80 -0.54 0.00 0.11 0.61 0.00
109.8 4229 1030 72 3265 -0.25 3.20 4.80 -0.54 0.00 0.47 0.67 0.00
110.8 2845 693 48 2196 -0.17 2.13 4.80 -0.54 0.00 0.31 0.44 0.00
111.8 1435 350 24 1108 -0.08 1.06 4.80 -0.54 0.00 0.15 0.22 0.00
L 112.8 0 0 0 0 -0.16 0.93 4.80 -0.54 0.00 0.29 0.19 0.00
Max: 0.58 0.47 0.67 0.46
Tensile
Stress
limit (ksi)
f_top f_bot
D/C ratio
(comp limit)
D/C
ratio(Ten
limit)
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit)
Moment
demands
DC3+DW (kip-
in)
Moment demands
DC4 (kip-in)
Moment
demands
LL(1+IM) (kip-
in)
f_top (ksi) f_Bot (ksi)Compressive
Stress limit (ksi)
Length
along
girder
(ft)
Moment
demands
DC1+DC2
(kip-in)
Service I : PS+Perm+LL*(1+IM)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders B Stress Page: of:
Job #: NO:
Note 1:
Note 2
f_bot SIM.
Note 3
Note 4
Check the stress to top of girder, so section modulus of the composite section, is the I_comp / y_tg, and y_tg
is the distance from comp. nuetral axis to the top of the girder.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders B Stress Page: of:
Job #: NO:
0 0.0 0 -0.16 0.93 4.80 -0.54 0.00 0.29 0.19 0.00
1.0 886 -0.09 1.07 4.80 -0.54 0.00 0.16 0.22 0.00
2.0 1757 -0.17 2.15 4.80 -0.54 0.00 0.32 0.45 0.00
3.0 2612 -0.26 3.23 4.80 -0.54 0.00 0.49 0.67 0.00
dv 5.0 4274 -0.03 2.92 4.80 -0.54 0.00 0.06 0.61 0.00
0.1L 11.3 9078 0.63 2.02 4.80 -0.54 0.13 0.00 0.42 0.00
13.0 10286 0.80 1.79 4.80 -0.54 0.17 0.00 0.37 0.00
14.0 10967 0.84 1.86 4.80 -0.54 0.18 0.00 0.39 0.00
15.0 11631 0.89 1.99 4.80 -0.54 0.19 0.00 0.42 0.00
16.0 12280 0.94 2.13 4.80 -0.54 0.20 0.00 0.44 0.00
0.2L 22.6 16139 1.47 1.41 4.80 -0.54 0.31 0.00 0.29 0.00
28.0 18825 1.84 0.92 4.80 -0.54 0.38 0.00 0.19 0.00
29.0 19267 1.88 0.93 4.80 -0.54 0.39 0.00 0.19 0.00
30.0 19694 1.91 0.98 4.80 -0.54 0.40 0.00 0.20 0.00
31.0 20104 1.95 1.03 4.80 -0.54 0.41 0.00 0.21 0.00
0.3L 33.8 21182 2.10 0.83 4.80 -0.54 0.44 0.00 0.17 0.00
0.4L 45.1 24208 2.52 0.26 4.80 -0.54 0.52 0.00 0.06 0.00
0.5L 56.4 25217 2.66 0.07 4.80 -0.54 0.55 0.00 0.01 0.00
0.6L 67.7 24208 2.52 0.26 4.80 -0.54 0.52 0.00 0.06 0.00
0.7L 78.9 21182 2.10 0.83 4.80 -0.54 0.44 0.00 0.17 0.00
81.8 20104 1.95 1.03 4.80 -0.54 0.41 0.00 0.21 0.00
82.8 19694 1.91 0.98 4.80 -0.54 0.40 0.00 0.20 0.00
83.8 19267 1.88 0.93 4.80 -0.54 0.39 0.00 0.19 0.00
84.8 18825 1.84 0.92 4.80 -0.54 0.38 0.00 0.19 0.00
0.8L 90.2 16139 1.47 1.41 4.80 -0.54 0.31 0.00 0.29 0.00
96.8 12280 0.94 2.13 4.80 -0.54 0.20 0.00 0.44 0.00
97.8 11631 0.89 1.99 4.80 -0.54 0.19 0.00 0.42 0.00
98.8 10967 0.84 1.86 4.80 -0.54 0.18 0.00 0.39 0.00
99.8 10286 0.80 1.79 4.80 -0.54 0.17 0.00 0.37 0.00
0.9L 101.5 9078 0.63 2.02 4.80 -0.54 0.13 0.00 0.42 0.00
dv 108.2 3964 -0.08 2.98 4.80 -0.54 0.00 0.14 0.62 0.00
109.8 2612 -0.26 3.23 4.80 -0.54 0.00 0.49 0.67 0.00
110.8 1757 -0.17 2.15 4.80 -0.54 0.00 0.32 0.45 0.00
111.8 886 -0.09 1.07 4.80 -0.54 0.00 0.16 0.22 0.00
L 112.8 0 -0.16 0.93 4.80 -0.54 0.00 0.29 0.19 0.00
Max: 0.55 0.49 0.67 0.00
f_Bot (ksi)
Compressiv
e Stress
limit (ksi)
Tensile
Stress limit
(ksi)
f_top f_bot
D/C ratio
(comp limit)
D/C ratio(Ten
limit)
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit)
Length along
girder (ft)
Moment
demands
0.8*LL(1+IM
) (kip-in)
f_top (ksi)
Service III : PS+Perm+0.8*LL*(1+IM)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders B Stress Page: of:
Job #: NO:
REQUIRED TOP REINFORCEMENT
0 0.0 -0.17 1.02 7.90 31.99 1.07 3
1.0 -0.18 1.32 6.70 28.92 0.96 3
2.0 -0.37 2.64 6.72 58.15 1.94 5
3.0 -0.55 3.97 6.73 87.70 2.92 7
dv 5.0 -0.47 3.88 5.91 65.12 2.17 5
0.1L 11.3 -0.22 3.64 3.14 16.29 0.54 2
13.0 -0.16 3.58 2.33 8.67 0.29 1
14.0 -0.18 3.77 2.52 10.71 0.36 1
15.0 -0.20 4.02 2.56 11.80 0.39 1
16.0 -0.21 4.28 2.60 13.00 0.43 1
0.2L 22.6 -0.01 4.08 0.19 0.06 0.00 1
28.0 0.12 3.95 0.00 0.00 0.00 0
29.0 0.12 4.03 0.00 0.00 0.00 0
30.0 0.12 4.15 0.00 0.00 0.00 0
31.0 0.11 4.28 0.00 0.00 0.00 0
0.3L 33.8 0.17 4.22 0.00 0.00 0.00 0
0.4L 45.1 0.32 4.07 0.00 0.00 0.00 0
0.5L 56.4 0.37 4.03 0.00 0.00 0.00 0
0.6L 67.7 0.32 4.07 0.00 0.00 0.00 0
0.7L 78.9 0.17 4.22 0.00 0.00 0.00 0
81.8 0.11 4.28 0.00 0.00 0.00 0
82.8 0.12 4.15 0.00 0.00 0.00 0
83.8 0.12 4.03 0.00 0.00 0.00 0
84.8 0.12 3.95 0.00 0.00 0.00 0
0.8L 90.2 -0.01 4.08 0.19 0.06 0.00 1
96.8 -0.21 4.28 2.60 13.00 0.43 1
97.8 -0.20 4.02 2.56 11.80 0.39 1
98.8 -0.18 3.77 2.52 10.71 0.36 1
99.8 -0.16 3.58 2.33 8.67 0.29 1
0.9L 101.5 -0.22 3.64 3.14 16.29 0.54 2
dv 108.2 -0.48 3.90 6.07 69.13 2.30 6
109.8 -0.55 3.97 6.73 87.70 2.92 7
110.8 -0.37 2.64 6.72 58.15 1.94 5
111.8 -0.18 1.32 6.70 28.92 0.96 3
L 112.8 -0.17 1.02 7.90 31.99 1.07 3
f_ci,top (ksi) f_ci,bot (ksi) x (in) T (kip) As (in^2)
# 6 rebars
(in^2)
Length along
girder (ft)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders C Design Page: of:
Job #: NO:
L, Bridge span length (ft) 112.38
Bridge Width (ft) Upper bound 78.16
Bridge Width (ft) Lower Bound 71.60
Bridge Width (ft) Average 74.88
Number of Lanes 4
m, Multipresent factor for LL 0.65
Nb, Number of Girder 8
S, Max Girder Spacing (ft) 10.05
Bridge Skew Angle (degree) 31
For the bridge girder:
f'ci at transfer (ksi) 6.7 AASHTO 5.4.2.3.1
f'c after 28 days (ksi) 8
E_ci (ksi) for girder @ transfer 4716
During the construction of the bridge, it is required to not interfere with train traffic,
thus, the bridge slab system is precast concrete panel in between girders, stitched with CIP Concrete.
Tendon diameter (in) 0.6
One strand area (in^2) 0.217
Debonding length (from end of beam to where bonding commence), ft
10
Girder Distribution factors for DL, LL moment, LL Shear
Type of deck CIP Concrete, Precast Concrete
Supporting Component Precast Concrete I or Bulb-tee section
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders C Design Page: of:
Job #: NO:
Common Deck superstructure Table 4.6.2.2.1-1
Typical Cross section K Table 4.6.2.2.1-1
Live Load Distribution Factor for Moment in Interior Beams Table 4.6.2.2.2b-1
Rang of Applicability
S, spacing of beams, ϵ [ 3.5, 16] ft ✔
L, Span Length, ϵ [20,240] ft ✔
Nb, number of beams >=4 ✔
ts, depth of concrete slab ϵ [ 4.5, 12] in ✔
Depth of concrete slab, ts (in) 8.00
kg, longitudinal stiffness factor, ϵ [10^4 , 7x10^6] ✔
kg= n( I + A*eg^2) 1576804.87 4.6.2.2.1-1
n= E_beam / E_deck 1.26491106
f'c_slab (ksi) 6
E_beam (ksi) 5,154
E_slab (ksi) 4,074
A, (non-composite) cross section area of girder (in^2) 925 Caltrans Design Aids, CA BT-55
I, (non-composite) inertia (in^4) 373,350 Caltrans Design Aids, CA BT-55
Yb, CG to bottom of girder (in) 28.4 Caltrans Design Aids, CA BT-55
D, girder height (in) 55.125 Caltrans Design Aids, CA BT-55
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders C Design Page: of:
Job #: NO:
eg, dist. Btw CL of beam & CL of deck (in) 30.725
b_eff, deck effective width of girder (ft) 9.08
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders C Design Page: of:
Job #: NO:
Per above table from AASHTO, the LL distribution factor for moment in Interior beams are calculated:
g_int, One design lane loaded: 0.52 lane / girder multiple presence factor included
g_int, Two or more lane loaded: 0.77 lane / girder per C4.6.2.2.2b
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders C Design Page: of:
Job #: NO:
Per above table from AASHTO, the LL distribution factor for moment in exterior beams are calculated:
de, horizontal distance from CL of ext. web of ext. beam @ deck level, to int. edge of curb of traffic barrier
de (ft) 2.30
e=0.77+de/9.1 1.02
g_ext, one design lane loaded 0.53 lane/girder
g_ext, two or more design lane loaded 0.79 lane/girder
Considering the span length, it is very likley that cross frames & end diaphraagm will be necessary.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders C Design Page: of:
Job #: NO:
Per AASHTO C4.6.2.2.2d-1, exterior girders have higher load distribution factors due to cross frames
One lane loaded:
NL 1
X_ext, (ft) 35.18
e (ft) 24.03
x_1 (ft) 5.03
x_2 (ft) 15.08
x_3 (ft) 25.13
x_4 (ft) 35.18
R 0.32
Adjust with 1.2 multiple presence factor 0.39
Two Lanes loaded:
NL 2
e1 (ft) 24.03
e2 (ft) 6.5
R 0.50
Adjust with 1.0 multiple presence factor 0.50
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders C Design Page: of:
Job #: NO:
Three or more Lanes loaded:
NL 3
e1 (ft) 24.03
e2 (ft) 6.5
e3 (ft) 12
R 0.68
Adjust with 0.85 multiple presence factor 0.58
Final design values for moment distribution factors :
Load Case Int. Girder (lane)
One lane 0.52 0.53
NA 0.39
2 lanes loaded NA 0.50
3 lanes loaded NA 0.58
Design Value
Moment
Distribution 0.77 0.79
Max: 0.79
Two values are close enough, use the
maximum value for all to be conservative.
Note that AASHTO 4.6.2.2.2.e for skewed bridge provides reduction factors for live load distribution factors for momen in longitudinal
beams. However, CA amendment ignores reduction. Thus, no reduction applies for moment
Ext. Girder (lane)
Moment Distribution factor
per Table 4.6.2.2.2 Two or more
lane
0.77 0.79
Moment D.F. for ext. girder per
C4.6.2.2.2d-1
one lane loaded
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders C Design Page: of:
Job #: NO:
LL distribution factor for Shear :
Per above table from AASHTO, the LL distribution factor for shear in Interior beams are calculated:
g_int, One design lane loaded: 0.76 lane / girder multiple presence factor included
g_int, Two or more lane loaded: 0.96 lane / girder per C4.6.2.2.2b
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders C Design Page: of:
Job #: NO:
Per above table from AASHTO, the LL distribution factor for shear in exterior beams are calculated:
de (ft) 2.30
e=0.77+de/9.1 1.02
g_ext, one design lane loaded 0.53 lane/girder use same as ext one-lane for moment
g_ext, two or more design lane loaded 0.98 lane/girder
Notes:
AASHTO 4.6.2.2.3 C-1 provides correction factors for live load distribution factors for support shear of the obtuse girder.
CA Amendment revised AASHTO Table 4.6.2.2.3c-1 with equations provide for exterior girder & first interior girder.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders C Design Page: of:
Job #: NO:
Design values for shear distribution factors (without skew correction factor)
Load Case Int. Girder (lane)
One lane 0.76 NA
NA
NA 0.53
NA 0.98
Design Value
Shear
Distribution
Factor
0.96 0.98
Max: 0.98
Skew Correction factors for shear:
Shear D.F. for ext. girder per
C4.6.2.2.3b-1
one lane loaded
Two or more
laneTwo values are close enough, use the
maximum value for all to be conservative.
Ext. Girder (lane)
Shear Distribution factor per
Table 4.6.2.2.3a-1 Two or more
lane
0.96
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders C Design Page: of:
Job #: NO:
The shear correction factors are applied between the point of support at the obtuse corner and mid-span.
May be decreased linearly to a value of 1.0 at mid-span.
Skew Factor 1.09
Design values for shear distribution factors@ obtuse angle
Load Case Int. Girder (lane)
Design Value Shear D.F. 1.04 1.07 Max: 1.07
Two values are close enough, use the
maximum value for all to be conservative.Ext. Girder (lane)
1.07
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders C Design Page: of:
Job #: NO:
Moment Demands Calculations
One lane
0 0.0 0 0 0 0 0 0 0
dv 5.0 259 316 52 10 637 88 566
0.1L 11.2 547 669 110 23 1349 186 1198
0.2L 22.5 973 1189 196 45 2403 331 2131
0.3L 33.7 1277 1561 257 68 3162 434 2796
0.4L 45.0 1459 1784 294 90 3627 496 3196
0.5L 56.2 1520 1858 306 113 3797 517 3329
0.6L 67.4 1459 1784 294 90 3627 496 3196
0.7L 78.7 1277 1561 257 68 3162 434 2796
0.8L 89.9 973 1189 196 45 2403 331 2131
0.9L 101.1 547 669 110 23 1349 186 1198
dv 107.4 259 316 52 10 637 88 566
L 112.4 0 0 0 0 0 0 0
dv Use 0.9h (AASHTO 5.8.2.9) 5.03 ft
LL+IM Use Caltrans Bridge Design Aids attached as following.
Span length Moment (k-ft) End Shear (kip)
110 3229 122.8
120 3652.4 126.7
112.4 3329.6 123.7
Lane Load included from Caltrans Table
0 0
942 0
445 0
2197 0
1674 0
2616 0
2511 0
2197 0
2511 0
1674 0
Min LL
0 0
445 0
942 0
Length along
girder (ft)
For Each Girder
M (k-ft) DC1 M (k-ft) DC2 M (k-ft) DC3
M (k-ft)
DC4
M (k-ft)
DC Total
M (k-ft)
DW
(HL-93) LL+IM -M (k-f)
Distr.Fact
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders C Design Page: of:
Job #: NO:
Moment Capacity Calculations@ Wet Concr. Deck Stage (NonComposite)
Note 1 Note 4 Note 3
0 0.0 8 8 8 6 4 2 2 48.16 8.25 0.68 N.A. @ TF
dv 5.0 8 8 8 6 4 2 2 48.16 8.25 0.68 N.A. @ TF
0.1L 11.2 8 8 8 6 4 2 2 48.16 8.25 0.68 N.A. @ TF
0.2L 22.5 10 10 10 8 4 2 2 48.38 9.98 0.82 N.A. @ TF
0.3L 33.7 10 12 12 8 4 2 2 48.46 10.85 0.89 N.A. @ TF
0.4L 45.0 10 12 12 8 4 2 2 48.46 10.85 0.89 N.A. @ TF
0.5L 56.2 10 12 12 8 4 2 2 48.46 10.85 0.89 N.A. @ TF
0.6L 67.4 10 12 12 8 4 2 2 48.46 10.85 0.89 N.A. @ TF
0.7L 78.7 10 12 12 8 4 2 2 48.46 10.85 0.89 N.A. @ TF
0.8L 89.9 10 10 10 8 4 2 2 48.38 9.98 0.82 N.A. @ TF
0.9L 101.1 8 8 8 6 4 2 2 48.16 8.25 0.68 N.A. @ TF
dv 107.4 8 8 8 6 4 2 2 48.16 8.25 0.68 N.A. @ TF
L 112.4 8 8 8 6 4 2 2 48.16 8.25 0.68 N.A. @ TF
0.6" diameter tendons are used
Reference: AASHTO 2014 LRFD 7th Edition
Note 1: Note 4:
Note 2: Note 5:
Note 3: Note 6:Calcuated "c" to determine location of section
N.A.
No. Tendon
at 12.75"
From Bot
No.
Tendon at
14.75"
From Bot
dp(in) to
Girder top
Aps(in^2) c (in)
Action Type:
Nuetral axis
location
Length
along
girder (ft)
No. Tendon
at 2.75"
From Bot
No.
Tendon at
4.75" from
Bot
No.
Tendon at
6.75"
From Bot
No.
Tendon at
8.75" From
Bot
No.
Tendon at
10.75"
From Bot
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders C Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Wet Concrete Deck Stage
Note 2 Note 5 Note 6 Note 7 Note 8
0 0.0 0.68 0.58 268.9 8848 0.2105 1.00 8848 0 8848 0
dv 5.0 0.68 0.58 268.9 8848 0.2105 1.00 8848 718 8848 0.08
0.1L 11.2 0.68 0.58 268.9 8848 0.2105 1.00 8848 1520 8848 0.17
0.2L 22.5 0.82 0.70 268.7 10736 0.1743 1.00 10736 2703 10736 0.25
0.3L 33.7 0.89 0.76 268.6 11676 0.1605 1.00 11676 3547 11676 0.30
0.4L 45.0 0.89 0.76 268.6 11676 0.1605 1.00 11676 4054 11676 0.35
0.5L 56.2 0.89 0.76 268.6 11676 0.1605 1.00 11676 4223 11676 0.36
0.6L 67.4 0.89 0.76 268.6 11676 0.1605 1.00 11676 4054 11676 0.35
0.7L 78.7 0.89 0.76 268.6 11676 0.1605 1.00 11676 3547 11676 0.30
0.8L 89.9 0.82 0.70 268.7 10736 0.1743 1.00 10736 2703 10736 0.25
0.9L 101.1 0.68 0.58 268.9 8848 0.2105 1.00 8848 1520 8848 0.17
dv 107.4 0.68 0.58 268.9 8848 0.2105 1.00 8848 718 8848 0.08
L 112.4 0.68 0.58 268.9 8848 0.2105 1.00 8848 0 8848 0.00
Note 7: Moment formula chosen depends on girder action type
Beta_1 =0.85 Per AASHTO 5.7.2.2
Value of k =0.28 Per Table C5.7.3.1.1.1
Note 8:
phi
factor φ
φMn(k-
ft)
For Each Girder
Mu (k-ft)
Strength I φMn(k-ft) D/C
Length
along
girder
(ft)
Update c (in) a (in) f_ps(ksi) Mn(k-ft)Epslon_t
ξ_t
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders C Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Wet Concrete Deck Stage
Mu=1.25 DC1+1.25DC2
Controlling Combination to design girders:
Strength I 1.25 DC+1.5 DW
0
2000
4000
6000
8000
10000
12000
14000
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Mo
me
nt
(k
-ft)
Length (ft)
Moment Plot along Span Length
Mu (k-ft) Strength I φMn(k-ft)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders C Design Page: of:
Job #: NO:
0 0.0 0 0 0 0 0 0 0
dv 5.0 259 316 52 10 637 88 1018
0.1L 11.2 547 669 110 23 1349 186 2155
0.2L 22.5 973 1189 196 45 2403 331 3832
0.3L 33.7 1277 1561 257 68 3162 434 5029
0.4L 45.0 1459 1784 294 90 3627 496 5748
0.5L 56.2 1520 1858 306 113 3797 517 5987
0.6L 67.4 1459 1784 294 90 3627 496 5748
0.7L 78.7 1277 1561 257 68 3162 434 5029
0.8L 89.9 973 1189 196 45 2403 331 3832
0.9L 101.1 547 669 110 23 1349 186 2155
dv 107.4 259 316 52 10 637 88 1018
L 112.4 0 0 0 0 0 0 0 0 0
3011 0
1694 0
800 0
4705 0
4516 0
3952 0
3011 0
3952 0
4516 0
Min LL
0 0
800 0
1694 0
Length along
girder (ft)M (k-ft) DC1 M (k-ft) DC2 M (k-ft) DC3
M (k-ft)
DC4
M (k-ft)
DC Total
For Each Girder
M (k-ft)
DW
(P-15) LL+IM -M (k-f)
One lane Distr.Fact
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders C Design Page: of:
Job #: NO:
Moment Capacity Calculations@ Final Stage Stage
0 0.0 8 8 8 6 4 2 2 8 56.16 8.25 5.50
dv 5.0 8 8 8 6 4 2 2 8 56.16 8.25 5.50
0.1L 11.2 8 8 8 6 4 2 2 8 56.16 8.25 5.50
0.2L 22.5 10 10 10 8 4 2 2 8 56.38 9.98 6.62
0.3L 33.7 10 12 12 8 4 2 2 8 56.46 10.85 7.18
0.4L 45.0 10 12 12 8 4 2 2 8 56.46 10.85 7.18
0.5L 56.2 10 12 12 8 4 2 2 8 56.46 10.85 7.18
0.6L 67.4 10 12 12 8 4 2 2 8 56.46 10.85 7.18
0.7L 78.7 10 12 12 8 4 2 2 8 56.46 10.85 7.18
0.8L 89.9 10 10 10 8 4 2 2 8 56.38 9.98 6.62
0.9L 101.1 8 8 8 6 4 2 2 8 56.16 8.25 5.50
dv 107.4 8 8 8 6 4 2 2 8 56.16 8.25 5.50
L 112.4 8 8 8 6 4 2 2 8 56.16 8.25 5.50
Considering the concrete deck is acting compositely with the CA BT 55 girders.
Also Conservatively igore the precast concrete panel's composite concrete reaction, due to lack of friction btw the panel surface.
c (in) No.
Tendon at
10.75"
From Bot
No. Tendon
at 12.75"
From Bot
No.
Tendon at
14.75"
From Bot
Composite
Deck THK
(in)
dp(in) to
Deck top
Aps(in^2)
Length
along
girder (ft)
No. Tendon
at 2.75"
From Bot
No.
Tendon at
4.75" from
Bot
No.
Tendon at
6.75"
From Bot
No.
Tendon at
8.75" From
Bot
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders C Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Final Stage
0 0.0 N.A. @ Deck 5.50 4.68 262.6 9713 0.0276 1.00 9713
dv 5.0 N.A. @ Deck 5.50 4.68 262.6 9713 0.0276 1.00 9713
0.1L 11.2 N.A. @ Deck 5.50 4.68 262.6 9713 0.0276 1.00 9713
0.2L 22.5 N.A. @ Deck 6.62 5.63 261.1 11634 0.0225 1.00 11634
0.3L 33.7 N.A. @ Deck 7.18 6.10 260.4 12573 0.0206 1.00 12573
0.4L 45.0 N.A. @ Deck 7.18 6.10 260.4 12573 0.0206 1.00 12573
0.5L 56.2 N.A. @ Deck 7.18 6.10 260.4 12573 0.0206 1.00 12573
0.6L 67.4 N.A. @ Deck 7.18 6.10 260.4 12573 0.0206 1.00 12573
0.7L 78.7 N.A. @ Deck 7.18 6.10 260.4 12573 0.0206 1.00 12573
0.8L 89.9 N.A. @ Deck 6.62 5.63 261.1 11634 0.0225 1.00 11634
0.9L 101.1 N.A. @ Deck 5.50 4.68 262.6 9713 0.0276 1.00 9713
dv 107.4 N.A. @ Deck 5.50 4.68 262.6 9713 0.0276 1.00 9713
L 112.4 N.A. @ Deck 5.50 4.68 262.6 9713 0.0276 1.00 9713
Mn(k-ft)Epslon_t
ξ_t
phi factor
φ φMn(k-ft)
Length
along
girder
(ft)
Action Type
(Neutral Axis
location)
Update
c (in)
from
deck
top
a (in) f_ps(ksi)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders C Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Final Stage
0 0.0 0 0 9713 0 0.00
dv 5.0 1706 2008 9713 0.18 0.21
0.1L 11.2 3613 4252 9713 0.37 0.44
0.2L 22.5 6430 7565 11634 0.55 0.65
0.3L 33.7 8450 9940 12573 0.67 0.79
0.4L 45.0 9673 11376 12573 0.77 0.90
0.5L 56.2 10100 11873 12573 0.80 0.94
0.6L 67.4 9673 11376 12573 0.77 0.90
0.7L 78.7 8450 9940 12573 0.67 0.79
0.8L 89.9 6430 7565 11634 0.55 0.65
0.9L 101.1 3613 4252 9713 0.37 0.44
dv 107.4 1706 2008 9713 0.18 0.21
L 112.4 0 0 9713 0.00 0.00
Strength I 1.25 DC+1.5 DW+1.75 LL
Strength II 1.25 DC+1.5 DW+1.35 LL-permit
17
Mu (k-ft)
Strength I
Mu (k-ft)
Strength II φMn(k-ft)
D/C for
Strength I
D/C for
Strength II
Length
along
girder (ft)
For Each Girder
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders C Design Page: of:
Job #: NO:
0
2000
4000
6000
8000
10000
12000
14000
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Mo
me
nt
(k
-ft)
Length (ft)
Moment Plot along Span Length
Mu (k-ft) Strength I
φMn(k-ft)
Mu (k-ft) Strength II
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders C Stress Page: of:
Job #: NO:
For the stress calc, negative stress is tensile stress; positive stress is compressive stress.
Stress Calculations @ Transfer Stage
Tendons f_pu (ksi) 270
Tendon f_pbt (ksi) 202.5 (AASHTO Table 5.9.3.1)
Tendon E_ps (ksi) 28,500
Girder Concrete E_pc (ksi) 5,154
n'-1 = E_ps/ E_pc -1 4.53
f'c (ksi) 8
f'ci (ksi) 6.7
CA BT 55, Ag (in^2) 925
CA BT 55, w (k/ft) 0.963
CA BT 55, Yt, CG to Top (in) 26.70
CA BT 55, Yb, CG to Bot (in) 28.40
CA BT 55, Ig (in^4) 373,350
Ƴ_h Say H= 70% 1
Ƴ_st 0.65
Δf_pR (ksi) 2.4
Transfer length l_t =60*db (in) 36
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders C Stress Page: of:
Job #: NO:
Stress Calculations @ Transfer Stage* debond included
Note 1 Note 2 Note 3 Note 4 Note 5 Note 6
0 0.0 8 8 8 6 4 2 2 8.25 48.16 21.46 0 19 183 ok 378
1.0 8 8 8 6 4 2 2 8.25 48.16 21.46 644 19 183 ok 504
2.0 8 8 8 6 4 2 2 8.25 48.16 21.46 1275 19 184 ok 1009
3.0 8 8 8 6 4 2 2 8.25 48.16 21.46 1896 19 184 ok 1515
dv 5.0 8 8 8 6 4 2 2 8.25 48.16 21.46 3102 18 184 ok 1518
0.1L 11.2 8 8 8 6 4 2 2 8.25 48.16 21.46 6567 17 185 ok 1526
13.0 8 8 8 6 4 2 2 8.25 48.16 21.46 7464 17 185 ok 1528
14.0 10 10 10 8 4 2 2 9.98 48.38 21.68 7958 21 182 ok 1603
15.0 10 10 10 8 4 2 2 9.98 48.38 21.68 8439 21 182 ok 1709
16.0 10 10 10 8 4 2 2 9.98 48.38 21.68 8910 21 182 ok 1815
0.2L 22.5 10 10 10 8 4 2 2 9.98 48.38 21.68 11674 20 183 ok 1823
28.0 10 10 10 8 4 2 2 9.98 48.38 21.68 13651 19 183 ok 1829
29.0 10 12 12 8 4 2 2 10.85 48.46 21.76 13970 21 181 ok 1864
30.0 10 12 12 8 4 2 2 10.85 48.46 21.76 14279 21 182 ok 1917
31.0 10 12 12 8 4 2 2 10.85 48.46 21.76 14576 21 182 ok 1970
0.3L 33.7 10 12 12 8 4 2 2 10.85 48.46 21.76 15323 21 182 ok 1973
0.4L 45.0 10 12 12 8 4 2 2 10.85 48.46 21.76 17512 20 182 ok 1979
0.5L 56.2 10 12 12 8 4 2 2 10.85 48.46 21.76 18241 20 183 ok 1982
0.6L 67.4 10 12 12 8 4 2 2 10.85 48.46 21.76 17512 20 182 ok 1979
0.7L 78.7 10 12 12 8 4 2 2 10.85 48.46 21.76 15323 21 182 ok 1973
81.4 10 12 12 8 4 2 2 10.85 48.46 21.76 14576 21 182 ok 1970
82.4 10 12 12 8 4 2 2 10.85 48.46 21.76 14279 21 182 ok 1917
83.4 10 12 12 8 4 2 2 10.85 48.46 21.76 13970 21 181 ok 1864
84.4 10 10 10 8 4 2 2 9.98 48.38 21.68 13651 19 183 ok 1829
0.8L 89.9 10 10 10 8 4 2 2 9.98 48.38 21.68 11674 20 183 ok 1823
96.4 10 10 10 8 4 2 2 9.98 48.38 21.68 8910 21 182 ok 1815
97.4 10 10 10 8 4 2 2 9.98 48.38 21.68 8439 21 182 ok 1709
98.4 10 10 10 8 4 2 2 9.98 48.38 21.68 7958 21 182 ok 1603
99.4 8 8 8 6 4 2 2 8.25 48.16 21.46 7464 17 185 ok 1528
0.9L 101.1 8 8 8 6 4 2 2 8.25 48.16 21.46 6567 17 185 ok 1526
dv 108.2 8 8 8 6 4 2 2 8.25 48.16 21.46 2634 19 184 ok 1517
109.4 8 8 8 6 4 2 2 8.25 48.16 21.46 1896 19 184 ok 1515
110.4 8 8 8 6 4 2 2 8.25 48.16 21.46 1275 19 184 ok 1009
111.4 8 8 8 6 4 2 2 8.25 48.16 21.46 644 19 183 ok 504
L 112.4 8 8 8 6 4 2 2 8.25 48.16 21.46 0 19 183 ok 378
Δf_pES
(ksi)
f_pi
(ksi)
Stress
limit for
tendon
0.8fpy
Jakcing
force
@transfer,
Pji (kip)
No. Tendon
at 12.75"
From Bot
No. Tendon
at 14.75"
From Bot
Aps(in^2)
Y_p,
Tendon
CG to Top
of Girder
(in)
e_ti (in)
Mg (kip-
in) Girder
Self
Weight
Length along
girder (ft) No. Tendon
at 2.75"
From Bot
No. Tendon
at 4.75"
from Bot
No.
Tendon at
6.75" From
Bot
No. Tendon
at 8.75"
From Bot
No. Tendon
at 10.75"
From Bot
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders C Stress Page: of:
Job #: NO:
Note 1: Eccencity equal to value of Y_p minus YtNote 2: Mg is the moment caused by the self weight of the girder+ Concrete deck
Note 4:
Note 3:
Note 5: fpy assumes to be 0.9fpu; Table 5.9.3-1 AASHTO
Note 7: Top fiber concr gider stress=P/A-P*e/(I/Yt)+Mg/(I/Yb) (+ is compression, - is tension)
Note 9:
Note 6: Jakcing force @ transfer taken as f_pi multiplies Aps (Total area of tendons)
Note 8: Bot. fiber concr gider stress=P/A+P*e/(I/Yt)-Mg/(I/Yb) (+ is cpmpression, - is tension )
Note 10:
Girder top bars: #4 Total of 6, 0.2x6=1.2in^2
f_pi is the value of f_pbt minus Δf_pES. Per AASHTO C5.9.5.2.3a, if the transformed
section properties are used, the Δf_pES should not be inlcuded in the prestressing force.
In this case, jacking force is calcuated as f_pbt minus short term elastic shortening loss,
and so the Gorss section properties of the concrete girder are used.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders C Stress Page: of:
Job #: NO:
0
500
1000
1500
2000
2500
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Jakcing force @transfer, Pji (kip)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders C Stress Page: of:
Job #: NO:
Stress Calculations @ Transfer Stage
Note 7 Note 8 Note 9 Note 10
0 0.0 -0.17 1.02 4.36 -0.62 0.00 0.28 0.24 0.00
1.0 -0.18 1.32 4.36 -0.62 0.00 0.29 0.30 0.00
2.0 -0.37 2.64 4.36 -0.62 0.00 0.59 0.61 0.00
3.0 -0.55 3.97 4.36 -0.62 0.00 0.89 0.91 0.00
dv 5.0 -0.47 3.88 4.36 -0.62 0.00 0.75 0.89 0.00
0.1L 11.2 -0.22 3.64 4.36 -0.62 0.00 0.36 0.84 0.00
13.0 -0.16 3.58 4.36 -0.62 0.00 0.26 0.82 0.00
14.0 -0.18 3.77 4.36 -0.62 0.00 0.29 0.87 0.00
15.0 -0.20 4.02 4.36 -0.62 0.00 0.32 0.92 0.00
16.0 -0.21 4.28 4.36 -0.62 0.00 0.34 0.98 0.00
0.2L 22.5 -0.02 4.09 4.36 -0.62 0.00 0.03 0.94 0.00
28.0 0.12 3.95 4.36 -0.62 0.03 0.00 0.91 0.00
29.0 0.11 4.04 4.36 -0.62 0.03 0.00 0.93 0.00
30.0 0.11 4.16 4.36 -0.62 0.03 0.00 0.95 0.00
31.0 0.11 4.28 4.36 -0.62 0.02 0.00 0.98 0.00
0.3L 33.7 0.16 4.23 4.36 -0.62 0.04 0.00 0.97 0.00
0.4L 45.0 0.31 4.08 4.36 -0.62 0.07 0.00 0.94 0.00
0.5L 56.2 0.36 4.03 4.36 -0.62 0.08 0.00 0.93 0.00
0.6L 67.4 0.31 4.08 4.36 -0.62 0.07 0.00 0.94 0.00
0.7L 78.7 0.16 4.23 4.36 -0.62 0.04 0.00 0.97 0.00
81.4 0.11 4.28 4.36 -0.62 0.02 0.00 0.98 0.00
82.4 0.11 4.16 4.36 -0.62 0.03 0.00 0.95 0.00
83.4 0.11 4.04 4.36 -0.62 0.03 0.00 0.93 0.00
84.4 0.12 3.95 4.36 -0.62 0.03 0.00 0.91 0.00
0.8L 89.9 -0.02 4.09 4.36 -0.62 0.00 0.03 0.94 0.00
96.4 -0.21 4.28 4.36 -0.62 0.00 0.34 0.98 0.00
97.4 -0.20 4.02 4.36 -0.62 0.00 0.32 0.92 0.00
98.4 -0.18 3.77 4.36 -0.62 0.00 0.29 0.87 0.00
99.4 -0.16 3.58 4.36 -0.62 0.00 0.26 0.82 0.00
0.9L 101.1 -0.22 3.64 4.36 -0.62 0.00 0.36 0.84 0.00
dv 108.2 -0.50 3.92 4.36 -0.62 0.00 0.80 0.90 0.00
109.4 -0.55 3.97 4.36 -0.62 0.00 0.89 0.91 0.00
110.4 -0.37 2.64 4.36 -0.62 0.00 0.59 0.61 0.00
111.4 -0.18 1.32 4.36 -0.62 0.00 0.29 0.30 0.00
L 112.4 -0.17 1.02 4.36 -0.62 0.00 0.28 0.24 0.00
Max: 0.08 0.89 0.98 0.00
f_bot (ksi) (comp limit
0.65f'ci)
(Ten limit -
0.24*sqrt(f
'ci) ksi)
f_top f_bot
D/C ratio
(comp
limit )
D/C
ratio(Ten
limit )
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit )
Length
along
girder (ft)
f_top
(ksi)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: Date:
Task: Girders C Stress Page: of:
Job #: NO:
For the stress calc, negative stress is tensile stress; positive stress is compressive stress.
Stress Calculations @ Transfer Stage
Tendons f_pu (ksi) 270
Tendon f_pbt (ksi) 203 (AASHTO Table 5.9.3.1)
Tendon E_ps (ksi) 28500
Girder Concrete E_pc (ksi) 5154
n'-1 = E_ps/ E_pc -1 5
f'c (ksi) 8.0
f'ci (ksi) 6.7
CA BT 55, Ag (in^2) 925
CA BT 55, w (k/ft) 1
CA BT 55, Yt, CG to Top (in) 27
CA BT 55, Yb, CG to Bot (in) 28
CA BT 55, Ig (in^4) 373350
Ƴ_h Say H= 70% 1
Ƴ_st 0.65
Δf_pR (ksi) 2.4
Transfer length l_t =60*db (in) 36
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: Date:
Task: Girders C Stress Page: of:
Job #: NO:
Stress Calculations @ PS + Perm load condition Transformed seciton properties
Note 1 Note 2 Note 3 Note 4 Note 5 Note 6 Note 7 Note 8
0 0.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
1.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
2.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
3.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
dv 5.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
0.1L 11.2 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
13.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
14.0 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
15.0 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
16.0 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
0.2L 22.5 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
28.0 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
29.0 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
30.0 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
31.0 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
0.3L 33.7 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
0.4L 45.0 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
0.5L 56.2 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
0.6L 67.4 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
0.7L 78.7 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
81.4 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
82.4 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
83.4 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
84.4 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
0.8L 89.9 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
96.4 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
97.4 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
98.4 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
99.4 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
0.9L 101.1 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
dv 108.2 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
109.4 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
110.4 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
111.4 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
L 112.4 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
Transfor
med
Y_ttop
(in)
Transfor
med
Y_tbot
(in)
Ʃ Ai*(Y_i-
Y_ttop)^
2
(in^4)
I_final(in
^4)
Transfor
med
S_ttop
(in^3)
Transfor
med
S_tbot
(in^3)
Aps(in^
2)
Y_p,
Tendon CG
to
GirderTop
(in)
Aps*(n'-
1)
(in^2)
Total
Aps*(n-
1)+Ag
(in^2) Ig (in^4)
ƩAi*Y_i
(in^3)
Length
along
girder
(ft)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: Date:
Task: Girders C Stress Page: of:
Job #: NO:
Note 1: Ignore moment of inertia I from prestrssing tendons, since it is too small compared to that of precast concrete Girder.
Note 2: Summation of tranformed strands area times CG of strands, and area of precast concrete girder times CG of the girder.
Note 3: Values of Note 2 divide by the total area of the transformed section to determine CG of the tranformed section (from top of the section)
Note 4: CG of the tranformed seciton (from bottom of the section)
Note 5:
Note 6: I_final =Ig + values at Note 5
Note 7: Transformed section modulus from top of seciton is I_final divide by Transformed Y_ttop
Note 8: Transformed section modulus from bottom of seciton is I_final divide by Transformed Y_tbot
Summation of tranformed area of strands times squrea of CG differenec between strands and the entire tranformed section, plus such value
for precast concrete girder component.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders C Stress Page: of:
Job #: NO:
Stress Calculations @ PS + Perm load condition * debond included
Note 9 Note 10 Note 11 Note 12 Note 13 Note 14 Note 15 Note 16
0 0.0 21 22 181 372 0 -0.16 0.93 3.60 -0.54 0.00 0.29 0.26 0.00
1.0 21 22 181 496 1430 -0.11 1.14 3.60 -0.54 0.00 0.20 0.32 0.00
2.0 21 22 181 993 2835 -0.21 2.28 3.60 -0.54 0.00 0.40 0.63 0.00
3.0 21 22 181 1489 4213 -0.32 3.42 3.60 -0.54 0.00 0.60 0.95 0.00
dv 5.0 21 22 181 1489 6894 -0.14 3.23 3.60 -0.54 0.00 0.25 0.90 0.00
0.1L 11.2 21 22 181 1489 14594 0.41 2.69 3.60 -0.54 0.11 0.00 0.75 0.00
13.0 21 22 181 1489 16589 0.55 2.55 3.60 -0.54 0.15 0.00 0.71 0.00
14.0 21 24 178 1572 17685 0.58 2.65 3.60 -0.54 0.16 0.00 0.74 0.00
15.0 21 24 178 1675 18756 0.61 2.83 3.60 -0.54 0.17 0.00 0.79 0.00
16.0 21 24 178 1778 19801 0.64 3.01 3.60 -0.54 0.18 0.00 0.84 0.00
0.2L 22.5 21 24 178 1778 25945 1.07 2.58 3.60 -0.54 0.30 0.00 0.72 0.00
28.0 21 24 178 1778 30337 1.38 2.28 3.60 -0.54 0.38 0.00 0.63 0.00
29.0 21 26 177 1817 31048 1.41 2.31 3.60 -0.54 0.39 0.00 0.64 0.00
30.0 21 26 177 1868 31734 1.44 2.39 3.60 -0.54 0.40 0.00 0.66 0.00
31.0 21 26 177 1919 32393 1.46 2.47 3.60 -0.54 0.41 0.00 0.69 0.00
0.3L 33.7 21 26 177 1919 34053 1.58 2.36 3.60 -0.54 0.44 0.00 0.65 0.00
0.4L 45.0 21 26 177 1919 38918 1.92 2.02 3.60 -0.54 0.53 0.00 0.56 0.00
0.5L 56.2 21 26 177 1919 40540 2.03 1.91 3.60 -0.54 0.56 0.00 0.53 0.00
0.6L 67.4 21 26 177 1919 38918 1.92 2.02 3.60 -0.54 0.53 0.00 0.56 0.00
0.7L 78.7 21 26 177 1919 34053 1.58 2.36 3.60 -0.54 0.44 0.00 0.65 0.00
81.4 21 26 177 1919 32393 1.46 2.47 3.60 -0.54 0.41 0.00 0.69 0.00
82.4 21 26 177 1868 31734 1.44 2.39 3.60 -0.54 0.40 0.00 0.66 0.00
83.4 21 26 177 1817 31048 1.41 2.31 3.60 -0.54 0.39 0.00 0.64 0.00
84.4 21 24 178 1778 30337 1.38 2.28 3.60 -0.54 0.38 0.00 0.63 0.00
0.8L 89.9 21 24 178 1778 25945 1.07 2.58 3.60 -0.54 0.30 0.00 0.72 0.00
96.4 21 24 178 1778 19801 0.64 3.01 3.60 -0.54 0.18 0.00 0.84 0.00
97.4 21 24 178 1675 18756 0.61 2.83 3.60 -0.54 0.17 0.00 0.79 0.00
98.4 21 24 178 1572 17685 0.58 2.65 3.60 -0.54 0.16 0.00 0.74 0.00
99.4 21 22 181 1489 16589 0.55 2.55 3.60 -0.54 0.15 0.00 0.71 0.00
0.9L 101.1 21 22 181 1489 14594 0.41 2.69 3.60 -0.54 0.11 0.00 0.75 0.00
dv 108.2 21 22 181 1489 5854 -0.21 3.31 3.60 -0.54 0.00 0.39 0.92 0.00
109.4 21 22 181 1489 4213 -0.32 3.42 3.60 -0.54 0.00 0.60 0.95 0.00
110.4 21 22 181 993 2835 -0.21 2.28 3.60 -0.54 0.00 0.40 0.63 0.00
111.4 21 22 181 496 1430 -0.11 1.14 3.60 -0.54 0.00 0.20 0.32 0.00
L 112.4 21 22 181 372 0 -0.16 0.93 3.60 -0.54 0.00 0.29 0.26 0.00
Max: 0.56 0.60 0.95 0.00
f_top
(ksi)
f_Bot
(ksi)
Compres
sive
Stress
limit (ksi)
Tensile
Stress
limit (ksi)
f_top f_bot
D/C ratio
(comp limit)
D/C
ratio(Ten
limit)
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit)
Length
along
girder
(ft)
e (in)Δf_pLT
(ksi)fpe (ksi) Pf (kiP)
Moment
demands
DC1+DC2
(kip-in)
PS+ Perm (DC1+DC2)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders C Stress Page: of:
Job #: NO:
Note 9: Eccentricity of the seciton is Y_p(in) from girder top subtracted by Transformed Y_ttop
Note 10
Note 11 fpe is stress at transfer minus long term loss Δf_pLT
Note 12 Prestressing force Pf, is fpe times area of the prestressing tendons, Aps.
Note 13
Note 14
Note 15
Note 16:
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders C Stress Page: of:
Job #: NO:
Tendons f_pu (ksi) 270
Tendon f_pbt (ksi) 202.5 (AASHTO Table 5.9.3.1)
CA BT 55, Ag (in^2) 925
CA BT 55, w (k/ft) 0.963
CA BT 55, Yt, CG to Top (in) 26.7
CA BT 55, Yb, CG to Bot (in) 28.4
CA BT 55, Ig (in^4) 373350
Tendon E_ps (ksi) 28,500
Girder Concrete E_pc (ksi) 5,154
n'-1 = E_ps/ E_pc -1 5
Girder f'c (ksi) 8
Girder f'ci (ksi) 6.7
Deck Concrete E_c (ksi) 4,074
Girder Concrete E_pc (ksi) 5,154
n= E_c/E_pc 0.79
CIP Deck f'c (ksi) 5
Deck effective width (ft) 9.08
Depth of concrete slab, ts (in) 8.00
Precast panel thickness (in) 3.50
Tranformed deck area (in^2) 768.74 (based on Ec of 8ksi concrete)
Tranformed effective deck width (in) 96.093 (based on Ec of 8ksi concrete)
Transfer length l_t =60*db (in) 36
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders C Stress Page: of:
Job #: NO:
Stress Calculations @ Service, composite section properties include the Deck Slab
Note 1
0 0.0 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 372
1.0 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 496
2.0 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 993
3.0 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
dv 5.0 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
0.1L 11.2 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
13.0 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
14.0 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1572
15.0 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1675
16.0 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1778
0.2L 22.5 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1778
28.0 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1778
29.0 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1817
30.0 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1868
31.0 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
0.3L 33.7 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
0.4L 45.0 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
0.5L 56.2 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
0.6L 67.4 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
0.7L 78.7 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
81.4 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
82.4 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1868
83.4 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1817
84.4 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1778
0.8L 89.9 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1778
96.4 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1778
97.4 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1675
98.4 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1572
99.4 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
0.9L 101.1 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
dv 108.2 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
109.4 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
110.4 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 993
111.4 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 496
L 112.4 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 372
e (in)
Δf_pLT
(ksi)
fpe
(ksi)
Pf
(kiP)
Yi to Top
of Deck
ƩAi*Y_i
(in^3)
Comp
Y_ttop
(in)
ToDec
kTop
Comp.
Y_tbot
(in)
I_comp
(in^4)
Comp.
S_tg
(in^3)
Comp S_tb
(in^3)
Length
along
girder (ft)
I_tg(in^4)Transformed
Y_ttop (in)
Transfor
med
Y_tbot
(in)
Tranfor
med
A_deck
(in^2)
A_deck+A
ps*(n'-
1)+Ag
(in^2)
From PS+Perm stress calc
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders C Stress Page: of:
Job #: NO:
Stress Calculations @ Service, composite section properties include the Deck Slab
* debond included Note 2 Note 3 Note 4
0 0.0 0 0 0 0 -0.16 0.93 4.80 -0.54 0.00 0.29 0.19 0.00
1.0 1430 348 24 1107 -0.08 1.06 4.80 -0.54 0.00 0.15 0.22 0.00
2.0 2835 691 48 2195 -0.17 2.13 4.80 -0.54 0.00 0.31 0.44 0.00
3.0 4213 1026 72 3263 -0.25 3.20 4.80 -0.54 0.00 0.47 0.67 0.00
dv 5.0 6894 1679 120 5338 -0.02 2.87 4.80 -0.54 0.00 0.03 0.60 0.00
0.1L 11.2 14594 3555 271 11301 0.66 1.92 4.80 -0.54 0.14 0.00 0.40 0.00
13.0 16589 4041 313 12845 0.83 1.67 4.80 -0.54 0.17 0.00 0.35 0.00
14.0 17685 4308 337 13694 0.88 1.73 4.80 -0.54 0.18 0.00 0.36 0.00
15.0 18756 4569 361 14523 0.93 1.85 4.80 -0.54 0.19 0.00 0.39 0.00
16.0 19801 4824 385 15333 0.98 1.98 4.80 -0.54 0.20 0.00 0.41 0.00
0.2L 22.5 25945 6320 541 20090 1.52 1.23 4.80 -0.54 0.32 0.00 0.26 0.00
28.0 30337 7390 674 23491 1.91 0.69 4.80 -0.54 0.40 0.00 0.14 0.00
29.0 31048 7563 698 24042 1.95 0.70 4.80 -0.54 0.41 0.00 0.15 0.00
30.0 31734 7730 722 24572 1.98 0.75 4.80 -0.54 0.41 0.00 0.16 0.00
31.0 32393 7891 746 25083 2.02 0.79 4.80 -0.54 0.42 0.00 0.16 0.00
0.3L 33.7 34053 8295 812 26369 2.17 0.59 4.80 -0.54 0.45 0.00 0.12 0.00
0.4L 45.0 38918 9481 1082 30136 2.59 -0.01 4.80 -0.54 0.54 0.00 0.00 0.01
0.5L 56.2 40540 9876 1353 31391 2.74 -0.22 4.80 -0.54 0.57 0.00 0.00 0.40
0.6L 67.4 38918 9481 1082 30136 2.59 -0.01 4.80 -0.54 0.54 0.00 0.00 0.01
0.7L 78.7 34053 8295 812 26369 2.17 0.59 4.80 -0.54 0.45 0.00 0.12 0.00
81.4 32393 7891 746 25083 2.02 0.79 4.80 -0.54 0.42 0.00 0.16 0.00
82.4 31734 7730 722 24572 1.98 0.75 4.80 -0.54 0.41 0.00 0.16 0.00
83.4 31048 7563 698 24042 1.95 0.70 4.80 -0.54 0.41 0.00 0.15 0.00
84.4 30337 7390 674 23491 1.91 0.69 4.80 -0.54 0.40 0.00 0.14 0.00
0.8L 89.9 25945 6320 541 20090 1.52 1.23 4.80 -0.54 0.32 0.00 0.26 0.00
96.4 19801 4824 385 15333 0.98 1.98 4.80 -0.54 0.20 0.00 0.41 0.00
97.4 18756 4569 361 14523 0.93 1.85 4.80 -0.54 0.19 0.00 0.39 0.00
98.4 17685 4308 337 13694 0.88 1.73 4.80 -0.54 0.18 0.00 0.36 0.00
99.4 16589 4041 313 12845 0.83 1.67 4.80 -0.54 0.17 0.00 0.35 0.00
0.9L 101.1 14594 3555 271 11301 0.66 1.92 4.80 -0.54 0.14 0.00 0.40 0.00
dv 108.2 5854 1426 101 4533 -0.11 3.00 4.80 -0.54 0.00 0.20 0.62 0.00
109.4 4213 1026 72 3263 -0.25 3.20 4.80 -0.54 0.00 0.47 0.67 0.00
110.4 2835 691 48 2195 -0.17 2.13 4.80 -0.54 0.00 0.31 0.44 0.00
111.4 1430 348 24 1107 -0.08 1.06 4.80 -0.54 0.00 0.15 0.22 0.00
L 112.4 0 0 0 0 -0.16 0.93 4.80 -0.54 0.00 0.29 0.19 0.00
Max: 0.57 0.47 0.67 0.40
Tensile
Stress
limit (ksi)
f_top f_bot
D/C ratio
(comp limit)
D/C
ratio(Ten
limit)
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit)
Moment
demands
DC3+DW (kip-
in)
Moment demands
DC4 (kip-in)
Moment
demands
LL(1+IM) (kip-
in)
f_top (ksi) f_Bot (ksi)Compressive
Stress limit (ksi)
Length
along
girder
(ft)
Moment
demands
DC1+DC2
(kip-in)
Service I : PS+Perm+LL*(1+IM)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders C Stress Page: of:
Job #: NO:
Note 1:
Note 2
f_bot SIM.
Note 3
Note 4
Check the stress to top of girder, so section modulus of the composite section, is the I_comp / y_tg, and y_tg
is the distance from comp. nuetral axis to the top of the girder.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: Date:
Task: Girders C Stress Page: of:
Job #: NO:
0 0.0 0 -0.16 0.93 4.80 -0.54 0.00 0.29 0.19 0.00
1.0 886 -0.09 1.08 4.80 -0.54 0.00 0.16 0.22 0.00
2.0 1756 -0.17 2.15 4.80 -0.54 0.00 0.32 0.45 0.00
3.0 2610 -0.26 3.23 4.80 -0.54 0.00 0.49 0.67 0.00
dv 5.0 4271 -0.03 2.92 4.80 -0.54 0.00 0.06 0.61 0.00
0.1L 11.2 9041 0.62 2.03 4.80 -0.54 0.13 0.00 0.42 0.00
13.0 10276 0.79 1.80 4.80 -0.54 0.17 0.00 0.38 0.00
14.0 10956 0.84 1.87 4.80 -0.54 0.17 0.00 0.39 0.00
15.0 11619 0.88 2.00 4.80 -0.54 0.18 0.00 0.42 0.00
16.0 12266 0.93 2.13 4.80 -0.54 0.19 0.00 0.44 0.00
0.2L 22.5 16072 1.45 1.43 4.80 -0.54 0.30 0.00 0.30 0.00
28.0 18793 1.83 0.93 4.80 -0.54 0.38 0.00 0.19 0.00
29.0 19233 1.87 0.94 4.80 -0.54 0.39 0.00 0.20 0.00
30.0 19658 1.90 0.99 4.80 -0.54 0.40 0.00 0.21 0.00
31.0 20067 1.94 1.04 4.80 -0.54 0.40 0.00 0.22 0.00
0.3L 33.7 21095 2.08 0.85 4.80 -0.54 0.43 0.00 0.18 0.00
0.4L 45.0 24109 2.49 0.29 4.80 -0.54 0.52 0.00 0.06 0.00
0.5L 56.2 25113 2.64 0.10 4.80 -0.54 0.55 0.00 0.02 0.00
0.6L 67.4 24109 2.49 0.29 4.80 -0.54 0.52 0.00 0.06 0.00
0.7L 78.7 21095 2.08 0.85 4.80 -0.54 0.43 0.00 0.18 0.00
81.4 20067 1.94 1.04 4.80 -0.54 0.40 0.00 0.22 0.00
82.4 19658 1.90 0.99 4.80 -0.54 0.40 0.00 0.21 0.00
83.4 19233 1.87 0.94 4.80 -0.54 0.39 0.00 0.20 0.00
84.4 18793 1.83 0.93 4.80 -0.54 0.38 0.00 0.19 0.00
0.8L 89.9 16072 1.45 1.43 4.80 -0.54 0.30 0.00 0.30 0.00
96.4 12266 0.93 2.13 4.80 -0.54 0.19 0.00 0.44 0.00
97.4 11619 0.88 2.00 4.80 -0.54 0.18 0.00 0.42 0.00
98.4 10956 0.84 1.87 4.80 -0.54 0.17 0.00 0.39 0.00
99.4 10276 0.79 1.80 4.80 -0.54 0.17 0.00 0.38 0.00
0.9L 101.1 9041 0.62 2.03 4.80 -0.54 0.13 0.00 0.42 0.00
dv 108.2 3626 -0.12 3.04 4.80 -0.54 0.00 0.23 0.63 0.00
109.4 2610 -0.26 3.23 4.80 -0.54 0.00 0.49 0.67 0.00
110.4 1756 -0.17 2.15 4.80 -0.54 0.00 0.32 0.45 0.00
111.4 886 -0.09 1.08 4.80 -0.54 0.00 0.16 0.22 0.00
L 112.4 0 -0.16 0.93 4.80 -0.54 0.00 0.29 0.19 0.00
Max: 0.55 0.49 0.67 0.00
f_Bot (ksi)
Compressiv
e Stress
limit (ksi)
Tensile
Stress limit
(ksi)
f_top f_bot
D/C ratio
(comp limit)
D/C ratio(Ten
limit)
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit)
Length along
girder (ft)
Moment
demands
0.8*LL(1+IM
) (kip-in)
f_top (ksi)
Service III : PS+Perm+0.8*LL*(1+IM)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/26/20
Subject: Design Calculations Checked: CL Date: 5/6/20
Task: Girders C Stress Page: of:
Job #: NO:
REQUIRED TOP REINFORCEMENT
0 0.0 -0.17 1.02 7.90 31.99 1.07 3
1.0 -0.18 1.32 6.71 28.97 0.97 3
2.0 -0.37 2.64 6.72 58.25 1.94 5
3.0 -0.55 3.97 6.73 87.84 2.93 7
dv 5.0 -0.47 3.88 5.92 65.33 2.18 5
0.1L 11.2 -0.22 3.64 3.18 16.77 0.56 2
13.0 -0.16 3.58 2.36 8.90 0.30 1
14.0 -0.18 3.77 2.55 10.98 0.37 1
15.0 -0.20 4.02 2.59 12.09 0.40 1
16.0 -0.21 4.28 2.63 13.31 0.44 2
0.2L 22.5 -0.02 4.09 0.27 0.13 0.00 1
28.0 0.12 3.95 0.00 0.00 0.00 0
29.0 0.11 4.04 0.00 0.00 0.00 0
30.0 0.11 4.16 0.00 0.00 0.00 0
31.0 0.11 4.28 0.00 0.00 0.00 0
0.3L 33.7 0.16 4.23 0.00 0.00 0.00 0
0.4L 45.0 0.31 4.08 0.00 0.00 0.00 0
0.5L 56.2 0.36 4.03 0.00 0.00 0.00 0
0.6L 67.4 0.31 4.08 0.00 0.00 0.00 0
0.7L 78.7 0.16 4.23 0.00 0.00 0.00 0
81.4 0.11 4.28 0.00 0.00 0.00 0
82.4 0.11 4.16 0.00 0.00 0.00 0
83.4 0.11 4.04 0.00 0.00 0.00 0
84.4 0.12 3.95 0.00 0.00 0.00 0
0.8L 89.9 -0.02 4.09 0.27 0.13 0.00 1
96.4 -0.21 4.28 2.63 13.31 0.44 2
97.4 -0.20 4.02 2.59 12.09 0.40 1
98.4 -0.18 3.77 2.55 10.98 0.37 1
99.4 -0.16 3.58 2.36 8.90 0.30 1
0.9L 101.1 -0.22 3.64 3.18 16.77 0.56 2
dv 108.2 -0.50 3.92 6.24 73.76 2.46 6
109.4 -0.55 3.97 6.73 87.84 2.93 7
110.4 -0.37 2.64 6.72 58.25 1.94 5
111.4 -0.18 1.32 6.71 28.97 0.97 3
L 112.4 -0.17 1.02 7.90 31.99 1.07 3
f_ci,top (ksi) f_ci,bot (ksi) x (in) T (kip) As (in^2)
# 6 rebars
(in^2)
Length along
girder (ft)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders D Design Page: of:
Job #: NO:
L, Bridge span length (ft) 111.98
Bridge Width (ft) Upper bound 78.16
Bridge Width (ft) Lower Bound 71.60
Bridge Width (ft) Average 74.88
Number of Lanes 4
m, Multipresent factor for LL 0.65
Nb, Number of Girder 8
S, Max Girder Spacing (ft) 10.05
Bridge Skew Angle (degree) 31
For the bridge girder:
f'ci at transfer (ksi) 6.7 AASHTO 5.4.2.3.1
f'c after 28 days (ksi) 8
E_ci (ksi) for girder @ transfer 4716
During the construction of the bridge, it is required to not interfere with train traffic,
thus, the bridge slab system is precast concrete panel in between girders, stitched with CIP Concrete.
Tendon diameter (in) 0.6
One strand area (in^2) 0.217
Debonding length (from end of beam to where bonding commence), ft
10
Girder Distribution factors for DL, LL moment, LL Shear
Type of deck CIP Concrete, Precast Concrete
Supporting Component Precast Concrete I or Bulb-tee section
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders D Design Page: of:
Job #: NO:
Common Deck superstructure Table 4.6.2.2.1-1
Typical Cross section K Table 4.6.2.2.1-1
Live Load Distribution Factor for Moment in Interior Beams Table 4.6.2.2.2b-1
Rang of Applicability
S, spacing of beams, ϵ [ 3.5, 16] ft ✔
L, Span Length, ϵ [20,240] ft ✔
Nb, number of beams >=4 ✔
ts, depth of concrete slab ϵ [ 4.5, 12] in ✔
Depth of concrete slab, ts (in) 8.00
kg, longitudinal stiffness factor, ϵ [10^4 , 7x10^6] ✔
kg= n( I + A*eg^2) 1576804.87 4.6.2.2.1-1
n= E_beam / E_deck 1.26491106
f'c_slab (ksi) 6
E_beam (ksi) 5,154
E_slab (ksi) 4,074
A, (non-composite) cross section area of girder (in^2) 925 Caltrans Design Aids, CA BT-55
I, (non-composite) inertia (in^4) 373,350 Caltrans Design Aids, CA BT-55
Yb, CG to bottom of girder (in) 28.4 Caltrans Design Aids, CA BT-55
D, girder height (in) 55.125 Caltrans Design Aids, CA BT-55
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders D Design Page: of:
Job #: NO:
eg, dist. Btw CL of beam & CL of deck (in) 30.725
b_eff, deck effective width of girder (ft) 9.08
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders D Design Page: of:
Job #: NO:
Per above table from AASHTO, the LL distribution factor for moment in Interior beams are calculated:
g_int, One design lane loaded: 0.52 lane / girder multiple presence factor included
g_int, Two or more lane loaded: 0.77 lane / girder per C4.6.2.2.2b
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders D Design Page: of:
Job #: NO:
Per above table from AASHTO, the LL distribution factor for moment in exterior beams are calculated:
de, horizontal distance from CL of ext. web of ext. beam @ deck level, to int. edge of curb of traffic barrier
de (ft) 2.30
e=0.77+de/9.1 1.02
g_ext, one design lane loaded 0.53 lane/girder
g_ext, two or more design lane loaded 0.79 lane/girder
Considering the span length, it is very likley that cross frames & end diaphraagm will be necessary.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders D Design Page: of:
Job #: NO:
Per AASHTO C4.6.2.2.2d-1, exterior girders have higher load distribution factors due to cross frames
One lane loaded:
NL 1
X_ext, (ft) 35.18
e (ft) 24.03
x_1 (ft) 5.03
x_2 (ft) 15.08
x_3 (ft) 25.13
x_4 (ft) 35.18
R 0.32
Adjust with 1.2 multiple presence factor 0.39
Two Lanes loaded:
NL 2
e1 (ft) 24.03
e2 (ft) 6.5
R 0.50
Adjust with 1.0 multiple presence factor 0.50
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders D Design Page: of:
Job #: NO:
Three or more Lanes loaded:
NL 3
e1 (ft) 24.03
e2 (ft) 6.5
e3 (ft) 12
R 0.68
Adjust with 0.85 multiple presence factor 0.58
Final design values for moment distribution factors :
Load Case Int. Girder (lane)
One lane 0.52 0.53
NA 0.39
2 lanes loaded NA 0.50
3 lanes loaded NA 0.58
Design Value
Moment
Distribution 0.77 0.79
Max: 0.79
Two values are close enough, use the
maximum value for all to be conservative.
Note that AASHTO 4.6.2.2.2.e for skewed bridge provides reduction factors for live load distribution factors for momen in longitudinal
beams. However, CA amendment ignores reduction. Thus, no reduction applies for moment
Ext. Girder (lane)
Moment Distribution factor
per Table 4.6.2.2.2 Two or more
lane
0.77 0.79
Moment D.F. for ext. girder per
C4.6.2.2.2d-1
one lane loaded
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders D Design Page: of:
Job #: NO:
LL distribution factor for Shear :
Per above table from AASHTO, the LL distribution factor for shear in Interior beams are calculated:
g_int, One design lane loaded: 0.76 lane / girder multiple presence factor included
g_int, Two or more lane loaded: 0.96 lane / girder per C4.6.2.2.2b
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders D Design Page: of:
Job #: NO:
Per above table from AASHTO, the LL distribution factor for shear in exterior beams are calculated:
de (ft) 2.30
e=0.77+de/9.1 1.02
g_ext, one design lane loaded 0.53 lane/girder use same as ext one-lane for moment
g_ext, two or more design lane loaded 0.98 lane/girder
Notes:
AASHTO 4.6.2.2.3 C-1 provides correction factors for live load distribution factors for support shear of the obtuse girder.
CA Amendment revised AASHTO Table 4.6.2.2.3c-1 with equations provide for exterior girder & first interior girder.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders D Design Page: of:
Job #: NO:
Design values for shear distribution factors (without skew correction factor)
Load Case Int. Girder (lane)
One lane 0.76 NA
NA
NA 0.53
NA 0.98
Design Value
Shear
Distribution
Factor
0.96 0.98
Max: 0.98
Skew Correction factors for shear:
Two values are close enough, use the
maximum value for all to be conservative.
Ext. Girder (lane)
Shear Distribution factor per
Table 4.6.2.2.3a-1 Two or more
lane
0.96
Shear D.F. for ext. girder per
C4.6.2.2.3b-1
one lane loaded
Two or more
lane
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders D Design Page: of:
Job #: NO:
The shear correction factors are applied between the point of support at the obtuse corner and mid-span.
May be decreased linearly to a value of 1.0 at mid-span.
Skew Factor 1.09
Design values for shear distribution factors@ obtuse angle
Load Case Int. Girder (lane)
Design Value Shear D.F. 1.04 1.07 Max: 1.07
Two values are close enough, use the
maximum value for all to be conservative.Ext. Girder (lane)
1.07
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders D Design Page: of:
Job #: NO:
Moment Demands Calculations
One lane
0 0.0 0 0 0 0 0 0 0
dv 5.0 258 315 52 10 634 88 565
0.1L 11.2 543 664 109 22 1339 185 1193
0.2L 22.4 966 1181 194 45 2386 329 2120
0.3L 33.6 1268 1550 255 67 3140 431 2783
0.4L 44.8 1449 1771 292 90 3602 493 3180
0.5L 56.0 1509 1845 304 112 3771 513 3313
0.6L 67.2 1449 1771 292 90 3602 493 3180
0.7L 78.4 1268 1550 255 67 3140 431 2783
0.8L 89.6 966 1181 194 45 2386 329 2120
0.9L 100.8 543 664 109 22 1339 185 1193
dv 107.0 258 315 52 10 634 88 565
L 112.0 0 0 0 0 0 0 0
dv Use 0.9h (AASHTO 5.8.2.9) 5.03 ft
LL+IM Use Caltrans Bridge Design Aids attached as following.
Span length Moment (k-ft) End Shear (kip)
110 3229 122.8
120 3652.4 126.7
112.0 3312.8 123.6
Lane Load included from Caltrans Table
0 0
938 0
445 0
2189 0
1668 0
2606 0
2502 0
2189 0
2502 0
1668 0
Min LL
0 0
445 0
938 0
Length along
girder (ft)
For Each Girder
M (k-ft) DC1 M (k-ft) DC2 M (k-ft) DC3
M (k-ft)
DC4
M (k-ft)
DC Total
M (k-ft)
DW
(HL-93) LL+IM -M (k-f)
Distr.Fact
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders D Design Page: of:
Job #: NO:
Moment Capacity Calculations@ Wet Concr. Deck Stage (NonComposite)
Note 1 Note 4 Note 3
0 0.0 8 8 8 6 4 2 2 48.16 8.25 0.68 N.A. @ TF
dv 5.0 8 8 8 6 4 2 2 48.16 8.25 0.68 N.A. @ TF
0.1L 11.2 8 8 8 6 4 2 2 48.16 8.25 0.68 N.A. @ TF
0.2L 22.4 10 10 10 8 4 2 2 48.38 9.98 0.82 N.A. @ TF
0.3L 33.6 10 12 12 8 4 2 2 48.46 10.85 0.89 N.A. @ TF
0.4L 44.8 10 12 12 8 4 2 2 48.46 10.85 0.89 N.A. @ TF
0.5L 56.0 10 12 12 8 4 2 2 48.46 10.85 0.89 N.A. @ TF
0.6L 67.2 10 12 12 8 4 2 2 48.46 10.85 0.89 N.A. @ TF
0.7L 78.4 10 12 12 8 4 2 2 48.46 10.85 0.89 N.A. @ TF
0.8L 89.6 10 10 10 8 4 2 2 48.38 9.98 0.82 N.A. @ TF
0.9L 100.8 8 8 8 6 4 2 2 48.16 8.25 0.68 N.A. @ TF
dv 107.0 8 8 8 6 4 2 2 48.16 8.25 0.68 N.A. @ TF
L 112.0 8 8 8 6 4 2 2 48.16 8.25 0.68 N.A. @ TF
0.6" diameter tendons are used
Reference: AASHTO 2014 LRFD 7th Edition
Note 1: Note 4:
Note 2: Note 5:
Note 3: Note 6:Calcuated "c" to determine location of section
N.A.
No.
Tendon
at 12.75"
From Bot
No.
Tendon at
14.75"
From Bot
dp(in) to
Girder top
Aps(in^2) c (in)
Action Type:
Nuetral axis
location
Length
along
girder (ft)
No. Tendon
at 2.75"
From Bot
No.
Tendon at
4.75" from
Bot
No.
Tendon at
6.75"
From Bot
No.
Tendon at
8.75" From
Bot
No.
Tendon at
10.75"
From Bot
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders D Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Wet Concrete Deck Stage
Note 2 Note 5 Note 6 Note 7 Note 8
0 0.0 0.68 0.58 268.9 8848 0.2105 1.00 8848 0 8848 0
dv 5.0 0.68 0.58 268.9 8848 0.2105 1.00 8848 715 8848 0.08
0.1L 11.2 0.68 0.58 268.9 8848 0.2105 1.00 8848 1510 8848 0.17
0.2L 22.4 0.82 0.70 268.7 10736 0.1743 1.00 10736 2684 10736 0.25
0.3L 33.6 0.89 0.76 268.6 11676 0.1605 1.00 11676 3522 11676 0.30
0.4L 44.8 0.89 0.76 268.6 11676 0.1605 1.00 11676 4025 11676 0.34
0.5L 56.0 0.89 0.76 268.6 11676 0.1605 1.00 11676 4193 11676 0.36
0.6L 67.2 0.89 0.76 268.6 11676 0.1605 1.00 11676 4025 11676 0.34
0.7L 78.4 0.89 0.76 268.6 11676 0.1605 1.00 11676 3522 11676 0.30
0.8L 89.6 0.82 0.70 268.7 10736 0.1743 1.00 10736 2684 10736 0.25
0.9L 100.8 0.68 0.58 268.9 8848 0.2105 1.00 8848 1510 8848 0.17
dv 107.0 0.68 0.58 268.9 8848 0.2105 1.00 8848 715 8848 0.08
L 112.0 0.68 0.58 268.9 8848 0.2105 1.00 8848 0 8848 0.00
Note 7: Moment formula chosen depends on girder action type
Beta_1 =0.85 Per AASHTO 5.7.2.2
Value of k =0.28 Per Table C5.7.3.1.1.1
Note 8:
phi
factor φ
φMn(k-
ft)
For Each Girder
Mu (k-ft)
Strength I φMn(k-ft) D/C
Length
along
girder
(ft)
Update c (in) a (in) f_ps(ksi) Mn(k-ft)Epslon_t
ξ_t
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders D Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Wet Concrete Deck Stage
Mu=1.25 DC1+1.25DC2
Controlling Combination to design girders:
Strength I 1.25 DC+1.5 DW
0
2000
4000
6000
8000
10000
12000
14000
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Mo
me
nt
(k
-ft)
Length (ft)
Moment Plot along Span Length
Mu (k-ft) Strength I φMn(k-ft)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders D Design Page: of:
Job #: NO:
0 0.0 0 0 0 0 0 0 0
dv 5.0 258 315 52 10 634 88 1014
0.1L 11.2 543 664 109 22 1339 185 2139
0.2L 22.4 966 1181 194 45 2386 329 3802
0.3L 33.6 1268 1550 255 67 3140 431 4990
0.4L 44.8 1449 1771 292 90 3602 493 5703
0.5L 56.0 1509 1845 304 112 3771 513 5941
0.6L 67.2 1449 1771 292 90 3602 493 5703
0.7L 78.4 1268 1550 255 67 3140 431 4990
0.8L 89.6 966 1181 194 45 2386 329 3802
0.9L 100.8 543 664 109 22 1339 185 2139
dv 107.0 258 315 52 10 634 88 1014
L 112.0 0 0 0 0 0 0 0 0 0
2991 0
1682 0
797 0
4673 0
4486 0
3925 0
2991 0
3925 0
4486 0
Min LL
0 0
797 0
1682 0
Length along
girder (ft)M (k-ft) DC1 M (k-ft) DC2 M (k-ft) DC3
M (k-ft)
DC4
M (k-ft)
DC Total
For Each Girder
M (k-ft)
DW
(P-15) LL+IM -M (k-f)
One lane Distr.Fact
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders D Design Page: of:
Job #: NO:
Moment Capacity Calculations@ Final Stage Stage
0 0.0 8 8 8 6 4 2 2 8 56.16 8.25 5.50
dv 5.0 8 8 8 6 4 2 2 8 56.16 8.25 5.50
0.1L 11.2 8 8 8 6 4 2 2 8 56.16 8.25 5.50
0.2L 22.4 10 10 10 8 4 2 2 8 56.38 9.98 6.62
0.3L 33.6 10 12 12 8 4 2 2 8 56.46 10.85 7.18
0.4L 44.8 10 12 12 8 4 2 2 8 56.46 10.85 7.18
0.5L 56.0 10 12 12 8 4 2 2 8 56.46 10.85 7.18
0.6L 67.2 10 12 12 8 4 2 2 8 56.46 10.85 7.18
0.7L 78.4 10 12 12 8 4 2 2 8 56.46 10.85 7.18
0.8L 89.6 10 10 10 8 4 2 2 8 56.38 9.98 6.62
0.9L 100.8 8 8 8 6 4 2 2 8 56.16 8.25 5.50
dv 107.0 8 8 8 6 4 2 2 8 56.16 8.25 5.50
L 112.0 8 8 8 6 4 2 2 8 56.16 8.25 5.50
Considering the concrete deck is acting compositely with the CA BT 55 girders.
Also Conservatively igore the precast concrete panel's composite concrete reaction, due to lack of friction btw the panel surface.
Aps(in^2) c (in) No.
Tendon at
10.75"
From Bot
No.
Tendon
at 12.75"
From Bot
No.
Tendon at
14.75"
From Bot
Composite
Deck THK
(in)
dp(in) to
Deck top
Length
along
girder (ft)
No. Tendon
at 2.75"
From Bot
No.
Tendon at
4.75" from
Bot
No.
Tendon at
6.75"
From Bot
No.
Tendon at
8.75" From
Bot
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders D Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Final Stage
0 0.0 N.A. @ Deck 5.50 4.68 262.6 9713 0.0276 1.00 9713
dv 5.0 N.A. @ Deck 5.50 4.68 262.6 9713 0.0276 1.00 9713
0.1L 11.2 N.A. @ Deck 5.50 4.68 262.6 9713 0.0276 1.00 9713
0.2L 22.4 N.A. @ Deck 6.62 5.63 261.1 11634 0.0225 1.00 11634
0.3L 33.6 N.A. @ Deck 7.18 6.10 260.4 12573 0.0206 1.00 12573
0.4L 44.8 N.A. @ Deck 7.18 6.10 260.4 12573 0.0206 1.00 12573
0.5L 56.0 N.A. @ Deck 7.18 6.10 260.4 12573 0.0206 1.00 12573
0.6L 67.2 N.A. @ Deck 7.18 6.10 260.4 12573 0.0206 1.00 12573
0.7L 78.4 N.A. @ Deck 7.18 6.10 260.4 12573 0.0206 1.00 12573
0.8L 89.6 N.A. @ Deck 6.62 5.63 261.1 11634 0.0225 1.00 11634
0.9L 100.8 N.A. @ Deck 5.50 4.68 262.6 9713 0.0276 1.00 9713
dv 107.0 N.A. @ Deck 5.50 4.68 262.6 9713 0.0276 1.00 9713
L 112.0 N.A. @ Deck 5.50 4.68 262.6 9713 0.0276 1.00 9713
Mn(k-ft)Epslon_t
ξ_t
phi factor
φ φMn(k-ft)
Length
along
girder
(ft)
Action Type
(Neutral Axis
location)
Update
c (in)
from
deck
top
a (in) f_ps(ksi)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders D Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Final Stage
0 0.0 0 0 9713 0 0.00
dv 5.0 1702 2001 9713 0.18 0.21
0.1L 11.2 3593 4223 9713 0.37 0.43
0.2L 22.4 6394 7513 11634 0.55 0.65
0.3L 33.6 8403 9871 12573 0.67 0.79
0.4L 44.8 9619 11298 12573 0.77 0.90
0.5L 56.0 10044 11792 12573 0.80 0.938
0.6L 67.2 9619 11298 12573 0.77 0.90
0.7L 78.4 8403 9871 12573 0.67 0.79
0.8L 89.6 6394 7513 11634 0.55 0.65
0.9L 100.8 3593 4223 9713 0.37 0.43
dv 107.0 1702 2001 9713 0.18 0.21
L 112.0 0 0 9713 0.00 0.00
Strength I 1.25 DC+1.5 DW+1.75 LL
Strength II 1.25 DC+1.5 DW+1.35 LL-permit
17
Mu (k-ft)
Strength I
Mu (k-ft)
Strength II φMn(k-ft)
D/C for
Strength I
D/C for
Strength II
Length
along
girder (ft)
For Each Girder
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders D Design Page: of:
Job #: NO:
0
2000
4000
6000
8000
10000
12000
14000
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Mo
me
nt
(k
-ft)
Length (ft)
Moment Plot along Span Length
Mu (k-ft) Strength I
φMn(k-ft)
Mu (k-ft) Strength II
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders D Stress Page: of:
Job #: NO:
For the stress calc, negative stress is tensile stress; positive stress is compressive stress.
Stress Calculations @ Transfer Stage
Tendons f_pu (ksi) 270
Tendon f_pbt (ksi) 202.5 (AASHTO Table 5.9.3.1)
Tendon E_ps (ksi) 28,500
Girder Concrete E_pc (ksi) 5,154
n'-1 = E_ps/ E_pc -1 4.53
f'c (ksi) 8
f'ci (ksi) 6.7
CA BT 55, Ag (in^2) 925
CA BT 55, w (k/ft) 0.963
CA BT 55, Yt, CG to Top (in) 26.70
CA BT 55, Yb, CG to Bot (in) 28.40
CA BT 55, Ig (in^4) 373,350
Ƴ_h Say H= 70% 1
Ƴ_st 0.65
Δf_pR (ksi) 2.4
Transfer length l_t =60*db (in) 36
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders D Stress Page: of:
Job #: NO:
Stress Calculations @ Transfer Stage* debond included
Note 1 Note 2 Note 3 Note 4 Note 5 Note 6
0 0.0 8 8 8 6 4 2 2 8.25 48.16 21.46 0 19 183 ok 378
1.0 8 8 8 6 4 2 2 8.25 48.16 21.46 641 19 183 ok 504
2.0 8 8 8 6 4 2 2 8.25 48.16 21.46 1271 19 184 ok 1009
3.0 8 8 8 6 4 2 2 8.25 48.16 21.46 1889 19 184 ok 1515
dv 5.0 8 8 8 6 4 2 2 8.25 48.16 21.46 3091 18 184 ok 1518
0.1L 11.2 8 8 8 6 4 2 2 8.25 48.16 21.46 6521 17 185 ok 1526
13.0 8 8 8 6 4 2 2 8.25 48.16 21.46 7435 17 185 ok 1528
14.0 10 10 10 8 4 2 2 9.98 48.38 21.68 7926 21 182 ok 1603
15.0 10 10 10 8 4 2 2 9.98 48.38 21.68 8405 21 182 ok 1709
16.0 10 10 10 8 4 2 2 9.98 48.38 21.68 8873 21 182 ok 1815
0.2L 22.4 10 10 10 8 4 2 2 9.98 48.38 21.68 11592 20 183 ok 1823
28.0 10 10 10 8 4 2 2 9.98 48.38 21.68 13586 19 183 ok 1829
29.0 10 12 12 8 4 2 2 10.85 48.46 21.76 13904 21 181 ok 1863
30.0 10 12 12 8 4 2 2 10.85 48.46 21.76 14210 21 182 ok 1917
31.0 10 12 12 8 4 2 2 10.85 48.46 21.76 14505 21 182 ok 1970
0.3L 33.6 10 12 12 8 4 2 2 10.85 48.46 21.76 15215 21 182 ok 1972
0.4L 44.8 10 12 12 8 4 2 2 10.85 48.46 21.76 17389 20 182 ok 1979
0.5L 56.0 10 12 12 8 4 2 2 10.85 48.46 21.76 18113 20 183 ok 1981
0.6L 67.2 10 12 12 8 4 2 2 10.85 48.46 21.76 17389 20 182 ok 1979
0.7L 78.4 10 12 12 8 4 2 2 10.85 48.46 21.76 15215 21 182 ok 1972
81.0 10 12 12 8 4 2 2 10.85 48.46 21.76 14505 21 182 ok 1970
82.0 10 12 12 8 4 2 2 10.85 48.46 21.76 14210 21 182 ok 1917
83.0 10 12 12 8 4 2 2 10.85 48.46 21.76 13904 21 181 ok 1863
84.0 10 10 10 8 4 2 2 9.98 48.38 21.68 13586 19 183 ok 1829
0.8L 89.6 10 10 10 8 4 2 2 9.98 48.38 21.68 11592 20 183 ok 1823
96.0 10 10 10 8 4 2 2 9.98 48.38 21.68 8873 21 182 ok 1815
97.0 10 10 10 8 4 2 2 9.98 48.38 21.68 8405 21 182 ok 1709
98.0 10 10 10 8 4 2 2 9.98 48.38 21.68 7926 21 182 ok 1603
99.0 8 8 8 6 4 2 2 8.25 48.16 21.46 7435 17 185 ok 1528
0.9L 100.8 8 8 8 6 4 2 2 8.25 48.16 21.46 6521 17 185 ok 1526
dv 108.2 8 8 8 6 4 2 2 8.25 48.16 21.46 2387 19 184 ok 1516
109.0 8 8 8 6 4 2 2 8.25 48.16 21.46 1889 19 184 ok 1515
110.0 8 8 8 6 4 2 2 8.25 48.16 21.46 1271 19 184 ok 1009
111.0 8 8 8 6 4 2 2 8.25 48.16 21.46 641 19 183 ok 504
L 112.0 8 8 8 6 4 2 2 8.25 48.16 21.46 0 19 183 ok 378
Length along
girder (ft) No. Tendon
at 2.75"
From Bot
No. Tendon
at 4.75"
from Bot
No.
Tendon at
6.75" From
Bot
No. Tendon
at 8.75"
From Bot
No. Tendon
at 10.75"
From Bot
Δf_pES
(ksi)
f_pi
(ksi)
Stress
limit for
tendon
0.8fpy
Jakcing
force
@transfer,
Pji (kip)
No. Tendon
at 12.75"
From Bot
No. Tendon
at 14.75"
From Bot
Aps(in^2)
Y_p,
Tendon
CG to Top
of Girder
(in)
e_ti (in)
Mg (kip-
in) Girder
Self
Weight
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders D Stress Page: of:
Job #: NO:
Note 1: Eccencity equal to value of Y_p minus YtNote 2: Mg is the moment caused by the self weight of the girder+ Concrete deck
Note 4:
Note 3:
Note 5: fpy assumes to be 0.9fpu; Table 5.9.3-1 AASHTO
Note 7: Top fiber concr gider stress=P/A-P*e/(I/Yt)+Mg/(I/Yb) (+ is compression, - is tension)
Note 9:
Note 6: Jakcing force @ transfer taken as f_pi multiplies Aps (Total area of tendons)
Note 8: Bot. fiber concr gider stress=P/A+P*e/(I/Yt)-Mg/(I/Yb) (+ is cpmpression, - is tension )
Note 10:
Girder top bars: #4 Total of 6, 0.2x6=1.2in^2
f_pi is the value of f_pbt minus Δf_pES. Per AASHTO C5.9.5.2.3a, if the transformed
section properties are used, the Δf_pES should not be inlcuded in the prestressing force.
In this case, jacking force is calcuated as f_pbt minus short term elastic shortening loss,
and so the Gorss section properties of the concrete girder are used.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders D Stress Page: of:
Job #: NO:
0
500
1000
1500
2000
2500
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Jakcing force @transfer, Pji (kip)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders D Stress Page: of:
Job #: NO:
Stress Calculations @ Transfer Stage
Note 7 Note 8 Note 9 Note 10
0 0.0 -0.17 1.02 4.36 -0.62 0.00 0.28 0.24 0.00
1.0 -0.18 1.32 4.36 -0.62 0.00 0.29 0.30 0.00
2.0 -0.37 2.64 4.36 -0.62 0.00 0.59 0.61 0.00
3.0 -0.55 3.97 4.36 -0.62 0.00 0.89 0.91 0.00
dv 5.0 -0.47 3.88 4.36 -0.62 0.00 0.75 0.89 0.00
0.1L 11.2 -0.23 3.64 4.36 -0.62 0.00 0.36 0.84 0.00
13.0 -0.16 3.58 4.36 -0.62 0.00 0.26 0.82 0.00
14.0 -0.18 3.77 4.36 -0.62 0.00 0.30 0.87 0.00
15.0 -0.20 4.03 4.36 -0.62 0.00 0.32 0.92 0.00
16.0 -0.22 4.28 4.36 -0.62 0.00 0.35 0.98 0.00
0.2L 22.4 -0.03 4.09 4.36 -0.62 0.00 0.04 0.94 0.00
28.0 0.11 3.96 4.36 -0.62 0.03 0.00 0.91 0.00
29.0 0.11 4.04 4.36 -0.62 0.03 0.00 0.93 0.00
30.0 0.11 4.16 4.36 -0.62 0.02 0.00 0.96 0.00
31.0 0.10 4.29 4.36 -0.62 0.02 0.00 0.98 0.00
0.3L 33.6 0.15 4.24 4.36 -0.62 0.03 0.00 0.97 0.00
0.4L 44.8 0.30 4.09 4.36 -0.62 0.07 0.00 0.94 0.00
0.5L 56.0 0.35 4.04 4.36 -0.62 0.08 0.00 0.93 0.00
0.6L 67.2 0.30 4.09 4.36 -0.62 0.07 0.00 0.94 0.00
0.7L 78.4 0.15 4.24 4.36 -0.62 0.03 0.00 0.97 0.00
81.0 0.10 4.29 4.36 -0.62 0.02 0.00 0.98 0.00
82.0 0.11 4.16 4.36 -0.62 0.02 0.00 0.96 0.00
83.0 0.11 4.04 4.36 -0.62 0.03 0.00 0.93 0.00
84.0 0.11 3.96 4.36 -0.62 0.03 0.00 0.91 0.00
0.8L 89.6 -0.03 4.09 4.36 -0.62 0.00 0.04 0.94 0.00
96.0 -0.22 4.28 4.36 -0.62 0.00 0.35 0.98 0.00
97.0 -0.20 4.03 4.36 -0.62 0.00 0.32 0.92 0.00
98.0 -0.18 3.77 4.36 -0.62 0.00 0.30 0.87 0.00
99.0 -0.16 3.58 4.36 -0.62 0.00 0.26 0.82 0.00
0.9L 100.8 -0.23 3.64 4.36 -0.62 0.00 0.36 0.84 0.00
dv 108.2 -0.52 3.93 4.36 -0.62 0.00 0.83 0.90 0.00
109.0 -0.55 3.97 4.36 -0.62 0.00 0.89 0.91 0.00
110.0 -0.37 2.64 4.36 -0.62 0.00 0.59 0.61 0.00
111.0 -0.18 1.32 4.36 -0.62 0.00 0.29 0.30 0.00
L 112.0 -0.17 1.02 4.36 -0.62 0.00 0.28 0.24 0.00
Max: 0.08 0.89 0.98 0.00
f_bot (ksi) (comp limit
0.65f'ci)
(Ten limit -
0.24*sqrt(f
'ci) ksi)
f_top f_bot
D/C ratio
(comp
limit )
D/C
ratio(Ten
limit )
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit )
Length
along
girder (ft)
f_top
(ksi)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders D Stress Page: of:
Job #: NO:
For the stress calc, negative stress is tensile stress; positive stress is compressive stress.
Stress Calculations @ Transfer Stage
Tendons f_pu (ksi) 270
Tendon f_pbt (ksi) 203 (AASHTO Table 5.9.3.1)
Tendon E_ps (ksi) 28500
Girder Concrete E_pc (ksi) 5154
n'-1 = E_ps/ E_pc -1 5
f'c (ksi) 8.0
f'ci (ksi) 6.7
CA BT 55, Ag (in^2) 925
CA BT 55, w (k/ft) 1
CA BT 55, Yt, CG to Top (in) 27
CA BT 55, Yb, CG to Bot (in) 28
CA BT 55, Ig (in^4) 373350
Ƴ_h Say H= 70% 1
Ƴ_st 0.65
Δf_pR (ksi) 2.4
Transfer length l_t =60*db (in) 36
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders D Stress Page: of:
Job #: NO:
Stress Calculations @ PS + Perm load condition Transformed seciton properties
Note 1 Note 2 Note 3 Note 4 Note 5 Note 6 Note 7 Note 8
0 0.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
1.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
2.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
3.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
dv 5.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
0.1L 11.2 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
13.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
14.0 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
15.0 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
16.0 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
0.2L 22.4 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
28.0 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
29.0 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
30.0 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
31.0 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
0.3L 33.6 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
0.4L 44.8 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
0.5L 56.0 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
0.6L 67.2 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
0.7L 78.4 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
81.0 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
82.0 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
83.0 10.85 48.46 49.15 974 373350 27079 27.79767 27 22089 395439 14226 14470
84.0 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
0.8L 89.6 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
96.0 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
97.0 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
98.0 9.98 48.38 45.22 970 373350 26885 27.71022 27 20254 393604 14204 14357
99.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
0.9L 100.8 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
dv 108.2 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
109.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
110.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
111.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
L 112.0 8.25 48.16 37.36 962 373350 26497 27.53318 28 16542 389892 14161 14131
Transfor
med
Y_ttop
(in)
Transfor
med
Y_tbot
(in)
Ʃ Ai*(Y_i-
Y_ttop)^
2
(in^4)
I_final(in
^4)
Transfor
med
S_ttop
(in^3)
Transfor
med
S_tbot
(in^3)
Total
Aps*(n-
1)+Ag
(in^2) Ig (in^4)
ƩAi*Y_i
(in^3)
Length
along
girder
(ft) Aps(in^
2)
Y_p,
Tendon CG
to
GirderTop
(in)
Aps*(n'-
1)
(in^2)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders D Stress Page: of:
Job #: NO:
Note 1: Ignore moment of inertia I from prestrssing tendons, since it is too small compared to that of precast concrete Girder.
Note 2: Summation of tranformed strands area times CG of strands, and area of precast concrete girder times CG of the girder.
Note 3: Values of Note 2 divide by the total area of the transformed section to determine CG of the tranformed section (from top of the section)
Note 4: CG of the tranformed seciton (from bottom of the section)
Note 5:
Note 6: I_final =Ig + values at Note 5
Note 7: Transformed section modulus from top of seciton is I_final divide by Transformed Y_ttop
Note 8: Transformed section modulus from bottom of seciton is I_final divide by Transformed Y_tbot
Summation of tranformed area of strands times squrea of CG differenec between strands and the entire tranformed section, plus such value
for precast concrete girder component.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders D Stress Page: of:
Job #: NO:
Stress Calculations @ PS + Perm load condition * debond included
Note 9 Note 10 Note 11 Note 12 Note 13 Note 14 Note 15 Note 16
0 0.0 21 22 181 372 0 -0.16 0.93 3.60 -0.54 0.00 0.29 0.26 0.00
1.0 21 22 181 496 1425 -0.11 1.14 3.60 -0.54 0.00 0.20 0.32 0.00
2.0 21 22 181 993 2825 -0.22 2.28 3.60 -0.54 0.00 0.40 0.63 0.00
3.0 21 22 181 1489 4198 -0.33 3.42 3.60 -0.54 0.00 0.61 0.95 0.00
dv 5.0 21 22 181 1489 6869 -0.14 3.24 3.60 -0.54 0.00 0.26 0.90 0.00
0.1L 11.2 21 22 181 1489 14492 0.40 2.70 3.60 -0.54 0.11 0.00 0.75 0.00
13.0 21 22 181 1489 16523 0.54 2.55 3.60 -0.54 0.15 0.00 0.71 0.00
14.0 21 24 178 1572 17614 0.57 2.66 3.60 -0.54 0.16 0.00 0.74 0.00
15.0 21 24 178 1675 18680 0.60 2.84 3.60 -0.54 0.17 0.00 0.79 0.00
16.0 21 24 178 1778 19720 0.63 3.02 3.60 -0.54 0.18 0.00 0.84 0.00
0.2L 22.4 21 24 178 1778 25763 1.06 2.60 3.60 -0.54 0.29 0.00 0.72 0.00
28.0 21 24 178 1778 30195 1.37 2.29 3.60 -0.54 0.38 0.00 0.64 0.00
29.0 21 26 177 1817 30901 1.40 2.32 3.60 -0.54 0.39 0.00 0.65 0.00
30.0 21 26 177 1868 31581 1.43 2.40 3.60 -0.54 0.40 0.00 0.67 0.00
31.0 21 26 177 1919 32236 1.45 2.48 3.60 -0.54 0.40 0.00 0.69 0.00
0.3L 33.6 21 26 177 1919 33814 1.56 2.37 3.60 -0.54 0.43 0.00 0.66 0.00
0.4L 44.8 21 26 177 1919 38644 1.90 2.04 3.60 -0.54 0.53 0.00 0.57 0.00
0.5L 56.0 21 26 177 1919 40255 2.01 1.93 3.60 -0.54 0.56 0.00 0.54 0.00
0.6L 67.2 21 26 177 1919 38644 1.90 2.04 3.60 -0.54 0.53 0.00 0.57 0.00
0.7L 78.4 21 26 177 1919 33814 1.56 2.37 3.60 -0.54 0.43 0.00 0.66 0.00
81.0 21 26 177 1919 32236 1.45 2.48 3.60 -0.54 0.40 0.00 0.69 0.00
82.0 21 26 177 1868 31581 1.43 2.40 3.60 -0.54 0.40 0.00 0.67 0.00
83.0 21 26 177 1817 30901 1.40 2.32 3.60 -0.54 0.39 0.00 0.65 0.00
84.0 21 24 178 1778 30195 1.37 2.29 3.60 -0.54 0.38 0.00 0.64 0.00
0.8L 89.6 21 24 178 1778 25763 1.06 2.60 3.60 -0.54 0.29 0.00 0.72 0.00
96.0 21 24 178 1778 19720 0.63 3.02 3.60 -0.54 0.18 0.00 0.84 0.00
97.0 21 24 178 1675 18680 0.60 2.84 3.60 -0.54 0.17 0.00 0.79 0.00
98.0 21 24 178 1572 17614 0.57 2.66 3.60 -0.54 0.16 0.00 0.74 0.00
99.0 21 22 181 1489 16523 0.54 2.55 3.60 -0.54 0.15 0.00 0.71 0.00
0.9L 100.8 21 22 181 1489 14492 0.40 2.70 3.60 -0.54 0.11 0.00 0.75 0.00
dv 108.2 21 22 181 1489 5304 -0.25 3.35 3.60 -0.54 0.00 0.46 0.93 0.00
109.0 21 22 181 1489 4198 -0.33 3.42 3.60 -0.54 0.00 0.61 0.95 0.00
110.0 21 22 181 993 2825 -0.22 2.28 3.60 -0.54 0.00 0.40 0.63 0.00
111.0 21 22 181 496 1425 -0.11 1.14 3.60 -0.54 0.00 0.20 0.32 0.00
L 112.0 21 22 181 372 0 -0.16 0.93 3.60 -0.54 0.00 0.29 0.26 0.00
Max: 0.56 0.61 0.95 0.00
f_top
(ksi)
f_Bot
(ksi)
Compres
sive
Stress
limit (ksi)
Tensile
Stress
limit (ksi)
f_top f_bot
D/C ratio
(comp limit)
D/C
ratio(Ten
limit)
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit)
Length
along
girder
(ft)
e (in)Δf_pLT
(ksi)fpe (ksi) Pf (kiP)
Moment
demands
DC1+DC2
(kip-in)
PS+ Perm (DC1+DC2)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders D Stress Page: of:
Job #: NO:
Note 9: Eccentricity of the seciton is Y_p(in) from girder top subtracted by Transformed Y_ttop
Note 10
Note 11 fpe is stress at transfer minus long term loss Δf_pLT
Note 12 Prestressing force Pf, is fpe times area of the prestressing tendons, Aps.
Note 13
Note 14
Note 15
Note 16:
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders D Stress Page: of:
Job #: NO:
Tendons f_pu (ksi) 270
Tendon f_pbt (ksi) 202.5 (AASHTO Table 5.9.3.1)
CA BT 55, Ag (in^2) 925
CA BT 55, w (k/ft) 0.963
CA BT 55, Yt, CG to Top (in) 26.7
CA BT 55, Yb, CG to Bot (in) 28.4
CA BT 55, Ig (in^4) 373350
Tendon E_ps (ksi) 28,500
Girder Concrete E_pc (ksi) 5,154
n'-1 = E_ps/ E_pc -1 5
Girder f'c (ksi) 8
Girder f'ci (ksi) 6.7
Deck Concrete E_c (ksi) 4,074
Girder Concrete E_pc (ksi) 5,154
n= E_c/E_pc 0.79
CIP Deck f'c (ksi) 5
Deck effective width (ft) 9.08
Depth of concrete slab, ts (in) 8.00
Precast panel thickness (in) 3.50
Tranformed deck area (in^2) 768.74 (based on Ec of 8ksi concrete)
Tranformed effective deck width (in) 96.093 (based on Ec of 8ksi concrete)
Transfer length l_t =60*db (in) 36
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders D Stress Page: of:
Job #: NO:
Stress Calculations @ Service, composite section properties include the Deck Slab
Note 1
0 0.0 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 372
1.0 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 496
2.0 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 993
3.0 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
dv 5.0 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
0.1L 11.2 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
13.0 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
14.0 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1572
15.0 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1675
16.0 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1778
0.2L 22.4 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1778
28.0 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1778
29.0 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1817
30.0 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1868
31.0 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
0.3L 33.6 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
0.4L 44.8 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
0.5L 56.0 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
0.6L 67.2 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
0.7L 78.4 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
81.0 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1919
82.0 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1868
83.0 395439 27.80 27.33 769 1743 37947 22 41 829877 60256 20068 21 26 177 1817
84.0 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1778
0.8L 89.6 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1778
96.0 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1778
97.0 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1675
98.0 393604 27.71 27.41 769 1739 37722 22 41 824885 60245 19909 21 24 178 1572
99.0 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
0.9L 100.8 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
dv 108.2 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
109.0 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 1489
110.0 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 993
111.0 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 496
L 112.0 389892 27.53 27.59 769 1731 37271 22 42 814836 60225 19590 21 22 181 372
e (in)
Δf_pLT
(ksi)
fpe
(ksi)
Pf
(kiP)
Yi to Top
of Deck
ƩAi*Y_i
(in^3)
Comp
Y_ttop
(in)
ToDec
kTop
Comp.
Y_tbot
(in)
I_comp
(in^4)
Comp.
S_tg
(in^3)
Comp S_tb
(in^3)
Length
along
girder (ft)
I_tg(in^4)Transformed
Y_ttop (in)
Transfor
med
Y_tbot
(in)
Tranfor
med
A_deck
(in^2)
A_deck+A
ps*(n'-
1)+Ag
(in^2)
From PS+Perm stress calc
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders D Stress Page: of:
Job #: NO:
Stress Calculations @ Service, composite section properties include the Deck Slab
* debond included Note 2 Note 3 Note 4
0 0.0 0 0 0 0 -0.16 0.93 4.80 -0.54 0.00 0.29 0.19 0.00
1.0 1425 347 24 1107 -0.08 1.06 4.80 -0.54 0.00 0.15 0.22 0.00
2.0 2825 688 48 2194 -0.17 2.13 4.80 -0.54 0.00 0.31 0.44 0.00
3.0 4198 1023 72 3261 -0.25 3.20 4.80 -0.54 0.00 0.47 0.67 0.00
dv 5.0 6869 1673 120 5336 -0.02 2.87 4.80 -0.54 0.00 0.03 0.60 0.00
0.1L 11.2 14492 3530 270 11257 0.65 1.93 4.80 -0.54 0.14 0.00 0.40 0.00
13.0 16523 4025 313 12835 0.83 1.68 4.80 -0.54 0.17 0.00 0.35 0.00
14.0 17614 4291 337 13683 0.88 1.74 4.80 -0.54 0.18 0.00 0.36 0.00
15.0 18680 4550 361 14511 0.93 1.86 4.80 -0.54 0.19 0.00 0.39 0.00
16.0 19720 4804 385 15318 0.97 1.99 4.80 -0.54 0.20 0.00 0.41 0.00
0.2L 22.4 25763 6276 539 20013 1.50 1.25 4.80 -0.54 0.31 0.00 0.26 0.00
28.0 30195 7355 674 23456 1.89 0.71 4.80 -0.54 0.39 0.00 0.15 0.00
29.0 30901 7527 698 24004 1.93 0.72 4.80 -0.54 0.40 0.00 0.15 0.00
30.0 31581 7693 722 24533 1.97 0.76 4.80 -0.54 0.41 0.00 0.16 0.00
31.0 32236 7853 746 25041 2.01 0.81 4.80 -0.54 0.42 0.00 0.17 0.00
0.3L 33.6 33814 8237 809 26267 2.15 0.61 4.80 -0.54 0.45 0.00 0.13 0.00
0.4L 44.8 38644 9414 1078 30019 2.57 0.02 4.80 -0.54 0.54 0.00 0.00 0.00
0.5L 56.0 40255 9806 1348 31270 2.72 -0.19 4.80 -0.54 0.57 0.00 0.00 0.35
0.6L 67.2 38644 9414 1078 30019 2.57 0.02 4.80 -0.54 0.54 0.00 0.00 0.00
0.7L 78.4 33814 8237 809 26267 2.15 0.61 4.80 -0.54 0.45 0.00 0.13 0.00
81.0 32236 7853 746 25041 2.01 0.81 4.80 -0.54 0.42 0.00 0.17 0.00
82.0 31581 7693 722 24533 1.97 0.76 4.80 -0.54 0.41 0.00 0.16 0.00
83.0 30901 7527 698 24004 1.93 0.72 4.80 -0.54 0.40 0.00 0.15 0.00
84.0 30195 7355 674 23456 1.89 0.71 4.80 -0.54 0.39 0.00 0.15 0.00
0.8L 89.6 25763 6276 539 20013 1.50 1.25 4.80 -0.54 0.31 0.00 0.26 0.00
96.0 19720 4804 385 15318 0.97 1.99 4.80 -0.54 0.20 0.00 0.41 0.00
97.0 18680 4550 361 14511 0.93 1.86 4.80 -0.54 0.19 0.00 0.39 0.00
98.0 17614 4291 337 13683 0.88 1.74 4.80 -0.54 0.18 0.00 0.36 0.00
99.0 16523 4025 313 12835 0.83 1.68 4.80 -0.54 0.17 0.00 0.35 0.00
0.9L 100.8 14492 3530 270 11257 0.65 1.93 4.80 -0.54 0.14 0.00 0.40 0.00
dv 108.2 5304 1292 92 4121 -0.16 3.07 4.80 -0.54 0.00 0.29 0.64 0.00
109.0 4198 1023 72 3261 -0.25 3.20 4.80 -0.54 0.00 0.47 0.67 0.00
110.0 2825 688 48 2194 -0.17 2.13 4.80 -0.54 0.00 0.31 0.44 0.00
111.0 1425 347 24 1107 -0.08 1.06 4.80 -0.54 0.00 0.15 0.22 0.00
L 112.0 0 0 0 0 -0.16 0.93 4.80 -0.54 0.00 0.29 0.19 0.00
Max: 0.57 0.47 0.67 0.35
Tensile
Stress
limit (ksi)
f_top f_bot
D/C ratio
(comp limit)
D/C
ratio(Ten
limit)
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit)
Moment
demands
DC3+DW (kip-
in)
Moment demands
DC4 (kip-in)
Moment
demands
LL(1+IM) (kip-
in)
f_top (ksi) f_Bot (ksi)Compressive
Stress limit (ksi)
Length
along
girder
(ft)
Moment
demands
DC1+DC2
(kip-in)
Service I : PS+Perm+LL*(1+IM)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders D Stress Page: of:
Job #: NO:
Note 1:
Note 2
f_bot SIM.
Note 3
Note 4
Check the stress to top of girder, so section modulus of the composite section, is the I_comp / y_tg, and y_tg
is the distance from comp. nuetral axis to the top of the girder.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders D Stress Page: of:
Job #: NO:
0 0.0 0 -0.16 0.93 4.80 -0.54 0.00 0.29 0.19 0.00
1.0 886 -0.09 1.08 4.80 -0.54 0.00 0.16 0.22 0.00
2.0 1755 -0.17 2.15 4.80 -0.54 0.00 0.32 0.45 0.00
3.0 2609 -0.26 3.24 4.80 -0.54 0.00 0.49 0.67 0.00
dv 5.0 4269 -0.04 2.93 4.80 -0.54 0.00 0.07 0.61 0.00
0.1L 11.2 9006 0.61 2.04 4.80 -0.54 0.13 0.00 0.43 0.00
13.0 10268 0.79 1.81 4.80 -0.54 0.16 0.00 0.38 0.00
14.0 10946 0.83 1.87 4.80 -0.54 0.17 0.00 0.39 0.00
15.0 11609 0.88 2.01 4.80 -0.54 0.18 0.00 0.42 0.00
16.0 12255 0.92 2.14 4.80 -0.54 0.19 0.00 0.45 0.00
0.2L 22.4 16010 1.44 1.45 4.80 -0.54 0.30 0.00 0.30 0.00
28.0 18765 1.82 0.94 4.80 -0.54 0.38 0.00 0.20 0.00
29.0 19203 1.85 0.96 4.80 -0.54 0.39 0.00 0.20 0.00
30.0 19626 1.89 1.00 4.80 -0.54 0.39 0.00 0.21 0.00
31.0 20033 1.92 1.06 4.80 -0.54 0.40 0.00 0.22 0.00
0.3L 33.6 21014 2.06 0.88 4.80 -0.54 0.43 0.00 0.18 0.00
0.4L 44.8 24016 2.47 0.32 4.80 -0.54 0.52 0.00 0.07 0.00
0.5L 56.0 25016 2.61 0.13 4.80 -0.54 0.54 0.00 0.03 0.00
0.6L 67.2 24016 2.47 0.32 4.80 -0.54 0.52 0.00 0.07 0.00
0.7L 78.4 21014 2.06 0.88 4.80 -0.54 0.43 0.00 0.18 0.00
81.0 20033 1.92 1.06 4.80 -0.54 0.40 0.00 0.22 0.00
82.0 19626 1.89 1.00 4.80 -0.54 0.39 0.00 0.21 0.00
83.0 19203 1.85 0.96 4.80 -0.54 0.39 0.00 0.20 0.00
84.0 18765 1.82 0.94 4.80 -0.54 0.38 0.00 0.20 0.00
0.8L 89.6 16010 1.44 1.45 4.80 -0.54 0.30 0.00 0.30 0.00
96.0 12255 0.92 2.14 4.80 -0.54 0.19 0.00 0.45 0.00
97.0 11609 0.88 2.01 4.80 -0.54 0.18 0.00 0.42 0.00
98.0 10946 0.83 1.87 4.80 -0.54 0.17 0.00 0.39 0.00
99.0 10268 0.79 1.81 4.80 -0.54 0.16 0.00 0.38 0.00
0.9L 100.8 9006 0.61 2.04 4.80 -0.54 0.13 0.00 0.43 0.00
dv 108.2 3296 -0.17 3.11 4.80 -0.54 0.00 0.32 0.65 0.00
109.0 2609 -0.26 3.24 4.80 -0.54 0.00 0.49 0.67 0.00
110.0 1755 -0.17 2.15 4.80 -0.54 0.00 0.32 0.45 0.00
111.0 886 -0.09 1.08 4.80 -0.54 0.00 0.16 0.22 0.00
L 112.0 0 -0.16 0.93 4.80 -0.54 0.00 0.29 0.19 0.00
Max: 0.54 0.49 0.67 0.00
f_Bot (ksi)
Compressiv
e Stress
limit (ksi)
Tensile
Stress limit
(ksi)
f_top f_bot
D/C ratio
(comp limit)
D/C ratio(Ten
limit)
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit)
Length along
girder (ft)
Moment
demands
0.8*LL(1+IM
) (kip-in)
f_top (ksi)
Service III : PS+Perm+0.8*LL*(1+IM)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders D Stress Page: of:
Job #: NO:
REQUIRED TOP REINFORCEMENT
0 0.0 -0.17 1.02 7.90 31.99 1.07 3
1.0 -0.18 1.32 6.71 29.01 0.97 3
2.0 -0.37 2.64 6.73 58.34 1.94 5
3.0 -0.55 3.97 6.74 87.97 2.93 7
dv 5.0 -0.47 3.88 5.93 65.53 2.18 5
0.1L 11.2 -0.23 3.64 3.22 17.23 0.57 2
13.0 -0.16 3.58 2.38 9.12 0.30 1
14.0 -0.18 3.77 2.57 11.24 0.37 1
15.0 -0.20 4.03 2.61 12.37 0.41 1
16.0 -0.22 4.28 2.66 13.62 0.45 2
0.2L 22.4 -0.03 4.09 0.35 0.21 0.01 1
28.0 0.11 3.96 0.00 0.00 0.00 0
29.0 0.11 4.04 0.00 0.00 0.00 0
30.0 0.11 4.16 0.00 0.00 0.00 0
31.0 0.10 4.29 0.00 0.00 0.00 0
0.3L 33.6 0.15 4.24 0.00 0.00 0.00 0
0.4L 44.8 0.30 4.09 0.00 0.00 0.00 0
0.5L 56.0 0.35 4.04 0.00 0.00 0.00 0
0.6L 67.2 0.30 4.09 0.00 0.00 0.00 0
0.7L 78.4 0.15 4.24 0.00 0.00 0.00 0
81.0 0.10 4.29 0.00 0.00 0.00 0
82.0 0.11 4.16 0.00 0.00 0.00 0
83.0 0.11 4.04 0.00 0.00 0.00 0
84.0 0.11 3.96 0.00 0.00 0.00 0
0.8L 89.6 -0.03 4.09 0.35 0.21 0.01 1
96.0 -0.22 4.28 2.66 13.62 0.45 2
97.0 -0.20 4.03 2.61 12.37 0.41 1
98.0 -0.18 3.77 2.57 11.24 0.37 1
99.0 -0.16 3.58 2.38 9.12 0.30 1
0.9L 100.8 -0.23 3.64 3.22 17.23 0.57 2
dv 108.2 -0.52 3.93 6.41 78.37 2.61 6
109.0 -0.55 3.97 6.74 87.97 2.93 7
110.0 -0.37 2.64 6.73 58.34 1.94 5
111.0 -0.18 1.32 6.71 29.01 0.97 3
L 112.0 -0.17 1.02 7.90 31.99 1.07 3
f_ci,top (ksi) f_ci,bot (ksi) x (in) T (kip) As (in^2)
# 6 rebars
(in^2)
Length along
girder (ft)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders E Design Page: of:
Job #: NO:
L, Bridge span length (ft) 111.58
Bridge Width (ft) Upper bound 78.16
Bridge Width (ft) Lower Bound 71.60
Bridge Width (ft) Average 74.88
Number of Lanes 4
m, Multipresent factor for LL 0.65
Nb, Number of Girder 8
S, Max Girder Spacing (ft) 10.05
Bridge Skew Angle (degree) 31
For the bridge girder:
f'ci at transfer (ksi) 6.7 AASHTO 5.4.2.3.1
f'c after 28 days (ksi) 8
E_ci (ksi) for girder @ transfer 4716
During the construction of the bridge, it is required to not interfere with train traffic,
thus, the bridge slab system is precast concrete panel in between girders, stitched with CIP Concrete.
Tendon diameter (in) 0.6
One strand area (in^2) 0.217
Debonding length (from end of beam to where bonding commence), ft
10
Girder Distribution factors for DL, LL moment, LL Shear
Type of deck CIP Concrete, Precast Concrete
Supporting Component Precast Concrete I or Bulb-tee section
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders E Design Page: of:
Job #: NO:
Common Deck superstructure Table 4.6.2.2.1-1
Typical Cross section K Table 4.6.2.2.1-1
Live Load Distribution Factor for Moment in Interior Beams Table 4.6.2.2.2b-1
Rang of Applicability
S, spacing of beams, ϵ [ 3.5, 16] ft ✔
L, Span Length, ϵ [20,240] ft ✔
Nb, number of beams >=4 ✔
ts, depth of concrete slab ϵ [ 4.5, 12] in ✔
Depth of concrete slab, ts (in) 8.00
kg, longitudinal stiffness factor, ϵ [10^4 , 7x10^6] ✔
kg= n( I + A*eg^2) 1576804.87 4.6.2.2.1-1
n= E_beam / E_deck 1.26491106
f'c_slab (ksi) 6
E_beam (ksi) 5,154
E_slab (ksi) 4,074
A, (non-composite) cross section area of girder (in^2) 925 Caltrans Design Aids, CA BT-55
I, (non-composite) inertia (in^4) 373,350 Caltrans Design Aids, CA BT-55
Yb, CG to bottom of girder (in) 28.4 Caltrans Design Aids, CA BT-55
D, girder height (in) 55.125 Caltrans Design Aids, CA BT-55
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders E Design Page: of:
Job #: NO:
eg, dist. Btw CL of beam & CL of deck (in) 30.725
b_eff, deck effective width of girder (ft) 9.08
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders E Design Page: of:
Job #: NO:
Per above table from AASHTO, the LL distribution factor for moment in Interior beams are calculated:
g_int, One design lane loaded: 0.52 lane / girder multiple presence factor included
g_int, Two or more lane loaded: 0.77 lane / girder per C4.6.2.2.2b
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders E Design Page: of:
Job #: NO:
Per above table from AASHTO, the LL distribution factor for moment in exterior beams are calculated:
de, horizontal distance from CL of ext. web of ext. beam @ deck level, to int. edge of curb of traffic barrier
de (ft) 2.30
e=0.77+de/9.1 1.02
g_ext, one design lane loaded 0.53 lane/girder
g_ext, two or more design lane loaded 0.79 lane/girder
Considering the span length, it is very likley that cross frames & end diaphraagm will be necessary.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders E Design Page: of:
Job #: NO:
Per AASHTO C4.6.2.2.2d-1, exterior girders have higher load distribution factors due to cross frames
One lane loaded:
NL 1
X_ext, (ft) 35.18
e (ft) 24.03
x_1 (ft) 5.03
x_2 (ft) 15.08
x_3 (ft) 25.13
x_4 (ft) 35.18
R 0.32
Adjust with 1.2 multiple presence factor 0.39
Two Lanes loaded:
NL 2
e1 (ft) 24.03
e2 (ft) 6.5
R 0.50
Adjust with 1.0 multiple presence factor 0.50
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders E Design Page: of:
Job #: NO:
Three or more Lanes loaded:
NL 3
e1 (ft) 24.03
e2 (ft) 6.5
e3 (ft) 12
R 0.68
Adjust with 0.85 multiple presence factor 0.58
Final design values for moment distribution factors :
Load Case Int. Girder (lane)
One lane 0.52 0.53
NA 0.39
2 lanes loaded NA 0.50
3 lanes loaded NA 0.58
Design Value
Moment
Distribution 0.77 0.79
Max: 0.79
Two values are close enough, use the
maximum value for all to be conservative.
Note that AASHTO 4.6.2.2.2.e for skewed bridge provides reduction factors for live load distribution factors for momen in longitudinal
beams. However, CA amendment ignores reduction. Thus, no reduction applies for moment
Ext. Girder (lane)
Moment Distribution factor
per Table 4.6.2.2.2 Two or more
lane
0.77 0.79
Moment D.F. for ext. girder per
C4.6.2.2.2d-1
one lane loaded
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders E Design Page: of:
Job #: NO:
LL distribution factor for Shear :
Per above table from AASHTO, the LL distribution factor for shear in Interior beams are calculated:
g_int, One design lane loaded: 0.76 lane / girder multiple presence factor included
g_int, Two or more lane loaded: 0.96 lane / girder per C4.6.2.2.2b
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders E Design Page: of:
Job #: NO:
Per above table from AASHTO, the LL distribution factor for shear in exterior beams are calculated:
de (ft) 2.30
e=0.77+de/9.1 1.02
g_ext, one design lane loaded 0.53 lane/girder use same as ext one-lane for moment
g_ext, two or more design lane loaded 0.98 lane/girder
Notes:
AASHTO 4.6.2.2.3 C-1 provides correction factors for live load distribution factors for support shear of the obtuse girder.
CA Amendment revised AASHTO Table 4.6.2.2.3c-1 with equations provide for exterior girder & first interior girder.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders E Design Page: of:
Job #: NO:
Design values for shear distribution factors (without skew correction factor)
Load Case Int. Girder (lane)
One lane 0.76 NA
NA
NA 0.53
NA 0.98
Design Value
Shear
Distribution
Factor
0.96 0.98
Max: 0.98
Skew Correction factors for shear:
Two values are close enough, use the
maximum value for all to be conservative.
Ext. Girder (lane)
Shear Distribution factor per
Table 4.6.2.2.3a-1 Two or more
lane
0.96
Shear D.F. for ext. girder per
C4.6.2.2.3b-1
one lane loaded
Two or more
lane
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders E Design Page: of:
Job #: NO:
The shear correction factors are applied between the point of support at the obtuse corner and mid-span.
May be decreased linearly to a value of 1.0 at mid-span.
Skew Factor 1.09
Design values for shear distribution factors@ obtuse angle
Load Case Int. Girder (lane)
Design Value Shear D.F. 1.04 1.07 Max: 1.07
Two values are close enough, use the
maximum value for all to be conservative.Ext. Girder (lane)
1.07
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders E Design Page: of:
Job #: NO:
Moment Demands Calculations
One lane
0 0.0 0 0 0 0 0 0 0
dv 5.0 257 314 52 10 632 87 564
0.1L 11.2 540 660 109 22 1330 184 1187
0.2L 22.3 959 1173 193 45 2370 326 2109
0.3L 33.5 1259 1539 253 67 3118 428 2769
0.4L 44.6 1439 1759 289 90 3577 489 3164
0.5L 55.8 1499 1832 302 112 3744 510 3296
0.6L 67.0 1439 1759 289 90 3577 489 3164
0.7L 78.1 1259 1539 253 67 3118 428 2769
0.8L 89.3 959 1173 193 45 2370 326 2109
0.9L 100.4 540 660 109 22 1330 184 1187
dv 106.6 257 314 52 10 632 87 564
L 111.6 0 0 0 0 0 0 0
dv Use 0.9h (AASHTO 5.8.2.9) 5.03 ft
LL+IM Use Caltrans Bridge Design Aids attached as following.
Span length Moment (k-ft) End Shear (kip)
110 3229 122.8
120 3652.4 126.7
111.6 3296.0 123.4
Lane Load included from Caltrans Table
0 0
934 0
444 0
2180 0
1661 0
2595 0
2491 0
2180 0
2491 0
1661 0
Min LL
0 0
444 0
934 0
Length along
girder (ft)
For Each Girder
M (k-ft) DC1 M (k-ft) DC2 M (k-ft) DC3
M (k-ft)
DC4
M (k-ft)
DC Total
M (k-ft)
DW
(HL-93) LL+IM -M (k-f)
Distr.Fact
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders E Design Page: of:
Job #: NO:
Moment Capacity Calculations@ Wet Concr. Deck Stage (NonComposite)
Note 1 Note 4 Note 3
0 0.0 8 8 8 6 4 2 0 48.60 7.81 0.64 N.A. @ TF
dv 5.0 8 8 8 6 4 2 0 48.60 7.81 0.64 N.A. @ TF
0.1L 11.2 8 8 8 6 4 2 0 48.60 7.81 0.64 N.A. @ TF
0.2L 22.3 10 10 10 8 4 2 0 48.74 9.55 0.78 N.A. @ TF
0.3L 33.5 10 12 12 8 4 2 0 48.79 10.42 0.85 N.A. @ TF
0.4L 44.6 10 12 12 8 4 2 0 48.79 10.42 0.85 N.A. @ TF
0.5L 55.8 10 12 12 8 4 2 0 48.79 10.42 0.85 N.A. @ TF
0.6L 67.0 10 12 12 8 4 2 0 48.79 10.42 0.85 N.A. @ TF
0.7L 78.1 10 12 12 8 4 2 0 48.79 10.42 0.85 N.A. @ TF
0.8L 89.3 10 10 10 8 4 2 0 48.74 9.55 0.78 N.A. @ TF
0.9L 100.4 8 8 8 6 4 2 0 48.60 7.81 0.64 N.A. @ TF
dv 106.6 8 8 8 6 4 2 0 48.60 7.81 0.64 N.A. @ TF
L 111.6 8 8 8 6 4 2 0 48.60 7.81 0.64 N.A. @ TF
0.6" diameter tendons are used
Reference: AASHTO 2014 LRFD 7th Edition
Note 1: Note 4:
Note 2: Note 5:
Note 3: Note 6:Calcuated "c" to determine location of section
N.A.
No.
Tendon
at 12.75"
From Bot
No.
Tendon at
14.75"
From Bot
dp(in) to
Girder top
Aps(in^2) c (in)
Action Type:
Nuetral axis
location
Length
along
girder (ft)
No. Tendon
at 2.75"
From Bot
No.
Tendon at
4.75" from
Bot
No.
Tendon at
6.75"
From Bot
No.
Tendon at
8.75" From
Bot
No.
Tendon at
10.75"
From Bot
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders E Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Wet Concrete Deck Stage
Note 2 Note 5 Note 6 Note 7 Note 8
0 0.0 0.64 0.55 269.0 8463 0.2244 1.00 8463 0 8463 0
dv 5.0 0.64 0.55 269.0 8463 0.2244 1.00 8463 713 8463 0.08
0.1L 11.2 0.64 0.55 269.0 8463 0.2244 1.00 8463 1499 8463 0.18
0.2L 22.3 0.78 0.67 268.8 10352 0.1837 1.00 10352 2665 10352 0.26
0.3L 33.5 0.85 0.73 268.7 11294 0.1684 1.00 11294 3497 11294 0.31
0.4L 44.6 0.85 0.73 268.7 11294 0.1684 1.00 11294 3997 11294 0.35
0.5L 55.8 0.85 0.73 268.7 11294 0.1684 1.00 11294 4164 11294 0.37
0.6L 67.0 0.85 0.73 268.7 11294 0.1684 1.00 11294 3997 11294 0.35
0.7L 78.1 0.85 0.73 268.7 11294 0.1684 1.00 11294 3497 11294 0.31
0.8L 89.3 0.78 0.67 268.8 10352 0.1837 1.00 10352 2665 10352 0.26
0.9L 100.4 0.64 0.55 269.0 8463 0.2244 1.00 8463 1499 8463 0.18
dv 106.6 0.64 0.55 269.0 8463 0.2244 1.00 8463 713 8463 0.08
L 111.6 0.64 0.55 269.0 8463 0.2244 1.00 8463 0 8463 0.00
Note 7: Moment formula chosen depends on girder action type
Beta_1 =0.85 Per AASHTO 5.7.2.2
Value of k =0.28 Per Table C5.7.3.1.1.1
Note 8:
phi
factor φ
φMn(k-
ft)
For Each Girder
Mu (k-ft)
Strength I φMn(k-ft) D/C
Length
along
girder
(ft)
Update c (in) a (in) f_ps(ksi) Mn(k-ft)Epslon_t
ξ_t
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders E Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Wet Concrete Deck Stage
Mu=1.25 DC1+1.25DC2
Controlling Combination to design girders:
Strength I 1.25 DC+1.5 DW
0
2000
4000
6000
8000
10000
12000
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Mo
me
nt
(k
-ft)
Length (ft)
Moment Plot along Span Length
Mu (k-ft) Strength I φMn(k-ft)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders E Design Page: of:
Job #: NO:
0 0.0 0 0 0 0 0 0 0
dv 5.0 257 314 52 10 632 87 1010
0.1L 11.2 540 660 109 22 1330 184 2124
0.2L 22.3 959 1173 193 45 2370 326 3777
0.3L 33.5 1259 1539 253 67 3118 428 4957
0.4L 44.6 1439 1759 289 90 3577 489 5665
0.5L 55.8 1499 1832 302 112 3744 510 5901
0.6L 67.0 1439 1759 289 90 3577 489 5665
0.7L 78.1 1259 1539 253 67 3118 428 4957
0.8L 89.3 959 1173 193 45 2370 326 3777
0.9L 100.4 540 660 109 22 1330 184 2124
dv 106.6 257 314 52 10 632 87 1010
L 111.6 0 0 0 0 0 0 0 0 0
2973 0
1673 0
795 0
4646 0
4460 0
3903 0
2973 0
3903 0
4460 0
Min LL
0 0
795 0
1673 0
Length along
girder (ft)M (k-ft) DC1 M (k-ft) DC2 M (k-ft) DC3
M (k-ft)
DC4
M (k-ft)
DC Total
For Each Girder
M (k-ft)
DW
(P-15) LL+IM -M (k-f)
One lane Distr.Fact
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders E Design Page: of:
Job #: NO:
Moment Capacity Calculations@ Final Stage Stage
0 0.0 8 8 8 6 4 2 0 8 56.60 7.81 5.22
dv 5.0 8 8 8 6 4 2 0 8 56.60 7.81 5.22
0.1L 11.2 8 8 8 6 4 2 0 8 56.60 7.81 5.22
0.2L 22.3 10 10 10 8 4 2 0 8 56.74 9.55 6.35
0.3L 33.5 10 12 12 8 4 2 0 8 56.79 10.42 6.90
0.4L 44.6 10 12 12 8 4 2 0 8 56.79 10.42 6.90
0.5L 55.8 10 12 12 8 4 2 0 8 56.79 10.42 6.90
0.6L 67.0 10 12 12 8 4 2 0 8 56.79 10.42 6.90
0.7L 78.1 10 12 12 8 4 2 0 8 56.79 10.42 6.90
0.8L 89.3 10 10 10 8 4 2 0 8 56.74 9.55 6.35
0.9L 100.4 8 8 8 6 4 2 0 8 56.60 7.81 5.22
dv 106.6 8 8 8 6 4 2 0 8 56.60 7.81 5.22
L 111.6 8 8 8 6 4 2 0 8 56.60 7.81 5.22
Considering the concrete deck is acting compositely with the CA BT 55 girders.
Also Conservatively igore the precast concrete panel's composite concrete reaction, due to lack of friction btw the panel surface.
Aps(in^2) c (in) No.
Tendon at
10.75"
From Bot
No.
Tendon
at 12.75"
From Bot
No.
Tendon at
14.75"
From Bot
Composite
Deck THK
(in)
dp(in) to
Deck top
Length
along
girder (ft)
No. Tendon
at 2.75"
From Bot
No.
Tendon at
4.75" from
Bot
No.
Tendon at
6.75"
From Bot
No.
Tendon at
8.75" From
Bot
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders E Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Final Stage
0 0.0 N.A. @ Deck 5.22 4.44 263.0 9311 0.0295 1.00 9311
dv 5.0 N.A. @ Deck 5.22 4.44 263.0 9311 0.0295 1.00 9311
0.1L 11.2 N.A. @ Deck 5.22 4.44 263.0 9311 0.0295 1.00 9311
0.2L 22.3 N.A. @ Deck 6.35 5.39 261.5 11246 0.0238 1.00 11246
0.3L 33.5 N.A. @ Deck 6.90 5.87 260.8 12192 0.0217 1.00 12192
0.4L 44.6 N.A. @ Deck 6.90 5.87 260.8 12192 0.0217 1.00 12192
0.5L 55.8 N.A. @ Deck 6.90 5.87 260.8 12192 0.0217 1.00 12192
0.6L 67.0 N.A. @ Deck 6.90 5.87 260.8 12192 0.0217 1.00 12192
0.7L 78.1 N.A. @ Deck 6.90 5.87 260.8 12192 0.0217 1.00 12192
0.8L 89.3 N.A. @ Deck 6.35 5.39 261.5 11246 0.0238 1.00 11246
0.9L 100.4 N.A. @ Deck 5.22 4.44 263.0 9311 0.0295 1.00 9311
dv 106.6 N.A. @ Deck 5.22 4.44 263.0 9311 0.0295 1.00 9311
L 111.6 N.A. @ Deck 5.22 4.44 263.0 9311 0.0295 1.00 9311
Mn(k-ft)Epslon_t
ξ_t
phi factor
φ φMn(k-ft)
Length
along
girder
(ft)
Action Type
(Neutral Axis
location)
Update
c (in)
from
deck
top
a (in) f_ps(ksi)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders E Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Final Stage
0 0.0 0 0 9311 0 0.00
dv 5.0 1698 1995 9311 0.18 0.21
0.1L 11.2 3573 4196 9311 0.38 0.45
0.2L 22.3 6358 7465 11246 0.57 0.66
0.3L 33.5 8355 9809 12192 0.69 0.80
0.4L 44.6 9565 11226 12192 0.78 0.92
0.5L 55.8 9986 11717 12192 0.82 0.96
0.6L 67.0 9565 11226 12192 0.78 0.92
0.7L 78.1 8355 9809 12192 0.69 0.80
0.8L 89.3 6358 7465 11246 0.57 0.66
0.9L 100.4 3573 4196 9311 0.38 0.45
dv 106.6 1698 1995 9311 0.18 0.21
L 111.6 0 0 9311 0.00 0.00
Strength I 1.25 DC+1.5 DW+1.75 LL
Strength II 1.25 DC+1.5 DW+1.35 LL-permit
17
Mu (k-ft)
Strength I
Mu (k-ft)
Strength II φMn(k-ft)
D/C for
Strength I
D/C for
Strength II
Length
along
girder (ft)
For Each Girder
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders E Design Page: of:
Job #: NO:
0
2000
4000
6000
8000
10000
12000
14000
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Mo
me
nt
(k
-ft)
Length (ft)
Moment Plot along Span Length
Mu (k-ft) Strength I
φMn(k-ft)
Mu (k-ft) Strength II
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders E Stress Page: of:
Job #: NO:
For the stress calc, negative stress is tensile stress; positive stress is compressive stress.
Stress Calculations @ Transfer Stage
Tendons f_pu (ksi) 270
Tendon f_pbt (ksi) 202.5 (AASHTO Table 5.9.3.1)
Tendon E_ps (ksi) 28,500
Girder Concrete E_pc (ksi) 5,154
n'-1 = E_ps/ E_pc -1 4.53
f'c (ksi) 8
f'ci (ksi) 6.7
CA BT 55, Ag (in^2) 925
CA BT 55, w (k/ft) 0.963
CA BT 55, Yt, CG to Top (in) 26.70
CA BT 55, Yb, CG to Bot (in) 28.40
CA BT 55, Ig (in^4) 373,350
Ƴ_h Say H= 70% 1
Ƴ_st 0.65
Δf_pR (ksi) 2.4
Transfer length l_t =60*db (in) 36
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders E Stress Page: of:
Job #: NO:
Stress Calculations @ Transfer Stage* debond included
Note 1 Note 2 Note 3 Note 4 Note 5 Note 6
0 0.0 8 8 8 6 4 2 0 7.81 48.60 21.90 0 19 184 ok 359
1.0 8 8 8 6 4 2 0 7.81 48.60 21.90 639 19 184 ok 479
2.0 8 8 8 6 4 2 0 7.81 48.60 21.90 1266 18 184 ok 959
3.0 8 8 8 6 4 2 0 7.81 48.60 21.90 1882 18 184 ok 1440
dv 5.0 8 8 8 6 4 2 0 7.81 48.60 21.90 3079 18 185 ok 1442
0.1L 11.2 8 8 8 6 4 2 0 7.81 48.60 21.90 6475 17 186 ok 1450
13.0 8 8 8 6 4 2 0 7.81 48.60 21.90 7405 17 186 ok 1452
14.0 10 10 10 8 4 2 0 9.55 48.74 22.04 7894 20 182 ok 1528
15.0 10 10 10 8 4 2 0 9.55 48.74 22.04 8371 20 182 ok 1635
16.0 10 10 10 8 4 2 0 9.55 48.74 22.04 8836 20 182 ok 1742
0.2L 22.3 10 10 10 8 4 2 0 9.55 48.74 22.04 11511 19 183 ok 1749
28.0 10 10 10 8 4 2 0 9.55 48.74 22.04 13522 19 184 ok 1755
29.0 10 12 12 8 4 2 0 10.42 48.79 22.09 13838 21 182 ok 1790
30.0 10 12 12 8 4 2 0 10.42 48.79 22.09 14142 20 182 ok 1844
31.0 10 12 12 8 4 2 0 10.42 48.79 22.09 14434 20 182 ok 1897
0.3L 33.5 10 12 12 8 4 2 0 10.42 48.79 22.09 15108 20 182 ok 1899
0.4L 44.6 10 12 12 8 4 2 0 10.42 48.79 22.09 17266 20 183 ok 1906
0.5L 55.8 10 12 12 8 4 2 0 10.42 48.79 22.09 17985 19 183 ok 1908
0.6L 67.0 10 12 12 8 4 2 0 10.42 48.79 22.09 17266 20 183 ok 1906
0.7L 78.1 10 12 12 8 4 2 0 10.42 48.79 22.09 15108 20 182 ok 1899
80.6 10 12 12 8 4 2 0 10.42 48.79 22.09 14434 20 182 ok 1897
81.6 10 12 12 8 4 2 0 10.42 48.79 22.09 14142 20 182 ok 1844
82.6 10 12 12 8 4 2 0 10.42 48.79 22.09 13838 21 182 ok 1790
83.6 10 10 10 8 4 2 0 9.55 48.74 22.04 13522 19 184 ok 1755
0.8L 89.3 10 10 10 8 4 2 0 9.55 48.74 22.04 11511 19 183 ok 1749
95.6 10 10 10 8 4 2 0 9.55 48.74 22.04 8836 20 182 ok 1742
96.6 10 10 10 8 4 2 0 9.55 48.74 22.04 8371 20 182 ok 1635
97.6 10 10 10 8 4 2 0 9.55 48.74 22.04 7894 20 182 ok 1528
98.6 8 8 8 6 4 2 0 7.81 48.60 21.90 7405 17 186 ok 1452
0.9L 100.4 8 8 8 6 4 2 0 7.81 48.60 21.90 6475 17 186 ok 1450
dv 108.2 8 8 8 6 4 2 0 7.81 48.60 21.90 2139 18 184 ok 1440
108.6 8 8 8 6 4 2 0 7.81 48.60 21.90 1882 18 184 ok 1440
109.6 8 8 8 6 4 2 0 7.81 48.60 21.90 1266 18 184 ok 959
110.6 8 8 8 6 4 2 0 7.81 48.60 21.90 639 19 184 ok 479
L 111.6 8 8 8 6 4 2 0 7.81 48.60 21.90 0 19 184 ok 359
Length along
girder (ft) No. Tendon
at 2.75"
From Bot
No. Tendon
at 4.75"
from Bot
No.
Tendon at
6.75" From
Bot
No. Tendon
at 8.75"
From Bot
No. Tendon
at 10.75"
From Bot
Δf_pES
(ksi)
f_pi
(ksi)
Stress
limit for
tendon
0.8fpy
Jakcing
force
@transfer,
Pji (kip)
No. Tendon
at 12.75"
From Bot
No. Tendon
at 14.75"
From Bot
Aps(in^2)
Y_p,
Tendon
CG to Top
of Girder
(in)
e_ti (in)
Mg (kip-
in) Girder
Self
Weight
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders E Stress Page: of:
Job #: NO:
Note 1: Eccencity equal to value of Y_p minus YtNote 2: Mg is the moment caused by the self weight of the girder+ Concrete deck
Note 4:
Note 3:
Note 5: fpy assumes to be 0.9fpu; Table 5.9.3-1 AASHTO
Note 7: Top fiber concr gider stress=P/A-P*e/(I/Yt)+Mg/(I/Yb) (+ is compression, - is tension)
Note 9:
Note 6: Jakcing force @ transfer taken as f_pi multiplies Aps (Total area of tendons)
Note 8: Bot. fiber concr gider stress=P/A+P*e/(I/Yt)-Mg/(I/Yb) (+ is cpmpression, - is tension )
Note 10:
Girder top bars: #4 Total of 6, 0.2x6=1.2in^2
f_pi is the value of f_pbt minus Δf_pES. Per AASHTO C5.9.5.2.3a, if the transformed
section properties are used, the Δf_pES should not be inlcuded in the prestressing force.
In this case, jacking force is calcuated as f_pbt minus short term elastic shortening loss,
and so the Gorss section properties of the concrete girder are used.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders E Stress Page: of:
Job #: NO:
0
500
1000
1500
2000
2500
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Jakcing force @transfer, Pji (kip)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders E Stress Page: of:
Job #: NO:
Stress Calculations @ Transfer Stage
Note 7 Note 8 Note 9 Note 10
0 0.0 -0.17 0.99 4.36 -0.62 0.00 0.28 0.23 0.00
1.0 -0.19 1.27 4.36 -0.62 0.00 0.30 0.29 0.00
2.0 -0.37 2.54 4.36 -0.62 0.00 0.60 0.58 0.00
3.0 -0.56 3.81 4.36 -0.62 0.00 0.91 0.88 0.00
dv 5.0 -0.48 3.73 4.36 -0.62 0.00 0.77 0.86 0.00
0.1L 11.2 -0.24 3.49 4.36 -0.62 0.00 0.39 0.80 0.00
13.0 -0.17 3.43 4.36 -0.62 0.00 0.28 0.79 0.00
14.0 -0.19 3.61 4.36 -0.62 0.00 0.31 0.83 0.00
15.0 -0.21 3.87 4.36 -0.62 0.00 0.34 0.89 0.00
16.0 -0.23 4.13 4.36 -0.62 0.00 0.37 0.95 0.00
0.2L 22.3 -0.04 3.95 4.36 -0.62 0.00 0.07 0.91 0.00
28.0 0.10 3.81 4.36 -0.62 0.02 0.00 0.87 0.00
29.0 0.10 3.89 4.36 -0.62 0.02 0.00 0.89 0.00
30.0 0.09 4.02 4.36 -0.62 0.02 0.00 0.92 0.00
31.0 0.09 4.14 4.36 -0.62 0.02 0.00 0.95 0.00
0.3L 33.5 0.13 4.10 4.36 -0.62 0.03 0.00 0.94 0.00
0.4L 44.6 0.28 3.95 4.36 -0.62 0.07 0.00 0.91 0.00
0.5L 55.8 0.33 3.90 4.36 -0.62 0.08 0.00 0.90 0.00
0.6L 67.0 0.28 3.95 4.36 -0.62 0.07 0.00 0.91 0.00
0.7L 78.1 0.13 4.10 4.36 -0.62 0.03 0.00 0.94 0.00
80.6 0.09 4.14 4.36 -0.62 0.02 0.00 0.95 0.00
81.6 0.09 4.02 4.36 -0.62 0.02 0.00 0.92 0.00
82.6 0.10 3.89 4.36 -0.62 0.02 0.00 0.89 0.00
83.6 0.10 3.81 4.36 -0.62 0.02 0.00 0.87 0.00
0.8L 89.3 -0.04 3.95 4.36 -0.62 0.00 0.07 0.91 0.00
95.6 -0.23 4.13 4.36 -0.62 0.00 0.37 0.95 0.00
96.6 -0.21 3.87 4.36 -0.62 0.00 0.34 0.89 0.00
97.6 -0.19 3.61 4.36 -0.62 0.00 0.31 0.83 0.00
98.6 -0.17 3.43 4.36 -0.62 0.00 0.28 0.79 0.00
0.9L 100.4 -0.24 3.49 4.36 -0.62 0.00 0.39 0.80 0.00
dv 108.2 -0.55 3.79 4.36 -0.62 0.00 0.88 0.87 0.00
108.6 -0.56 3.81 4.36 -0.62 0.00 0.91 0.88 0.00
109.6 -0.37 2.54 4.36 -0.62 0.00 0.60 0.58 0.00
110.6 -0.19 1.27 4.36 -0.62 0.00 0.30 0.29 0.00
L 111.6 -0.17 0.99 4.36 -0.62 0.00 0.28 0.23 0.00
Max: 0.08 0.91 0.95 0.00
f_bot (ksi) (comp limit
0.65f'ci)
(Ten limit -
0.24*sqrt(f
'ci) ksi)
f_top f_bot
D/C ratio
(comp
limit )
D/C
ratio(Ten
limit )
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit )
Length
along
girder (ft)
f_top
(ksi)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders E Stress Page: of:
Job #: NO:
For the stress calc, negative stress is tensile stress; positive stress is compressive stress.
Stress Calculations @ Transfer Stage
Tendons f_pu (ksi) 270
Tendon f_pbt (ksi) 203 (AASHTO Table 5.9.3.1)
Tendon E_ps (ksi) 28500
Girder Concrete E_pc (ksi) 5154
n'-1 = E_ps/ E_pc -1 5
f'c (ksi) 8.0
f'ci (ksi) 6.7
CA BT 55, Ag (in^2) 925
CA BT 55, w (k/ft) 1
CA BT 55, Yt, CG to Top (in) 27
CA BT 55, Yb, CG to Bot (in) 28
CA BT 55, Ig (in^4) 373350
Ƴ_h Say H= 70% 1
Ƴ_st 0.65
Δf_pR (ksi) 2.4
Transfer length l_t =60*db (in) 36
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders E Stress Page: of:
Job #: NO:
Stress Calculations @ PS + Perm load condition Transformed seciton properties
Note 1 Note 2 Note 3 Note 4 Note 5 Note 6 Note 7 Note 8
0 0.0 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
1.0 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
2.0 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
3.0 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
dv 5.0 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
0.1L 11.2 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
13.0 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
14.0 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
15.0 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
16.0 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
0.2L 22.3 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
28.0 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
29.0 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
30.0 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
31.0 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
0.3L 33.5 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
0.4L 44.6 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
0.5L 55.8 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
0.6L 67.0 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
0.7L 78.1 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
80.6 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
81.6 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
82.6 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
83.6 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
0.8L 89.3 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
95.6 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
96.6 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
97.6 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
98.6 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
0.9L 100.4 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
dv 108.2 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
108.6 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
109.6 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
110.6 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
L 111.6 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
Transfor
med
Y_ttop
(in)
Transfor
med
Y_tbot
(in)
Ʃ Ai*(Y_i-
Y_ttop)^
2
(in^4)
I_final(in
^4)
Transfor
med
S_ttop
(in^3)
Transfor
med
S_tbot
(in^3)
Total
Aps*(n-
1)+Ag
(in^2) Ig (in^4)
ƩAi*Y_i
(in^3)
Length
along
girder
(ft) Aps(in^
2)
Y_p,
Tendon CG
to
GirderTop
(in)
Aps*(n'-
1)
(in^2)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders E Stress Page: of:
Job #: NO:
Note 1: Ignore moment of inertia I from prestrssing tendons, since it is too small compared to that of precast concrete Girder.
Note 2: Summation of tranformed strands area times CG of strands, and area of precast concrete girder times CG of the girder.
Note 3: Values of Note 2 divide by the total area of the transformed section to determine CG of the tranformed section (from top of the section)
Note 4: CG of the tranformed seciton (from bottom of the section)
Note 5:
Note 6: I_final =Ig + values at Note 5
Note 7: Transformed section modulus from top of seciton is I_final divide by Transformed Y_ttop
Note 8: Transformed section modulus from bottom of seciton is I_final divide by Transformed Y_tbot
Summation of tranformed area of strands times squrea of CG differenec between strands and the entire tranformed section, plus such value
for precast concrete girder component.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders E Stress Page: of:
Job #: NO:
Stress Calculations @ PS + Perm load condition * debond included
Note 9 Note 10 Note 11 Note 12 Note 13 Note 14 Note 15 Note 16
0 0.0 21 21 181 354 0 -0.16 0.90 3.60 -0.54 0.00 0.29 0.25 0.00
1.0 21 21 181 472 1420 -0.11 1.10 3.60 -0.54 0.00 0.21 0.30 0.00
2.0 21 21 181 944 2814 -0.22 2.19 3.60 -0.54 0.00 0.42 0.61 0.00
3.0 21 21 181 1416 4183 -0.34 3.29 3.60 -0.54 0.00 0.63 0.91 0.00
dv 5.0 21 21 181 1416 6843 -0.15 3.10 3.60 -0.54 0.00 0.28 0.86 0.00
0.1L 11.2 21 21 181 1416 14389 0.38 2.57 3.60 -0.54 0.11 0.00 0.71 0.00
13.0 21 21 181 1416 16457 0.53 2.42 3.60 -0.54 0.15 0.00 0.67 0.00
14.0 21 24 179 1500 17543 0.56 2.53 3.60 -0.54 0.16 0.00 0.70 0.00
15.0 21 24 179 1603 18604 0.59 2.71 3.60 -0.54 0.16 0.00 0.75 0.00
16.0 21 24 179 1707 19638 0.62 2.90 3.60 -0.54 0.17 0.00 0.81 0.00
0.2L 22.3 21 24 179 1707 25581 1.03 2.48 3.60 -0.54 0.29 0.00 0.69 0.00
28.0 21 24 179 1707 30052 1.35 2.17 3.60 -0.54 0.37 0.00 0.60 0.00
29.0 21 25 178 1746 30753 1.38 2.21 3.60 -0.54 0.38 0.00 0.61 0.00
30.0 21 25 178 1797 31429 1.40 2.29 3.60 -0.54 0.39 0.00 0.64 0.00
31.0 21 25 178 1849 32078 1.43 2.37 3.60 -0.54 0.40 0.00 0.66 0.00
0.3L 33.5 21 25 178 1849 33575 1.53 2.27 3.60 -0.54 0.43 0.00 0.63 0.00
0.4L 44.6 21 25 178 1849 38372 1.87 1.94 3.60 -0.54 0.52 0.00 0.54 0.00
0.5L 55.8 21 25 178 1849 39971 1.98 1.83 3.60 -0.54 0.55 0.00 0.51 0.00
0.6L 67.0 21 25 178 1849 38372 1.87 1.94 3.60 -0.54 0.52 0.00 0.54 0.00
0.7L 78.1 21 25 178 1849 33575 1.53 2.27 3.60 -0.54 0.43 0.00 0.63 0.00
80.6 21 25 178 1849 32078 1.43 2.37 3.60 -0.54 0.40 0.00 0.66 0.00
81.6 21 25 178 1797 31429 1.40 2.29 3.60 -0.54 0.39 0.00 0.64 0.00
82.6 21 25 178 1746 30753 1.38 2.21 3.60 -0.54 0.38 0.00 0.61 0.00
83.6 21 24 179 1707 30052 1.35 2.17 3.60 -0.54 0.37 0.00 0.60 0.00
0.8L 89.3 21 24 179 1707 25581 1.03 2.48 3.60 -0.54 0.29 0.00 0.69 0.00
95.6 21 24 179 1707 19638 0.62 2.90 3.60 -0.54 0.17 0.00 0.81 0.00
96.6 21 24 179 1603 18604 0.59 2.71 3.60 -0.54 0.16 0.00 0.75 0.00
97.6 21 24 179 1500 17543 0.56 2.53 3.60 -0.54 0.16 0.00 0.70 0.00
98.6 21 21 181 1416 16457 0.53 2.42 3.60 -0.54 0.15 0.00 0.67 0.00
0.9L 100.4 21 21 181 1416 14389 0.38 2.57 3.60 -0.54 0.11 0.00 0.71 0.00
dv 108.2 21 21 181 1416 4755 -0.30 3.25 3.60 -0.54 0.00 0.55 0.90 0.00
108.6 21 21 181 1416 4183 -0.34 3.29 3.60 -0.54 0.00 0.63 0.91 0.00
109.6 21 21 181 944 2814 -0.22 2.19 3.60 -0.54 0.00 0.42 0.61 0.00
110.6 21 21 181 472 1420 -0.11 1.10 3.60 -0.54 0.00 0.21 0.30 0.00
L 111.6 21 21 181 354 0 -0.16 0.90 3.60 -0.54 0.00 0.29 0.25 0.00
Max: 0.55 0.63 0.91 0.00
f_top
(ksi)
f_Bot
(ksi)
Compres
sive
Stress
limit (ksi)
Tensile
Stress
limit (ksi)
f_top f_bot
D/C ratio
(comp limit)
D/C
ratio(Ten
limit)
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit)
Length
along
girder
(ft)
e (in)Δf_pLT
(ksi)fpe (ksi) Pf (kiP)
Moment
demands
DC1+DC2
(kip-in)
PS+ Perm (DC1+DC2)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders E Stress Page: of:
Job #: NO:
Note 9: Eccentricity of the seciton is Y_p(in) from girder top subtracted by Transformed Y_ttop
Note 10
Note 11 fpe is stress at transfer minus long term loss Δf_pLT
Note 12 Prestressing force Pf, is fpe times area of the prestressing tendons, Aps.
Note 13
Note 14
Note 15
Note 16:
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders E Stress Page: of:
Job #: NO:
Tendons f_pu (ksi) 270
Tendon f_pbt (ksi) 202.5 (AASHTO Table 5.9.3.1)
CA BT 55, Ag (in^2) 925
CA BT 55, w (k/ft) 0.963
CA BT 55, Yt, CG to Top (in) 26.7
CA BT 55, Yb, CG to Bot (in) 28.4
CA BT 55, Ig (in^4) 373350
Tendon E_ps (ksi) 28,500
Girder Concrete E_pc (ksi) 5,154
n'-1 = E_ps/ E_pc -1 5
Girder f'c (ksi) 8
Girder f'ci (ksi) 6.7
Deck Concrete E_c (ksi) 4,074
Girder Concrete E_pc (ksi) 5,154
n= E_c/E_pc 0.79
CIP Deck f'c (ksi) 5
Deck effective width (ft) 9.08
Depth of concrete slab, ts (in) 8.00
Precast panel thickness (in) 3.50
Tranformed deck area (in^2) 768.74 (based on Ec of 8ksi concrete)
Tranformed effective deck width (in) 96.093 (based on Ec of 8ksi concrete)
Transfer length l_t =60*db (in) 36
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders E Stress Page: of:
Job #: NO:
Stress Calculations @ Service, composite section properties include the Deck Slab
Note 1
0 0.0 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 354
1.0 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 472
2.0 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 944
3.0 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
dv 5.0 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
0.1L 11.2 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
13.0 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
14.0 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1500
15.0 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1603
16.0 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1707
0.2L 22.3 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1707
28.0 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1707
29.0 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1746
30.0 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1797
31.0 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
0.3L 33.5 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
0.4L 44.6 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
0.5L 55.8 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
0.6L 67.0 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
0.7L 78.1 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
80.6 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
81.6 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1797
82.6 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1746
83.6 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1707
0.8L 89.3 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1707
95.6 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1707
96.6 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1603
97.6 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1500
98.6 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
0.9L 100.4 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
dv 108.2 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
108.6 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
109.6 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 944
110.6 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 472
L 111.6 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 354
e (in)
Δf_pLT
(ksi)
fpe
(ksi)
Pf
(kiP)
Yi to Top
of Deck
ƩAi*Y_i
(in^3)
Comp
Y_ttop
(in)
ToDec
kTop
Comp.
Y_tbot
(in)
I_comp
(in^4)
Comp.
S_tg
(in^3)
Comp S_tb
(in^3)
Length
along
girder (ft)
I_tg(in^4)Transformed
Y_ttop (in)
Transfor
med
Y_tbot
(in)
Tranfor
med
A_deck
(in^2)
A_deck+A
ps*(n'-
1)+Ag
(in^2)
From PS+Perm stress calc
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders E Stress Page: of:
Job #: NO:
Stress Calculations @ Service, composite section properties include the Deck Slab
* debond included Note 2 Note 3 Note 4
0 0.0 0 0 0 0 -0.16 0.90 4.80 -0.54 0.00 0.29 0.19 0.00
1.0 1420 346 24 1106 -0.09 1.02 4.80 -0.54 0.00 0.16 0.21 0.00
2.0 2814 686 48 2193 -0.18 2.04 4.80 -0.54 0.00 0.33 0.43 0.00
3.0 4183 1019 72 3259 -0.27 3.07 4.80 -0.54 0.00 0.49 0.64 0.00
dv 5.0 6843 1667 120 5331 -0.03 2.74 4.80 -0.54 0.00 0.06 0.57 0.00
0.1L 11.2 14389 3505 269 11210 0.63 1.80 4.80 -0.54 0.13 0.00 0.38 0.00
13.0 16457 4009 313 12821 0.81 1.55 4.80 -0.54 0.17 0.00 0.32 0.00
14.0 17543 4274 337 13667 0.86 1.61 4.80 -0.54 0.18 0.00 0.33 0.00
15.0 18604 4532 361 14493 0.91 1.74 4.80 -0.54 0.19 0.00 0.36 0.00
16.0 19638 4784 385 15300 0.96 1.87 4.80 -0.54 0.20 0.00 0.39 0.00
0.2L 22.3 25581 6232 537 19929 1.48 1.14 4.80 -0.54 0.31 0.00 0.24 0.00
28.0 30052 7321 674 23413 1.87 0.59 4.80 -0.54 0.39 0.00 0.12 0.00
29.0 30753 7492 698 23959 1.91 0.60 4.80 -0.54 0.40 0.00 0.13 0.00
30.0 31429 7656 722 24485 1.95 0.65 4.80 -0.54 0.41 0.00 0.13 0.00
31.0 32078 7814 746 24991 1.98 0.70 4.80 -0.54 0.41 0.00 0.14 0.00
0.3L 33.5 33575 8179 806 26157 2.11 0.51 4.80 -0.54 0.44 0.00 0.11 0.00
0.4L 44.6 38372 9347 1075 29894 2.54 -0.08 4.80 -0.54 0.53 0.00 0.00 0.14
0.5L 55.8 39971 9737 1343 31140 2.68 -0.28 4.80 -0.54 0.56 0.00 0.00 0.53
0.6L 67.0 38372 9347 1075 29894 2.54 -0.08 4.80 -0.54 0.53 0.00 0.00 0.14
0.7L 78.1 33575 8179 806 26157 2.11 0.51 4.80 -0.54 0.44 0.00 0.11 0.00
80.6 32078 7814 746 24991 1.98 0.70 4.80 -0.54 0.41 0.00 0.14 0.00
81.6 31429 7656 722 24485 1.95 0.65 4.80 -0.54 0.41 0.00 0.13 0.00
82.6 30753 7492 698 23959 1.91 0.60 4.80 -0.54 0.40 0.00 0.13 0.00
83.6 30052 7321 674 23413 1.87 0.59 4.80 -0.54 0.39 0.00 0.12 0.00
0.8L 89.3 25581 6232 537 19929 1.48 1.14 4.80 -0.54 0.31 0.00 0.24 0.00
95.6 19638 4784 385 15300 0.96 1.87 4.80 -0.54 0.20 0.00 0.39 0.00
96.6 18604 4532 361 14493 0.91 1.74 4.80 -0.54 0.19 0.00 0.36 0.00
97.6 17543 4274 337 13667 0.86 1.61 4.80 -0.54 0.18 0.00 0.33 0.00
98.6 16457 4009 313 12821 0.81 1.55 4.80 -0.54 0.17 0.00 0.32 0.00
0.9L 100.4 14389 3505 269 11210 0.63 1.80 4.80 -0.54 0.13 0.00 0.38 0.00
dv 108.2 4755 1158 82 3704 -0.22 3.00 4.80 -0.54 0.00 0.40 0.62 0.00
108.6 4183 1019 72 3259 -0.27 3.07 4.80 -0.54 0.00 0.49 0.64 0.00
109.6 2814 686 48 2193 -0.18 2.04 4.80 -0.54 0.00 0.33 0.43 0.00
110.6 1420 346 24 1106 -0.09 1.02 4.80 -0.54 0.00 0.16 0.21 0.00
L 111.6 0 0 0 0 -0.16 0.90 4.80 -0.54 0.00 0.29 0.19 0.00
Max: 0.56 0.49 0.64 0.53
Tensile
Stress
limit (ksi)
f_top f_bot
D/C ratio
(comp limit)
D/C
ratio(Ten
limit)
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit)
Moment
demands
DC3+DW (kip-
in)
Moment demands
DC4 (kip-in)
Moment
demands
LL(1+IM) (kip-
in)
f_top (ksi) f_Bot (ksi)Compressive
Stress limit (ksi)
Length
along
girder
(ft)
Moment
demands
DC1+DC2
(kip-in)
Service I : PS+Perm+LL*(1+IM)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders E Stress Page: of:
Job #: NO:
Note 1:
Note 2
f_bot SIM.
Note 3
Note 4
Check the stress to top of girder, so section modulus of the composite section, is the I_comp / y_tg, and y_tg
is the distance from comp. nuetral axis to the top of the girder.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders E Stress Page: of:
Job #: NO:
0 0.0 0 -0.16 0.90 4.80 -0.54 0.00 0.29 0.19 0.00
1.0 885 -0.09 1.03 4.80 -0.54 0.00 0.17 0.21 0.00
2.0 1754 -0.18 2.07 4.80 -0.54 0.00 0.34 0.43 0.00
3.0 2607 -0.28 3.10 4.80 -0.54 0.00 0.51 0.65 0.00
dv 5.0 4265 -0.05 2.80 4.80 -0.54 0.00 0.09 0.58 0.00
0.1L 11.2 8968 0.59 1.92 4.80 -0.54 0.12 0.00 0.40 0.00
13.0 10257 0.77 1.68 4.80 -0.54 0.16 0.00 0.35 0.00
14.0 10934 0.82 1.75 4.80 -0.54 0.17 0.00 0.36 0.00
15.0 11595 0.86 1.88 4.80 -0.54 0.18 0.00 0.39 0.00
16.0 12240 0.90 2.02 4.80 -0.54 0.19 0.00 0.42 0.00
0.2L 22.3 15944 1.41 1.34 4.80 -0.54 0.29 0.00 0.28 0.00
28.0 18730 1.79 0.83 4.80 -0.54 0.37 0.00 0.17 0.00
29.0 19167 1.83 0.84 4.80 -0.54 0.38 0.00 0.18 0.00
30.0 19588 1.87 0.89 4.80 -0.54 0.39 0.00 0.19 0.00
31.0 19993 1.90 0.95 4.80 -0.54 0.40 0.00 0.20 0.00
0.3L 33.5 20926 2.03 0.77 4.80 -0.54 0.42 0.00 0.16 0.00
0.4L 44.6 23915 2.44 0.22 4.80 -0.54 0.51 0.00 0.05 0.00
0.5L 55.8 24912 2.58 0.03 4.80 -0.54 0.54 0.00 0.01 0.00
0.6L 67.0 23915 2.44 0.22 4.80 -0.54 0.51 0.00 0.05 0.00
0.7L 78.1 20926 2.03 0.77 4.80 -0.54 0.42 0.00 0.16 0.00
80.6 19993 1.90 0.95 4.80 -0.54 0.40 0.00 0.20 0.00
81.6 19588 1.87 0.89 4.80 -0.54 0.39 0.00 0.19 0.00
82.6 19167 1.83 0.84 4.80 -0.54 0.38 0.00 0.18 0.00
83.6 18730 1.79 0.83 4.80 -0.54 0.37 0.00 0.17 0.00
0.8L 89.3 15944 1.41 1.34 4.80 -0.54 0.29 0.00 0.28 0.00
95.6 12240 0.90 2.02 4.80 -0.54 0.19 0.00 0.42 0.00
96.6 11595 0.86 1.88 4.80 -0.54 0.18 0.00 0.39 0.00
97.6 10934 0.82 1.75 4.80 -0.54 0.17 0.00 0.36 0.00
98.6 10257 0.77 1.68 4.80 -0.54 0.16 0.00 0.35 0.00
0.9L 100.4 8968 0.59 1.92 4.80 -0.54 0.12 0.00 0.40 0.00
dv 108.2 2963 -0.23 3.04 4.80 -0.54 0.00 0.42 0.63 0.00
108.6 2607 -0.28 3.10 4.80 -0.54 0.00 0.51 0.65 0.00
109.6 1754 -0.18 2.07 4.80 -0.54 0.00 0.34 0.43 0.00
110.6 885 -0.09 1.03 4.80 -0.54 0.00 0.17 0.21 0.00
L 111.6 0 -0.16 0.90 4.80 -0.54 0.00 0.29 0.19 0.00
Max: 0.54 0.51 0.65 0.00
f_Bot (ksi)
Compressiv
e Stress
limit (ksi)
Tensile
Stress limit
(ksi)
f_top f_bot
D/C ratio
(comp limit)
D/C ratio(Ten
limit)
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit)
Length along
girder (ft)
Moment
demands
0.8*LL(1+IM
) (kip-in)
f_top (ksi)
Service III : PS+Perm+0.8*LL*(1+IM)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders E Stress Page: of:
Job #: NO:
REQUIRED TOP REINFORCEMENT
0 0.0 -0.17 0.99 8.27 34.00 1.13 3
1.0 -0.19 1.27 7.07 31.18 1.04 3
2.0 -0.37 2.54 7.09 62.68 2.09 5
3.0 -0.56 3.81 7.10 94.51 3.15 8
dv 5.0 -0.48 3.73 6.28 71.08 2.37 6
0.1L 11.2 -0.24 3.49 3.55 20.13 0.67 2
13.0 -0.17 3.43 2.67 11.03 0.37 1
14.0 -0.19 3.61 2.78 12.62 0.42 1
15.0 -0.21 3.87 2.85 14.17 0.47 2
16.0 -0.23 4.13 2.91 15.84 0.53 2
0.2L 22.3 -0.04 3.95 0.59 0.60 0.02 1
28.0 0.10 3.81 0.00 0.00 0.00 0
29.0 0.10 3.89 0.00 0.00 0.00 0
30.0 0.09 4.02 0.00 0.00 0.00 0
31.0 0.09 4.14 0.00 0.00 0.00 0
0.3L 33.5 0.13 4.10 0.00 0.00 0.00 0
0.4L 44.6 0.28 3.95 0.00 0.00 0.00 0
0.5L 55.8 0.33 3.90 0.00 0.00 0.00 0
0.6L 67.0 0.28 3.95 0.00 0.00 0.00 0
0.7L 78.1 0.13 4.10 0.00 0.00 0.00 0
80.6 0.09 4.14 0.00 0.00 0.00 0
81.6 0.09 4.02 0.00 0.00 0.00 0
82.6 0.10 3.89 0.00 0.00 0.00 0
83.6 0.10 3.81 0.00 0.00 0.00 0
0.8L 89.3 -0.04 3.95 0.59 0.60 0.02 1
95.6 -0.23 4.13 2.91 15.84 0.53 2
96.6 -0.21 3.87 2.85 14.17 0.47 2
97.6 -0.19 3.61 2.78 12.62 0.42 1
98.6 -0.17 3.43 2.67 11.03 0.37 1
0.9L 100.4 -0.24 3.49 3.55 20.13 0.67 2
dv 108.2 -0.55 3.79 6.93 89.27 2.98 7
108.6 -0.56 3.81 7.10 94.51 3.15 8
109.6 -0.37 2.54 7.09 62.68 2.09 5
110.6 -0.19 1.27 7.07 31.18 1.04 3
L 111.6 -0.17 0.99 8.27 34.00 1.13 3
f_ci,top (ksi) f_ci,bot (ksi) x (in) T (kip) As (in^2)
# 6 rebars
(in^2)
Length along
girder (ft)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders F Design Page: of:
Job #: NO:
L, Bridge span length (ft) 111.19
Bridge Width (ft) Upper bound 78.16
Bridge Width (ft) Lower Bound 71.60
Bridge Width (ft) Average 74.88
Number of Lanes 4
m, Multipresent factor for LL 0.65
Nb, Number of Girder 8
S, Max Girder Spacing (ft) 10.05
Bridge Skew Angle (degree) 31
For the bridge girder:
f'ci at transfer (ksi) 6.7 AASHTO 5.4.2.3.1
f'c after 28 days (ksi) 8
E_ci (ksi) for girder @ transfer 4716
During the construction of the bridge, it is required to not interfere with train traffic,
thus, the bridge slab system is precast concrete panel in between girders, stitched with CIP Concrete.
Tendon diameter (in) 0.6
One strand area (in^2) 0.217
Debonding length (from end of beam to where bonding commence), ft
10
Girder Distribution factors for DL, LL moment, LL Shear
Type of deck CIP Concrete, Precast Concrete
Supporting Component Precast Concrete I or Bulb-tee section
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders F Design Page: of:
Job #: NO:
Common Deck superstructure Table 4.6.2.2.1-1
Typical Cross section K Table 4.6.2.2.1-1
Live Load Distribution Factor for Moment in Interior Beams Table 4.6.2.2.2b-1
Rang of Applicability
S, spacing of beams, ϵ [ 3.5, 16] ft ✔
L, Span Length, ϵ [20,240] ft ✔
Nb, number of beams >=4 ✔
ts, depth of concrete slab ϵ [ 4.5, 12] in ✔
Depth of concrete slab, ts (in) 8.00
kg, longitudinal stiffness factor, ϵ [10^4 , 7x10^6] ✔
kg= n( I + A*eg^2) 1576804.87 4.6.2.2.1-1
n= E_beam / E_deck 1.26491106
f'c_slab (ksi) 6
E_beam (ksi) 5,154
E_slab (ksi) 4,074
A, (non-composite) cross section area of girder (in^2) 925 Caltrans Design Aids, CA BT-55
I, (non-composite) inertia (in^4) 373,350 Caltrans Design Aids, CA BT-55
Yb, CG to bottom of girder (in) 28.4 Caltrans Design Aids, CA BT-55
D, girder height (in) 55.125 Caltrans Design Aids, CA BT-55
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders F Design Page: of:
Job #: NO:
eg, dist. Btw CL of beam & CL of deck (in) 30.725
b_eff, deck effective width of girder (ft) 9.08
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders F Design Page: of:
Job #: NO:
Per above table from AASHTO, the LL distribution factor for moment in Interior beams are calculated:
g_int, One design lane loaded: 0.52 lane / girder multiple presence factor included
g_int, Two or more lane loaded: 0.77 lane / girder per C4.6.2.2.2b
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders F Design Page: of:
Job #: NO:
Per above table from AASHTO, the LL distribution factor for moment in exterior beams are calculated:
de, horizontal distance from CL of ext. web of ext. beam @ deck level, to int. edge of curb of traffic barrier
de (ft) 2.30
e=0.77+de/9.1 1.02
g_ext, one design lane loaded 0.54 lane/girder
g_ext, two or more design lane loaded 0.79 lane/girder
Considering the span length, it is very likley that cross frames & end diaphraagm will be necessary.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders F Design Page: of:
Job #: NO:
Per AASHTO C4.6.2.2.2d-1, exterior girders have higher load distribution factors due to cross frames
One lane loaded:
NL 1
X_ext, (ft) 35.18
e (ft) 24.03
x_1 (ft) 5.03
x_2 (ft) 15.08
x_3 (ft) 25.13
x_4 (ft) 35.18
R 0.32
Adjust with 1.2 multiple presence factor 0.39
Two Lanes loaded:
NL 2
e1 (ft) 24.03
e2 (ft) 6.5
R 0.50
Adjust with 1.0 multiple presence factor 0.50
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders F Design Page: of:
Job #: NO:
Three or more Lanes loaded:
NL 3
e1 (ft) 24.03
e2 (ft) 6.5
e3 (ft) 12
R 0.68
Adjust with 0.85 multiple presence factor 0.58
Final design values for moment distribution factors :
Load Case Int. Girder (lane)
One lane 0.52 0.54
NA 0.39
2 lanes loaded NA 0.50
3 lanes loaded NA 0.58
Design Value
Moment
Distribution 0.77 0.79
Max: 0.79
Two values are close enough, use the
maximum value for all to be conservative.
Note that AASHTO 4.6.2.2.2.e for skewed bridge provides reduction factors for live load distribution factors for momen in longitudinal
beams. However, CA amendment ignores reduction. Thus, no reduction applies for moment
Ext. Girder (lane)
Moment Distribution factor
per Table 4.6.2.2.2 Two or more
lane
0.77 0.79
Moment D.F. for ext. girder per
C4.6.2.2.2d-1
one lane loaded
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders F Design Page: of:
Job #: NO:
LL distribution factor for Shear :
Per above table from AASHTO, the LL distribution factor for shear in Interior beams are calculated:
g_int, One design lane loaded: 0.76 lane / girder multiple presence factor included
g_int, Two or more lane loaded: 0.96 lane / girder per C4.6.2.2.2b
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders F Design Page: of:
Job #: NO:
Per above table from AASHTO, the LL distribution factor for shear in exterior beams are calculated:
de (ft) 2.30
e=0.77+de/9.1 1.02
g_ext, one design lane loaded 0.54 lane/girder use same as ext one-lane for moment
g_ext, two or more design lane loaded 0.98 lane/girder
Notes:
AASHTO 4.6.2.2.3 C-1 provides correction factors for live load distribution factors for support shear of the obtuse girder.
CA Amendment revised AASHTO Table 4.6.2.2.3c-1 with equations provide for exterior girder & first interior girder.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders F Design Page: of:
Job #: NO:
Design values for shear distribution factors (without skew correction factor)
Load Case Int. Girder (lane)
One lane 0.76 NA
NA
NA 0.54
NA 0.98
Design Value
Shear
Distribution
Factor
0.96 0.98
Max: 0.98
Skew Correction factors for shear:
Two values are close enough, use the
maximum value for all to be conservative.
Ext. Girder (lane)
Shear Distribution factor per
Table 4.6.2.2.3a-1 Two or more
lane
0.96
Shear D.F. for ext. girder per
C4.6.2.2.3b-1
one lane loaded
Two or more
lane
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders F Design Page: of:
Job #: NO:
The shear correction factors are applied between the point of support at the obtuse corner and mid-span.
May be decreased linearly to a value of 1.0 at mid-span.
Skew Factor 1.09
Design values for shear distribution factors@ obtuse angle
Load Case Int. Girder (lane)
Design Value Shear D.F. 1.04 1.07 Max: 1.07
Two values are close enough, use the
maximum value for all to be conservative.Ext. Girder (lane)
1.07
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders F Design Page: of:
Job #: NO:
Moment Demands Calculations
One lane
0 0.0 0 0 0 0 0 0 0
dv 5.0 256 313 51 10 630 87 563
0.1L 11.1 536 655 108 22 1321 182 1180
0.2L 22.2 952 1164 192 45 2353 324 2099
0.3L 33.4 1250 1528 252 67 3097 425 2754
0.4L 44.5 1429 1746 287 89 3552 486 3148
0.5L 55.6 1488 1819 299 112 3718 506 3279
0.6L 66.7 1429 1746 287 89 3552 486 3148
0.7L 77.8 1250 1528 252 67 3097 425 2754
0.8L 89.0 952 1164 192 45 2353 324 2099
0.9L 100.1 536 655 108 22 1321 182 1180
dv 106.2 256 313 51 10 630 87 563
L 111.2 0 0 0 0 0 0 0
dv Use 0.9h (AASHTO 5.8.2.9) 5.03 ft
LL+IM Use Caltrans Bridge Design Aids attached as following.
Span length Moment (k-ft) End Shear (kip)
110 3229 122.8
120 3652.4 126.7
111.2 3279.3 123.3
Lane Load included from Caltrans Table
0 0
930 0
444 0
2171 0
1654 0
2584 0
2481 0
2171 0
2481 0
1654 0
Min LL
0 0
444 0
930 0
Length along
girder (ft)
For Each Girder
M (k-ft) DC1 M (k-ft) DC2 M (k-ft) DC3
M (k-ft)
DC4
M (k-ft)
DC Total
M (k-ft)
DW
(HL-93) LL+IM -M (k-f)
Distr.Fact
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders F Design Page: of:
Job #: NO:
Moment Capacity Calculations@ Wet Concr. Deck Stage (NonComposite)
Note 1 Note 4 Note 3
0 0.0 8 8 8 6 4 2 0 48.60 7.81 0.64 N.A. @ TF
dv 5.0 8 8 8 6 4 2 0 48.60 7.81 0.64 N.A. @ TF
0.1L 11.1 8 8 8 6 4 2 0 48.60 7.81 0.64 N.A. @ TF
0.2L 22.2 10 10 10 8 4 2 0 48.74 9.55 0.78 N.A. @ TF
0.3L 33.4 10 12 12 8 4 2 0 48.79 10.42 0.85 N.A. @ TF
0.4L 44.5 10 12 12 8 4 2 0 48.79 10.42 0.85 N.A. @ TF
0.5L 55.6 10 12 12 8 4 2 0 48.79 10.42 0.85 N.A. @ TF
0.6L 66.7 10 12 12 8 4 2 0 48.79 10.42 0.85 N.A. @ TF
0.7L 77.8 10 12 12 8 4 2 0 48.79 10.42 0.85 N.A. @ TF
0.8L 89.0 10 10 10 8 4 2 0 48.74 9.55 0.78 N.A. @ TF
0.9L 100.1 8 8 8 6 4 2 0 48.60 7.81 0.64 N.A. @ TF
dv 106.2 8 8 8 6 4 2 0 48.60 7.81 0.64 N.A. @ TF
L 111.2 8 8 8 6 4 2 0 48.60 7.81 0.64 N.A. @ TF
0.6" diameter tendons are used
Reference: AASHTO 2014 LRFD 7th Edition
Note 1: Note 4:
Note 2: Note 5:
Note 3: Note 6:Calcuated "c" to determine location of section
N.A.
No.
Tendon
at 12.75"
From Bot
No.
Tendon at
14.75"
From Bot
dp(in) to
Girder top
Aps(in^2) c (in)
Action Type:
Nuetral axis
location
Length
along
girder (ft)
No. Tendon
at 2.75"
From Bot
No.
Tendon at
4.75" from
Bot
No.
Tendon at
6.75"
From Bot
No.
Tendon at
8.75" From
Bot
No.
Tendon at
10.75"
From Bot
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders F Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Wet Concrete Deck Stage
Note 2 Note 5 Note 6 Note 7 Note 8
0 0.0 0.64 0.55 269.0 8463 0.2244 1.00 8463 0 8463 0
dv 5.0 0.64 0.55 269.0 8463 0.2244 1.00 8463 710 8463 0.08
0.1L 11.1 0.64 0.55 269.0 8463 0.2244 1.00 8463 1488 8463 0.18
0.2L 22.2 0.78 0.67 268.8 10352 0.1837 1.00 10352 2646 10352 0.26
0.3L 33.4 0.85 0.73 268.7 11294 0.1684 1.00 11294 3473 11294 0.31
0.4L 44.5 0.85 0.73 268.7 11294 0.1684 1.00 11294 3969 11294 0.35
0.5L 55.6 0.85 0.73 268.7 11294 0.1684 1.00 11294 4134 11294 0.37
0.6L 66.7 0.85 0.73 268.7 11294 0.1684 1.00 11294 3969 11294 0.35
0.7L 77.8 0.85 0.73 268.7 11294 0.1684 1.00 11294 3473 11294 0.31
0.8L 89.0 0.78 0.67 268.8 10352 0.1837 1.00 10352 2646 10352 0.26
0.9L 100.1 0.64 0.55 269.0 8463 0.2244 1.00 8463 1488 8463 0.18
dv 106.2 0.64 0.55 269.0 8463 0.2244 1.00 8463 710 8463 0.08
L 111.2 0.64 0.55 269.0 8463 0.2244 1.00 8463 0 8463 0.00
Note 7: Moment formula chosen depends on girder action type
Beta_1 =0.85 Per AASHTO 5.7.2.2
Value of k =0.28 Per Table C5.7.3.1.1.1
Note 8:
phi
factor φ
φMn(k-
ft)
For Each Girder
Mu (k-ft)
Strength I φMn(k-ft) D/C
Length
along
girder
(ft)
Update c (in) a (in) f_ps(ksi) Mn(k-ft)Epslon_t
ξ_t
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders F Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Wet Concrete Deck Stage
Mu=1.25 DC1+1.25DC2
Controlling Combination to design girders:
Strength I 1.25 DC+1.5 DW
0
2000
4000
6000
8000
10000
12000
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Mo
me
nt
(k
-ft)
Length (ft)
Moment Plot along Span Length
Mu (k-ft) Strength I φMn(k-ft)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders F Design Page: of:
Job #: NO:
0 0.0 0 0 0 0 0 0 0
dv 5.0 256 313 51 10 630 87 1007
0.1L 11.1 536 655 108 22 1321 182 2110
0.2L 22.2 952 1164 192 45 2353 324 3751
0.3L 33.4 1250 1528 252 67 3097 425 4923
0.4L 44.5 1429 1746 287 89 3552 486 5627
0.5L 55.6 1488 1819 299 112 3718 506 5861
0.6L 66.7 1429 1746 287 89 3552 486 5627
0.7L 77.8 1250 1528 252 67 3097 425 4923
0.8L 89.0 952 1164 192 45 2353 324 3751
0.9L 100.1 536 655 108 22 1321 182 2110
dv 106.2 256 313 51 10 630 87 1007
L 111.2 0 0 0 0 0 0 0 0 0
2956 0
1663 0
793 0
4619 0
4434 0
3880 0
2956 0
3880 0
4434 0
Min LL
0 0
793 0
1663 0
Length along
girder (ft)M (k-ft) DC1 M (k-ft) DC2 M (k-ft) DC3
M (k-ft)
DC4
M (k-ft)
DC Total
For Each Girder
M (k-ft)
DW
(P-15) LL+IM -M (k-f)
One lane Distr.Fact
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders F Design Page: of:
Job #: NO:
Moment Capacity Calculations@ Final Stage Stage
0 0.0 8 8 8 6 4 2 0 8 56.60 7.81 5.22
dv 5.0 8 8 8 6 4 2 0 8 56.60 7.81 5.22
0.1L 11.1 8 8 8 6 4 2 0 8 56.60 7.81 5.22
0.2L 22.2 10 10 10 8 4 2 0 8 56.74 9.55 6.35
0.3L 33.4 10 12 12 8 4 2 0 8 56.79 10.42 6.90
0.4L 44.5 10 12 12 8 4 2 0 8 56.79 10.42 6.90
0.5L 55.6 10 12 12 8 4 2 0 8 56.79 10.42 6.90
0.6L 66.7 10 12 12 8 4 2 0 8 56.79 10.42 6.90
0.7L 77.8 10 12 12 8 4 2 0 8 56.79 10.42 6.90
0.8L 89.0 10 10 10 8 4 2 0 8 56.74 9.55 6.35
0.9L 100.1 8 8 8 6 4 2 0 8 56.60 7.81 5.22
dv 106.2 8 8 8 6 4 2 0 8 56.60 7.81 5.22
L 111.2 8 8 8 6 4 2 0 8 56.60 7.81 5.22
Considering the concrete deck is acting compositely with the CA BT 55 girders.
Also Conservatively igore the precast concrete panel's composite concrete reaction, due to lack of friction btw the panel surface.
Aps(in^2) c (in) No.
Tendon at
10.75"
From Bot
No.
Tendon
at 12.75"
From Bot
No.
Tendon at
14.75"
From Bot
Composite
Deck THK
(in)
dp(in) to
Deck top
Length
along
girder (ft)
No. Tendon
at 2.75"
From Bot
No.
Tendon at
4.75" from
Bot
No.
Tendon at
6.75"
From Bot
No.
Tendon at
8.75" From
Bot
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders F Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Final Stage
0 0.0 N.A. @ Deck 5.22 4.44 263.0 9311 0.0295 1.00 9311
dv 5.0 N.A. @ Deck 5.22 4.44 263.0 9311 0.0295 1.00 9311
0.1L 11.1 N.A. @ Deck 5.22 4.44 263.0 9311 0.0295 1.00 9311
0.2L 22.2 N.A. @ Deck 6.35 5.39 261.5 11246 0.0238 1.00 11246
0.3L 33.4 N.A. @ Deck 6.90 5.87 260.8 12192 0.0217 1.00 12192
0.4L 44.5 N.A. @ Deck 6.90 5.87 260.8 12192 0.0217 1.00 12192
0.5L 55.6 N.A. @ Deck 6.90 5.87 260.8 12192 0.0217 1.00 12192
0.6L 66.7 N.A. @ Deck 6.90 5.87 260.8 12192 0.0217 1.00 12192
0.7L 77.8 N.A. @ Deck 6.90 5.87 260.8 12192 0.0217 1.00 12192
0.8L 89.0 N.A. @ Deck 6.35 5.39 261.5 11246 0.0238 1.00 11246
0.9L 100.1 N.A. @ Deck 5.22 4.44 263.0 9311 0.0295 1.00 9311
dv 106.2 N.A. @ Deck 5.22 4.44 263.0 9311 0.0295 1.00 9311
L 111.2 N.A. @ Deck 5.22 4.44 263.0 9311 0.0295 1.00 9311
Mn(k-ft)Epslon_t
ξ_t
phi factor
φ φMn(k-ft)
Length
along
girder
(ft)
Action Type
(Neutral Axis
location)
Update
c (in)
from
deck
top
a (in) f_ps(ksi)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders F Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Final Stage
0 0.0 0 0 9311 0 0.00
dv 5.0 1694 1989 9311 0.18 0.21
0.1L 11.1 3552 4169 9311 0.38 0.45
0.2L 22.2 6321 7418 11246 0.56 0.66
0.3L 33.4 8307 9746 12192 0.68 0.80
0.4L 44.5 9510 11155 12192 0.78 0.91
0.5L 55.6 9929 11643 12192 0.81 0.95
0.6L 66.7 9510 11155 12192 0.78 0.91
0.7L 77.8 8307 9746 12192 0.68 0.80
0.8L 89.0 6321 7418 11246 0.56 0.66
0.9L 100.1 3552 4169 9311 0.38 0.45
dv 106.2 1694 1989 9311 0.18 0.21
L 111.2 0 0 9311 0.00 0.00
Strength I 1.25 DC+1.5 DW+1.75 LL
Strength II 1.25 DC+1.5 DW+1.35 LL-permit
17
Mu (k-ft)
Strength I
Mu (k-ft)
Strength II φMn(k-ft)
D/C for
Strength I
D/C for
Strength II
Length
along
girder (ft)
For Each Girder
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders F Design Page: of:
Job #: NO:
0
2000
4000
6000
8000
10000
12000
14000
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Mo
me
nt
(k
-ft)
Length (ft)
Moment Plot along Span Length
Mu (k-ft) Strength I
φMn(k-ft)
Mu (k-ft) Strength II
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders F Stress Page: of:
Job #: NO:
For the stress calc, negative stress is tensile stress; positive stress is compressive stress.
Stress Calculations @ Transfer Stage
Tendons f_pu (ksi) 270
Tendon f_pbt (ksi) 202.5 (AASHTO Table 5.9.3.1)
Tendon E_ps (ksi) 28,500
Girder Concrete E_pc (ksi) 5,154
n'-1 = E_ps/ E_pc -1 4.53
f'c (ksi) 8
f'ci (ksi) 6.7
CA BT 55, Ag (in^2) 925
CA BT 55, w (k/ft) 0.963
CA BT 55, Yt, CG to Top (in) 26.70
CA BT 55, Yb, CG to Bot (in) 28.40
CA BT 55, Ig (in^4) 373,350
Ƴ_h Say H= 70% 1
Ƴ_st 0.65
Δf_pR (ksi) 2.4
Transfer length l_t =60*db (in) 36
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders F Stress Page: of:
Job #: NO:
Stress Calculations @ Transfer Stage* debond included
Note 1 Note 2 Note 3 Note 4 Note 5 Note 6
0 0.0 8 8 8 6 4 2 0 7.81 48.60 21.90 0 19 184 ok 359
1.0 8 8 8 6 4 2 0 7.81 48.60 21.90 637 19 184 ok 479
2.0 8 8 8 6 4 2 0 7.81 48.60 21.90 1262 18 184 ok 959
3.0 8 8 8 6 4 2 0 7.81 48.60 21.90 1875 18 184 ok 1440
dv 5.0 8 8 8 6 4 2 0 7.81 48.60 21.90 3068 18 185 ok 1442
0.1L 11.1 8 8 8 6 4 2 0 7.81 48.60 21.90 6429 17 186 ok 1450
13.0 8 8 8 6 4 2 0 7.81 48.60 21.90 7375 17 186 ok 1452
14.0 10 10 10 8 4 2 0 9.55 48.74 22.04 7862 20 182 ok 1528
15.0 10 10 10 8 4 2 0 9.55 48.74 22.04 8337 20 182 ok 1635
16.0 10 10 10 8 4 2 0 9.55 48.74 22.04 8800 20 182 ok 1742
0.2L 22.2 10 10 10 8 4 2 0 9.55 48.74 22.04 11429 19 183 ok 1749
28.0 10 10 10 8 4 2 0 9.55 48.74 22.04 13458 19 184 ok 1755
29.0 10 12 12 8 4 2 0 10.42 48.79 22.09 13772 21 182 ok 1790
30.0 10 12 12 8 4 2 0 10.42 48.79 22.09 14073 20 182 ok 1844
31.0 10 12 12 8 4 2 0 10.42 48.79 22.09 14363 20 182 ok 1897
0.3L 33.4 10 12 12 8 4 2 0 10.42 48.79 22.09 15001 20 182 ok 1899
0.4L 44.5 10 12 12 8 4 2 0 10.42 48.79 22.09 17144 20 183 ok 1906
0.5L 55.6 10 12 12 8 4 2 0 10.42 48.79 22.09 17858 19 183 ok 1908
0.6L 66.7 10 12 12 8 4 2 0 10.42 48.79 22.09 17144 20 183 ok 1906
0.7L 77.8 10 12 12 8 4 2 0 10.42 48.79 22.09 15001 20 182 ok 1899
80.2 10 12 12 8 4 2 0 10.42 48.79 22.09 14363 20 182 ok 1897
81.2 10 12 12 8 4 2 0 10.42 48.79 22.09 14073 20 182 ok 1844
82.2 10 12 12 8 4 2 0 10.42 48.79 22.09 13772 21 182 ok 1790
83.2 10 10 10 8 4 2 0 9.55 48.74 22.04 13458 19 184 ok 1755
0.8L 89.0 10 10 10 8 4 2 0 9.55 48.74 22.04 11429 19 183 ok 1749
95.2 10 10 10 8 4 2 0 9.55 48.74 22.04 8800 20 182 ok 1742
96.2 10 10 10 8 4 2 0 9.55 48.74 22.04 8337 20 182 ok 1635
97.2 10 10 10 8 4 2 0 9.55 48.74 22.04 7862 20 182 ok 1528
98.2 8 8 8 6 4 2 0 7.81 48.60 21.90 7375 17 186 ok 1452
0.9L 100.1 8 8 8 6 4 2 0 7.81 48.60 21.90 6429 17 186 ok 1450
dv 108.2 8 8 8 6 4 2 0 7.81 48.60 21.90 1892 18 184 ok 1440
108.2 8 8 8 6 4 2 0 7.81 48.60 21.90 1875 18 184 ok 1440
109.2 8 8 8 6 4 2 0 7.81 48.60 21.90 1262 18 184 ok 959
110.2 8 8 8 6 4 2 0 7.81 48.60 21.90 637 19 184 ok 479
L 111.2 8 8 8 6 4 2 0 7.81 48.60 21.90 0 19 184 ok 359
Length along
girder (ft) No. Tendon
at 2.75"
From Bot
No. Tendon
at 4.75"
from Bot
No.
Tendon at
6.75" From
Bot
No. Tendon
at 8.75"
From Bot
No. Tendon
at 10.75"
From Bot
Δf_pES
(ksi)
f_pi
(ksi)
Stress
limit for
tendon
0.8fpy
Jakcing
force
@transfer,
Pji (kip)
No. Tendon
at 12.75"
From Bot
No. Tendon
at 14.75"
From Bot
Aps(in^2)
Y_p,
Tendon
CG to Top
of Girder
(in)
e_ti (in)
Mg (kip-
in) Girder
Self
Weight
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders F Stress Page: of:
Job #: NO:
Note 1: Eccencity equal to value of Y_p minus YtNote 2: Mg is the moment caused by the self weight of the girder+ Concrete deck
Note 4:
Note 3:
Note 5: fpy assumes to be 0.9fpu; Table 5.9.3-1 AASHTO
Note 7: Top fiber concr gider stress=P/A-P*e/(I/Yt)+Mg/(I/Yb) (+ is compression, - is tension)
Note 9:
Note 6: Jakcing force @ transfer taken as f_pi multiplies Aps (Total area of tendons)
Note 8: Bot. fiber concr gider stress=P/A+P*e/(I/Yt)-Mg/(I/Yb) (+ is cpmpression, - is tension )
Note 10:
Girder top bars: #4 Total of 6, 0.2x6=1.2in^2
f_pi is the value of f_pbt minus Δf_pES. Per AASHTO C5.9.5.2.3a, if the transformed
section properties are used, the Δf_pES should not be inlcuded in the prestressing force.
In this case, jacking force is calcuated as f_pbt minus short term elastic shortening loss,
and so the Gorss section properties of the concrete girder are used.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders F Stress Page: of:
Job #: NO:
0
500
1000
1500
2000
2500
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Jakcing force @transfer, Pji (kip)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders F Stress Page: of:
Job #: NO:
Stress Calculations @ Transfer Stage
Note 7 Note 8 Note 9 Note 10
0 0.0 -0.17 0.99 4.36 -0.62 0.00 0.28 0.23 0.00
1.0 -0.19 1.27 4.36 -0.62 0.00 0.30 0.29 0.00
2.0 -0.37 2.54 4.36 -0.62 0.00 0.60 0.58 0.00
3.0 -0.56 3.81 4.36 -0.62 0.00 0.91 0.88 0.00
dv 5.0 -0.48 3.73 4.36 -0.62 0.00 0.77 0.86 0.00
0.1L 11.1 -0.24 3.49 4.36 -0.62 0.00 0.39 0.80 0.00
13.0 -0.18 3.43 4.36 -0.62 0.00 0.28 0.79 0.00
14.0 -0.19 3.62 4.36 -0.62 0.00 0.31 0.83 0.00
15.0 -0.21 3.87 4.36 -0.62 0.00 0.34 0.89 0.00
16.0 -0.23 4.13 4.36 -0.62 0.00 0.37 0.95 0.00
0.2L 22.2 -0.05 3.95 4.36 -0.62 0.00 0.08 0.91 0.00
28.0 0.09 3.81 4.36 -0.62 0.02 0.00 0.88 0.00
29.0 0.09 3.90 4.36 -0.62 0.02 0.00 0.89 0.00
30.0 0.09 4.02 4.36 -0.62 0.02 0.00 0.92 0.00
31.0 0.08 4.15 4.36 -0.62 0.02 0.00 0.95 0.00
0.3L 33.4 0.13 4.10 4.36 -0.62 0.03 0.00 0.94 0.00
0.4L 44.5 0.28 3.96 4.36 -0.62 0.06 0.00 0.91 0.00
0.5L 55.6 0.33 3.91 4.36 -0.62 0.07 0.00 0.90 0.00
0.6L 66.7 0.28 3.96 4.36 -0.62 0.06 0.00 0.91 0.00
0.7L 77.8 0.13 4.10 4.36 -0.62 0.03 0.00 0.94 0.00
80.2 0.08 4.15 4.36 -0.62 0.02 0.00 0.95 0.00
81.2 0.09 4.02 4.36 -0.62 0.02 0.00 0.92 0.00
82.2 0.09 3.90 4.36 -0.62 0.02 0.00 0.89 0.00
83.2 0.09 3.81 4.36 -0.62 0.02 0.00 0.88 0.00
0.8L 89.0 -0.05 3.95 4.36 -0.62 0.00 0.08 0.91 0.00
95.2 -0.23 4.13 4.36 -0.62 0.00 0.37 0.95 0.00
96.2 -0.21 3.87 4.36 -0.62 0.00 0.34 0.89 0.00
97.2 -0.19 3.62 4.36 -0.62 0.00 0.31 0.83 0.00
98.2 -0.18 3.43 4.36 -0.62 0.00 0.28 0.79 0.00
0.9L 100.1 -0.24 3.49 4.36 -0.62 0.00 0.39 0.80 0.00
dv 108.2 -0.56 3.81 4.36 -0.62 0.00 0.91 0.87 0.00
108.2 -0.56 3.81 4.36 -0.62 0.00 0.91 0.88 0.00
109.2 -0.37 2.54 4.36 -0.62 0.00 0.60 0.58 0.00
110.2 -0.19 1.27 4.36 -0.62 0.00 0.30 0.29 0.00
L 111.2 -0.17 0.99 4.36 -0.62 0.00 0.28 0.23 0.00
Max: 0.07 0.91 0.95 0.00
f_bot (ksi) (comp limit
0.65f'ci)
(Ten limit -
0.24*sqrt(f
'ci) ksi)
f_top f_bot
D/C ratio
(comp
limit )
D/C
ratio(Ten
limit )
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit )
Length
along
girder (ft)
f_top
(ksi)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders F Stress Page: of:
Job #: NO:
For the stress calc, negative stress is tensile stress; positive stress is compressive stress.
Stress Calculations @ Transfer Stage
Tendons f_pu (ksi) 270
Tendon f_pbt (ksi) 203 (AASHTO Table 5.9.3.1)
Tendon E_ps (ksi) 28500
Girder Concrete E_pc (ksi) 5154
n'-1 = E_ps/ E_pc -1 5
f'c (ksi) 8
f'ci (ksi) 6.7
CA BT 55, Ag (in^2) 925
CA BT 55, w (k/ft) 1
CA BT 55, Yt, CG to Top (in) 27
CA BT 55, Yb, CG to Bot (in) 28
CA BT 55, Ig (in^4) 373350
Ƴ_h Say H= 70% 1
Ƴ_st 0.65
Δf_pR (ksi) 2.4
Transfer length l_t =60*db (in) 36
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders F Stress Page: of:
Job #: NO:
Stress Calculations @ PS + Perm load condition Transformed seciton properties
Note 1 Note 2 Note 3 Note 4 Note 5 Note 6 Note 7 Note 8
0 0.0 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
1.0 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
2.0 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
3.0 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
dv 5.0 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
0.1L 11.1 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
13.0 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
14.0 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
15.0 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
16.0 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
0.2L 22.2 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
28.0 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
29.0 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
30.0 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
31.0 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
0.3L 33.4 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
0.4L 44.5 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
0.5L 55.6 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
0.6L 66.7 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
0.7L 77.8 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
80.2 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
81.2 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
82.2 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
83.2 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
0.8L 89.0 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
95.2 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
96.2 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
97.2 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
98.2 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
0.9L 100.1 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
dv 108.2 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
108.2 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
109.2 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
110.2 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
L 111.2 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
Transfor
med
Y_ttop
(in)
Transfor
med
Y_tbot
(in)
Ʃ Ai*(Y_i-
Y_ttop)^
2
(in^4)
I_final(in
^4)
Transfor
med
S_ttop
(in^3)
Transfor
med
S_tbot
(in^3)
Total
Aps*(n-
1)+Ag
(in^2) Ig (in^4)
ƩAi*Y_i
(in^3)
Length
along
girder
(ft) Aps(in^
2)
Y_p,
Tendon CG
to
GirderTop
(in)
Aps*(n'-
1)
(in^2)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders F Stress Page: of:
Job #: NO:
Note 1: Ignore moment of inertia I from prestrssing tendons, since it is too small compared to that of precast concrete Girder.
Note 2: Summation of tranformed strands area times CG of strands, and area of precast concrete girder times CG of the girder.
Note 3: Values of Note 2 divide by the total area of the transformed section to determine CG of the tranformed section (from top of the section)
Note 4: CG of the tranformed seciton (from bottom of the section)
Note 5:
Note 6: I_final =Ig + values at Note 5
Note 7: Transformed section modulus from top of seciton is I_final divide by Transformed Y_ttop
Note 8: Transformed section modulus from bottom of seciton is I_final divide by Transformed Y_tbot
Summation of tranformed area of strands times squrea of CG differenec between strands and the entire tranformed section, plus such value
for precast concrete girder component.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders F Stress Page: of:
Job #: NO:
Stress Calculations @ PS + Perm load condition * debond included
Note 9 Note 10 Note 11 Note 12 Note 13 Note 14 Note 15 Note 16
0 0.0 21 21 181 354 0 -0.16 0.90 3.60 -0.54 0.00 0.29 0.25 0.00
1.0 21 21 181 472 1415 -0.11 1.10 3.60 -0.54 0.00 0.21 0.30 0.00
2.0 21 21 181 944 2804 -0.22 2.19 3.60 -0.54 0.00 0.42 0.61 0.00
3.0 21 21 181 1416 4168 -0.34 3.29 3.60 -0.54 0.00 0.63 0.92 0.00
dv 5.0 21 21 181 1416 6818 -0.15 3.11 3.60 -0.54 0.00 0.28 0.86 0.00
0.1L 11.1 21 21 181 1416 14287 0.38 2.58 3.60 -0.54 0.10 0.00 0.72 0.00
13.0 21 21 181 1416 16391 0.52 2.43 3.60 -0.54 0.15 0.00 0.67 0.00
14.0 21 24 179 1500 17472 0.56 2.53 3.60 -0.54 0.15 0.00 0.70 0.00
15.0 21 24 179 1603 18527 0.58 2.72 3.60 -0.54 0.16 0.00 0.75 0.00
16.0 21 24 179 1707 19557 0.61 2.90 3.60 -0.54 0.17 0.00 0.81 0.00
0.2L 22.2 21 24 179 1707 25400 1.02 2.50 3.60 -0.54 0.28 0.00 0.69 0.00
28.0 21 24 179 1707 29910 1.34 2.18 3.60 -0.54 0.37 0.00 0.61 0.00
29.0 21 25 178 1746 30606 1.37 2.22 3.60 -0.54 0.38 0.00 0.62 0.00
30.0 21 25 178 1797 31276 1.39 2.30 3.60 -0.54 0.39 0.00 0.64 0.00
31.0 21 25 178 1849 31921 1.41 2.38 3.60 -0.54 0.39 0.00 0.66 0.00
0.3L 33.4 21 25 178 1849 33337 1.51 2.28 3.60 -0.54 0.42 0.00 0.63 0.00
0.4L 44.5 21 25 178 1849 38100 1.85 1.95 3.60 -0.54 0.51 0.00 0.54 0.00
0.5L 55.6 21 25 178 1849 39687 1.96 1.84 3.60 -0.54 0.54 0.00 0.51 0.00
0.6L 66.7 21 25 178 1849 38100 1.85 1.95 3.60 -0.54 0.51 0.00 0.54 0.00
0.7L 77.8 21 25 178 1849 33337 1.51 2.28 3.60 -0.54 0.42 0.00 0.63 0.00
80.2 21 25 178 1849 31921 1.41 2.38 3.60 -0.54 0.39 0.00 0.66 0.00
81.2 21 25 178 1797 31276 1.39 2.30 3.60 -0.54 0.39 0.00 0.64 0.00
82.2 21 25 178 1746 30606 1.37 2.22 3.60 -0.54 0.38 0.00 0.62 0.00
83.2 21 24 179 1707 29910 1.34 2.18 3.60 -0.54 0.37 0.00 0.61 0.00
0.8L 89.0 21 24 179 1707 25400 1.02 2.50 3.60 -0.54 0.28 0.00 0.69 0.00
95.2 21 24 179 1707 19557 0.61 2.90 3.60 -0.54 0.17 0.00 0.81 0.00
96.2 21 24 179 1603 18527 0.58 2.72 3.60 -0.54 0.16 0.00 0.75 0.00
97.2 21 24 179 1500 17472 0.56 2.53 3.60 -0.54 0.15 0.00 0.70 0.00
98.2 21 21 181 1416 16391 0.52 2.43 3.60 -0.54 0.15 0.00 0.67 0.00
0.9L 100.1 21 21 181 1416 14287 0.38 2.58 3.60 -0.54 0.10 0.00 0.72 0.00
dv 108.2 21 21 181 1416 4205 -0.34 3.29 3.60 -0.54 0.00 0.63 0.91 0.00
108.2 21 21 181 1416 4168 -0.34 3.29 3.60 -0.54 0.00 0.63 0.92 0.00
109.2 21 21 181 944 2804 -0.22 2.19 3.60 -0.54 0.00 0.42 0.61 0.00
110.2 21 21 181 472 1415 -0.11 1.10 3.60 -0.54 0.00 0.21 0.30 0.00
L 111.2 21 21 181 354 0 -0.16 0.90 3.60 -0.54 0.00 0.29 0.25 0.00
Max: 0.54 0.63 0.92 0.00
f_top
(ksi)
f_Bot
(ksi)
Compres
sive
Stress
limit (ksi)
Tensile
Stress
limit (ksi)
f_top f_bot
D/C ratio
(comp limit)
D/C
ratio(Ten
limit)
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit)
Length
along
girder
(ft)
e (in)Δf_pLT
(ksi)fpe (ksi) Pf (kiP)
Moment
demands
DC1+DC2
(kip-in)
PS+ Perm (DC1+DC2)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders F Stress Page: of:
Job #: NO:
Note 9: Eccentricity of the seciton is Y_p(in) from girder top subtracted by Transformed Y_ttop
Note 10
Note 11 fpe is stress at transfer minus long term loss Δf_pLT
Note 12 Prestressing force Pf, is fpe times area of the prestressing tendons, Aps.
Note 13
Note 14
Note 15
Note 16:
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders F Stress Page: of:
Job #: NO:
Tendons f_pu (ksi) 270
Tendon f_pbt (ksi) 202.5 (AASHTO Table 5.9.3.1)
CA BT 55, Ag (in^2) 925
CA BT 55, w (k/ft) 0.963
CA BT 55, Yt, CG to Top (in) 26.7
CA BT 55, Yb, CG to Bot (in) 28.4
CA BT 55, Ig (in^4) 373350
Tendon E_ps (ksi) 28,500
Girder Concrete E_pc (ksi) 5,154
n'-1 = E_ps/ E_pc -1 5
Girder f'c (ksi) 8
Girder f'ci (ksi) 6.7
Deck Concrete E_c (ksi) 4,074
Girder Concrete E_pc (ksi) 5,154
n= E_c/E_pc 0.79
CIP Deck f'c (ksi) 5
Deck effective width (ft) 9.08
Depth of concrete slab, ts (in) 8.00
Precast panel thickness (in) 3.50
Tranformed deck area (in^2) 768.74 (based on Ec of 8ksi concrete)
Tranformed effective deck width (in) 96.093 (based on Ec of 8ksi concrete)
Transfer length l_t =60*db (in) 36
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders F Stress Page: of:
Job #: NO:
Stress Calculations @ Service, composite section properties include the Deck Slab
Note 1
0 0.0 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 354
1.0 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 472
2.0 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 944
3.0 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
dv 5.0 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
0.1L 11.1 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
13.0 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
14.0 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1500
15.0 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1603
16.0 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1707
0.2L 22.2 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1707
28.0 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1707
29.0 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1746
30.0 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1797
31.0 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
0.3L 33.4 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
0.4L 44.5 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
0.5L 55.6 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
0.6L 66.7 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
0.7L 77.8 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
80.2 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
81.2 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1797
82.2 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1746
83.2 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1707
0.8L 89.0 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1707
95.2 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1707
96.2 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1603
97.2 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1500
98.2 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
0.9L 100.1 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
dv 108.2 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
108.2 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
109.2 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 944
110.2 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 472
L 111.2 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 354
e (in)
Δf_pLT
(ksi)
fpe
(ksi)
Pf
(kiP)
Yi to Top
of Deck
ƩAi*Y_i
(in^3)
Comp
Y_ttop
(in)
ToDec
kTop
Comp.
Y_tbot
(in)
I_comp
(in^4)
Comp.
S_tg
(in^3)
Comp S_tb
(in^3)
Length
along
girder (ft)
I_tg(in^4)Transformed
Y_ttop (in)
Transfor
med
Y_tbot
(in)
Tranfor
med
A_deck
(in^2)
A_deck+A
ps*(n'-
1)+Ag
(in^2)
From PS+Perm stress calc
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders F Stress Page: of:
Job #: NO:
Stress Calculations @ Service, composite section properties include the Deck Slab
* debond included Note 2 Note 3 Note 4
0 0.0 0 0 0 0 -0.16 0.90 4.80 -0.54 0.00 0.29 0.19 0.00
1.0 1415 345 24 1106 -0.09 1.02 4.80 -0.54 0.00 0.16 0.21 0.00
2.0 2804 683 48 2191 -0.18 2.04 4.80 -0.54 0.00 0.33 0.43 0.00
3.0 4168 1015 72 3256 -0.27 3.07 4.80 -0.54 0.00 0.50 0.64 0.00
dv 5.0 6818 1661 120 5327 -0.03 2.74 4.80 -0.54 0.00 0.06 0.57 0.00
0.1L 11.1 14287 3480 268 11163 0.62 1.81 4.80 -0.54 0.13 0.00 0.38 0.00
13.0 16391 3993 313 12807 0.81 1.55 4.80 -0.54 0.17 0.00 0.32 0.00
14.0 17472 4256 337 13651 0.86 1.61 4.80 -0.54 0.18 0.00 0.34 0.00
15.0 18527 4513 361 14476 0.91 1.74 4.80 -0.54 0.19 0.00 0.36 0.00
16.0 19557 4764 385 15280 0.95 1.88 4.80 -0.54 0.20 0.00 0.39 0.00
0.2L 22.2 25400 6187 535 19846 1.46 1.16 4.80 -0.54 0.30 0.00 0.24 0.00
28.0 29910 7286 674 23370 1.86 0.61 4.80 -0.54 0.39 0.00 0.13 0.00
29.0 30606 7456 698 23913 1.90 0.62 4.80 -0.54 0.40 0.00 0.13 0.00
30.0 31276 7619 722 24437 1.94 0.66 4.80 -0.54 0.40 0.00 0.14 0.00
31.0 31921 7776 746 24940 1.97 0.71 4.80 -0.54 0.41 0.00 0.15 0.00
0.3L 33.4 33337 8121 803 26047 2.09 0.54 4.80 -0.54 0.44 0.00 0.11 0.00
0.4L 44.5 38100 9281 1071 29769 2.51 -0.05 4.80 -0.54 0.52 0.00 0.00 0.09
0.5L 55.6 39687 9668 1339 31009 2.66 -0.25 4.80 -0.54 0.55 0.00 0.00 0.47
0.6L 66.7 38100 9281 1071 29769 2.51 -0.05 4.80 -0.54 0.52 0.00 0.00 0.09
0.7L 77.8 33337 8121 803 26047 2.09 0.54 4.80 -0.54 0.44 0.00 0.11 0.00
80.2 31921 7776 746 24940 1.97 0.71 4.80 -0.54 0.41 0.00 0.15 0.00
81.2 31276 7619 722 24437 1.94 0.66 4.80 -0.54 0.40 0.00 0.14 0.00
82.2 30606 7456 698 23913 1.90 0.62 4.80 -0.54 0.40 0.00 0.13 0.00
83.2 29910 7286 674 23370 1.86 0.61 4.80 -0.54 0.39 0.00 0.13 0.00
0.8L 89.0 25400 6187 535 19846 1.46 1.16 4.80 -0.54 0.30 0.00 0.24 0.00
95.2 19557 4764 385 15280 0.95 1.88 4.80 -0.54 0.20 0.00 0.39 0.00
96.2 18527 4513 361 14476 0.91 1.74 4.80 -0.54 0.19 0.00 0.36 0.00
97.2 17472 4256 337 13651 0.86 1.61 4.80 -0.54 0.18 0.00 0.34 0.00
98.2 16391 3993 313 12807 0.81 1.55 4.80 -0.54 0.17 0.00 0.32 0.00
0.9L 100.1 14287 3480 268 11163 0.62 1.81 4.80 -0.54 0.13 0.00 0.38 0.00
dv 108.2 4205 1024 73 3285 -0.26 3.07 4.80 -0.54 0.00 0.49 0.64 0.00
108.2 4168 1015 72 3256 -0.27 3.07 4.80 -0.54 0.00 0.50 0.64 0.00
109.2 2804 683 48 2191 -0.18 2.04 4.80 -0.54 0.00 0.33 0.43 0.00
110.2 1415 345 24 1106 -0.09 1.02 4.80 -0.54 0.00 0.16 0.21 0.00
L 111.2 0 0 0 0 -0.16 0.90 4.80 -0.54 0.00 0.29 0.19 0.00
Max: 0.55 0.50 0.64 0.47
Tensile
Stress
limit (ksi)
f_top f_bot
D/C ratio
(comp limit)
D/C
ratio(Ten
limit)
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit)
Moment
demands
DC3+DW (kip-
in)
Moment demands
DC4 (kip-in)
Moment
demands
LL(1+IM) (kip-
in)
f_top (ksi) f_Bot (ksi)Compressive
Stress limit (ksi)
Length
along
girder
(ft)
Moment
demands
DC1+DC2
(kip-in)
Service I : PS+Perm+LL*(1+IM)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders F Stress Page: of:
Job #: NO:
Note 1:
Note 2
f_bot SIM.
Note 3
Note 4
Check the stress to top of girder, so section modulus of the composite section, is the I_comp / y_tg, and y_tg
is the distance from comp. nuetral axis to the top of the girder.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders F Stress Page: of:
Job #: NO:
0 0.0 0 -0.16 0.90 4.80 -0.54 0.00 0.29 0.19 0.00
1.0 884 -0.09 1.03 4.80 -0.54 0.00 0.17 0.22 0.00
2.0 1753 -0.18 2.07 4.80 -0.54 0.00 0.34 0.43 0.00
3.0 2605 -0.28 3.11 4.80 -0.54 0.00 0.52 0.65 0.00
dv 5.0 4262 -0.05 2.80 4.80 -0.54 0.00 0.10 0.58 0.00
0.1L 11.1 8931 0.59 1.93 4.80 -0.54 0.12 0.00 0.40 0.00
13.0 10245 0.77 1.68 4.80 -0.54 0.16 0.00 0.35 0.00
14.0 10921 0.81 1.75 4.80 -0.54 0.17 0.00 0.36 0.00
15.0 11581 0.86 1.89 4.80 -0.54 0.18 0.00 0.39 0.00
16.0 12224 0.90 2.03 4.80 -0.54 0.19 0.00 0.42 0.00
0.2L 22.2 15877 1.40 1.36 4.80 -0.54 0.29 0.00 0.28 0.00
28.0 18696 1.78 0.84 4.80 -0.54 0.37 0.00 0.18 0.00
29.0 19131 1.82 0.86 4.80 -0.54 0.38 0.00 0.18 0.00
30.0 19549 1.85 0.91 4.80 -0.54 0.39 0.00 0.19 0.00
31.0 19952 1.89 0.96 4.80 -0.54 0.39 0.00 0.20 0.00
0.3L 33.4 20838 2.01 0.80 4.80 -0.54 0.42 0.00 0.17 0.00
0.4L 44.5 23815 2.41 0.25 4.80 -0.54 0.50 0.00 0.05 0.00
0.5L 55.6 24807 2.55 0.06 4.80 -0.54 0.53 0.00 0.01 0.00
0.6L 66.7 23815 2.41 0.25 4.80 -0.54 0.50 0.00 0.05 0.00
0.7L 77.8 20838 2.01 0.80 4.80 -0.54 0.42 0.00 0.17 0.00
80.2 19952 1.89 0.96 4.80 -0.54 0.39 0.00 0.20 0.00
81.2 19549 1.85 0.91 4.80 -0.54 0.39 0.00 0.19 0.00
82.2 19131 1.82 0.86 4.80 -0.54 0.38 0.00 0.18 0.00
83.2 18696 1.78 0.84 4.80 -0.54 0.37 0.00 0.18 0.00
0.8L 89.0 15877 1.40 1.36 4.80 -0.54 0.29 0.00 0.28 0.00
95.2 12224 0.90 2.03 4.80 -0.54 0.19 0.00 0.42 0.00
96.2 11581 0.86 1.89 4.80 -0.54 0.18 0.00 0.39 0.00
97.2 10921 0.81 1.75 4.80 -0.54 0.17 0.00 0.36 0.00
98.2 10245 0.77 1.68 4.80 -0.54 0.16 0.00 0.35 0.00
0.9L 100.1 8931 0.59 1.93 4.80 -0.54 0.12 0.00 0.40 0.00
dv 108.2 2628 -0.27 3.10 4.80 -0.54 0.00 0.51 0.65 0.00
108.2 2605 -0.28 3.11 4.80 -0.54 0.00 0.52 0.65 0.00
109.2 1753 -0.18 2.07 4.80 -0.54 0.00 0.34 0.43 0.00
110.2 884 -0.09 1.03 4.80 -0.54 0.00 0.17 0.22 0.00
L 111.2 0 -0.16 0.90 4.80 -0.54 0.00 0.29 0.19 0.00
Max: 0.53 0.52 0.65 0.00
f_Bot (ksi)
Compressiv
e Stress
limit (ksi)
Tensile
Stress limit
(ksi)
f_top f_bot
D/C ratio
(comp limit)
D/C ratio(Ten
limit)
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit)
Length along
girder (ft)
Moment
demands
0.8*LL(1+IM
) (kip-in)
f_top (ksi)
Service III : PS+Perm+0.8*LL*(1+IM)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders F Stress Page: of:
Job #: NO:
REQUIRED TOP REINFORCEMENT
0 0.0 -0.17 0.99 8.27 34.00 1.13 3
1.0 -0.19 1.27 7.08 31.22 1.04 3
2.0 -0.37 2.54 7.09 62.78 2.09 5
3.0 -0.56 3.81 7.10 94.65 3.16 8
dv 5.0 -0.48 3.73 6.29 71.29 2.38 6
0.1L 11.1 -0.24 3.49 3.59 20.64 0.69 2
13.0 -0.18 3.43 2.70 11.28 0.38 1
14.0 -0.19 3.62 2.81 12.91 0.43 1
15.0 -0.21 3.87 2.87 14.48 0.48 2
16.0 -0.23 4.13 2.94 16.18 0.54 2
0.2L 22.2 -0.05 3.95 0.67 0.76 0.03 1
28.0 0.09 3.81 0.00 0.00 0.00 0
29.0 0.09 3.90 0.00 0.00 0.00 0
30.0 0.09 4.02 0.00 0.00 0.00 0
31.0 0.08 4.15 0.00 0.00 0.00 0
0.3L 33.4 0.13 4.10 0.00 0.00 0.00 0
0.4L 44.5 0.28 3.96 0.00 0.00 0.00 0
0.5L 55.6 0.33 3.91 0.00 0.00 0.00 0
0.6L 66.7 0.28 3.96 0.00 0.00 0.00 0
0.7L 77.8 0.13 4.10 0.00 0.00 0.00 0
80.2 0.08 4.15 0.00 0.00 0.00 0
81.2 0.09 4.02 0.00 0.00 0.00 0
82.2 0.09 3.90 0.00 0.00 0.00 0
83.2 0.09 3.81 0.00 0.00 0.00 0
0.8L 89.0 -0.05 3.95 0.67 0.76 0.03 1
95.2 -0.23 4.13 2.94 16.18 0.54 2
96.2 -0.21 3.87 2.87 14.48 0.48 2
97.2 -0.19 3.62 2.81 12.91 0.43 1
98.2 -0.18 3.43 2.70 11.28 0.38 1
0.9L 100.1 -0.24 3.49 3.59 20.64 0.69 2
dv 108.2 -0.56 3.81 7.09 94.31 3.14 8
108.2 -0.56 3.81 7.10 94.65 3.16 8
109.2 -0.37 2.54 7.09 62.78 2.09 5
110.2 -0.19 1.27 7.08 31.22 1.04 3
L 111.2 -0.17 0.99 8.27 34.00 1.13 3
f_ci,top (ksi) f_ci,bot (ksi) x (in) T (kip) As (in^2)
# 6 rebars
(in^2)
Length along
girder (ft)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders G Design Page: of:
Job #: NO:
L, Bridge span length (ft) 110.80
Bridge Width (ft) Upper bound 78.16
Bridge Width (ft) Lower Bound 71.60
Bridge Width (ft) Average 74.88
Number of Lanes 4
m, Multipresent factor for LL 0.65
Nb, Number of Girder 8
S, Max Girder Spacing (ft) 10.05
Bridge Skew Angle (degree) 31
For the bridge girder:
f'ci at transfer (ksi) 6.7 AASHTO 5.4.2.3.1
f'c after 28 days (ksi) 8
E_ci (ksi) for girder @ transfer 4716
During the construction of the bridge, it is required to not interfere with train traffic,
thus, the bridge slab system is precast concrete panel in between girders, stitched with CIP Concrete.
Tendon diameter (in) 0.6
One strand area (in^2) 0.217
Debonding length (from end of beam to where bonding commence), ft
10
Girder Distribution factors for DL, LL moment, LL Shear
Type of deck CIP Concrete, Precast Concrete
Supporting Component Precast Concrete I or Bulb-tee section
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders G Design Page: of:
Job #: NO:
Common Deck superstructure Table 4.6.2.2.1-1
Typical Cross section K Table 4.6.2.2.1-1
Live Load Distribution Factor for Moment in Interior Beams Table 4.6.2.2.2b-1
Rang of Applicability
S, spacing of beams, ϵ [ 3.5, 16] ft ✔
L, Span Length, ϵ [20,240] ft ✔
Nb, number of beams >=4 ✔
ts, depth of concrete slab ϵ [ 4.5, 12] in ✔
Depth of concrete slab, ts (in) 8.00
kg, longitudinal stiffness factor, ϵ [10^4 , 7x10^6] ✔
kg= n( I + A*eg^2) 1576804.87 4.6.2.2.1-1
n= E_beam / E_deck 1.26491106
f'c_slab (ksi) 6
E_beam (ksi) 5,154
E_slab (ksi) 4,074
A, (non-composite) cross section area of girder (in^2) 925 Caltrans Design Aids, CA BT-55
I, (non-composite) inertia (in^4) 373,350 Caltrans Design Aids, CA BT-55
Yb, CG to bottom of girder (in) 28.4 Caltrans Design Aids, CA BT-55
D, girder height (in) 55.125 Caltrans Design Aids, CA BT-55
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders G Design Page: of:
Job #: NO:
eg, dist. Btw CL of beam & CL of deck (in) 30.725
b_eff, deck effective width of girder (ft) 9.08
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders G Design Page: of:
Job #: NO:
Per above table from AASHTO, the LL distribution factor for moment in Interior beams are calculated:
g_int, One design lane loaded: 0.52 lane / girder multiple presence factor included
g_int, Two or more lane loaded: 0.77 lane / girder per C4.6.2.2.2b
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders G Design Page: of:
Job #: NO:
Per above table from AASHTO, the LL distribution factor for moment in exterior beams are calculated:
de, horizontal distance from CL of ext. web of ext. beam @ deck level, to int. edge of curb of traffic barrier
de (ft) 2.30
e=0.77+de/9.1 1.02
g_ext, one design lane loaded 0.54 lane/girder
g_ext, two or more design lane loaded 0.79 lane/girder
Considering the span length, it is very likley that cross frames & end diaphraagm will be necessary.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders G Design Page: of:
Job #: NO:
Per AASHTO C4.6.2.2.2d-1, exterior girders have higher load distribution factors due to cross frames
One lane loaded:
NL 1
X_ext, (ft) 35.18
e (ft) 24.03
x_1 (ft) 5.03
x_2 (ft) 15.08
x_3 (ft) 25.13
x_4 (ft) 35.18
R 0.32
Adjust with 1.2 multiple presence factor 0.39
Two Lanes loaded:
NL 2
e1 (ft) 24.03
e2 (ft) 6.5
R 0.50
Adjust with 1.0 multiple presence factor 0.50
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders G Design Page: of:
Job #: NO:
Three or more Lanes loaded:
NL 3
e1 (ft) 24.03
e2 (ft) 6.5
e3 (ft) 12
R 0.68
Adjust with 0.85 multiple presence factor 0.58
Final design values for moment distribution factors :
Load Case Int. Girder (lane)
One lane 0.52 0.54
NA 0.39
2 lanes loaded NA 0.50
3 lanes loaded NA 0.58
Design Value
Moment
Distribution 0.77 0.79
Max: 0.79
Two values are close enough, use the
maximum value for all to be conservative.
Note that AASHTO 4.6.2.2.2.e for skewed bridge provides reduction factors for live load distribution factors for momen in longitudinal
beams. However, CA amendment ignores reduction. Thus, no reduction applies for moment
Ext. Girder (lane)
Moment Distribution factor
per Table 4.6.2.2.2 Two or more
lane
0.77 0.79
Moment D.F. for ext. girder per
C4.6.2.2.2d-1
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders G Design Page: of:
Job #: NO:
LL distribution factor for Shear :
Per above table from AASHTO, the LL distribution factor for shear in Interior beams are calculated:
g_int, One design lane loaded: 0.76 lane / girder multiple presence factor included
g_int, Two or more lane loaded: 0.96 lane / girder per C4.6.2.2.2b
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders G Design Page: of:
Job #: NO:
Per above table from AASHTO, the LL distribution factor for shear in exterior beams are calculated:
de (ft) 2.30
e=0.77+de/9.1 1.02
g_ext, one design lane loaded 0.54 lane/girder use same as ext one-lane for moment
g_ext, two or more design lane loaded 0.98 lane/girder
Notes:
AASHTO 4.6.2.2.3 C-1 provides correction factors for live load distribution factors for support shear of the obtuse girder.
CA Amendment revised AASHTO Table 4.6.2.2.3c-1 with equations provide for exterior girder & first interior girder.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders G Design Page: of:
Job #: NO:
Design values for shear distribution factors (without skew correction factor)
Load Case Int. Girder (lane)
One lane 0.76 NA
NA
NA 0.54
NA 0.98
Design Value
Shear
Distribution
Factor
0.96 0.98
Max: 0.98
Skew Correction factors for shear:
Two values are close enough, use the
maximum value for all to be conservative.
Ext. Girder (lane)
Shear Distribution factor per
Table 4.6.2.2.3a-1 Two or more
lane
0.96
Shear D.F. for ext. girder per
C4.6.2.2.3b-1
one lane loaded
Two or more
lane
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders G Design Page: of:
Job #: NO:
The shear correction factors are applied between the point of support at the obtuse corner and mid-span.
May be decreased linearly to a value of 1.0 at mid-span.
Skew Factor 1.09
Design values for shear distribution factors@ obtuse angle
Load Case Int. Girder (lane)
Design Value Shear D.F. 1.04 1.07 Max: 1.07
Two values are close enough, use the
maximum value for all to be conservative.Ext. Girder (lane)
1.07
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders G Design Page: of:
Job #: NO:
Moment Demands Calculations
One lane
0 0.0 0 0 0 0 0 0 0
dv 5.0 255 311 51 10 627 87 562
0.1L 11.1 532 650 107 22 1312 181 1175
0.2L 22.2 946 1156 190 44 2337 322 2088
0.3L 33.2 1241 1517 250 67 3075 422 2741
0.4L 44.3 1419 1734 285 89 3527 483 3132
0.5L 55.4 1478 1807 297 111 3693 503 3263
0.6L 66.5 1419 1734 285 89 3527 483 3132
0.7L 77.6 1241 1517 250 67 3075 422 2741
0.8L 88.6 946 1156 190 44 2337 322 2088
0.9L 99.7 532 650 107 22 1312 181 1175
dv 105.8 255 311 51 10 627 87 562
L 110.8 0 0 0 0 0 0 0
dv Use 0.9h (AASHTO 5.8.2.9) 5.03 ft
LL+IM Use Caltrans Bridge Design Aids attached as following.
Span length Moment (k-ft) End Shear (kip)
110 3229 122.8
120 3652.4 126.7
110.8 3263.0 123.1
Lane Load included from Caltrans Table
0 0
927 0
444 0
2162 0
1647 0
2574 0
2471 0
2162 0
2471 0
1647 0
Min LL
0 0
444 0
927 0
Length along
girder (ft)
For Each Girder
M (k-ft) DC1 M (k-ft) DC2 M (k-ft) DC3
M (k-ft)
DC4
M (k-ft)
DC Total
M (k-ft)
DW
(HL-93) LL+IM -M (k-f)
Distr.Fact
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders G Design Page: of:
Job #: NO:
Moment Capacity Calculations@ Wet Concr. Deck Stage (NonComposite)
Note 1 Note 4 Note 3
0 0.0 8 8 8 6 4 2 0 48.60 7.81 0.64 N.A. @ TF
dv 5.0 8 8 8 6 4 2 0 48.60 7.81 0.64 N.A. @ TF
0.1L 11.1 8 8 8 6 4 2 0 48.60 7.81 0.64 N.A. @ TF
0.2L 22.2 10 10 10 8 4 2 0 48.74 9.55 0.78 N.A. @ TF
0.3L 33.2 10 12 12 8 4 2 0 48.79 10.42 0.85 N.A. @ TF
0.4L 44.3 10 12 12 8 4 2 0 48.79 10.42 0.85 N.A. @ TF
0.5L 55.4 10 12 12 8 4 2 0 48.79 10.42 0.85 N.A. @ TF
0.6L 66.5 10 12 12 8 4 2 0 48.79 10.42 0.85 N.A. @ TF
0.7L 77.6 10 12 12 8 4 2 0 48.79 10.42 0.85 N.A. @ TF
0.8L 88.6 10 10 10 8 4 2 0 48.74 9.55 0.78 N.A. @ TF
0.9L 99.7 8 8 8 6 4 2 0 48.60 7.81 0.64 N.A. @ TF
dv 105.8 8 8 8 6 4 2 0 48.60 7.81 0.64 N.A. @ TF
L 110.8 8 8 8 6 4 2 0 48.60 7.81 0.64 N.A. @ TF
0.6" diameter tendons are used
Reference: AASHTO 2014 LRFD 7th Edition
Note 1: Note 4:
Note 2: Note 5:
Note 3: Note 6:Calcuated "c" to determine location of section
N.A.
No.
Tendon
at 12.75"
From Bot
No.
Tendon at
14.75"
From Bot
dp(in) to
Girder top
Aps(in^2) c (in)
Action Type:
Nuetral axis
location
Length
along
girder (ft)
No. Tendon
at 2.75"
From Bot
No.
Tendon at
4.75" from
Bot
No.
Tendon at
6.75"
From Bot
No.
Tendon at
8.75" From
Bot
No.
Tendon at
10.75"
From Bot
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders G Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Wet Concrete Deck Stage
Note 2 Note 5 Note 6 Note 7 Note 8
0 0.0 0.64 0.55 269.0 8463 0.2244 1.00 8463 0 8463 0
dv 5.0 0.64 0.55 269.0 8463 0.2244 1.00 8463 708 8463 0.08
0.1L 11.1 0.64 0.55 269.0 8463 0.2244 1.00 8463 1478 8463 0.17
0.2L 22.2 0.78 0.67 268.8 10352 0.1837 1.00 10352 2628 10352 0.25
0.3L 33.2 0.85 0.73 268.7 11294 0.1684 1.00 11294 3449 11294 0.31
0.4L 44.3 0.85 0.73 268.7 11294 0.1684 1.00 11294 3941 11294 0.35
0.5L 55.4 0.85 0.73 268.7 11294 0.1684 1.00 11294 4106 11294 0.36
0.6L 66.5 0.85 0.73 268.7 11294 0.1684 1.00 11294 3941 11294 0.35
0.7L 77.6 0.85 0.73 268.7 11294 0.1684 1.00 11294 3449 11294 0.31
0.8L 88.6 0.78 0.67 268.8 10352 0.1837 1.00 10352 2628 10352 0.25
0.9L 99.7 0.64 0.55 269.0 8463 0.2244 1.00 8463 1478 8463 0.17
dv 105.8 0.64 0.55 269.0 8463 0.2244 1.00 8463 708 8463 0.08
L 110.8 0.64 0.55 269.0 8463 0.2244 1.00 8463 0 8463 0.00
Note 7: Moment formula chosen depends on girder action type
Beta_1 =0.85 Per AASHTO 5.7.2.2
Value of k =0.28 Per Table C5.7.3.1.1.1
Note 8:
phi
factor φ
φMn(k-
ft)
For Each Girder
Mu (k-ft)
Strength I φMn(k-ft) D/C
Length
along
girder
(ft)
Update c (in) a (in) f_ps(ksi) Mn(k-ft)Epslon_t
ξ_t
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders G Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Wet Concrete Deck Stage
Mu=1.25 DC1+1.25DC2
Controlling Combination to design girders:
Strength I 1.25 DC+1.5 DW
0
2000
4000
6000
8000
10000
12000
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Mo
me
nt
(k
-ft)
Length (ft)
Moment Plot along Span Length
Mu (k-ft) Strength I φMn(k-ft)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders G Design Page: of:
Job #: NO:
0 0.0 0 0 0 0 0 0 0
dv 5.0 255 311 51 10 627 87 1003
0.1L 11.1 532 650 107 22 1312 181 2095
0.2L 22.2 946 1156 190 44 2337 322 3725
0.3L 33.2 1241 1517 250 67 3075 422 4889
0.4L 44.3 1419 1734 285 89 3527 483 5587
0.5L 55.4 1478 1807 297 111 3693 503 5820
0.6L 66.5 1419 1734 285 89 3527 483 5587
0.7L 77.6 1241 1517 250 67 3075 422 4889
0.8L 88.6 946 1156 190 44 2337 322 3725
0.9L 99.7 532 650 107 22 1312 181 2095
dv 105.8 255 311 51 10 627 87 1003
L 110.8 0 0 0 0 0 0 0 0 0
2938 0
1653 0
791 0
4591 0
4407 0
3856 0
2938 0
3856 0
4407 0
Min LL
0 0
791 0
1653 0
Length along
girder (ft)M (k-ft) DC1 M (k-ft) DC2 M (k-ft) DC3
M (k-ft)
DC4
M (k-ft)
DC Total
For Each Girder
M (k-ft)
DW
(P-15) LL+IM -M (k-f)
One lane Distr.Fact
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders G Design Page: of:
Job #: NO:
Moment Capacity Calculations@ Final Stage Stage
0 0.0 8 8 8 6 4 2 0 8 56.60 7.81 5.22
dv 5.0 8 8 8 6 4 2 0 8 56.60 7.81 5.22
0.1L 11.1 8 8 8 6 4 2 0 8 56.60 7.81 5.22
0.2L 22.2 10 10 10 8 4 2 0 8 56.74 9.55 6.35
0.3L 33.2 10 12 12 8 4 2 0 8 56.79 10.42 6.90
0.4L 44.3 10 12 12 8 4 2 0 8 56.79 10.42 6.90
0.5L 55.4 10 12 12 8 4 2 0 8 56.79 10.42 6.90
0.6L 66.5 10 12 12 8 4 2 0 8 56.79 10.42 6.90
0.7L 77.6 10 12 12 8 4 2 0 8 56.79 10.42 6.90
0.8L 88.6 10 10 10 8 4 2 0 8 56.74 9.55 6.35
0.9L 99.7 8 8 8 6 4 2 0 8 56.60 7.81 5.22
dv 105.8 8 8 8 6 4 2 0 8 56.60 7.81 5.22
L 110.8 8 8 8 6 4 2 0 8 56.60 7.81 5.22
Considering the concrete deck is acting compositely with the CA BT 55 girders.
Also Conservatively igore the precast concrete panel's composite concrete reaction, due to lack of friction btw the panel surface.
Aps(in^2) c (in) No.
Tendon at
10.75"
From Bot
No.
Tendon
at 12.75"
From Bot
No.
Tendon at
14.75"
From Bot
Composite
Deck THK
(in)
dp(in) to
Deck top
Length
along
girder (ft)
No. Tendon
at 2.75"
From Bot
No.
Tendon at
4.75" from
Bot
No.
Tendon at
6.75"
From Bot
No.
Tendon at
8.75" From
Bot
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders G Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Final Stage
0 0.0 N.A. @ Deck 5.22 4.44 263.0 9311 0.0295 1.00 9311
dv 5.0 N.A. @ Deck 5.22 4.44 263.0 9311 0.0295 1.00 9311
0.1L 11.1 N.A. @ Deck 5.22 4.44 263.0 9311 0.0295 1.00 9311
0.2L 22.2 N.A. @ Deck 6.35 5.39 261.5 11246 0.0238 1.00 11246
0.3L 33.2 N.A. @ Deck 6.90 5.87 260.8 12192 0.0217 1.00 12192
0.4L 44.3 N.A. @ Deck 6.90 5.87 260.8 12192 0.0217 1.00 12192
0.5L 55.4 N.A. @ Deck 6.90 5.87 260.8 12192 0.0217 1.00 12192
0.6L 66.5 N.A. @ Deck 6.90 5.87 260.8 12192 0.0217 1.00 12192
0.7L 77.6 N.A. @ Deck 6.90 5.87 260.8 12192 0.0217 1.00 12192
0.8L 88.6 N.A. @ Deck 6.35 5.39 261.5 11246 0.0238 1.00 11246
0.9L 99.7 N.A. @ Deck 5.22 4.44 263.0 9311 0.0295 1.00 9311
dv 105.8 N.A. @ Deck 5.22 4.44 263.0 9311 0.0295 1.00 9311
L 110.8 N.A. @ Deck 5.22 4.44 263.0 9311 0.0295 1.00 9311
Mn(k-ft)Epslon_t
ξ_t
phi factor
φ φMn(k-ft)
Length
along
girder
(ft)
Action Type
(Neutral Axis
location)
Update
c (in)
from
deck
top
a (in) f_ps(ksi)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders G Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Final Stage
0 0.0 0 0 9311 0 0.00
dv 5.0 1691 1982 9311 0.18 0.21
0.1L 11.1 3533 4142 9311 0.38 0.44
0.2L 22.2 6286 7370 11246 0.56 0.66
0.3L 33.2 8261 9684 12192 0.68 0.79
0.4L 44.3 9457 11083 12192 0.78 0.91
0.5L 55.4 9875 11568 12192 0.81 0.95
0.6L 66.5 9457 11083 12192 0.78 0.91
0.7L 77.6 8261 9684 12192 0.68 0.79
0.8L 88.6 6286 7370 11246 0.56 0.66
0.9L 99.7 3533 4142 9311 0.38 0.44
dv 105.8 1691 1982 9311 0.18 0.21
L 110.8 0 0 9311 0.00 0.00
Strength I 1.25 DC+1.5 DW+1.75 LL
Strength II 1.25 DC+1.5 DW+1.35 LL-permit
17
Mu (k-ft)
Strength I
Mu (k-ft)
Strength II φMn(k-ft)
D/C for
Strength I
D/C for
Strength II
Length
along
girder (ft)
For Each Girder
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders G Design Page: of:
Job #: NO:
0
2000
4000
6000
8000
10000
12000
14000
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Mo
me
nt
(k
-ft)
Length (ft)
Moment Plot along Span Length
Mu (k-ft) Strength I
φMn(k-ft)
Mu (k-ft) Strength II
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders G Stress Page: of:
Job #: NO:
For the stress calc, negative stress is tensile stress; positive stress is compressive stress.
Stress Calculations @ Transfer Stage
Tendons f_pu (ksi) 270
Tendon f_pbt (ksi) 202.5 (AASHTO Table 5.9.3.1)
Tendon E_ps (ksi) 28,500
Girder Concrete E_pc (ksi) 5,154
n'-1 = E_ps/ E_pc -1 4.53
f'c (ksi) 8
f'ci (ksi) 6.7
CA BT 55, Ag (in^2) 925
CA BT 55, w (k/ft) 0.963
CA BT 55, Yt, CG to Top (in) 26.70
CA BT 55, Yb, CG to Bot (in) 28.40
CA BT 55, Ig (in^4) 373,350
Ƴ_h Say H= 70% 1
Ƴ_st 0.65
Δf_pR (ksi) 2.4
Transfer length l_t =60*db (in) 36
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders G Stress Page: of:
Job #: NO:
Stress Calculations @ Transfer Stage* debond included
Note 1 Note 2 Note 3 Note 4 Note 5 Note 6
0 0.0 8 8 8 6 4 2 0 7.81 48.60 21.90 0 19 184 ok 359
1.0 8 8 8 6 4 2 0 7.81 48.60 21.90 634 19 184 ok 479
2.0 8 8 8 6 4 2 0 7.81 48.60 21.90 1257 18 184 ok 959
3.0 8 8 8 6 4 2 0 7.81 48.60 21.90 1869 18 184 ok 1440
dv 5.0 8 8 8 6 4 2 0 7.81 48.60 21.90 3057 18 185 ok 1442
0.1L 11.1 8 8 8 6 4 2 0 7.81 48.60 21.90 6384 17 186 ok 1450
13.0 8 8 8 6 4 2 0 7.81 48.60 21.90 7346 17 186 ok 1452
14.0 10 10 10 8 4 2 0 9.55 48.74 22.04 7831 20 182 ok 1528
15.0 10 10 10 8 4 2 0 9.55 48.74 22.04 8303 20 182 ok 1635
16.0 10 10 10 8 4 2 0 9.55 48.74 22.04 8764 20 182 ok 1742
0.2L 22.2 10 10 10 8 4 2 0 9.55 48.74 22.04 11350 19 183 ok 1749
28.0 10 10 10 8 4 2 0 9.55 48.74 22.04 13396 19 184 ok 1755
29.0 10 12 12 8 4 2 0 10.42 48.79 22.09 13707 21 182 ok 1790
30.0 10 12 12 8 4 2 0 10.42 48.79 22.09 14006 20 182 ok 1843
31.0 10 12 12 8 4 2 0 10.42 48.79 22.09 14294 20 182 ok 1897
0.3L 33.2 10 12 12 8 4 2 0 10.42 48.79 22.09 14897 20 182 ok 1899
0.4L 44.3 10 12 12 8 4 2 0 10.42 48.79 22.09 17025 20 183 ok 1905
0.5L 55.4 10 12 12 8 4 2 0 10.42 48.79 22.09 17734 19 183 ok 1907
0.6L 66.5 10 12 12 8 4 2 0 10.42 48.79 22.09 17025 20 183 ok 1905
0.7L 77.6 10 12 12 8 4 2 0 10.42 48.79 22.09 14897 20 182 ok 1899
79.8 10 12 12 8 4 2 0 10.42 48.79 22.09 14294 20 182 ok 1897
80.8 10 12 12 8 4 2 0 10.42 48.79 22.09 14006 20 182 ok 1843
81.8 10 12 12 8 4 2 0 10.42 48.79 22.09 13707 21 182 ok 1790
82.8 10 10 10 8 4 2 0 9.55 48.74 22.04 13396 19 184 ok 1755
0.8L 88.6 10 10 10 8 4 2 0 9.55 48.74 22.04 11350 19 183 ok 1749
94.8 10 10 10 8 4 2 0 9.55 48.74 22.04 8764 20 182 ok 1742
95.8 10 10 10 8 4 2 0 9.55 48.74 22.04 8303 20 182 ok 1635
96.8 10 10 10 8 4 2 0 9.55 48.74 22.04 7831 20 182 ok 1528
97.8 8 8 8 6 4 2 0 7.81 48.60 21.90 7346 17 186 ok 1452
0.9L 99.7 8 8 8 6 4 2 0 7.81 48.60 21.90 6384 17 186 ok 1450
dv 108.2 8 8 8 6 4 2 0 7.81 48.60 21.90 1651 18 184 ok 1439
107.8 8 8 8 6 4 2 0 7.81 48.60 21.90 1869 18 184 ok 1440
108.8 8 8 8 6 4 2 0 7.81 48.60 21.90 1257 18 184 ok 959
109.8 8 8 8 6 4 2 0 7.81 48.60 21.90 634 19 184 ok 479
L 110.8 8 8 8 6 4 2 0 7.81 48.60 21.90 0 19 184 ok 359
Length along
girder (ft) No. Tendon
at 2.75"
From Bot
No. Tendon
at 4.75"
from Bot
No.
Tendon at
6.75" From
Bot
No. Tendon
at 8.75"
From Bot
No. Tendon
at 10.75"
From Bot
Δf_pES
(ksi)
f_pi
(ksi)
Stress
limit for
tendon
0.8fpy
Jakcing
force
@transfer,
Pji (kip)
No. Tendon
at 12.75"
From Bot
No. Tendon
at 14.75"
From Bot
Aps(in^2)
Y_p,
Tendon
CG to Top
of Girder
(in)
e_ti (in)
Mg (kip-
in) Girder
Self
Weight
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders G Stress Page: of:
Job #: NO:
Note 1: Eccencity equal to value of Y_p minus YtNote 2: Mg is the moment caused by the self weight of the girder+ Concrete deck
Note 4:
Note 3:
Note 5: fpy assumes to be 0.9fpu; Table 5.9.3-1 AASHTO
Note 7: Top fiber concr gider stress=P/A-P*e/(I/Yt)+Mg/(I/Yb) (+ is compression, - is tension)
Note 9:
Note 6: Jakcing force @ transfer taken as f_pi multiplies Aps (Total area of tendons)
Note 8: Bot. fiber concr gider stress=P/A+P*e/(I/Yt)-Mg/(I/Yb) (+ is cpmpression, - is tension )
Note 10:
Girder top bars: #4 Total of 6, 0.2x6=1.2in^2
f_pi is the value of f_pbt minus Δf_pES. Per AASHTO C5.9.5.2.3a, if the transformed
section properties are used, the Δf_pES should not be inlcuded in the prestressing force.
In this case, jacking force is calcuated as f_pbt minus short term elastic shortening loss,
and so the Gorss section properties of the concrete girder are used.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders G Stress Page: of:
Job #: NO:
0
500
1000
1500
2000
2500
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Jakcing force @transfer, Pji (kip)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders G Stress Page: of:
Job #: NO:
Stress Calculations @ Transfer Stage
Note 7 Note 8 Note 9 Note 10
0 0.0 -0.17 0.99 4.36 -0.62 0.00 0.28 0.23 0.00
1.0 -0.19 1.27 4.36 -0.62 0.00 0.30 0.29 0.00
2.0 -0.37 2.54 4.36 -0.62 0.00 0.60 0.58 0.00
3.0 -0.56 3.81 4.36 -0.62 0.00 0.91 0.88 0.00
dv 5.0 -0.48 3.73 4.36 -0.62 0.00 0.77 0.86 0.00
0.1L 11.1 -0.25 3.50 4.36 -0.62 0.00 0.40 0.80 0.00
13.0 -0.18 3.43 4.36 -0.62 0.00 0.29 0.79 0.00
14.0 -0.20 3.62 4.36 -0.62 0.00 0.32 0.83 0.00
15.0 -0.22 3.88 4.36 -0.62 0.00 0.35 0.89 0.00
16.0 -0.24 4.14 4.36 -0.62 0.00 0.38 0.95 0.00
0.2L 22.2 -0.05 3.96 4.36 -0.62 0.00 0.09 0.91 0.00
28.0 0.09 3.82 4.36 -0.62 0.02 0.00 0.88 0.00
29.0 0.09 3.90 4.36 -0.62 0.02 0.00 0.90 0.00
30.0 0.08 4.03 4.36 -0.62 0.02 0.00 0.92 0.00
31.0 0.08 4.15 4.36 -0.62 0.02 0.00 0.95 0.00
0.3L 33.2 0.12 4.11 4.36 -0.62 0.03 0.00 0.94 0.00
0.4L 44.3 0.27 3.97 4.36 -0.62 0.06 0.00 0.91 0.00
0.5L 55.4 0.32 3.92 4.36 -0.62 0.07 0.00 0.90 0.00
0.6L 66.5 0.27 3.97 4.36 -0.62 0.06 0.00 0.91 0.00
0.7L 77.6 0.12 4.11 4.36 -0.62 0.03 0.00 0.94 0.00
79.8 0.08 4.15 4.36 -0.62 0.02 0.00 0.95 0.00
80.8 0.08 4.03 4.36 -0.62 0.02 0.00 0.92 0.00
81.8 0.09 3.90 4.36 -0.62 0.02 0.00 0.90 0.00
82.8 0.09 3.82 4.36 -0.62 0.02 0.00 0.88 0.00
0.8L 88.6 -0.05 3.96 4.36 -0.62 0.00 0.09 0.91 0.00
94.8 -0.24 4.14 4.36 -0.62 0.00 0.38 0.95 0.00
95.8 -0.22 3.88 4.36 -0.62 0.00 0.35 0.89 0.00
96.8 -0.20 3.62 4.36 -0.62 0.00 0.32 0.83 0.00
97.8 -0.18 3.43 4.36 -0.62 0.00 0.29 0.79 0.00
0.9L 99.7 -0.25 3.50 4.36 -0.62 0.00 0.40 0.80 0.00
dv 108.2 -0.58 3.83 4.36 -0.62 0.00 0.93 0.88 0.00
107.8 -0.56 3.81 4.36 -0.62 0.00 0.91 0.88 0.00
108.8 -0.37 2.54 4.36 -0.62 0.00 0.60 0.58 0.00
109.8 -0.19 1.27 4.36 -0.62 0.00 0.30 0.29 0.00
L 110.8 -0.17 0.99 4.36 -0.62 0.00 0.28 0.23 0.00
Max: 0.07 0.93 0.95 0.00
f_bot (ksi) (comp limit
0.65f'ci)
(Ten limit -
0.24*sqrt(f
'ci) ksi)
f_top f_bot
D/C ratio
(comp
limit )
D/C
ratio(Ten
limit )
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit )
Length
along
girder (ft)
f_top
(ksi)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders G Stress Page: of:
Job #: NO:
For the stress calc, negative stress is tensile stress; positive stress is compressive stress.
Stress Calculations @ Transfer Stage
Tendons f_pu (ksi) 270
Tendon f_pbt (ksi) 203 (AASHTO Table 5.9.3.1)
Tendon E_ps (ksi) 28500
Girder Concrete E_pc (ksi) 5154
n'-1 = E_ps/ E_pc -1 5
f'c (ksi) 8
f'ci (ksi) 6.7
CA BT 55, Ag (in^2) 925
CA BT 55, w (k/ft) 1
CA BT 55, Yt, CG to Top (in) 27
CA BT 55, Yb, CG to Bot (in) 28
CA BT 55, Ig (in^4) 373350
Ƴ_h Say H= 70% 1
Ƴ_st 0.65
Δf_pR (ksi) 2.4
Transfer length l_t =60*db (in) 36
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders G Stress Page: of:
Job #: NO:
Stress Calculations @ PS + Perm load condition Transformed seciton properties
Note 1 Note 2 Note 3 Note 4 Note 5 Note 6 Note 7 Note 8
0 0.0 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
1.0 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
2.0 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
3.0 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
dv 5.0 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
0.1L 11.1 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
13.0 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
14.0 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
15.0 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
16.0 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
0.2L 22.2 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
28.0 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
29.0 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
30.0 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
31.0 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
0.3L 33.2 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
0.4L 44.3 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
0.5L 55.4 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
0.6L 66.5 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
0.7L 77.6 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
79.8 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
80.8 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
81.8 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
82.8 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
0.8L 88.6 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
94.8 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
95.8 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
96.8 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
97.8 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
0.9L 99.7 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
dv 108.2 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
107.8 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
108.8 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
109.8 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
L 110.8 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
Transfor
med
Y_ttop
(in)
Transfor
med
Y_tbot
(in)
Ʃ Ai*(Y_i-
Y_ttop)^
2
(in^4)
I_final(in
^4)
Transfor
med
S_ttop
(in^3)
Transfor
med
S_tbot
(in^3)
Total
Aps*(n-
1)+Ag
(in^2) Ig (in^4)
ƩAi*Y_i
(in^3)
Length
along
girder
(ft) Aps(in^
2)
Y_p,
Tendon CG
to
GirderTop
(in)
Aps*(n'-
1)
(in^2)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders G Stress Page: of:
Job #: NO:
Note 1: Ignore moment of inertia I from prestrssing tendons, since it is too small compared to that of precast concrete Girder.
Note 2: Summation of tranformed strands area times CG of strands, and area of precast concrete girder times CG of the girder.
Note 3: Values of Note 2 divide by the total area of the transformed section to determine CG of the tranformed section (from top of the section)
Note 4: CG of the tranformed seciton (from bottom of the section)
Note 5:
Note 6: I_final =Ig + values at Note 5
Note 7: Transformed section modulus from top of seciton is I_final divide by Transformed Y_ttop
Note 8: Transformed section modulus from bottom of seciton is I_final divide by Transformed Y_tbot
Summation of tranformed area of strands times squrea of CG differenec between strands and the entire tranformed section, plus such value
for precast concrete girder component.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders G Stress Page: of:
Job #: NO:
Stress Calculations @ PS + Perm load condition * debond included
Note 9 Note 10 Note 11 Note 12 Note 13 Note 14 Note 15 Note 16
0 0.0 21 21 181 354 0 -0.16 0.90 3.60 -0.54 0.00 0.29 0.25 0.00
1.0 21 21 181 472 1410 -0.11 1.10 3.60 -0.54 0.00 0.21 0.30 0.00
2.0 21 21 181 944 2794 -0.23 2.20 3.60 -0.54 0.00 0.42 0.61 0.00
3.0 21 21 181 1416 4153 -0.34 3.30 3.60 -0.54 0.00 0.63 0.92 0.00
dv 5.0 21 21 181 1416 6793 -0.15 3.11 3.60 -0.54 0.00 0.29 0.86 0.00
0.1L 11.1 21 21 181 1416 14189 0.37 2.58 3.60 -0.54 0.10 0.00 0.72 0.00
13.0 21 21 181 1416 16326 0.52 2.43 3.60 -0.54 0.14 0.00 0.68 0.00
14.0 21 24 179 1500 17403 0.55 2.54 3.60 -0.54 0.15 0.00 0.70 0.00
15.0 21 24 179 1603 18453 0.58 2.72 3.60 -0.54 0.16 0.00 0.76 0.00
16.0 21 24 179 1707 19478 0.60 2.91 3.60 -0.54 0.17 0.00 0.81 0.00
0.2L 22.2 21 24 179 1707 25224 1.01 2.51 3.60 -0.54 0.28 0.00 0.70 0.00
28.0 21 24 179 1707 29772 1.33 2.19 3.60 -0.54 0.37 0.00 0.61 0.00
29.0 21 25 178 1746 30462 1.36 2.23 3.60 -0.54 0.38 0.00 0.62 0.00
30.0 21 25 178 1797 31128 1.38 2.31 3.60 -0.54 0.38 0.00 0.64 0.00
31.0 21 25 178 1849 31767 1.40 2.39 3.60 -0.54 0.39 0.00 0.66 0.00
0.3L 33.2 21 25 178 1849 33107 1.50 2.30 3.60 -0.54 0.42 0.00 0.64 0.00
0.4L 44.3 21 25 178 1849 37836 1.83 1.97 3.60 -0.54 0.51 0.00 0.55 0.00
0.5L 55.4 21 25 178 1849 39413 1.94 1.86 3.60 -0.54 0.54 0.00 0.52 0.00
0.6L 66.5 21 25 178 1849 37836 1.83 1.97 3.60 -0.54 0.51 0.00 0.55 0.00
0.7L 77.6 21 25 178 1849 33107 1.50 2.30 3.60 -0.54 0.42 0.00 0.64 0.00
79.8 21 25 178 1849 31767 1.40 2.39 3.60 -0.54 0.39 0.00 0.66 0.00
80.8 21 25 178 1797 31128 1.38 2.31 3.60 -0.54 0.38 0.00 0.64 0.00
81.8 21 25 178 1746 30462 1.36 2.23 3.60 -0.54 0.38 0.00 0.62 0.00
82.8 21 24 179 1707 29772 1.33 2.19 3.60 -0.54 0.37 0.00 0.61 0.00
0.8L 88.6 21 24 179 1707 25224 1.01 2.51 3.60 -0.54 0.28 0.00 0.70 0.00
94.8 21 24 179 1707 19478 0.60 2.91 3.60 -0.54 0.17 0.00 0.81 0.00
95.8 21 24 179 1603 18453 0.58 2.72 3.60 -0.54 0.16 0.00 0.76 0.00
96.8 21 24 179 1500 17403 0.55 2.54 3.60 -0.54 0.15 0.00 0.70 0.00
97.8 21 21 181 1416 16326 0.52 2.43 3.60 -0.54 0.14 0.00 0.68 0.00
0.9L 99.7 21 21 181 1416 14189 0.37 2.58 3.60 -0.54 0.10 0.00 0.72 0.00
dv 108.2 21 21 181 1416 3670 -0.37 3.33 3.60 -0.54 0.00 0.70 0.92 0.00
107.8 21 21 181 1416 4153 -0.34 3.30 3.60 -0.54 0.00 0.63 0.92 0.00
108.8 21 21 181 944 2794 -0.23 2.20 3.60 -0.54 0.00 0.42 0.61 0.00
109.8 21 21 181 472 1410 -0.11 1.10 3.60 -0.54 0.00 0.21 0.30 0.00
L 110.8 21 21 181 354 0 -0.16 0.90 3.60 -0.54 0.00 0.29 0.25 0.00
Max: 0.54 0.70 0.92 0.00
f_top
(ksi)
f_Bot
(ksi)
Compres
sive
Stress
limit (ksi)
Tensile
Stress
limit (ksi)
f_top f_bot
D/C ratio
(comp limit)
D/C
ratio(Ten
limit)
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit)
Length
along
girder
(ft)
e (in)Δf_pLT
(ksi)fpe (ksi) Pf (kiP)
Moment
demands
DC1+DC2
(kip-in)
PS+ Perm (DC1+DC2)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders G Stress Page: of:
Job #: NO:
Note 9: Eccentricity of the seciton is Y_p(in) from girder top subtracted by Transformed Y_ttop
Note 10
Note 11 fpe is stress at transfer minus long term loss Δf_pLT
Note 12 Prestressing force Pf, is fpe times area of the prestressing tendons, Aps.
Note 13
Note 14
Note 15
Note 16:
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders G Stress Page: of:
Job #: NO:
Tendons f_pu (ksi) 270
Tendon f_pbt (ksi) 202.5 (AASHTO Table 5.9.3.1)
CA BT 55, Ag (in^2) 925
CA BT 55, w (k/ft) 0.963
CA BT 55, Yt, CG to Top (in) 26.7
CA BT 55, Yb, CG to Bot (in) 28.4
CA BT 55, Ig (in^4) 373350
Tendon E_ps (ksi) 28,500
Girder Concrete E_pc (ksi) 5,154
n'-1 = E_ps/ E_pc -1 5
Girder f'c (ksi) 8
Girder f'ci (ksi) 6.7
Deck Concrete E_c (ksi) 4,074
Girder Concrete E_pc (ksi) 5,154
n= E_c/E_pc 0.79
CIP Deck f'c (ksi) 5
Deck effective width (ft) 9.08
Depth of concrete slab, ts (in) 8.00
Precast panel thickness (in) 3.50
Tranformed deck area (in^2) 768.74 (based on Ec of 8ksi concrete)
Tranformed effective deck width (in) 96.093 (based on Ec of 8ksi concrete)
Transfer length l_t =60*db (in) 36
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders G Stress Page: of:
Job #: NO:
Stress Calculations @ Service, composite section properties include the Deck Slab
Note 1
0 0.0 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 354
1.0 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 472
2.0 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 944
3.0 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
dv 5.0 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
0.1L 11.1 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
13.0 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
14.0 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1500
15.0 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1603
16.0 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1707
0.2L 22.2 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1707
28.0 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1707
29.0 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1746
30.0 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1797
31.0 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
0.3L 33.2 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
0.4L 44.3 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
0.5L 55.4 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
0.6L 66.5 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
0.7L 77.6 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
79.8 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
80.8 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1797
81.8 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1746
82.8 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1707
0.8L 88.6 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1707
94.8 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1707
95.8 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1603
96.8 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1500
97.8 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
0.9L 99.7 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
dv 108.2 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
107.8 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
108.8 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 944
109.8 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 472
L 110.8 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 354
e (in)
Δf_pLT
(ksi)
fpe
(ksi)
Pf
(kiP)
Yi to Top
of Deck
ƩAi*Y_i
(in^3)
Comp
Y_ttop
(in)
ToDec
kTop
Comp.
Y_tbot
(in)
I_comp
(in^4)
Comp.
S_tg
(in^3)
Comp S_tb
(in^3)
Length
along
girder (ft)
I_tg(in^4)Transformed
Y_ttop (in)
Transfor
med
Y_tbot
(in)
Tranfor
med
A_deck
(in^2)
A_deck+A
ps*(n'-
1)+Ag
(in^2)
From PS+Perm stress calc
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders G Stress Page: of:
Job #: NO:
Stress Calculations @ Service, composite section properties include the Deck Slab
* debond included Note 2 Note 3 Note 4
0 0.0 0 0 0 0 -0.16 0.90 4.80 -0.54 0.00 0.29 0.19 0.00
1.0 1410 343 24 1105 -0.09 1.02 4.80 -0.54 0.00 0.16 0.21 0.00
2.0 2794 681 48 2190 -0.18 2.05 4.80 -0.54 0.00 0.33 0.43 0.00
3.0 4153 1012 72 3254 -0.27 3.07 4.80 -0.54 0.00 0.50 0.64 0.00
dv 5.0 6793 1655 120 5324 -0.04 2.75 4.80 -0.54 0.00 0.07 0.57 0.00
0.1L 11.1 14189 3456 267 11119 0.61 1.82 4.80 -0.54 0.13 0.00 0.38 0.00
13.0 16326 3977 313 12795 0.80 1.56 4.80 -0.54 0.17 0.00 0.32 0.00
14.0 17403 4239 337 13638 0.85 1.62 4.80 -0.54 0.18 0.00 0.34 0.00
15.0 18453 4495 361 14461 0.90 1.75 4.80 -0.54 0.19 0.00 0.36 0.00
16.0 19478 4745 385 15264 0.94 1.88 4.80 -0.54 0.20 0.00 0.39 0.00
0.2L 22.2 25224 6145 534 19767 1.45 1.18 4.80 -0.54 0.30 0.00 0.25 0.00
28.0 29772 7252 674 23331 1.85 0.62 4.80 -0.54 0.38 0.00 0.13 0.00
29.0 30462 7421 698 23872 1.89 0.63 4.80 -0.54 0.39 0.00 0.13 0.00
30.0 31128 7583 722 24394 1.92 0.68 4.80 -0.54 0.40 0.00 0.14 0.00
31.0 31767 7738 746 24895 1.96 0.73 4.80 -0.54 0.41 0.00 0.15 0.00
0.3L 33.2 33107 8065 800 25945 2.07 0.56 4.80 -0.54 0.43 0.00 0.12 0.00
0.4L 44.3 37836 9217 1067 29651 2.49 -0.02 4.80 -0.54 0.52 0.00 0.00 0.04
0.5L 55.4 39413 9601 1334 30887 2.63 -0.23 4.80 -0.54 0.55 0.00 0.00 0.42
0.6L 66.5 37836 9217 1067 29651 2.49 -0.02 4.80 -0.54 0.52 0.00 0.00 0.04
0.7L 77.6 33107 8065 800 25945 2.07 0.56 4.80 -0.54 0.43 0.00 0.12 0.00
79.8 31767 7738 746 24895 1.96 0.73 4.80 -0.54 0.41 0.00 0.15 0.00
80.8 31128 7583 722 24394 1.92 0.68 4.80 -0.54 0.40 0.00 0.14 0.00
81.8 30462 7421 698 23872 1.89 0.63 4.80 -0.54 0.39 0.00 0.13 0.00
82.8 29772 7252 674 23331 1.85 0.62 4.80 -0.54 0.38 0.00 0.13 0.00
0.8L 88.6 25224 6145 534 19767 1.45 1.18 4.80 -0.54 0.30 0.00 0.25 0.00
94.8 19478 4745 385 15264 0.94 1.88 4.80 -0.54 0.20 0.00 0.39 0.00
95.8 18453 4495 361 14461 0.90 1.75 4.80 -0.54 0.19 0.00 0.36 0.00
96.8 17403 4239 337 13638 0.85 1.62 4.80 -0.54 0.18 0.00 0.34 0.00
97.8 16326 3977 313 12795 0.80 1.56 4.80 -0.54 0.17 0.00 0.32 0.00
0.9L 99.7 14189 3456 267 11119 0.61 1.82 4.80 -0.54 0.13 0.00 0.38 0.00
dv 108.2 3670 894 64 2876 -0.31 3.13 4.80 -0.54 0.00 0.58 0.65 0.00
107.8 4153 1012 72 3254 -0.27 3.07 4.80 -0.54 0.00 0.50 0.64 0.00
108.8 2794 681 48 2190 -0.18 2.05 4.80 -0.54 0.00 0.33 0.43 0.00
109.8 1410 343 24 1105 -0.09 1.02 4.80 -0.54 0.00 0.16 0.21 0.00
L 110.8 0 0 0 0 -0.16 0.90 4.80 -0.54 0.00 0.29 0.19 0.00
Max: 0.55 0.58 0.65 0.42
Tensile
Stress
limit (ksi)
f_top f_bot
D/C ratio
(comp limit)
D/C
ratio(Ten
limit)
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit)
Moment
demands
DC3+DW (kip-
in)
Moment demands
DC4 (kip-in)
Moment
demands
LL(1+IM) (kip-
in)
f_top (ksi) f_Bot (ksi)Compressive
Stress limit (ksi)
Length
along
girder
(ft)
Moment
demands
DC1+DC2
(kip-in)
Service I : PS+Perm+LL*(1+IM)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders G Stress Page: of:
Job #: NO:
Note 1:
Note 2
f_bot SIM.
Note 3
Note 4
Check the stress to top of girder, so section modulus of the composite section, is the I_comp / y_tg, and y_tg
is the distance from comp. nuetral axis to the top of the girder.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders G Stress Page: of:
Job #: NO:
0 0.0 0 -0.16 0.90 4.80 -0.54 0.00 0.29 0.19 0.00
1.0 884 -0.09 1.03 4.80 -0.54 0.00 0.17 0.22 0.00
2.0 1752 -0.18 2.07 4.80 -0.54 0.00 0.34 0.43 0.00
3.0 2604 -0.28 3.11 4.80 -0.54 0.00 0.52 0.65 0.00
dv 5.0 4259 -0.05 2.80 4.80 -0.54 0.00 0.10 0.58 0.00
0.1L 11.1 8895 0.58 1.94 4.80 -0.54 0.12 0.00 0.40 0.00
13.0 10236 0.76 1.69 4.80 -0.54 0.16 0.00 0.35 0.00
14.0 10910 0.81 1.76 4.80 -0.54 0.17 0.00 0.37 0.00
15.0 11569 0.85 1.90 4.80 -0.54 0.18 0.00 0.39 0.00
16.0 12211 0.89 2.04 4.80 -0.54 0.19 0.00 0.42 0.00
0.2L 22.2 15814 1.38 1.38 4.80 -0.54 0.29 0.00 0.29 0.00
28.0 18665 1.77 0.85 4.80 -0.54 0.37 0.00 0.18 0.00
29.0 19098 1.81 0.87 4.80 -0.54 0.38 0.00 0.18 0.00
30.0 19515 1.84 0.92 4.80 -0.54 0.38 0.00 0.19 0.00
31.0 19916 1.87 0.97 4.80 -0.54 0.39 0.00 0.20 0.00
0.3L 33.2 20756 1.99 0.82 4.80 -0.54 0.41 0.00 0.17 0.00
0.4L 44.3 23721 2.39 0.27 4.80 -0.54 0.50 0.00 0.06 0.00
0.5L 55.4 24709 2.53 0.08 4.80 -0.54 0.53 0.00 0.02 0.00
0.6L 66.5 23721 2.39 0.27 4.80 -0.54 0.50 0.00 0.06 0.00
0.7L 77.6 20756 1.99 0.82 4.80 -0.54 0.41 0.00 0.17 0.00
79.8 19916 1.87 0.97 4.80 -0.54 0.39 0.00 0.20 0.00
80.8 19515 1.84 0.92 4.80 -0.54 0.38 0.00 0.19 0.00
81.8 19098 1.81 0.87 4.80 -0.54 0.38 0.00 0.18 0.00
82.8 18665 1.77 0.85 4.80 -0.54 0.37 0.00 0.18 0.00
0.8L 88.6 15814 1.38 1.38 4.80 -0.54 0.29 0.00 0.29 0.00
94.8 12211 0.89 2.04 4.80 -0.54 0.19 0.00 0.42 0.00
95.8 11569 0.85 1.90 4.80 -0.54 0.18 0.00 0.39 0.00
96.8 10910 0.81 1.76 4.80 -0.54 0.17 0.00 0.37 0.00
97.8 10236 0.76 1.69 4.80 -0.54 0.16 0.00 0.35 0.00
0.9L 99.7 8895 0.58 1.94 4.80 -0.54 0.12 0.00 0.40 0.00
dv 108.2 2301 -0.32 3.16 4.80 -0.54 0.00 0.60 0.66 0.00
107.8 2604 -0.28 3.11 4.80 -0.54 0.00 0.52 0.65 0.00
108.8 1752 -0.18 2.07 4.80 -0.54 0.00 0.34 0.43 0.00
109.8 884 -0.09 1.03 4.80 -0.54 0.00 0.17 0.22 0.00
L 110.8 0 -0.16 0.90 4.80 -0.54 0.00 0.29 0.19 0.00
Max: 0.53 0.60 0.66 0.00
f_Bot (ksi)
Compressiv
e Stress
limit (ksi)
Tensile
Stress limit
(ksi)
f_top f_bot
D/C ratio
(comp limit)
D/C ratio(Ten
limit)
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit)
Length along
girder (ft)
Moment
demands
0.8*LL(1+IM
) (kip-in)
f_top (ksi)
Service III : PS+Perm+0.8*LL*(1+IM)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders G Stress Page: of:
Job #: NO:
REQUIRED TOP REINFORCEMENT
0 0.0 -0.17 0.99 8.27 34.00 1.13 3
1.0 -0.19 1.27 7.08 31.27 1.04 3
2.0 -0.37 2.54 7.10 62.87 2.10 5
3.0 -0.56 3.81 7.11 94.79 3.16 8
dv 5.0 -0.48 3.73 6.30 71.50 2.38 6
0.1L 11.1 -0.25 3.50 3.63 21.14 0.70 2
13.0 -0.18 3.43 2.73 11.53 0.38 1
14.0 -0.20 3.62 2.84 13.18 0.44 1
15.0 -0.22 3.88 2.90 14.78 0.49 2
16.0 -0.24 4.14 2.97 16.51 0.55 2
0.2L 22.2 -0.05 3.96 0.74 0.95 0.03 1
28.0 0.09 3.82 0.00 0.00 0.00 0
29.0 0.09 3.90 0.00 0.00 0.00 0
30.0 0.08 4.03 0.00 0.00 0.00 0
31.0 0.08 4.15 0.00 0.00 0.00 0
0.3L 33.2 0.12 4.11 0.00 0.00 0.00 0
0.4L 44.3 0.27 3.97 0.00 0.00 0.00 0
0.5L 55.4 0.32 3.92 0.00 0.00 0.00 0
0.6L 66.5 0.27 3.97 0.00 0.00 0.00 0
0.7L 77.6 0.12 4.11 0.00 0.00 0.00 0
79.8 0.08 4.15 0.00 0.00 0.00 0
80.8 0.08 4.03 0.00 0.00 0.00 0
81.8 0.09 3.90 0.00 0.00 0.00 0
82.8 0.09 3.82 0.00 0.00 0.00 0
0.8L 88.6 -0.05 3.96 0.74 0.95 0.03 1
94.8 -0.24 4.14 2.97 16.51 0.55 2
95.8 -0.22 3.88 2.90 14.78 0.49 2
96.8 -0.20 3.62 2.84 13.18 0.44 1
97.8 -0.18 3.43 2.73 11.53 0.38 1
0.9L 99.7 -0.25 3.50 3.63 21.14 0.70 2
dv 108.2 -0.58 3.83 7.25 99.31 3.31 8
107.8 -0.56 3.81 7.11 94.79 3.16 8
108.8 -0.37 2.54 7.10 62.87 2.10 5
109.8 -0.19 1.27 7.08 31.27 1.04 3
L 110.8 -0.17 0.99 8.27 34.00 1.13 3
f_ci,top (ksi) f_ci,bot (ksi) x (in) T (kip) As (in^2)
# 6 rebars
(in^2)
Length along
girder (ft)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders H Design Page: of:
Job #: NO:
L, Bridge span length (ft) 110.42
Bridge Width (ft) Upper bound 78.16
Bridge Width (ft) Lower Bound 71.60
Bridge Width (ft) Average 74.88
Number of Lanes 4
m, Multipresent factor for LL 0.65
Nb, Number of Girder 8
S, Max Girder Spacing (ft) 10.05
Bridge Skew Angle (degree) 31
For the bridge girder:
f'ci at transfer (ksi) 6.7 AASHTO 5.4.2.3.1
f'c after 28 days (ksi) 8
E_ci (ksi) for girder @ transfer 4716
During the construction of the bridge, it is required to not interfere with train traffic,
thus, the bridge slab system is precast concrete panel in between girders, stitched with CIP Concrete.
Tendon diameter (in) 0.6
One strand area (in^2) 0.217
Debonding length (from end of beam to where bonding commence), ft
10
Girder Distribution factors for DL, LL moment, LL Shear
Type of deck CIP Concrete, Precast Concrete
Supporting Component Precast Concrete I or Bulb-tee section
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders H Design Page: of:
Job #: NO:
Common Deck superstructure Table 4.6.2.2.1-1
Typical Cross section K Table 4.6.2.2.1-1
Live Load Distribution Factor for Moment in Interior Beams Table 4.6.2.2.2b-1
Rang of Applicability
S, spacing of beams, ϵ [ 3.5, 16] ft ✔
L, Span Length, ϵ [20,240] ft ✔
Nb, number of beams >=4 ✔
ts, depth of concrete slab ϵ [ 4.5, 12] in ✔
Depth of concrete slab, ts (in) 8.00
kg, longitudinal stiffness factor, ϵ [10^4 , 7x10^6] ✔
kg= n( I + A*eg^2) 1576804.87 4.6.2.2.1-1
n= E_beam / E_deck 1.26491106
f'c_slab (ksi) 6
E_beam (ksi) 5,154
E_slab (ksi) 4,074
A, (non-composite) cross section area of girder (in^2) 925 Caltrans Design Aids, CA BT-55
I, (non-composite) inertia (in^4) 373,350 Caltrans Design Aids, CA BT-55
Yb, CG to bottom of girder (in) 28.4 Caltrans Design Aids, CA BT-55
D, girder height (in) 55.125 Caltrans Design Aids, CA BT-55
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders H Design Page: of:
Job #: NO:
eg, dist. Btw CL of beam & CL of deck (in) 30.725
b_eff, deck effective width of girder (ft) 9.08
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders H Design Page: of:
Job #: NO:
Per above table from AASHTO, the LL distribution factor for moment in Interior beams are calculated:
g_int, One design lane loaded: 0.52 lane / girder multiple presence factor included
g_int, Two or more lane loaded: 0.77 lane / girder per C4.6.2.2.2b
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders H Design Page: of:
Job #: NO:
Per above table from AASHTO, the LL distribution factor for moment in exterior beams are calculated:
de, horizontal distance from CL of ext. web of ext. beam @ deck level, to int. edge of curb of traffic barrier
de (ft) 2.30
e=0.77+de/9.1 1.02
g_ext, one design lane loaded 0.54 lane/girder
g_ext, two or more design lane loaded 0.79 lane/girder
Considering the span length, it is very likley that cross frames & end diaphraagm will be necessary.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders H Design Page: of:
Job #: NO:
Per AASHTO C4.6.2.2.2d-1, exterior girders have higher load distribution factors due to cross frames
One lane loaded:
NL 1
X_ext, (ft) 35.18
e (ft) 24.03
x_1 (ft) 5.03
x_2 (ft) 15.08
x_3 (ft) 25.13
x_4 (ft) 35.18
R 0.32
Adjust with 1.2 multiple presence factor 0.39
Two Lanes loaded:
NL 2
e1 (ft) 24.03
e2 (ft) 6.5
R 0.50
Adjust with 1.0 multiple presence factor 0.50
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders H Design Page: of:
Job #: NO:
Three or more Lanes loaded:
NL 3
e1 (ft) 24.03
e2 (ft) 6.5
e3 (ft) 12
R 0.68
Adjust with 0.85 multiple presence factor 0.58
Final design values for moment distribution factors :
Load Case Int. Girder (lane)
One lane 0.52 0.54
NA 0.39
2 lanes loaded NA 0.50
3 lanes loaded NA 0.58
Design Value
Moment
Distribution 0.77 0.79
Max: 0.79
Two values are close enough, use the
maximum value for all to be conservative.
Note that AASHTO 4.6.2.2.2.e for skewed bridge provides reduction factors for live load distribution factors for momen in longitudinal
beams. However, CA amendment ignores reduction. Thus, no reduction applies for moment
Ext. Girder (lane)
Moment Distribution factor
per Table 4.6.2.2.2 Two or more
lane
0.77 0.79
Moment D.F. for ext. girder per
C4.6.2.2.2d-1
one lane loaded
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders H Design Page: of:
Job #: NO:
LL distribution factor for Shear :
Per above table from AASHTO, the LL distribution factor for shear in Interior beams are calculated:
g_int, One design lane loaded: 0.76 lane / girder multiple presence factor included
g_int, Two or more lane loaded: 0.96 lane / girder per C4.6.2.2.2b
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders H Design Page: of:
Job #: NO:
Per above table from AASHTO, the LL distribution factor for shear in exterior beams are calculated:
de (ft) 2.30
e=0.77+de/9.1 1.02
g_ext, one design lane loaded 0.54 lane/girder use same as ext one-lane for moment
g_ext, two or more design lane loaded 0.98 lane/girder
Notes:
AASHTO 4.6.2.2.3 C-1 provides correction factors for live load distribution factors for support shear of the obtuse girder.
CA Amendment revised AASHTO Table 4.6.2.2.3c-1 with equations provide for exterior girder & first interior girder.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders H Design Page: of:
Job #: NO:
Design values for shear distribution factors (without skew correction factor)
Load Case Int. Girder (lane)
One lane 0.76 NA
NA
NA 0.54
NA 0.98
Design Value
Shear
Distribution
Factor
0.96 0.98
Max: 0.98
Skew Correction factors for shear:
Two values are close enough, use the
maximum value for all to be conservative.
Ext. Girder (lane)
Shear Distribution factor per
Table 4.6.2.2.3a-1 Two or more
lane
0.96
Shear D.F. for ext. girder per
C4.6.2.2.3b-1
one lane loaded
Two or more
lane
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders H Design Page: of:
Job #: NO:
The shear correction factors are applied between the point of support at the obtuse corner and mid-span.
May be decreased linearly to a value of 1.0 at mid-span.
Skew Factor 1.09
Design values for shear distribution factors@ obtuse angle
Load Case Int. Girder (lane)
Design Value Shear D.F. 1.04 1.07 Max: 1.07
Two values are close enough, use the
maximum value for all to be conservative.Ext. Girder (lane)
1.07
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders H Design Page: of:
Job #: NO:
Moment Demands Calculations
One lane
0 0.0 0 0 0 0 0 0 0
dv 5.0 254 310 51 10 625 86 561
0.1L 11.0 528 646 106 22 1303 180 1169
0.2L 22.1 939 1148 189 44 2321 320 2077
0.3L 33.1 1233 1507 248 66 3054 419 2727
0.4L 44.2 1409 1722 283 89 3503 479 3116
0.5L 55.2 1468 1794 295 111 3668 499 3246
0.6L 66.3 1409 1722 283 89 3503 479 3116
0.7L 77.3 1233 1507 248 66 3054 419 2727
0.8L 88.3 939 1148 189 44 2321 320 2077
0.9L 99.4 528 646 106 22 1303 180 1169
dv 105.4 254 310 51 10 625 86 561
L 110.4 0 0 0 0 0 0 0
dv Use 0.9h (AASHTO 5.8.2.9) 5.03 ft
LL+IM Use Caltrans Bridge Design Aids attached as following.
Span length Moment (k-ft) End Shear (kip)
110 3229 122.8
120 3652.4 126.7
110.4 3246.6 123.0
Lane Load included from Caltrans Table
0 0
923 0
443 0
2153 0
1640 0
2563 0
2460 0
2153 0
2460 0
1640 0
Min LL
0 0
443 0
923 0
Length along
girder (ft)
For Each Girder
M (k-ft) DC1 M (k-ft) DC2 M (k-ft) DC3
M (k-ft)
DC4
M (k-ft)
DC Total
M (k-ft)
DW
(HL-93) LL+IM -M (k-f)
Distr.Fact
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders H Design Page: of:
Job #: NO:
Moment Capacity Calculations@ Wet Concr. Deck Stage (NonComposite)
Note 1 Note 4 Note 3
0 0.0 8 8 8 6 4 2 0 48.60 7.81 0.64 N.A. @ TF
dv 5.0 8 8 8 6 4 2 0 48.60 7.81 0.64 N.A. @ TF
0.1L 11.0 8 8 8 6 4 2 0 48.60 7.81 0.64 N.A. @ TF
0.2L 22.1 10 10 10 8 4 2 0 48.74 9.55 0.78 N.A. @ TF
0.3L 33.1 10 12 12 8 4 2 0 48.79 10.42 0.85 N.A. @ TF
0.4L 44.2 10 12 12 8 4 2 0 48.79 10.42 0.85 N.A. @ TF
0.5L 55.2 10 12 12 8 4 2 0 48.79 10.42 0.85 N.A. @ TF
0.6L 66.3 10 12 12 8 4 2 0 48.79 10.42 0.85 N.A. @ TF
0.7L 77.3 10 12 12 8 4 2 0 48.79 10.42 0.85 N.A. @ TF
0.8L 88.3 10 10 10 8 4 2 0 48.74 9.55 0.78 N.A. @ TF
0.9L 99.4 8 8 8 6 4 2 0 48.60 7.81 0.64 N.A. @ TF
dv 105.4 8 8 8 6 4 2 0 48.60 7.81 0.64 N.A. @ TF
L 110.4 8 8 8 6 4 2 0 48.60 7.81 0.64 N.A. @ TF
0.6" diameter tendons are used
Reference: AASHTO 2014 LRFD 7th Edition
Note 1: Note 4:
Note 2: Note 5:
Note 3: Note 6:Calcuated "c" to determine location of section
N.A.
No.
Tendon
at 12.75"
From Bot
No.
Tendon at
14.75"
From Bot
dp(in) to
Girder top
Aps(in^2) c (in)
Action Type:
Nuetral axis
location
Length
along
girder (ft)
No. Tendon
at 2.75"
From Bot
No.
Tendon at
4.75" from
Bot
No.
Tendon at
6.75"
From Bot
No.
Tendon at
8.75" From
Bot
No.
Tendon at
10.75"
From Bot
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders H Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Wet Concrete Deck Stage
Note 2 Note 5 Note 6 Note 7 Note 8
0 0.0 0.64 0.55 269.0 8463 0.2244 1.00 8463 0 8463 0
dv 5.0 0.64 0.55 269.0 8463 0.2244 1.00 8463 705 8463 0.08
0.1L 11.0 0.64 0.55 269.0 8463 0.2244 1.00 8463 1468 8463 0.17
0.2L 22.1 0.78 0.67 268.8 10352 0.1837 1.00 10352 2609 10352 0.25
0.3L 33.1 0.85 0.73 268.7 11294 0.1684 1.00 11294 3425 11294 0.30
0.4L 44.2 0.85 0.73 268.7 11294 0.1684 1.00 11294 3914 11294 0.35
0.5L 55.2 0.85 0.73 268.7 11294 0.1684 1.00 11294 4077 11294 0.36
0.6L 66.3 0.85 0.73 268.7 11294 0.1684 1.00 11294 3914 11294 0.35
0.7L 77.3 0.85 0.73 268.7 11294 0.1684 1.00 11294 3425 11294 0.30
0.8L 88.3 0.78 0.67 268.8 10352 0.1837 1.00 10352 2609 10352 0.25
0.9L 99.4 0.64 0.55 269.0 8463 0.2244 1.00 8463 1468 8463 0.17
dv 105.4 0.64 0.55 269.0 8463 0.2244 1.00 8463 705 8463 0.08
L 110.4 0.64 0.55 269.0 8463 0.2244 1.00 8463 0 8463 0.00
Note 7: Moment formula chosen depends on girder action type
Beta_1 =0.85 Per AASHTO 5.7.2.2
Value of k =0.28 Per Table C5.7.3.1.1.1
Note 8:
phi
factor φ
φMn(k-
ft)
For Each Girder
Mu (k-ft)
Strength I φMn(k-ft) D/C
Length
along
girder
(ft)
Update c (in) a (in) f_ps(ksi) Mn(k-ft)Epslon_t
ξ_t
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders H Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Wet Concrete Deck Stage
Mu=1.25 DC1+1.25DC2
Controlling Combination to design girders:
Strength I 1.25 DC+1.5 DW
0
2000
4000
6000
8000
10000
12000
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Mo
me
nt
(k
-ft)
Length (ft)
Moment Plot along Span Length
Mu (k-ft) Strength I φMn(k-ft)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders H Design Page: of:
Job #: NO:
0 0.0 0 0 0 0 0 0 0
dv 5.0 254 310 51 10 625 86 1000
0.1L 11.0 528 646 106 22 1303 180 2081
0.2L 22.1 939 1148 189 44 2321 320 3699
0.3L 33.1 1233 1507 248 66 3054 419 4855
0.4L 44.2 1409 1722 283 89 3503 479 5549
0.5L 55.2 1468 1794 295 111 3668 499 5780
0.6L 66.3 1409 1722 283 89 3503 479 5549
0.7L 77.3 1233 1507 248 66 3054 419 4855
0.8L 88.3 939 1148 189 44 2321 320 3699
0.9L 99.4 528 646 106 22 1303 180 2081
dv 105.4 254 310 51 10 625 86 1000
L 110.4 0 0 0 0 0 0 0 0 0
2921 0
1643 0
789 0
4564 0
4381 0
3833 0
2921 0
3833 0
4381 0
Min LL
0 0
789 0
1643 0
Length along
girder (ft)M (k-ft) DC1 M (k-ft) DC2 M (k-ft) DC3
M (k-ft)
DC4
M (k-ft)
DC Total
For Each Girder
M (k-ft)
DW
(P-15) LL+IM -M (k-f)
One lane Distr.Fact
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders H Design Page: of:
Job #: NO:
Moment Capacity Calculations@ Final Stage Stage
0 0.0 8 8 8 6 4 2 0 8 56.60 7.81 5.22
dv 5.0 8 8 8 6 4 2 0 8 56.60 7.81 5.22
0.1L 11.0 8 8 8 6 4 2 0 8 56.60 7.81 5.22
0.2L 22.1 10 10 10 8 4 2 0 8 56.74 9.55 6.35
0.3L 33.1 10 12 12 8 4 2 0 8 56.79 10.42 6.90
0.4L 44.2 10 12 12 8 4 2 0 8 56.79 10.42 6.90
0.5L 55.2 10 12 12 8 4 2 0 8 56.79 10.42 6.90
0.6L 66.3 10 12 12 8 4 2 0 8 56.79 10.42 6.90
0.7L 77.3 10 12 12 8 4 2 0 8 56.79 10.42 6.90
0.8L 88.3 10 10 10 8 4 2 0 8 56.74 9.55 6.35
0.9L 99.4 8 8 8 6 4 2 0 8 56.60 7.81 5.22
dv 105.4 8 8 8 6 4 2 0 8 56.60 7.81 5.22
L 110.4 8 8 8 6 4 2 0 8 56.60 7.81 5.22
Considering the concrete deck is acting compositely with the CA BT 55 girders.
Also Conservatively igore the precast concrete panel's composite concrete reaction, due to lack of friction btw the panel surface.
Aps(in^2) c (in) No.
Tendon at
10.75"
From Bot
No.
Tendon
at 12.75"
From Bot
No.
Tendon at
14.75"
From Bot
Composite
Deck THK
(in)
dp(in) to
Deck top
Length
along
girder (ft)
No. Tendon
at 2.75"
From Bot
No.
Tendon at
4.75" from
Bot
No.
Tendon at
6.75"
From Bot
No.
Tendon at
8.75" From
Bot
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders H Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Final Stage
0 0.0 N.A. @ Deck 5.22 4.44 263.0 9311 0.0295 1.00 9311
dv 5.0 N.A. @ Deck 5.22 4.44 263.0 9311 0.0295 1.00 9311
0.1L 11.0 N.A. @ Deck 5.22 4.44 263.0 9311 0.0295 1.00 9311
0.2L 22.1 N.A. @ Deck 6.35 5.39 261.5 11246 0.0238 1.00 11246
0.3L 33.1 N.A. @ Deck 6.90 5.87 260.8 12192 0.0217 1.00 12192
0.4L 44.2 N.A. @ Deck 6.90 5.87 260.8 12192 0.0217 1.00 12192
0.5L 55.2 N.A. @ Deck 6.90 5.87 260.8 12192 0.0217 1.00 12192
0.6L 66.3 N.A. @ Deck 6.90 5.87 260.8 12192 0.0217 1.00 12192
0.7L 77.3 N.A. @ Deck 6.90 5.87 260.8 12192 0.0217 1.00 12192
0.8L 88.3 N.A. @ Deck 6.35 5.39 261.5 11246 0.0238 1.00 11246
0.9L 99.4 N.A. @ Deck 5.22 4.44 263.0 9311 0.0295 1.00 9311
dv 105.4 N.A. @ Deck 5.22 4.44 263.0 9311 0.0295 1.00 9311
L 110.4 N.A. @ Deck 5.22 4.44 263.0 9311 0.0295 1.00 9311
Mn(k-ft)Epslon_t
ξ_t
phi factor
φ φMn(k-ft)
Length
along
girder
(ft)
Action Type
(Neutral Axis
location)
Update
c (in)
from
deck
top
a (in) f_ps(ksi)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders H Design Page: of:
Job #: NO:
Moment Demands & Capacity Plots @ Final Stage
0 0.0 0 0 9311 0 0.00
dv 5.0 1687 1976 9311 0.18 0.21
0.1L 11.0 3513 4116 9311 0.38 0.44
0.2L 22.1 6251 7323 11246 0.56 0.65
0.3L 33.1 8214 9622 12192 0.67 0.79
0.4L 44.2 9404 11012 12192 0.77 0.90
0.5L 55.2 9818 11494 12192 0.81 0.94
0.6L 66.3 9404 11012 12192 0.77 0.90
0.7L 77.3 8214 9622 12192 0.67 0.79
0.8L 88.3 6251 7323 11246 0.56 0.65
0.9L 99.4 3513 4116 9311 0.38 0.44
dv 105.4 1687 1976 9311 0.18 0.21
L 110.4 0 0 9311 0.00 0.00
Strength I 1.25 DC+1.5 DW+1.75 LL
Strength II 1.25 DC+1.5 DW+1.35 LL-permit
17
Mu (k-ft)
Strength I
Mu (k-ft)
Strength II φMn(k-ft)
D/C for
Strength I
D/C for
Strength II
Length
along
girder (ft)
For Each Girder
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/18/20
Subject: Design Calculations Checked: CL Date: 5/3/20
Task: Girders H Design Page: of:
Job #: NO:
0
2000
4000
6000
8000
10000
12000
14000
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Mo
me
nt
(k
-ft)
Length (ft)
Moment Plot along Span Length
Mu (k-ft) Strength I
φMn(k-ft)
Mu (k-ft) Strength II
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders H Stress Page: of:
Job #: NO:
For the stress calc, negative stress is tensile stress; positive stress is compressive stress.
Stress Calculations @ Transfer Stage
Tendons f_pu (ksi) 270
Tendon f_pbt (ksi) 202.5 (AASHTO Table 5.9.3.1)
Tendon E_ps (ksi) 28,500
Girder Concrete E_pc (ksi) 5,154
n'-1 = E_ps/ E_pc -1 4.53
f'c (ksi) 8
f'ci (ksi) 6.7
CA BT 55, Ag (in^2) 925
CA BT 55, w (k/ft) 0.963
CA BT 55, Yt, CG to Top (in) 26.70
CA BT 55, Yb, CG to Bot (in) 28.40
CA BT 55, Ig (in^4) 373,350
Ƴ_h Say H= 70% 1
Ƴ_st 0.65
Δf_pR (ksi) 2.4
Transfer length l_t =60*db (in) 36
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders H Stress Page: of:
Job #: NO:
Stress Calculations @ Transfer Stage* debond included
Note 1 Note 2 Note 3 Note 4 Note 5 Note 6
0 0.0 8 8 8 6 4 2 0 7.81 48.60 21.90 0 19 184 ok 359
1.0 8 8 8 6 4 2 0 7.81 48.60 21.90 632 19 184 ok 479
2.0 8 8 8 6 4 2 0 7.81 48.60 21.90 1253 18 184 ok 959
3.0 8 8 8 6 4 2 0 7.81 48.60 21.90 1862 18 184 ok 1440
dv 5.0 8 8 8 6 4 2 0 7.81 48.60 21.90 3045 18 185 ok 1442
0.1L 11.0 8 8 8 6 4 2 0 7.81 48.60 21.90 6340 17 186 ok 1450
13.0 8 8 8 6 4 2 0 7.81 48.60 21.90 7317 17 186 ok 1452
14.0 10 10 10 8 4 2 0 9.55 48.74 22.04 7799 20 182 ok 1528
15.0 10 10 10 8 4 2 0 9.55 48.74 22.04 8270 20 182 ok 1635
16.0 10 10 10 8 4 2 0 9.55 48.74 22.04 8729 20 182 ok 1742
0.2L 22.1 10 10 10 8 4 2 0 9.55 48.74 22.04 11271 19 183 ok 1749
28.0 10 10 10 8 4 2 0 9.55 48.74 22.04 13334 19 184 ok 1754
29.0 10 12 12 8 4 2 0 10.42 48.79 22.09 13642 21 182 ok 1790
30.0 10 12 12 8 4 2 0 10.42 48.79 22.09 13939 20 182 ok 1843
31.0 10 12 12 8 4 2 0 10.42 48.79 22.09 14225 20 182 ok 1897
0.3L 33.1 10 12 12 8 4 2 0 10.42 48.79 22.09 14793 20 182 ok 1898
0.4L 44.2 10 12 12 8 4 2 0 10.42 48.79 22.09 16907 20 183 ok 1905
0.5L 55.2 10 12 12 8 4 2 0 10.42 48.79 22.09 17611 19 183 ok 1907
0.6L 66.3 10 12 12 8 4 2 0 10.42 48.79 22.09 16907 20 183 ok 1905
0.7L 77.3 10 12 12 8 4 2 0 10.42 48.79 22.09 14793 20 182 ok 1898
79.4 10 12 12 8 4 2 0 10.42 48.79 22.09 14225 20 182 ok 1897
80.4 10 12 12 8 4 2 0 10.42 48.79 22.09 13939 20 182 ok 1843
81.4 10 12 12 8 4 2 0 10.42 48.79 22.09 13642 21 182 ok 1790
82.4 10 10 10 8 4 2 0 9.55 48.74 22.04 13334 19 184 ok 1754
0.8L 88.3 10 10 10 8 4 2 0 9.55 48.74 22.04 11271 19 183 ok 1749
94.4 10 10 10 8 4 2 0 9.55 48.74 22.04 8729 20 182 ok 1742
95.4 10 10 10 8 4 2 0 9.55 48.74 22.04 8270 20 182 ok 1635
96.4 10 10 10 8 4 2 0 9.55 48.74 22.04 7799 20 182 ok 1528
97.4 8 8 8 6 4 2 0 7.81 48.60 21.90 7317 17 186 ok 1452
0.9L 99.4 8 8 8 6 4 2 0 7.81 48.60 21.90 6340 17 186 ok 1450
dv 108.2 8 8 8 6 4 2 0 7.81 48.60 21.90 1410 18 184 ok 1439
107.4 8 8 8 6 4 2 0 7.81 48.60 21.90 1862 18 184 ok 1440
108.4 8 8 8 6 4 2 0 7.81 48.60 21.90 1253 18 184 ok 959
109.4 8 8 8 6 4 2 0 7.81 48.60 21.90 632 19 184 ok 479
L 110.4 8 8 8 6 4 2 0 7.81 48.60 21.90 0 19 184 ok 359
Length along
girder (ft) No. Tendon
at 2.75"
From Bot
No. Tendon
at 4.75"
from Bot
No.
Tendon at
6.75" From
Bot
No. Tendon
at 8.75"
From Bot
No. Tendon
at 10.75"
From Bot
Δf_pES
(ksi)
f_pi
(ksi)
Stress
limit for
tendon
0.8fpy
Jakcing
force
@transfer,
Pji (kip)
No. Tendon
at 12.75"
From Bot
No. Tendon
at 14.75"
From Bot
Aps(in^2)
Y_p,
Tendon
CG to Top
of Girder
(in)
e_ti (in)
Mg (kip-
in) Girder
Self
Weight
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders H Stress Page: of:
Job #: NO:
Note 1: Eccencity equal to value of Y_p minus YtNote 2: Mg is the moment caused by the self weight of the girder+ Concrete deck
Note 4:
Note 3:
Note 5: fpy assumes to be 0.9fpu; Table 5.9.3-1 AASHTO
Note 7: Top fiber concr gider stress=P/A-P*e/(I/Yt)+Mg/(I/Yb) (+ is compression, - is tension)
Note 9:
Note 6: Jakcing force @ transfer taken as f_pi multiplies Aps (Total area of tendons)
Note 8: Bot. fiber concr gider stress=P/A+P*e/(I/Yt)-Mg/(I/Yb) (+ is cpmpression, - is tension )
Note 10:
Girder top bars: #4 Total of 6, 0.2x6=1.2in^2
f_pi is the value of f_pbt minus Δf_pES. Per AASHTO C5.9.5.2.3a, if the transformed
section properties are used, the Δf_pES should not be inlcuded in the prestressing force.
In this case, jacking force is calcuated as f_pbt minus short term elastic shortening loss,
and so the Gorss section properties of the concrete girder are used.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders H Stress Page: of:
Job #: NO:
0
500
1000
1500
2000
2500
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Jakcing force @transfer, Pji (kip)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders H Stress Page: of:
Job #: NO:
Stress Calculations @ Transfer Stage
Note 7 Note 8 Note 9 Note 10
0 0.0 -0.17 0.99 4.36 -0.62 0.00 0.28 0.23 0.00
1.0 -0.19 1.27 4.36 -0.62 0.00 0.30 0.29 0.00
2.0 -0.38 2.54 4.36 -0.62 0.00 0.60 0.58 0.00
3.0 -0.56 3.81 4.36 -0.62 0.00 0.91 0.88 0.00
dv 5.0 -0.48 3.73 4.36 -0.62 0.00 0.78 0.86 0.00
0.1L 11.0 -0.25 3.50 4.36 -0.62 0.00 0.40 0.80 0.00
13.0 -0.18 3.43 4.36 -0.62 0.00 0.29 0.79 0.00
14.0 -0.20 3.62 4.36 -0.62 0.00 0.32 0.83 0.00
15.0 -0.22 3.88 4.36 -0.62 0.00 0.35 0.89 0.00
16.0 -0.24 4.14 4.36 -0.62 0.00 0.38 0.95 0.00
0.2L 22.1 -0.06 3.96 4.36 -0.62 0.00 0.10 0.91 0.00
28.0 0.09 3.82 4.36 -0.62 0.02 0.00 0.88 0.00
29.0 0.08 3.90 4.36 -0.62 0.02 0.00 0.90 0.00
30.0 0.08 4.03 4.36 -0.62 0.02 0.00 0.93 0.00
31.0 0.07 4.16 4.36 -0.62 0.02 0.00 0.95 0.00
0.3L 33.1 0.11 4.12 4.36 -0.62 0.03 0.00 0.95 0.00
0.4L 44.2 0.26 3.97 4.36 -0.62 0.06 0.00 0.91 0.00
0.5L 55.2 0.31 3.93 4.36 -0.62 0.07 0.00 0.90 0.00
0.6L 66.3 0.26 3.97 4.36 -0.62 0.06 0.00 0.91 0.00
0.7L 77.3 0.11 4.12 4.36 -0.62 0.03 0.00 0.95 0.00
79.4 0.07 4.16 4.36 -0.62 0.02 0.00 0.95 0.00
80.4 0.08 4.03 4.36 -0.62 0.02 0.00 0.93 0.00
81.4 0.08 3.90 4.36 -0.62 0.02 0.00 0.90 0.00
82.4 0.09 3.82 4.36 -0.62 0.02 0.00 0.88 0.00
0.8L 88.3 -0.06 3.96 4.36 -0.62 0.00 0.10 0.91 0.00
94.4 -0.24 4.14 4.36 -0.62 0.00 0.38 0.95 0.00
95.4 -0.22 3.88 4.36 -0.62 0.00 0.35 0.89 0.00
96.4 -0.20 3.62 4.36 -0.62 0.00 0.32 0.83 0.00
97.4 -0.18 3.43 4.36 -0.62 0.00 0.29 0.79 0.00
0.9L 99.4 -0.25 3.50 4.36 -0.62 0.00 0.40 0.80 0.00
dv 108.2 -0.60 3.84 4.36 -0.62 0.00 0.96 0.88 0.00
107.4 -0.56 3.81 4.36 -0.62 0.00 0.91 0.88 0.00
108.4 -0.38 2.54 4.36 -0.62 0.00 0.60 0.58 0.00
109.4 -0.19 1.27 4.36 -0.62 0.00 0.30 0.29 0.00
L 110.4 -0.17 0.99 4.36 -0.62 0.00 0.28 0.23 0.00
Max: 0.07 0.96 0.95 0.00
f_bot (ksi) (comp limit
0.65f'ci)
(Ten limit -
0.24*sqrt(f
'ci) ksi)
f_top f_bot
D/C ratio
(comp
limit )
D/C
ratio(Ten
limit )
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit )
Length
along
girder (ft)
f_top
(ksi)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders H Stress Page: of:
Job #: NO:
For the stress calc, negative stress is tensile stress; positive stress is compressive stress.
Stress Calculations @ Transfer Stage
Tendons f_pu (ksi) 270
Tendon f_pbt (ksi) 203 (AASHTO Table 5.9.3.1)
Tendon E_ps (ksi) 28500
Girder Concrete E_pc (ksi) 5154
n'-1 = E_ps/ E_pc -1 5
f'c (ksi) 8
f'ci (ksi) 6.7
CA BT 55, Ag (in^2) 925
CA BT 55, w (k/ft) 1
CA BT 55, Yt, CG to Top (in) 27
CA BT 55, Yb, CG to Bot (in) 28
CA BT 55, Ig (in^4) 373350
Ƴ_h Say H= 70% 1
Ƴ_st 0.65
Δf_pR (ksi) 2.4
Transfer length l_t =60*db (in) 36
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders H Stress Page: of:
Job #: NO:
Stress Calculations @ PS + Perm load condition Transformed seciton properties
Note 1 Note 2 Note 3 Note 4 Note 5 Note 6 Note 7 Note 8
0 0.0 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
1.0 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
2.0 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
3.0 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
dv 5.0 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
0.1L 11.0 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
13.0 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
14.0 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
15.0 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
16.0 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
0.2L 22.1 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
28.0 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
29.0 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
30.0 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
31.0 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
0.3L 33.1 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
0.4L 44.2 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
0.5L 55.2 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
0.6L 66.3 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
0.7L 77.3 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
79.4 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
80.4 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
81.4 10.42 48.79 47.19 972 373350 27000 27.77223 27 21911 395261 14232 14450
82.4 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
0.8L 88.3 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
94.4 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
95.4 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
96.4 9.55 48.74 43.25 968 373350 26806 27.6845 27 20070 393420 14211 14337
97.4 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
0.9L 99.4 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
dv 108.2 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
107.4 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
108.4 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
109.4 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
L 110.4 7.81 48.60 35.39 960 373350 26417 27.50689 28 16343 389693 14167 14110
Transfor
med
Y_ttop
(in)
Transfor
med
Y_tbot
(in)
Ʃ Ai*(Y_i-
Y_ttop)^
2
(in^4)
I_final(in
^4)
Transfor
med
S_ttop
(in^3)
Transfor
med
S_tbot
(in^3)
Total
Aps*(n-
1)+Ag
(in^2) Ig (in^4)
ƩAi*Y_i
(in^3)
Length
along
girder
(ft) Aps(in^
2)
Y_p,
Tendon CG
to
GirderTop
(in)
Aps*(n'-
1)
(in^2)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders H Stress Page: of:
Job #: NO:
Note 1: Ignore moment of inertia I from prestrssing tendons, since it is too small compared to that of precast concrete Girder.
Note 2: Summation of tranformed strands area times CG of strands, and area of precast concrete girder times CG of the girder.
Note 3: Values of Note 2 divide by the total area of the transformed section to determine CG of the tranformed section (from top of the section)
Note 4: CG of the tranformed seciton (from bottom of the section)
Note 5:
Note 6: I_final =Ig + values at Note 5
Note 7: Transformed section modulus from top of seciton is I_final divide by Transformed Y_ttop
Note 8: Transformed section modulus from bottom of seciton is I_final divide by Transformed Y_tbot
Summation of tranformed area of strands times squrea of CG differenec between strands and the entire tranformed section, plus such value
for precast concrete girder component.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders H Stress Page: of:
Job #: NO:
Stress Calculations @ PS + Perm load condition * debond included
Note 9 Note 10 Note 11 Note 12 Note 13 Note 14 Note 15 Note 16
0 0.0 21 21 181 354 0 -0.16 0.90 3.60 -0.54 0.00 0.29 0.25 0.00
1.0 21 21 181 472 1405 -0.11 1.10 3.60 -0.54 0.00 0.21 0.30 0.00
2.0 21 21 181 944 2784 -0.23 2.20 3.60 -0.54 0.00 0.42 0.61 0.00
3.0 21 21 181 1416 4138 -0.34 3.30 3.60 -0.54 0.00 0.64 0.92 0.00
dv 5.0 21 21 181 1416 6768 -0.16 3.11 3.60 -0.54 0.00 0.29 0.86 0.00
0.1L 11.0 21 21 181 1416 14090 0.36 2.59 3.60 -0.54 0.10 0.00 0.72 0.00
13.0 21 21 181 1416 16262 0.51 2.44 3.60 -0.54 0.14 0.00 0.68 0.00
14.0 21 24 179 1500 17333 0.55 2.54 3.60 -0.54 0.15 0.00 0.71 0.00
15.0 21 24 179 1603 18379 0.57 2.73 3.60 -0.54 0.16 0.00 0.76 0.00
16.0 21 24 179 1707 19399 0.60 2.92 3.60 -0.54 0.17 0.00 0.81 0.00
0.2L 22.1 21 24 179 1707 25049 1.00 2.52 3.60 -0.54 0.28 0.00 0.70 0.00
28.0 21 24 179 1707 29633 1.32 2.20 3.60 -0.54 0.37 0.00 0.61 0.00
29.0 21 25 178 1746 30319 1.35 2.24 3.60 -0.54 0.37 0.00 0.62 0.00
30.0 21 25 178 1797 30979 1.37 2.32 3.60 -0.54 0.38 0.00 0.64 0.00
31.0 21 25 178 1849 31614 1.39 2.40 3.60 -0.54 0.39 0.00 0.67 0.00
0.3L 33.1 21 25 178 1849 32877 1.48 2.32 3.60 -0.54 0.41 0.00 0.64 0.00
0.4L 44.2 21 25 178 1849 37574 1.81 1.99 3.60 -0.54 0.50 0.00 0.55 0.00
0.5L 55.2 21 25 178 1849 39139 1.92 1.88 3.60 -0.54 0.53 0.00 0.52 0.00
0.6L 66.3 21 25 178 1849 37574 1.81 1.99 3.60 -0.54 0.50 0.00 0.55 0.00
0.7L 77.3 21 25 178 1849 32877 1.48 2.32 3.60 -0.54 0.41 0.00 0.64 0.00
79.4 21 25 178 1849 31614 1.39 2.40 3.60 -0.54 0.39 0.00 0.67 0.00
80.4 21 25 178 1797 30979 1.37 2.32 3.60 -0.54 0.38 0.00 0.64 0.00
81.4 21 25 178 1746 30319 1.35 2.24 3.60 -0.54 0.37 0.00 0.62 0.00
82.4 21 24 179 1707 29633 1.32 2.20 3.60 -0.54 0.37 0.00 0.61 0.00
0.8L 88.3 21 24 179 1707 25049 1.00 2.52 3.60 -0.54 0.28 0.00 0.70 0.00
94.4 21 24 179 1707 19399 0.60 2.92 3.60 -0.54 0.17 0.00 0.81 0.00
95.4 21 24 179 1603 18379 0.57 2.73 3.60 -0.54 0.16 0.00 0.76 0.00
96.4 21 24 179 1500 17333 0.55 2.54 3.60 -0.54 0.15 0.00 0.71 0.00
97.4 21 21 181 1416 16262 0.51 2.44 3.60 -0.54 0.14 0.00 0.68 0.00
0.9L 99.4 21 21 181 1416 14090 0.36 2.59 3.60 -0.54 0.10 0.00 0.72 0.00
dv 108.2 21 21 181 1416 3134 -0.41 3.37 3.60 -0.54 0.00 0.77 0.94 0.00
107.4 21 21 181 1416 4138 -0.34 3.30 3.60 -0.54 0.00 0.64 0.92 0.00
108.4 21 21 181 944 2784 -0.23 2.20 3.60 -0.54 0.00 0.42 0.61 0.00
109.4 21 21 181 472 1405 -0.11 1.10 3.60 -0.54 0.00 0.21 0.30 0.00
L 110.4 21 21 181 354 0 -0.16 0.90 3.60 -0.54 0.00 0.29 0.25 0.00
Max: 0.53 0.77 0.94 0.00
f_top
(ksi)
f_Bot
(ksi)
Compres
sive
Stress
limit (ksi)
Tensile
Stress
limit (ksi)
f_top f_bot
D/C ratio
(comp limit)
D/C
ratio(Ten
limit)
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit)
Length
along
girder
(ft)
e (in)Δf_pLT
(ksi)fpe (ksi) Pf (kiP)
Moment
demands
DC1+DC2
(kip-in)
PS+ Perm (DC1+DC2)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders H Stress Page: of:
Job #: NO:
Note 9: Eccentricity of the seciton is Y_p(in) from girder top subtracted by Transformed Y_ttop
Note 10
Note 11 fpe is stress at transfer minus long term loss Δf_pLT
Note 12 Prestressing force Pf, is fpe times area of the prestressing tendons, Aps.
Note 13
Note 14
Note 15
Note 16:
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders H Stress Page: of:
Job #: NO:
Tendons f_pu (ksi) 270
Tendon f_pbt (ksi) 202.5 (AASHTO Table 5.9.3.1)
CA BT 55, Ag (in^2) 925
CA BT 55, w (k/ft) 0.963
CA BT 55, Yt, CG to Top (in) 26.7
CA BT 55, Yb, CG to Bot (in) 28.4
CA BT 55, Ig (in^4) 373350
Tendon E_ps (ksi) 28,500
Girder Concrete E_pc (ksi) 5,154
n'-1 = E_ps/ E_pc -1 5
Girder f'c (ksi) 8
Girder f'ci (ksi) 6.7
Deck Concrete E_c (ksi) 4,074
Girder Concrete E_pc (ksi) 5,154
n= E_c/E_pc 0.79
CIP Deck f'c (ksi) 5
Deck effective width (ft) 9.08
Depth of concrete slab, ts (in) 8.00
Precast panel thickness (in) 3.50
Tranformed deck area (in^2) 768.74 (based on Ec of 8ksi concrete)
Tranformed effective deck width (in) 96.093 (based on Ec of 8ksi concrete)
Transfer length l_t =60*db (in) 36
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders H Stress Page: of:
Job #: NO:
Stress Calculations @ Service, composite section properties include the Deck Slab
Note 1
0 0 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 354
1 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 472
2 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 944
3 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
dv 5 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
0.1L 11 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
13 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
14 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1500
15 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1603
16 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1707
0.2L 22 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1707
28 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1707
29 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1746
30 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1797
31 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
0.3L 33 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
0.4L 44 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
0.5L 55 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
0.6L 66 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
0.7L 77 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
79 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1849
80 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1797
81 395261 27.77 27.35 769 1741 37852 22 41 828618 60296 20023 21 25 178 1746
82 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1707
0.8L 88 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1707
94 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1707
95 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1603
96 393420 27.68 27.44 769 1737 37627 22 41 823615 60286 19864 21 24 179 1500
97 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
0.9L 99 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
dv 108 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
107 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 1416
108 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 944
109 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 472
L 110 389693 27.51 27.62 769 1729 37175 21 42 813543 60265 19544 21 21 181 354
e (in)
Δf_pLT
(ksi)
fpe
(ksi)
Pf
(kiP)
Yi to Top
of Deck
ƩAi*Y_i
(in^3)
Comp
Y_ttop
(in)
ToDec
kTop
Comp.
Y_tbot
(in)
I_comp
(in^4)
Comp.
S_tg
(in^3)
Comp S_tb
(in^3)
Length
along
girder (ft)
I_tg(in^4)Transformed
Y_ttop (in)
Transfor
med
Y_tbot
(in)
Tranfor
med
A_deck
(in^2)
A_deck+A
ps*(n'-
1)+Ag
(in^2)
From PS+Perm stress calc
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders H Stress Page: of:
Job #: NO:
Stress Calculations @ Service, composite section properties include the Deck Slab
* debond included Note 2 Note 3 Note 4
0 0.0 0 0 0 0 -0.16 0.90 4.80 -0.54 0.00 0.29 0.19 0.00
1.0 1405 342 24 1104 -0.09 1.02 4.80 -0.54 0.00 0.16 0.21 0.00
2.0 2784 678 48 2188 -0.18 2.05 4.80 -0.54 0.00 0.33 0.43 0.00
3.0 4138 1008 72 3252 -0.27 3.07 4.80 -0.54 0.00 0.50 0.64 0.00
dv 5.0 6768 1649 120 5318 -0.04 2.75 4.80 -0.54 0.00 0.07 0.57 0.00
0.1L 11.0 14090 3432 266 11072 0.61 1.84 4.80 -0.54 0.13 0.00 0.38 0.00
13.0 16262 3961 313 12778 0.80 1.56 4.80 -0.54 0.17 0.00 0.33 0.00
14.0 17333 4222 337 13620 0.85 1.63 4.80 -0.54 0.18 0.00 0.34 0.00
15.0 18379 4477 361 14442 0.89 1.76 4.80 -0.54 0.19 0.00 0.37 0.00
16.0 19399 4726 385 15243 0.94 1.89 4.80 -0.54 0.20 0.00 0.39 0.00
0.2L 22.1 25049 6102 532 19683 1.43 1.20 4.80 -0.54 0.30 0.00 0.25 0.00
28.0 29633 7219 674 23285 1.84 0.63 4.80 -0.54 0.38 0.00 0.13 0.00
29.0 30319 7386 698 23824 1.88 0.64 4.80 -0.54 0.39 0.00 0.13 0.00
30.0 30979 7547 722 24343 1.91 0.69 4.80 -0.54 0.40 0.00 0.14 0.00
31.0 31614 7701 746 24841 1.94 0.74 4.80 -0.54 0.41 0.00 0.15 0.00
0.3L 33.1 32877 8009 798 25834 2.06 0.59 4.80 -0.54 0.43 0.00 0.12 0.00
0.4L 44.2 37574 9153 1063 29525 2.47 0.01 4.80 -0.54 0.51 0.00 0.00 0.00
0.5L 55.2 39139 9534 1329 30755 2.61 -0.20 4.80 -0.54 0.54 0.00 0.00 0.36
0.6L 66.3 37574 9153 1063 29525 2.47 0.01 4.80 -0.54 0.51 0.00 0.00 0.00
0.7L 77.3 32877 8009 798 25834 2.06 0.59 4.80 -0.54 0.43 0.00 0.12 0.00
79.4 31614 7701 746 24841 1.94 0.74 4.80 -0.54 0.41 0.00 0.15 0.00
80.4 30979 7547 722 24343 1.91 0.69 4.80 -0.54 0.40 0.00 0.14 0.00
81.4 30319 7386 698 23824 1.88 0.64 4.80 -0.54 0.39 0.00 0.13 0.00
82.4 29633 7219 674 23285 1.84 0.63 4.80 -0.54 0.38 0.00 0.13 0.00
0.8L 88.3 25049 6102 532 19683 1.43 1.20 4.80 -0.54 0.30 0.00 0.25 0.00
94.4 19399 4726 385 15243 0.94 1.89 4.80 -0.54 0.20 0.00 0.39 0.00
95.4 18379 4477 361 14442 0.89 1.76 4.80 -0.54 0.19 0.00 0.37 0.00
96.4 17333 4222 337 13620 0.85 1.63 4.80 -0.54 0.18 0.00 0.34 0.00
97.4 16262 3961 313 12778 0.80 1.56 4.80 -0.54 0.17 0.00 0.33 0.00
0.9L 99.4 14090 3432 266 11072 0.61 1.84 4.80 -0.54 0.13 0.00 0.38 0.00
dv 108.2 3134 764 54 2463 -0.36 3.20 4.80 -0.54 0.00 0.67 0.67 0.00
107.4 4138 1008 72 3252 -0.27 3.07 4.80 -0.54 0.00 0.50 0.64 0.00
108.4 2784 678 48 2188 -0.18 2.05 4.80 -0.54 0.00 0.33 0.43 0.00
109.4 1405 342 24 1104 -0.09 1.02 4.80 -0.54 0.00 0.16 0.21 0.00
L 110.4 0 0 0 0 -0.16 0.90 4.80 -0.54 0.00 0.29 0.19 0.00
Max: 0.54 0.67 0.67 0.36
Tensile
Stress
limit (ksi)
f_top f_bot
D/C ratio
(comp limit)
D/C
ratio(Ten
limit)
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit)
Moment
demands
DC3+DW (kip-
in)
Moment demands
DC4 (kip-in)
Moment
demands
LL(1+IM) (kip-
in)
f_top (ksi) f_Bot (ksi)Compressive
Stress limit (ksi)
Length
along
girder
(ft)
Moment
demands
DC1+DC2
(kip-in)
Service I : PS+Perm+LL*(1+IM)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders H Stress Page: of:
Job #: NO:
Note 1:
Note 2
f_bot SIM.
Note 3
Note 4
Check the stress to top of girder, so section modulus of the composite section, is the I_comp / y_tg, and y_tg
is the distance from comp. nuetral axis to the top of the girder.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders H Stress Page: of:
Job #: NO:
0 0.0 0 -0.16 0.90 4.80 -0.54 0.00 0.29 0.19 0.00
1.0 883 -0.09 1.03 4.80 -0.54 0.00 0.17 0.22 0.00
2.0 1750 -0.18 2.07 4.80 -0.54 0.00 0.34 0.43 0.00
3.0 2601 -0.28 3.11 4.80 -0.54 0.00 0.52 0.65 0.00
dv 5.0 4255 -0.06 2.80 4.80 -0.54 0.00 0.10 0.58 0.00
0.1L 11.0 8857 0.57 1.95 4.80 -0.54 0.12 0.00 0.41 0.00
13.0 10223 0.76 1.70 4.80 -0.54 0.16 0.00 0.35 0.00
14.0 10896 0.80 1.76 4.80 -0.54 0.17 0.00 0.37 0.00
15.0 11553 0.85 1.90 4.80 -0.54 0.18 0.00 0.40 0.00
16.0 12194 0.89 2.04 4.80 -0.54 0.18 0.00 0.43 0.00
0.2L 22.1 15746 1.37 1.39 4.80 -0.54 0.29 0.00 0.29 0.00
28.0 18628 1.76 0.87 4.80 -0.54 0.37 0.00 0.18 0.00
29.0 19059 1.80 0.88 4.80 -0.54 0.37 0.00 0.18 0.00
30.0 19474 1.83 0.93 4.80 -0.54 0.38 0.00 0.19 0.00
31.0 19873 1.86 0.99 4.80 -0.54 0.39 0.00 0.21 0.00
0.3L 33.1 20667 1.97 0.84 4.80 -0.54 0.41 0.00 0.18 0.00
0.4L 44.2 23620 2.37 0.30 4.80 -0.54 0.49 0.00 0.06 0.00
0.5L 55.2 24604 2.51 0.11 4.80 -0.54 0.52 0.00 0.02 0.00
0.6L 66.3 23620 2.37 0.30 4.80 -0.54 0.49 0.00 0.06 0.00
0.7L 77.3 20667 1.97 0.84 4.80 -0.54 0.41 0.00 0.18 0.00
79.4 19873 1.86 0.99 4.80 -0.54 0.39 0.00 0.21 0.00
80.4 19474 1.83 0.93 4.80 -0.54 0.38 0.00 0.19 0.00
81.4 19059 1.80 0.88 4.80 -0.54 0.37 0.00 0.18 0.00
82.4 18628 1.76 0.87 4.80 -0.54 0.37 0.00 0.18 0.00
0.8L 88.3 15746 1.37 1.39 4.80 -0.54 0.29 0.00 0.29 0.00
94.4 12194 0.89 2.04 4.80 -0.54 0.18 0.00 0.43 0.00
95.4 11553 0.85 1.90 4.80 -0.54 0.18 0.00 0.40 0.00
96.4 10896 0.80 1.76 4.80 -0.54 0.17 0.00 0.37 0.00
97.4 10223 0.76 1.70 4.80 -0.54 0.16 0.00 0.35 0.00
0.9L 99.4 8857 0.57 1.95 4.80 -0.54 0.12 0.00 0.41 0.00
dv 108.2 1970 -0.37 3.22 4.80 -0.54 0.00 0.68 0.67 0.00
107.4 2601 -0.28 3.11 4.80 -0.54 0.00 0.52 0.65 0.00
108.4 1750 -0.18 2.07 4.80 -0.54 0.00 0.34 0.43 0.00
109.4 883 -0.09 1.03 4.80 -0.54 0.00 0.17 0.22 0.00
L 110.4 0 -0.16 0.90 4.80 -0.54 0.00 0.29 0.19 0.00
Max: 0.52 0.68 0.67 0.00
f_Bot (ksi)
Compressiv
e Stress
limit (ksi)
Tensile
Stress limit
(ksi)
f_top f_bot
D/C ratio
(comp limit)
D/C ratio(Ten
limit)
D/C ratio
(comp
limit)
D/C
ratio(Ten
limit)
Length along
girder (ft)
Moment
demands
0.8*LL(1+IM
) (kip-in)
f_top (ksi)
Service III : PS+Perm+0.8*LL*(1+IM)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/12/20
Subject: Design Calculations Checked: CL Date: 4/20/20
Task: Girders H Stress Page: of:
Job #: NO:
REQUIRED TOP REINFORCEMENT
0 0.0 -0.17 0.99 8.27 34.00 1.13 3
1.0 -0.19 1.27 7.09 31.32 1.04 3
2.0 -0.38 2.54 7.10 62.96 2.10 5
3.0 -0.56 3.81 7.11 94.93 3.16 8
dv 5.0 -0.48 3.73 6.30 71.71 2.39 6
0.1L 11.0 -0.25 3.50 3.67 21.64 0.72 2
13.0 -0.18 3.43 2.76 11.78 0.39 1
14.0 -0.20 3.62 2.87 13.47 0.45 2
15.0 -0.22 3.88 2.93 15.09 0.50 2
16.0 -0.24 4.14 3.00 16.84 0.56 2
0.2L 22.1 -0.06 3.96 0.82 1.15 0.04 1
28.0 0.09 3.82 0.00 0.00 0.00 0
29.0 0.08 3.90 0.00 0.00 0.00 0
30.0 0.08 4.03 0.00 0.00 0.00 0
31.0 0.07 4.16 0.00 0.00 0.00 0
0.3L 33.1 0.11 4.12 0.00 0.00 0.00 0
0.4L 44.2 0.26 3.97 0.00 0.00 0.00 0
0.5L 55.2 0.31 3.93 0.00 0.00 0.00 0
0.6L 66.3 0.26 3.97 0.00 0.00 0.00 0
0.7L 77.3 0.11 4.12 0.00 0.00 0.00 0
79.4 0.07 4.16 0.00 0.00 0.00 0
80.4 0.08 4.03 0.00 0.00 0.00 0
81.4 0.08 3.90 0.00 0.00 0.00 0
82.4 0.09 3.82 0.00 0.00 0.00 0
0.8L 88.3 -0.06 3.96 0.82 1.15 0.04 1
94.4 -0.24 4.14 3.00 16.84 0.56 2
95.4 -0.22 3.88 2.93 15.09 0.50 2
96.4 -0.20 3.62 2.87 13.47 0.45 2
97.4 -0.18 3.43 2.76 11.78 0.39 1
0.9L 99.4 -0.25 3.50 3.67 21.64 0.72 2
dv 108.2 -0.60 3.84 7.41 104.41 3.48 8
107.4 -0.56 3.81 7.11 94.93 3.16 8
108.4 -0.38 2.54 7.10 62.96 2.10 5
109.4 -0.19 1.27 7.09 31.32 1.04 3
L 110.4 -0.17 0.99 8.27 34.00 1.13 3
f_ci,top (ksi) f_ci,bot (ksi) x (in) T (kip) As (in^2)
# 6 rebars
(in^2)
Length along
girder (ft)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
Shear Demands Calculations
0 0.0 54 67 11 2 134 19 0 -124 121
dv 5.0 50 61 10 2 122 17 2 -119 116
0.1L 11.3 44 53 9 2 108 15 5 -101 99
0.2L 22.6 33 40 7 2 81 11 14 -86 84
0.3L 33.9 22 27 4 2 55 7 25 -71 69
0.4L 45.3 11 13 2 2 28 4 37 -57 55
0.5L 56.6 0 0 0 2 2 0 50 -43 42
0.6L 67.9 -11 -13 -2 2 -24 -4 64 -31 30
0.7L 79.2 -22 -27 -4 2 -51 -7 78 -19 18
0.8L 90.5 -33 -40 -7 2 -77 -11 93 -9 8
0.9L 101.8 -44 -53 -9 2 -104 -15 109 -2 2
dv 108.2 -50 -61 -10 2 -118 -17 119 -1 1
L 113.2 -54 -67 -11 2 -130 -19 124 0 0
18
-62
-76
-91
Length along
girder (ft)
max min D.F. MinV (kip) DC3 V (kip) DC4
V (kip)
DC Total
V (kip)
DWV (kip) DC1 V (kip) DC2
-116
D.F. Max
-121
-49
-107
0
-2
(HL-93) LL+IM-V (kip)
For Each Girder
-5
-13
-24
-36
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
Shear Capacity Calculations 5.8.3.4.2 General procedure As=0, Vp=0, f_po=0.7 f_pu, Nu=0 .
Note 1 Note 2 Note 3
0 0.0 56.2 53 -0.0014 0.1779 24.7000 2.6300 99 3 0.62
dv 5.0 56.2 53 -0.0019 0.1615 23.2000 2.7300 103 4 0.62
0.1L 11.3 56.2 53 -0.0005 0.1354 27.2146 7.7744 292 4 0.62
0.2L 22.6 56.4 53 0.0008 0.1058 31.6500 3.0615 114 6 0.62
0.3L 33.9 56.5 53 0.0016 0.0781 34.7502 2.1504 80 8 0.62
0.4L 45.3 56.5 53 0.0024 0.0532 37.5130 1.6996 63 8 0.62
0.5L 56.6 56.5 53 0.0026 0.0340 38.0530 1.6327 61 10 0.62
0.6L 67.9 56.5 53 0.0025 0.0584 37.7167 1.6737 62 8 0.62
0.7L 79.2 56.5 53 0.0017 0.0849 35.0190 2.0963 78 8 0.62
0.8L 90.5 56.4 53 0.0008 0.1128 31.9492 2.9412 110 6 0.62
0.9L 101.8 56.2 53 -0.0004 0.1439 27.6540 6.7457 254 4 0.62
dv 108.2 56.2 53 -0.0019 0.1601 23.2000 2.7300 103 4 0.62
L 113.2 56.2 53 -0.0014 0.1765 24.7000 2.6300 99 3 0.62
Ignore harped tendons contribution to shear capacity; it is conservative to do so. Stirup Design, use 2-leg # 5 0.62 in^2
bv=bw= 7.875 in
Note 1:
Note 2:
Note 3:
Length
along
girder (ft) de(in) dv (in) ϵ_s v_u/f'c θ ß Vc(kip)
Table B5.2.1 & 5.8.3.4.2s(transv.
Reinf
space, in)
Stirup Area,
Av (in^2)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
Note 4 Note 5
0 0.0 134 19 0.0 -247.1 0 241 1440 1539 841 841
dv 5.0 122 17 3.4 -223.8 -3 219 1159 1262 841 841
0.1L 11.3 108 15 6.7 -183.3 -7 179 966 1258 841 841
0.2L 22.6 81 11 16.3 -145.8 -16 142 534 648 836 648
0.3L 33.9 55 7 29.8 -112.1 -29 109 354 434 833 434
0.4L 45.3 28 4 48.8 -84.1 -48 82 320 383 833 383
0.5L 56.6 2 0 70.6 -58.9 -69 58 251 312 833 312
0.6L 67.9 -24 -4 97.6 -38.7 -95 38 318 380 833 380
0.7L 79.2 -51 -7 128.9 -23.0 -126 22 351 429 833 429
0.8L 90.5 -77 -11 163.0 -10.1 -159 10 528 637 836 637
0.9L 101.8 -104 -15 203.5 -3.4 -199 3 948 1202 841 841
dv 108.2 -118 -17 223.7 -2.9 -219 3 1159 1262 841 841
L 113.2 -130 -19 247.1 0.0 -241 0 1440 1539 841 841
Note 4:
Note 5:
(P-15) LL+IM-V (kip)
Final Vn
(kip)
V (kip) DC
Total
V (kip)
DW min D.F. Min Vs (kip) Vc+Vs (kip)
Length
along
girder
(ft)
max D.F. Max 0.25*f'c*b
v*dv (kip)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
0 0.0 757 195 408 408 195 618 618 -757 757 0.54 0.82
dv 5.0 757 175 381 381 173 561 561 -757 757 0.50 0.74
0.1L 11.3 757 149 330 330 145 470 470 -757 757 0.44 0.62
0.2L 22.6 583 95 265 265 90 368 368 -583 583 0.45 0.63
0.3L 33.9 391 38 201 201 29 271 271 -391 391 0.51 0.69
0.4L 45.3 345 -22 138 138 -42 185 185 -345 345 0.40 0.54
0.5L 56.6 281 -83 77 -83 -118 103 -118 -281 281 0.30 0.42
0.6L 67.9 342 -145 16 -145 -203 30 -203 -342 342 0.42 0.59
0.7L 79.2 386 -208 -43 -208 -295 -35 -295 -386 386 0.54 0.76
0.8L 90.5 574 -273 -99 -273 -392 -96 -392 -574 574 0.48 0.68
0.9L 101.8 757 -339 -148 -339 -500 -146 -500 -757 757 0.45 0.66
dv 108.2 757 -376 -171 -376 -556 -168 -556 -757 757 0.50 0.73
L 113.2 757 -403 -190 -403 -613 -190 -613 -757 757 0.53 0.81
Strength II
D/C
Vu-Min (kip)
Strength II
Vu-Max
(kip)
Strength II
Vu (kip)
Strength II-1* φVn(kip) φVn(kip)
Vu-Min
(kip)
Strength I
Vu-Max (kip)
Strength I
Vu (kip)
Strength I
Length
along
girder
(ft)
φVn
(kip)
For Each Girder
Strength
I D/C
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
-1000
-800
-600
-400
-200
0
200
400
600
800
1000
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Sh
ea
r (k
ip)
Length (ft)
Shear Plot along Span Length
-1* φVn(kip) φVn(kip) Vu (kip) Strength I Vu (kip) Strength II
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
Say conservatively put obtuse agle distributed factor for all, and check if the stirup arrangement will work.
Shear Demands Calculations
0 0.0 54 67 11 2 134 19 0 -124 133
dv 5.0 50 61 10 2 122 17 2 -119 127
0.1L 11.3 44 53 9 2 108 15 5 -101 108
0.2L 22.6 33 40 7 2 81 11 14 -86 92
0.3L 33.9 22 27 4 2 55 7 25 -71 76
0.4L 45.3 11 13 2 2 28 4 37 -57 61
0.5L 56.6 0 0 0 2 2 0 50 -43 46
0.6L 67.9 -11 -13 -2 2 -24 -4 64 -31 33
0.7L 79.2 -22 -27 -4 2 -51 -7 78 -19 20
0.8L 90.5 -33 -40 -7 2 -77 -11 93 -9 9
0.9L 101.8 -44 -53 -9 2 -104 -15 109 -2 2
dv 108.2 -50 -61 -10 2 -118 -17 119 -1 1
L 113.2 -54 -67 -11 2 -130 -19 124 0 0-133
0
-2
-5
-14
-26
-39
-53
-68
-100
-84
-117
-127
D.F. Min
(HL-93) LL+IM-V (kip)
D.F. Maxmax min
Length along
girder (ft)
For Each Girder
V (kip) DC1 V (kip) DC2 V (kip) DC3V (kip)
DC Total
V (kip)
DWV (kip) DC4
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
0 0.0 134 19 0.0 -247.1 0 264
dv 5.0 122 17 3.4 -223.8 -4 239
0.1L 11.3 108 15 6.7 -183.3 -7 196
0.2L 22.6 81 11 16.3 -145.8 -17 156
0.3L 33.9 55 7 29.8 -112.1 -32 120
0.4L 45.3 28 4 48.8 -84.1 -52 90
0.5L 56.6 2 0 70.6 -58.9 -75 63
0.6L 67.9 -24 -4 97.6 -38.7 -104 41
0.7L 79.2 -51 -7 128.9 -23.0 -138 25
0.8L 90.5 -77 -11 163.0 -10.1 -174 11
0.9L 101.8 -104 -15 203.5 -3.4 -217 4
dv 108.2 -118 -17 223.7 -2.9 -239 3
L 113.2 -130 -19 247.1 0.0 -264 0
Length
along
girder
(ft)
V (kip) DC
Total
V (kip)
DW max min D.F. Min D.F. Max
(P-15) LL+IM-V (kip)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
Shear Demands & Capacity D/C ratio
0 0.0 757 195 427 427 195 658 658 -757 757 0.56 0.87
dv 5.0 757 174 400 400 172 597 597 -757 757 0.53 0.79
0.1L 11.3 757 148 346 346 144 500 500 -757 757 0.46 0.66
0.2L 22.6 583 93 278 278 88 391 391 -583 583 0.48 0.67
0.3L 33.9 391 34 212 212 24 289 289 -391 391 0.54 0.74
0.4L 45.3 345 -28 147 147 -50 198 198 -345 345 0.43 0.57
0.5L 56.6 281 -91 84 -91 -130 113 -130 -281 281 0.32 0.46
0.6L 67.9 342 -155 21 -155 -219 36 -219 -342 342 0.45 0.64
0.7L 79.2 386 -221 -40 -221 -316 -32 -316 -386 386 0.57 0.82
0.8L 90.5 574 -288 -97 -288 -418 -94 -418 -574 574 0.50 0.73
0.9L 101.8 757 -356 -147 -356 -532 -145 -532 -757 757 0.47 0.70
dv 108.2 757 -395 -171 -395 -592 -168 -592 -757 757 0.52 0.78
L 113.2 757 -422 -190 -422 -653 -190 -653 -757 757 0.56 0.86
For Each Girder
Length
along
girder
(ft)
Vu-Min
(kip)
Strength I
Vu-Max (kip)
Strength I
Vu (kip)
Strength I
Vu-Min (kip)
Strength II
Vu-Max
(kip)
Strength II
Vu (kip)
Strength II-1* φVn(kip) φVn(kip)
Strength
I D/C
Strength II
D/C
φVn
(kip)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 3/20/20
Subject: Design Calculations Checked: CL Date: 4/14/20
Task: Girders A Design Page: of:
Job #: NO:
-1000
-800
-600
-400
-200
0
200
400
600
800
1000
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Sh
ea
r (k
ip)
Length (ft)
Shear Plot along Span Length
Vu (kip) Strength II φVn(kip) -1* φVn(kip)
3.1.2 Girder Camber and Deflection
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Using AVG girder
spacing Girder A Girder B Girder C Girder D Girder E Girder F Girder G Girder H
CL Brg to CL brg length
(ft)113.19 112.78 112.38 111.98 111.58 111.19 110.80 110.42
Deck thk (in) 8.50 8.00 8.00 8.00 8.00 8.00 8.00 8.50
Haunch thk (in) 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00
Tributary deck width (ft)8.90 9.70 9.70 9.70 9.70 9.70 9.70 8.90
Haunch (klf) 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10
Deck slab (klf) 0.98 1.00 1.00 1.00 1.00 1.00 1.00 0.98
sum (klf) 1.08 1.10 1.10 1.10 1.10 1.10 1.10 1.08
Diaphramg (kip) 2.29 4.59 4.59 4.59 4.59 4.59 4.59 2.29
Ec (ksi) 5,154 5,154 5,154 5,154 5,154 5,154 5,154 5,154
CABT55 I_g (in^4) 373,350 373,350 373,350 373,350 373,350 373,350 373,350 373,350
∆_slab+haunch (in) 2.07 2.09 2.06 2.03 2.00 1.97 1.95 1.88
∆_diaphragm (in) 0.06 0.12 0.12 0.12 0.12 0.12 0.12 0.06
∆_deck (in) 2.13 2.21 2.18 2.15 2.12 2.09 2.06 1.93
Barrier distr. % 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25
Barrier +railing+median
(klf) 0.775 0.775 0.775 0.775 0.775 0.775 0.775 0.775
I_comp (in^4) 814,836 814,836 814,836 814,836 814,836 814,836 814,836 814,836
∆_rail (in) 0.17 0.17 0.17 0.16 0.16 0.16 0.16 0.15
DW (klf) 0.31 0.34 0.34 0.34 0.34 0.34 0.34 0.31
∆_DW (in) 0.27 0.29 0.29 0.29 0.28 0.28 0.27 0.25
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Using MIN girder
spacing Girder A Girder B Girder C Girder D Girder E Girder F Girder G Girder H
CL Brg to CL brg length
(ft)113.19 112.78 112.38 111.98 111.58 111.19 110.80 110.42
Deck thk (in) 8.50 8.00 8.00 8.00 8.00 8.00 8.00 8.50
Haunch thk (in) 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00
Tributary deck width
(ft)8.73 9.35 9.35 9.35 9.35 9.35 9.35 8.73
Haunch (klf) 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10
Deck slab (klf) 0.96 0.97 0.97 0.97 0.97 0.97 0.97 0.96
sum (klf) 1.06 1.07 1.07 1.07 1.07 1.07 1.07 1.06
Diaphramg (kip) 2.29 4.59 4.59 4.59 4.59 4.59 4.59 2.29
Ec (ksi) 5,154 5,154 5,154 5,154 5,154 5,154 5,154 5,154
CABT55 I_g (in^4) 373,350 373,350 373,350 373,350 373,350 373,350 373,350 373,350
∆_slab+haunch (in) 2.03 2.02 1.99 1.96 1.94 1.91 1.88 1.84
∆_diaphragm (in) 0.06 0.12 0.12 0.12 0.12 0.12 0.12 0.06
∆_deck (in) 2.10 2.14 2.11 2.08 2.06 2.03 2.00 1.90
Barrier distr. % 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25
Barrier
+railing+median (klf) 0.775 0.775 0.775 0.775 0.775 0.775 0.775 0.775
I_comp (in^4) 814,836 814,836 814,836 814,836 814,836 814,836 814,836 814,836
∆_rail (in) 0.17 0.17 0.17 0.16 0.16 0.16 0.16 0.15
DW (klf) 0.31 0.33 0.33 0.33 0.33 0.33 0.33 0.31
∆_DW (in) 0.27 0.28 0.28 0.28 0.27 0.27 0.26 0.24
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Using Max girder
spacing Girder A Girder B Girder C Girder D Girder E Girder F Girder G Girder H
CL Brg to CL brg
length (ft)113.19 112.78 112.38 111.98 111.58 111.19 110.80 110.42
Deck thk (in) 8.50 8.00 8.00 8.00 8.00 8.00 8.00 8.50
Haunch thk (in) 2.00 2.00 2.00 2.00 2.00 2.00 2.00 2.00
Tributary deck
width (ft)9.08 10.05 10.05 10.05 10.05 10.05 10.05 9.08
Haunch (klf) 0.10 0.10 0.10 0.10 0.10 0.10 0.10 0.10
Deck slab (klf) 1.00 1.04 1.04 1.04 1.04 1.04 1.04 1.00
sum (klf) 1.10 1.14 1.14 1.14 1.14 1.14 1.14 1.10
Diaphramg (kip) 2.29 4.59 4.59 4.59 4.59 4.59 4.59 2.29
Ec (ksi) 5,154 5,154 5,154 5,154 5,154 5,154 5,154 5,154
CABT55 I_g (in^4) 373,350 373,350 373,350 373,350 373,350 373,350 373,350 373,350
∆_slab+haunch (in) 2.11 2.16 2.13 2.10 2.07 2.04 2.01 1.91
∆_diaphragm (in) 0.06 0.12 0.12 0.12 0.12 0.12 0.12 0.06
∆_deck (in) 2.17 2.28 2.25 2.22 2.19 2.16 2.13 1.97
Barrier distr. % 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25
Barrier
+railing+median 0.775 0.775 0.775 0.775 0.775 0.775 0.775 0.775
I_comp (in^4) 814,836 814,836 814,836 814,836 814,836 814,836 814,836 814,836
∆_rail (in) 0.17 0.17 0.17 0.16 0.16 0.16 0.16 0.15
DW (klf) 0.32 0.35 0.35 0.35 0.35 0.35 0.35 0.32
∆_DW (in) 0.28 0.30 0.30 0.30 0.29 0.29 0.28 0.25
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Girder self weight (plf) 963
Concrete slab (plf) from previous table
Diaphramg (kip) from previous table
haunch (plf) 203
Barrier + railing (plf) from previous table
Median (plf) 300 (only between girder D & E )
E_ci (ksi) 4,716
I_g (in^4) 373,350
E_c (ksi) 5154
I_comp (in^4) 814,836
* Adjusted distributed factors are applied to the final deflection, for the varied girder spacing.
0, W 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
dv 5.00 0.28 0.06 0.27 0.28 0.27 0.01 0.03 0.05 0.05 0.05
0.1L 11.32 0.63 0.13 0.58 0.61 0.58 0.01 0.06 0.10 0.10 0.10
0.2L 22.63 1.20 0.25 1.03 1.08 1.04 0.02 0.11 0.17 0.18 0.17
0.3L 33.95 1.64 0.35 1.35 1.41 1.37 0.04 0.14 0.23 0.23 0.23
0.4L 45.26 1.92 0.41 1.54 1.61 1.57 0.05 0.16 0.26 0.27 0.26
0.5L 56.58 2.02 0.43 1.61 1.68 1.65 0.06 0.17 0.27 0.28 0.27
0.6L 67.90 1.92 0.41 1.54 1.61 1.59 0.05 0.16 0.26 0.27 0.26
0.7L 79.21 1.64 0.35 1.35 1.41 1.39 0.04 0.14 0.23 0.23 0.23
0.8L 90.53 1.20 0.25 1.03 1.08 1.07 0.02 0.11 0.17 0.18 0.18
0.9L 101.84 0.63 0.13 0.58 0.61 0.60 0.01 0.06 0.10 0.10 0.10
dv 108.16 0.28 0.06 0.27 0.28 0.28 0.00 0.03 0.05 0.05 0.05
L, E 113.16 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
∆ (in)
haunch
Length along girder (ft)
Girder A ∆ (in) self
weight
∆ (in) DW
(Min. girder
space)
∆ (in) DW
(Max. girder
space)
* ∆ (in) DW
(Final)
Use E_ci Use E_c
∆ (in) Barrier
+railing+median
∆ (in) Deck
(Min. girder
space)
∆ (in) Deck
(Max. girder
space)
* ∆ (in)
Deck (Final)
∆ (in)
diaphragm
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Transfer & development length of the tendons.
Per AASHTO the stress in strands increase linearly from zero to f_pe, within transfer length region.
When the strands reach f_pe, the stress will increase linearly within development length region
Transfer length l_t =60*db (in) 36
f_pi= f_pbt -Δf_pES (ksi) 183
fpe, from Girder calualtion, (ksi) 181
fps, from Girder calualtion, (ksi) 269
ҡ 1.6
Min l_d, (in) 143 eqv to 11.9 ft
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Divide the tendons into 3 groups, the first goup is bonded straight strands
The second and third groups are the debonded strands.
0, W 0.00 8 8 8 6 4 2 2 38 8 4
dv 5.00 8 8 8 6 4 2 2 38 8 4
0.1L 11.32 8 8 8 6 4 2 2 38 8 4
0.2L 22.63 10 10 10 8 4 2 2 38 8 4
0.3L 33.95 10 12 12 8 4 2 2 38 8 4
0.4L 45.26 10 12 12 8 4 2 2 38 8 4
0.5L 56.58 10 12 12 8 4 2 2 38 8 4
0.6L 67.90 10 12 12 8 4 2 2 38 8 4
0.7L 79.21 10 12 12 8 4 2 2 38 8 4
0.8L 90.53 10 10 10 8 4 2 2 38 8 4
0.9L 101.84 8 8 8 6 4 2 2 38 8 4
dv 108.16 8 8 8 6 4 2 2 38 8 4
L, E 113.16 8 8 8 6 4 2 2 38 8 4
No.
Tendon at
2.75" From
Bot
Girder A
Length along girder (ft)
No.
Tendon at
4.75"
from Bot
No. Tendon
at 10.75"
From Bot
No. Tendon
at 12.75"
From Bot
No. Tendon at
14.75" From Bot
No. Tendon
at 6.75" From
Bot
No. Tendon at
8.75" From
Bot
Group 2
partially
bonded #
tendons(13')
Group 3
partially
bonded #
tendons(28')
Group 1
Fully bonded
# tendons
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Prestressing strand forces -Initial Prestressing Force @ Transfer
Positive sign--> updward ; negative sign--> downdward
0, W 0.00 45 0 0 372 0 0 0.00 0.00 0.00
dv 5.00 183 0 0 1510 0 0 0.72 0.14 0.05
0.1L 11.32 183 61 0 1510 106 0 1.53 0.30 0.12
0.2L 22.63 183 183 0 1510 318 0 2.72 0.53 0.21
0.3L 33.95 183 183 183 1510 318 159 3.56 0.70 0.27
0.4L 45.26 183 183 183 1510 318 159 4.07 0.80 0.31
0.5L 56.58 183 183 183 1510 318 159 4.24 0.83 0.33
0.6L 67.90 183 183 183 1510 318 159 4.07 0.80 0.31
0.7L 79.21 183 183 183 1510 318 159 3.56 0.70 0.27
0.8L 90.53 183 183 0 1510 318 0 2.72 0.53 0.21
0.9L 101.84 183 61 0 1510 106 0 1.53 0.30 0.12
dv 108.16 183 0 0 1510 0 0 0.72 0.14 0.05
L, E 113.16 45 0 0 372 0 0 0.00 0.00 0.00
Girder A
Length along girder (ft)Group 1
tendons (kip)
Group 1
tendons
(ksi)
Group 2
tendons
(ksi)
Group 3
tendons (ksi)
Group 2
tendons
(kip)
Group 3
tendons
(kip) Group 1 ∆p/s,1 (in)
Group 2 ∆p/s,2
(in)
Group 3 ∆p/s,3
(in)
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
V, Volumn of girder (in^3/ft length ) 11100
S, surface area (in^2/ft length) 2976
Ks 0.965
Controlling, Ks 1
k_hc 1.08
H , % 60
k_f 0.65
k_td 1
t, maturity of concrete, (day) 40
t_i, age of concr. When loading (day) 1
Cr, creep factor 0.72
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
K M J T= J+K+M
0, W 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
dv 5.0 0.91 0.63 1.08 0.71 -0.34 -0.03 1.08 0.71
0.1L 11.3 1.95 1.31 2.25 1.47 -0.73 -0.06 2.25 1.47
0.2L 22.6 3.46 2.26 3.88 2.46 -1.32 -0.11 3.88 2.46
0.3L 33.9 4.54 2.90 4.98 3.08 -1.75 -0.14 4.98 3.08
0.4L 45.3 5.19 3.27 5.61 3.42 -2.03 -0.16 5.61 3.42
0.5L 56.6 5.40 3.39 5.82 3.51 -2.13 -0.17 5.82 3.51
0.6L 67.9 5.19 3.27 5.61 3.41 -2.04 -0.16 5.61 3.41
0.7L 79.2 4.54 2.90 4.98 3.06 -1.78 -0.14 4.98 3.06
0.8L 90.5 3.46 2.26 3.88 2.43 -1.34 -0.11 3.88 2.43
0.9L 101.8 1.95 1.31 2.25 1.44 -0.75 -0.06 2.25 1.44
dv 108.2 0.91 0.63 1.08 0.71 -0.34 -0.03 1.08 0.71
L, E 113.2 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
K M
0.00 0.00
0.34 0.03
0.73 0.06
1.32 0.11
1.75 0.14
2.03 0.16
2.13 0.17
2.04 0.16
1.78 0.14
1.34 0.11
0.75 0.06
0.34 0.03
0.00 0.00
CiA, initial
camber
adjusted
creep, Ci*Cr (in)
Cf, final
camber, CiA+∆
DC (in)
Ci, initial
camber
∆p/s+ ∆ self
weight(in)
Cf, final
camber,
CiA+∆ DC
(in)
Girder A
Length along girder (ft)
∆ (in)
haunch+dec
k+diaphrag
m
∆ (in)
barrier+raili
ng+median
CiA, initial camber
adjusted creep,
Ci*Cr (in)
Total initial
defelction
from
prestress
∆p/s (in)
0.00
0.71
1.47
2.46
3.08
3.423.51
3.41
3.06
2.43
1.44
0.71
0.000.00
1.08
2.25
3.88
4.98
5.615.82
5.61
4.98
3.88
2.25
1.08
0.000.00
0.34
0.73
1.32
1.75
2.032.13
2.04
1.78
1.34
0.75
0.34
0.000.00 0.03 0.06 0.11 0.14 0.16 0.17 0.16 0.14 0.11 0.06 0.03 0.000.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Girder A Camber
T= J+K+M J K M
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Girder A For Drafting
0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L L
J 0.00 2.25 3.88 4.98 5.61 5.82 5.61 4.98 3.88 2.25 0.00
K 0.00 -0.73 -1.32 -1.75 -2.03 -2.13 -2.04 -1.78 -1.34 -0.75 0.00
M 0.00 -0.06 -0.11 -0.14 -0.16 -0.17 -0.16 -0.14 -0.11 -0.06 0.00
T 0.00 1.47 2.46 3.08 3.42 3.51 3.41 3.06 2.43 1.44 0.00
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Girder self weight (plf) 963
Concrete slab (plf) from previous table
Diaphramg (kip) from previous table
haunch (plf) 203
Barrier + railing (plf) from previous table
Median (plf) 300
E_ci (ksi) 4716
I_g (in^4) 373350
E_c (ksi) 5154
I_comp (in^4) 814836
* Adjusted distributed factors are applied to the final deflection, for the varied girder spacing.
0, W 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
dv 5.00 0.28 0.06 0.27 0.29 0.27 0.01 0.03 0.05 0.05 0.05
0.1L 11.28 0.62 0.13 0.58 0.63 0.58 0.02 0.06 0.10 0.11 0.10
0.2L 22.56 1.18 0.25 1.02 1.11 1.04 0.05 0.11 0.18 0.20 0.18
0.3L 33.83 1.62 0.34 1.34 1.46 1.38 0.07 0.14 0.24 0.26 0.24
0.4L 45.11 1.90 0.40 1.54 1.67 1.59 0.10 0.16 0.27 0.29 0.28
0.5L 56.39 1.99 0.42 1.60 1.74 1.67 0.12 0.17 0.28 0.30 0.29
0.6L 67.67 1.90 0.40 1.54 1.67 1.61 0.10 0.16 0.27 0.29 0.28
0.7L 78.95 1.62 0.34 1.34 1.46 1.42 0.07 0.14 0.24 0.26 0.25
0.8L 90.23 1.18 0.25 1.02 1.11 1.09 0.05 0.11 0.18 0.20 0.19
0.9L 101.50 0.62 0.13 0.58 0.63 0.62 0.02 0.06 0.10 0.11 0.11
dv 107.78 0.28 0.06 0.27 0.29 0.29 0.00 0.03 0.05 0.05 0.05
L, E 112.78 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Length along girder
(ft) Girder B
Use E_ci Use E_c
∆ (in) self
weight
∆ (in)
haunch
∆ (in) Deck
(Min. girder
space)
∆ (in) Deck
(Max. girder
space)
* ∆ (in)
Deck (Final)
∆ (in)
diaphragm
∆ (in) Barrier
+railing+median
∆ (in) DW
(Min. girder
space)
∆ (in) DW
(Max. girder
space)
* ∆ (in)
DW
(Final)
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Transfer & development length of the tendons.
Per AASHTO the stress in strands increase linearly from zero to f_pe, within transfer length region.
When the strands reach f_pe, the stress will increase linearly within development length region
Transfer length l_t =60*db (in) 36
f_pi= f_pbt -Δf_pES (ksi) 183
fpe, from Girder calualtion, (ksi) 181
fps, from Girder calualtion, (ksi) 269
ҡ 1.6
Min l_d, (in) 143 eqv to 11.9 ft
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Divide the tendons into 3 groups, the first goup is bonded straight strands
The second and third groups are the debonded strands.
0, W 0.00 8 8 8 6 4 2 2 38 8 4
dv 5.00 8 8 8 6 4 2 2 38 8 4
0.1L 11.28 8 8 8 6 4 2 2 38 8 4
0.2L 22.56 10 10 10 8 4 2 2 38 8 4
0.3L 33.83 10 12 12 8 4 2 2 38 8 4
0.4L 45.11 10 12 12 8 4 2 2 38 8 4
0.5L 56.39 10 12 12 8 4 2 2 38 8 4
0.6L 67.67 10 12 12 8 4 2 2 38 8 4
0.7L 78.95 10 12 12 8 4 2 2 38 8 4
0.8L 90.23 10 10 10 8 4 2 2 38 8 4
0.9L 101.50 8 8 8 6 4 2 2 38 8 4
dv 107.78 8 8 8 6 4 2 2 38 8 4
L, E 112.78 8 8 8 6 4 2 2 38 8 4
Group 1 Fully
bonded #
tendons
Group 3
partially
bonded #
tendons(
28')
No.
Tendon at
4.75" from
Bot
No. Tendon at
6.75" From Bot
No. Tendon
at 8.75"
From Bot
Group 2
partially
bonded #
tendons(13')
No. Tendon at
14.75" From Bot
No. Tendon
at 10.75"
From Bot
No. Tendon
at 12.75"
From Bot
Girder B
Length along girder
(ft)
No. Tendon at
2.75" From
Bot
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Prestressing strand forces -Initial Prestressing Force @ Transfer
Positive sign--> updward ; negative sign--> downdward
0, W 0.00 45 0 0 372 0 0 0.00 0.00 0.00
dv 5.00 183 0 0 1510 0 0 0.71 0.14 0.05
0.1L 11.28 183 61 0 1510 106 0 1.52 0.30 0.12
0.2L 22.56 183 183 0 1510 318 0 2.70 0.53 0.21
0.3L 33.83 183 183 183 1510 318 159 3.54 0.70 0.27
0.4L 45.11 183 183 183 1510 318 159 4.05 0.80 0.31
0.5L 56.39 183 183 183 1510 318 159 4.22 0.83 0.32
0.6L 67.67 183 183 183 1510 318 159 4.05 0.80 0.31
0.7L 78.95 183 183 183 1510 318 159 3.54 0.70 0.27
0.8L 90.23 183 183 0 1510 318 0 2.70 0.53 0.21
0.9L 101.50 183 61 0 1510 106 0 1.52 0.30 0.12
dv 107.78 183 0 0 1510 0 0 0.71 0.14 0.05
L, E 112.78 45 0 0 372 0 0 0.00 0.00 0.00
Group 1
tendons (ksi)
Group 2
tendons
(ksi)
Group 3
tendons (ksi)
Girder B
Length along girder
(ft)
Group 2
tendons
(kip)
Group 3
tendons
(kip) Group 1 ∆p/s,1 (in)
Group 2 ∆p/s,2
(in)
Group 3 ∆p/s,3
(in)
Group 1
tendons
(kip)
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
V, Volumn of girder (in^3/ft length ) 11100
S, surface area (in^2/ft length) 2976
Ks 0.965
Controlling, Ks 1
k_hc 1.08
H , % 60
k_f 0.65
k_td 1
t, maturity of concrete, (day) 40
t_i, age of concr. When loading (day) 1
Cr, creep factor 0.72
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
K M J T= J+K+M
0, W 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
dv 5.0 0.91 0.63 1.08 0.71 -0.34 -0.03 1.08 0.71
0.1L 11.3 1.93 1.31 2.25 1.45 -0.74 -0.06 2.25 1.45
0.2L 22.6 3.43 2.25 3.87 2.42 -1.34 -0.11 3.87 2.42
0.3L 33.8 4.51 2.89 4.96 3.03 -1.79 -0.14 4.96 3.03
0.4L 45.1 5.15 3.26 5.59 3.35 -2.09 -0.16 5.59 3.35
0.5L 56.4 5.37 3.38 5.80 3.42 -2.21 -0.17 5.80 3.42
0.6L 67.7 5.15 3.26 5.59 3.32 -2.11 -0.16 5.59 3.32
0.7L 78.9 4.51 2.89 4.96 2.98 -1.84 -0.14 4.96 2.98
0.8L 90.2 3.43 2.25 3.87 2.37 -1.39 -0.11 3.87 2.37
0.9L 101.5 1.93 1.31 2.25 1.41 -0.78 -0.06 2.25 1.41
dv 107.8 0.91 0.63 1.08 0.70 -0.35 -0.03 1.08 0.70
L, E 112.8 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
K M
0.00 0.00
0.34 0.03
0.74 0.06
1.34 0.11
1.79 0.14
2.09 0.16
2.21 0.17
2.11 0.16
1.84 0.14
1.39 0.11
0.78 0.06
0.35 0.03
0.00 0.00
Girder B
Length along girder
(ft)
∆ (in)
haunch+dec
k+diaphrag
m
∆ (in)
barrier+raili
ng+median
CiA, initial
camber adjusted
creep, Ci*Cr (in)
Cf, final
camber, CiA+∆
DC (in)
Total initial
defelction
from prestress
∆p/s (in)
Ci, initial
camber
∆p/s+ ∆ self
weight(in)
CiA, initial
camber
adjusted creep,
Ci*Cr (in)
Cf, final
camber,
CiA+∆ DC
(in)
0.00
0.71
1.45
2.42
3.03
3.35 3.423.32
2.98
2.37
1.41
0.70
0.000.00
1.08
2.25
3.87
4.96
5.595.80
5.59
4.96
3.87
2.25
1.08
0.000.00
0.34
0.74
1.34
1.79
2.092.21
2.11
1.84
1.39
0.78
0.35
0.000.00 0.03 0.06 0.11 0.14 0.16 0.17 0.16 0.14 0.11 0.06 0.03 0.000.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Girder B Camber
T= J+K+M J K M
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Girder B For Drafting
0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L L
J 0.00 2.25 3.87 4.96 5.59 5.80 5.59 4.96 3.87 2.25 0.00
K 0.00 -0.74 -1.34 -1.79 -2.09 -2.21 -2.11 -1.84 -1.39 -0.78 0.00
M 0.00 -0.06 -0.11 -0.14 -0.16 -0.17 -0.16 -0.14 -0.11 -0.06 0.00
T 0.00 1.45 2.42 3.03 3.35 3.42 3.32 2.98 2.37 1.41 0.00
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Girder self weight (plf) 963
Concrete slab (plf) from previous table
Diaphramg (kip) from previous table
haunch (plf) 203
Barrier + railing (plf) from previous table
Median (plf) 300
E_ci (ksi) 4716
I_g (in^4) 373350
E_c (ksi) 5154
I_comp (in^4) 814836
* Adjusted distributed factors are applied to the final deflection, for the varied girder spacing.
0, W 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
dv 5.00 0.28 0.06 0.27 0.29 0.27 0.01 0.03 0.05 0.05 0.05
0.1L 11.24 0.62 0.13 0.57 0.61 0.57 0.02 0.06 0.10 0.11 0.10
0.2L 22.48 1.17 0.25 1.01 1.09 1.02 0.05 0.11 0.18 0.19 0.18
0.3L 33.71 1.60 0.34 1.32 1.43 1.35 0.07 0.14 0.23 0.25 0.24
0.4L 44.95 1.87 0.39 1.51 1.64 1.56 0.10 0.16 0.27 0.29 0.28
0.5L 56.19 1.96 0.42 1.57 1.71 1.64 0.12 0.17 0.28 0.30 0.29
0.6L 67.43 1.87 0.39 1.51 1.64 1.59 0.10 0.16 0.27 0.29 0.28
0.7L 78.66 1.60 0.34 1.32 1.43 1.40 0.07 0.14 0.23 0.25 0.25
0.8L 89.90 1.17 0.25 1.01 1.09 1.07 0.05 0.11 0.18 0.19 0.19
0.9L 101.14 0.62 0.13 0.57 0.61 0.61 0.02 0.06 0.10 0.11 0.11
dv 107.38 0.28 0.06 0.27 0.29 0.29 0.01 0.03 0.05 0.05 0.05
L, E 112.38 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Length along
girder (ft) Girder
C
Use E_ci Use E_c
∆ (in) self
weight ∆ (in) haunch
∆ (in) Deck
(Min. girder
space)
∆ (in) Deck
(Max.
girder
space)
* ∆ (in) Deck
(Final)
∆ (in)
diaphragm
∆ (in) Barrier
+railing+medi
an
∆ (in) DW
(Min. girder
space)
∆ (in) DW
(Max. girder
space)
* ∆ (in) DW
(Final)
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Transfer & development length of the tendons.
Per AASHTO the stress in strands increase linearly from zero to f_pe, within transfer length region.
When the strands reach f_pe, the stress will increase linearly within development length region
Transfer length l_t =60*db (in) 36
f_pi= f_pbt -Δf_pES (ksi) 183
fpe, from Girder calualtion, (ksi) 181
fps, from Girder calualtion, (ksi) 269
ҡ 1.6
Min l_d, (in) 143 eqv to 11.9 ft
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Divide the tendons into 3 groups, the first goup is bonded straight strands
The second and third groups are the debonded strands.
0, W 0.00 8 8 8 6 4 2 2 38 8 4
dv 5.00 8 8 8 6 4 2 2 38 8 4
0.1L 11.24 8 8 8 6 4 2 2 38 8 4
0.2L 22.48 10 10 10 8 4 2 2 38 8 4
0.3L 33.71 10 12 12 8 4 2 2 38 8 4
0.4L 44.95 10 12 12 8 4 2 2 38 8 4
0.5L 56.19 10 12 12 8 4 2 2 38 8 4
0.6L 67.43 10 12 12 8 4 2 2 38 8 4
0.7L 78.66 10 12 12 8 4 2 2 38 8 4
0.8L 89.90 10 10 10 8 4 2 2 38 8 4
0.9L 101.14 8 8 8 6 4 2 2 38 8 4
dv 107.38 8 8 8 6 4 2 2 38 8 4
L, E 112.38 8 8 8 6 4 2 2 38 8 4
No. Tendon
at 4.75"
from Bot
No. Tendon
at 6.75" From
Bot
No.
Tendon at
8.75"
From Bot
Group 1 Fully
bonded #
tendons
Group 2
partially
bonded #
tendons(13')
Group 3
partially
bonded #
tendons(28
')
No. Tendon
at 10.75"
From Bot
No. Tendon
at 12.75"
From Bot
No. Tendon at
14.75" From
Bot
Girder C
Length along
girder (ft)
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Prestressing strand forces -Initial Prestressing Force @ Transfer
Positive sign--> updward ; negative sign--> downdward
0, W 0.00 45 0 0 372 0 0 0.00 0.00 0.00
dv 5.00 183 0 0 1510 0 0 0.71 0.14 0.05
0.1L 11.24 183 61 0 1510 106 0 1.51 0.30 0.11
0.2L 22.48 183 183 0 1510 318 0 2.68 0.53 0.20
0.3L 33.71 183 183 183 1510 318 159 3.52 0.69 0.27
0.4L 44.95 183 183 183 1510 318 159 4.02 0.79 0.31
0.5L 56.19 183 183 183 1510 318 159 4.18 0.82 0.32
0.6L 67.43 183 183 183 1510 318 159 4.02 0.79 0.31
0.7L 78.66 183 183 183 1510 318 159 3.52 0.69 0.27
0.8L 89.90 183 183 0 1510 318 0 2.68 0.53 0.20
0.9L 101.14 183 61 0 1510 106 0 1.51 0.30 0.11
dv 107.38 183 0 0 1510 0 0 0.71 0.14 0.05
L, E 112.38 45 0 0 372 0 0 0.00 0.00 0.00
Group 3
tendons (ksi)
Girder C
Length along
girder (ft)
Group 1
tendons
(kip)
Group 2
tendons (kip)
Group 3
tendons
(kip)
Group 1
tendons (ksi)
Group 2
tendons (ksi)
Group 1
∆p/s,1 (in)
Group 2
∆p/s,2 (in)
Group 3
∆p/s,3 (in)
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
V, Volumn of girder (in^3/ft length ) 11100
S, surface area (in^2/ft length) 2976
Ks 0.965
Controlling, Ks 1
k_hc 1.08
H , % 60
k_f 0.65
k_td 1
t, maturity of concrete, (day) 40
t_i, age of concr. When loading (day) 1
Cr, creep factor 0.72
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
K M J T= J+K+M
0, W 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
dv 5.0 0.91 0.63 1.08 0.71 -0.34 -0.03 1.08 0.71
0.1L 11.2 1.92 1.30 2.24 1.45 -0.73 -0.06 2.24 1.45
0.2L 22.5 3.41 2.24 3.85 2.43 -1.32 -0.11 3.85 2.43
0.3L 33.7 4.47 2.88 4.95 3.04 -1.76 -0.14 4.95 3.04
0.4L 45.0 5.11 3.24 5.58 3.36 -2.05 -0.16 5.58 3.36
0.5L 56.2 5.33 3.36 5.78 3.43 -2.18 -0.17 5.78 3.43
0.6L 67.4 5.11 3.24 5.58 3.34 -2.08 -0.16 5.58 3.34
0.7L 78.7 4.47 2.88 4.95 3.00 -1.81 -0.14 4.95 3.00
0.8L 89.9 3.41 2.24 3.85 2.38 -1.37 -0.11 3.85 2.38
0.9L 101.1 1.92 1.30 2.24 1.41 -0.76 -0.06 2.24 1.41
dv 107.4 0.91 0.63 1.08 0.69 -0.36 -0.03 1.08 0.69
L, E 112.4 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
K M
0.00 0.00
0.34 0.03
0.73 0.06
1.32 0.11
1.76 0.14
2.05 0.16
2.18 0.17
2.08 0.16
1.81 0.14
1.37 0.11
0.76 0.06
0.36 0.03
0.00 0.00
Girder C
Length along
girder (ft)
∆ (in)
haunch+deck
+diaphragm
∆ (in)
barrier+raili
ng+median
CiA, initial
camber
adjusted
creep, Ci*Cr
(in)
Cf, final
camber,
CiA+∆ DC (in)
Total initial
defelction
from prestress
∆p/s (in)
Ci, initial
camber
∆p/s+ ∆ self
weight(in)
CiA, initial
camber
adjusted
creep, Ci*Cr
(in)
Cf, final
camber,
CiA+∆ DC
(in)
0.00
0.71
1.45
2.43
3.04
3.36 3.433.34
3.00
2.38
1.41
0.69
0.000.00
1.08
2.24
3.85
4.95
5.585.78
5.58
4.95
3.85
2.24
1.08
0.000.00
0.34
0.73
1.32
1.76
2.052.18
2.08
1.81
1.37
0.76
0.36
0.000.00 0.03 0.06 0.11 0.14 0.16 0.17 0.16 0.14 0.11 0.06 0.03 0.000.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Girder C Camber
T= J+K+M J K M
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Girder C For Drafting
0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L L
J 0.00 2.24 3.85 4.95 5.58 5.78 5.58 4.95 3.85 2.24 0.00
K 0.00 -0.73 -1.32 -1.76 -2.05 -2.18 -2.08 -1.81 -1.37 -0.76 0.00
M 0.00 -0.06 -0.11 -0.14 -0.16 -0.17 -0.16 -0.14 -0.11 -0.06 0.00
T 0.00 1.45 2.43 3.04 3.36 3.43 3.34 3.00 2.38 1.41 0.00
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Girder self weight (plf) 963
Concrete slab (plf) from previous table
Diaphramg (kip) from previous table
haunch (plf) 203
Barrier + railing (plf) from previous table
Median (plf) 300
E_ci (ksi) 4716
I_g (in^4) 373350
E_c (ksi) 5154
I_comp (in^4) 814836
* Adjusted distributed factors are applied to the final deflection, for the varied girder spacing.
0, W 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
dv 5.00 0.28 0.06 0.27 0.29 0.27 0.01 0.03 0.05 0.05 0.05
0.1L 11.20 0.61 0.13 0.56 0.61 0.56 0.02 0.06 0.10 0.11 0.10
0.2L 22.40 1.15 0.24 1.00 1.08 1.01 0.05 0.10 0.18 0.19 0.18
0.3L 33.59 1.57 0.33 1.31 1.42 1.34 0.07 0.14 0.23 0.25 0.24
0.4L 44.79 1.84 0.39 1.49 1.62 1.54 0.10 0.16 0.26 0.28 0.27
0.5L 55.99 1.93 0.41 1.56 1.69 1.62 0.12 0.16 0.28 0.30 0.29
0.6L 67.19 1.84 0.39 1.49 1.62 1.57 0.10 0.16 0.26 0.28 0.28
0.7L 78.39 1.57 0.33 1.31 1.42 1.38 0.07 0.14 0.23 0.25 0.24
0.8L 89.58 1.15 0.24 1.00 1.08 1.06 0.05 0.10 0.18 0.19 0.19
0.9L 100.78 0.61 0.13 0.56 0.61 0.60 0.02 0.06 0.10 0.11 0.11
dv 106.98 0.28 0.06 0.27 0.29 0.29 0.01 0.03 0.05 0.05 0.05
L, E 111.98 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Length along
girder (ft)
Girder D
Use E_ci Use E_c
∆ (in) self
weight
∆ (in)
haunch
∆ (in) Deck
(Min. girder
space)
∆ (in) Deck
(Max. girder
space)
* ∆ (in) Deck
(Final)
∆ (in)
diaphragm
∆ (in) Barrier
+railing+medi
an
∆ (in) DW
(Min. girder
space)
∆ (in) DW
(Max. girder
space)
* ∆ (in)
DW
(Final)
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Transfer & development length of the tendons.
Per AASHTO the stress in strands increase linearly from zero to f_pe, within transfer length region.
When the strands reach f_pe, the stress will increase linearly within development length region
Transfer length l_t =60*db (in) 36
f_pi= f_pbt -Δf_pES (ksi) 183
fpe, from Girder calualtion, (ksi) 181
fps, from Girder calualtion, (ksi) 269
ҡ 1.6
Min l_d, (in) 143 eqv to 11.9 ft
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Divide the tendons into 3 groups, the first goup is bonded straight strands
The second and third groups are the debonded strands.
0, W 0.00 8 8 8 6 4 2 2 38 8 4
dv 5.00 8 8 8 6 4 2 2 38 8 4
0.1L 11.20 8 8 8 6 4 2 2 38 8 4
0.2L 22.40 10 10 10 8 4 2 2 38 8 4
0.3L 33.59 10 12 12 8 4 2 2 38 8 4
0.4L 44.79 10 12 12 8 4 2 2 38 8 4
0.5L 55.99 10 12 12 8 4 2 2 38 8 4
0.6L 67.19 10 12 12 8 4 2 2 38 8 4
0.7L 78.39 10 12 12 8 4 2 2 38 8 4
0.8L 89.58 10 10 10 8 4 2 2 38 8 4
0.9L 100.78 8 8 8 6 4 2 2 38 8 4
dv 106.98 8 8 8 6 4 2 2 38 8 4
L, E 111.98 8 8 8 6 4 2 2 38 8 4
No. Tendon
at 4.75"
from Bot
No. Tendon at
6.75" From
Bot
No. Tendon at
8.75" From Bot
Group 1
Fully bonded
# tendons
Group 2
partially
bonded #
tendons(13')
Group 3
partially
bonded #
tendons(
28')
Girder D
Length along
girder (ft)
No. Tendon
at 2.75"
From Bot
No. Tendon at
10.75" From
Bot
No. Tendon
at 12.75"
From Bot
No. Tendon at
14.75" From
Bot
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Prestressing strand forces -Initial Prestressing Force @ Transfer
Positive sign--> updward ; negative sign--> downdward
0, W 0.00 45 0 0 372 0 0 0.00 0.00 0.00
dv 5.00 183 0 0 1510 0 0 0.71 0.14 0.05
0.1L 11.20 183 61 0 1510 106 0 1.50 0.29 0.11
0.2L 22.40 183 183 0 1510 318 0 2.66 0.52 0.20
0.3L 33.59 183 183 183 1510 318 159 3.49 0.69 0.27
0.4L 44.79 183 183 183 1510 318 159 3.99 0.78 0.30
0.5L 55.99 183 183 183 1510 318 159 4.16 0.82 0.32
0.6L 67.19 183 183 183 1510 318 159 3.99 0.78 0.30
0.7L 78.39 183 183 183 1510 318 159 3.49 0.69 0.27
0.8L 89.58 183 183 0 1510 318 0 2.66 0.52 0.20
0.9L 100.78 183 61 0 1510 106 0 1.50 0.29 0.11
dv 106.98 183 0 0 1510 0 0 0.71 0.14 0.05
L, E 111.98 45 0 0 372 0 0 0.00 0.00 0.00
Group 2
tendons
(ksi)
Group 1
∆p/s,1 (in)
Group 2
∆p/s,2 (in)
Group 3
∆p/s,3 (in)
Group 3
tendons (ksi)
Girder D
Length along
girder (ft)
Group 1
tendons (kip)
Group 2
tendons (kip)
Group 3
tendons
(kip)
Group 1
tendons (ksi)
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
V, Volumn of girder (in^3/ft length ) 11100
S, surface area (in^2/ft length) 2976
Ks 0.965
Controlling, Ks 1
k_hc 1.08
H , % 60
k_f 0.65
k_td 1
t, maturity of concrete, (day) 40
t_i, age of concr. When loading (day) 1
Cr, creep factor 0.72
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
K M J T= J+K+M
0, W 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
dv 5.0 0.90 0.63 1.08 0.71 -0.34 -0.03 1.08 0.71
0.1L 11.2 1.90 1.30 2.23 1.45 -0.72 -0.06 2.23 1.45
0.2L 22.4 3.38 2.24 3.84 2.43 -1.30 -0.10 3.84 2.43
0.3L 33.6 4.44 2.87 4.93 3.05 -1.74 -0.14 4.93 3.05
0.4L 44.8 5.08 3.23 5.56 3.37 -2.03 -0.16 5.56 3.37
0.5L 56.0 5.29 3.35 5.76 3.45 -2.15 -0.16 5.76 3.45
0.6L 67.2 5.08 3.23 5.56 3.34 -2.06 -0.16 5.56 3.34
0.7L 78.4 4.44 2.87 4.93 3.00 -1.79 -0.14 4.93 3.00
0.8L 89.6 3.38 2.24 3.84 2.38 -1.35 -0.10 3.84 2.38
0.9L 100.8 1.90 1.30 2.23 1.41 -0.76 -0.06 2.23 1.41
dv 107.0 0.90 0.63 1.08 0.69 -0.36 -0.03 1.08 0.69
L, E 112.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
K M
0.00 0.00
0.34 0.03
0.72 0.06
1.30 0.10
1.74 0.14
2.03 0.16
2.15 0.16
2.06 0.16
1.79 0.14
1.35 0.10
0.76 0.06
0.36 0.03
0.00 0.00
Girder D
Length along
girder (ft)
∆ (in)
haunch+deck
+diaphragm
∆ (in)
barrier+railin
g+median
CiA, initial
camber
adjusted
creep, Ci*Cr
(in)
Cf, final
camber,
CiA+∆ DC
(in)
Total initial
defelction
from
prestress
∆p/s (in)
Ci, initial
camber
∆p/s+ ∆ self
weight(in)
CiA, initial
camber
adjusted
creep, Ci*Cr
(in)
Cf, final
camber, CiA+∆
DC (in)
0.00
0.71
1.45
2.43
3.05
3.37 3.453.34
3.00
2.38
1.41
0.69
0.000.00
1.08
2.23
3.84
4.93
5.565.76
5.56
4.93
3.84
2.23
1.08
0.000.00
0.34
0.72
1.30
1.74
2.032.15
2.06
1.79
1.35
0.76
0.36
0.000.00 0.03 0.06 0.10 0.14 0.16 0.16 0.16 0.14 0.10 0.06 0.03 0.000.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Girder D Camber
T= J+K+M J K M
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Girder D For Drafting
0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L L
J 0.00 2.23 3.84 4.93 5.56 5.76 5.56 4.93 3.84 2.23 0.00
K 0.00 -0.72 -1.30 -1.74 -2.03 -2.15 -2.06 -1.79 -1.35 -0.76 0.00
M 0.00 -0.06 -0.10 -0.14 -0.16 -0.16 -0.16 -0.14 -0.10 -0.06 0.00
T 0.00 1.45 2.43 3.05 3.37 3.45 3.34 3.00 2.38 1.41 0.00
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Girder self weight (plf) 963
Concrete slab (plf) from previous table
Diaphramg (kip) from previous table
haunch (plf) 203
Barrier + railing (plf) from previous table
Median (plf) 300
E_ci (ksi) 4716
I_g (in^4) 373350
E_c (ksi) 5154
I_comp (in^4) 814836
* Adjusted distributed factors are applied to the final deflection, for the varied girder spacing.
0, W 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
dv 5.00 0.27 0.06 0.26 0.28 0.26 0.01 0.03 0.05 0.05 0.05
0.1L 11.16 0.60 0.13 0.55 0.60 0.56 0.02 0.06 0.10 0.11 0.10
0.2L 22.32 1.13 0.24 0.98 1.06 1.00 0.05 0.10 0.17 0.19 0.18
0.3L 33.48 1.55 0.33 1.29 1.40 1.32 0.07 0.14 0.23 0.25 0.23
0.4L 44.63 1.82 0.38 1.47 1.60 1.52 0.10 0.15 0.26 0.28 0.27
0.5L 55.79 1.91 0.40 1.53 1.66 1.60 0.12 0.16 0.27 0.29 0.28
0.6L 66.95 1.82 0.38 1.47 1.60 1.55 0.10 0.15 0.26 0.28 0.27
0.7L 78.11 1.55 0.33 1.29 1.40 1.36 0.07 0.14 0.23 0.25 0.24
0.8L 89.27 1.13 0.24 0.98 1.06 1.05 0.05 0.10 0.17 0.19 0.18
0.9L 100.43 0.60 0.13 0.55 0.60 0.59 0.02 0.06 0.10 0.11 0.10
dv 106.58 0.27 0.06 0.26 0.28 0.28 0.01 0.03 0.05 0.05 0.05
L, E 111.58 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Length along
girder (ft)
Girder E
Use E_ci Use E_c
∆ (in) self
weight ∆ (in) haunch
∆ (in) Deck
(Min. girder
space)
∆ (in) Deck (Max.
girder space)
* ∆ (in) Deck
(Final) ∆ (in) diaphragm
∆ (in) Barrier
+railing+medi
an
∆ (in) DW
(Min. girder
space)
∆ (in) DW
(Max. girder
space)
* ∆ (in) DW
(Final)
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Transfer & development length of the tendons.
Per AASHTO the stress in strands increase linearly from zero to f_pe, within transfer length region.
When the strands reach f_pe, the stress will increase linearly within development length region
Transfer length l_t =60*db (in) 36
f_pi= f_pbt -Δf_pES (ksi) 183
fpe, from Girder calualtion, (ksi) 181
fps, from Girder calualtion, (ksi) 269
ҡ 1.6
Min l_d, (in) 143 eqv to 11.9 ft
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Divide the tendons into 3 groups, the first goup is bonded straight strands
The second and third groups are the debonded strands.
0, W 0.00 8 8 8 6 4 2 0 36 8 4
dv 5.00 8 8 8 6 4 2 0 36 8 4
0.1L 11.16 8 8 8 6 4 2 0 36 8 4
0.2L 22.32 10 10 10 8 4 2 0 36 8 4
0.3L 33.48 10 12 12 8 4 2 0 36 8 4
0.4L 44.63 10 12 12 8 4 2 0 36 8 4
0.5L 55.79 10 12 12 8 4 2 0 36 8 4
0.6L 66.95 10 12 12 8 4 2 0 36 8 4
0.7L 78.11 10 12 12 8 4 2 0 36 8 4
0.8L 89.27 10 10 10 8 4 2 0 36 8 4
0.9L 100.43 8 8 8 6 4 2 0 36 8 4
dv 106.58 8 8 8 6 4 2 0 36 8 4
L, E 111.58 8 8 8 6 4 2 0 36 8 4
No. Tendon at
4.75" from
Bot
No. Tendon at
6.75" From Bot
No. Tendon at
8.75" From Bot
Group 1 Fully
bonded #
tendons
Group 2
partially
bonded #
tendons
Group 3
partially
bonded #
tendons
Girder E
Length along
girder (ft)
No. Tendon
at 2.75" From
Bot
No. Tendon at
10.75" From Bot
No. Tendon at
12.75" From Bot
No. Tendon
at 14.75"
From Bot
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Prestressing strand forces -Initial Prestressing Force @ Transfer
Positive sign--> updward ; negative sign--> downdward
0, W 0.00 45 0 0 353 0 0 0.00 0.00 0.00
dv 5.00 183 0 0 1431 0 0 0.67 0.14 0.05
0.1L 11.16 183 61 0 1431 106 0 1.41 0.29 0.11
0.2L 22.32 183 183 0 1431 318 0 2.50 0.52 0.20
0.3L 33.48 183 183 183 1431 318 159 3.28 0.68 0.26
0.4L 44.63 183 183 183 1431 318 159 3.75 0.78 0.30
0.5L 55.79 183 183 183 1431 318 159 3.91 0.81 0.31
0.6L 66.95 183 183 183 1431 318 159 3.75 0.78 0.30
0.7L 78.11 183 183 183 1431 318 159 3.28 0.68 0.26
0.8L 89.27 183 183 0 1431 318 0 2.50 0.52 0.20
0.9L 100.43 183 61 0 1431 106 0 1.41 0.29 0.11
dv 106.58 183 0 0 1431 0 0 0.67 0.14 0.05
L, E 111.58 45 0 0 353 0 0 0.00 0.00 0.00
Group 3
tendons (ksi)
Girder E
Length along
girder (ft)
Group 2 tendons
(kip)
Group 3 tendons
(kip)
Group 1
∆p/s,1 (in)
Group 2
∆p/s,2 (in)
Group 1
tendons (ksi)
Group 2
tendons (ksi)
Group 1 tendons
(kip)
Group 3
∆p/s,3 (in)
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
V, Volumn of girder (in^3/ft length ) 11100
S, surface area (in^2/ft length) 2976
Ks 0.965
Controlling, Ks 1
k_hc 1.08
H , % 60
k_f 0.65
k_td 1
t, maturity of concrete, (day) 40
t_i, age of concr. When loading (day) 1
Cr, creep factor 0.72
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
K M J T= J+K+M
0, W 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
dv 5.0 0.86 0.59 1.01 0.65 -0.33 -0.03 1.01 0.65
0.1L 11.2 1.81 1.21 2.08 1.32 -0.71 -0.06 2.08 1.32
0.2L 22.3 3.22 2.09 3.59 2.20 -1.29 -0.10 3.59 2.20
0.3L 33.5 4.23 2.68 4.60 2.74 -1.72 -0.14 4.60 2.74
0.4L 44.6 4.83 3.01 5.18 3.02 -2.00 -0.15 5.18 3.02
0.5L 55.8 5.03 3.12 5.37 3.09 -2.12 -0.16 5.37 3.09
0.6L 67.0 4.83 3.01 5.18 3.00 -2.03 -0.15 5.18 3.00
0.7L 78.1 4.23 2.68 4.60 2.70 -1.76 -0.14 4.60 2.70
0.8L 89.3 3.22 2.09 3.59 2.15 -1.34 -0.10 3.59 2.15
0.9L 100.4 1.81 1.21 2.08 1.28 -0.74 -0.06 2.08 1.28
dv 106.6 0.86 0.59 1.01 0.63 -0.35 -0.03 1.01 0.63
L, E 111.6 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
K M
0.00 0.00
0.33 0.03
0.71 0.06
1.29 0.10
1.72 0.14
2.00 0.15
2.12 0.16
2.03 0.15
1.76 0.14
1.34 0.10
0.74 0.06
0.35 0.03
0.00 0.00
Girder E
Length along
girder (ft)
∆ (in)
haunch+deck+diap
hragm
∆ (in)
barrier+railing+m
edian
CiA, initial
camber
adjusted
creep, Ci*Cr
(in)
Cf, final
camber, CiA+∆
DC (in)
Total initial
defelction
from
prestress
∆p/s (in)
Ci, initial
camber ∆p/s+
∆ self
weight(in)
CiA, initial
camber
adjusted creep,
Ci*Cr (in)
Cf, final camber,
CiA+∆ DC (in)
0.00
0.65
1.32
2.20
2.74
3.02 3.093.00
2.70
2.15
1.28
0.63
0.000.00
1.01
2.08
3.59
4.60
5.185.37
5.18
4.60
3.59
2.08
1.01
0.000.00
0.33
0.71
1.29
1.72
2.002.12
2.03
1.76
1.34
0.74
0.35
0.000.00 0.03 0.06 0.10 0.14 0.15 0.16 0.15 0.14 0.10 0.06 0.03 0.000.00
1.00
2.00
3.00
4.00
5.00
6.00
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Girder E Camber
T= J+K+M J K M
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Girder E For Drafting
0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L L
J 0.00 2.08 3.59 4.60 5.18 5.37 5.18 4.60 3.59 2.08 0.00
K 0.00 -0.71 -1.29 -1.72 -2.00 -2.12 -2.03 -1.76 -1.34 -0.74 0.00
M 0.00 -0.06 -0.10 -0.14 -0.15 -0.16 -0.15 -0.14 -0.10 -0.06 0.00
T 0.00 1.32 2.20 2.74 3.02 3.09 3.00 2.70 2.15 1.28 0.00
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Girder self weight (plf) 963
Concrete slab (plf) from previous table
Diaphramg (kip) from previous table
haunch (plf) 203
Barrier + railing (plf) from previous table
Median (plf) 300
E_ci (ksi) 4716
I_g (in^4) 373350
E_c (ksi) 5154
I_comp (in^4) 814836
* Adjusted distributed factors are applied to the final deflection, for the varied girder spacing.
0, W 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
dv 5.00 0.27 0.06 0.26 0.28 0.26 0.01 0.03 0.05 0.05 0.05
0.1L 11.12 0.59 0.12 0.54 0.59 0.55 0.02 0.06 0.10 0.10 0.10
0.2L 22.24 1.12 0.24 0.97 1.05 0.98 0.05 0.10 0.17 0.18 0.17
0.3L 33.36 1.53 0.32 1.27 1.38 1.30 0.07 0.13 0.23 0.24 0.23
0.4L 44.48 1.79 0.38 1.45 1.57 1.50 0.09 0.15 0.26 0.28 0.27
0.5L 55.59 1.88 0.40 1.51 1.64 1.58 0.12 0.16 0.27 0.29 0.28
0.6L 66.71 1.79 0.38 1.45 1.57 1.53 0.09 0.15 0.26 0.28 0.27
0.7L 77.83 1.53 0.32 1.27 1.38 1.35 0.07 0.13 0.23 0.24 0.24
0.8L 88.95 1.12 0.24 0.97 1.05 1.03 0.05 0.10 0.17 0.18 0.18
0.9L 100.07 0.59 0.12 0.54 0.59 0.59 0.02 0.06 0.10 0.10 0.10
dv 106.19 0.27 0.06 0.26 0.28 0.28 0.01 0.03 0.05 0.05 0.05
L, E 111.19 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Length along
girder (ft)
Girder F
Use E_ci Use E_c
∆ (in) self
weight ∆ (in) haunch
∆ (in) Deck
(Min. girder
space)
∆ (in) Deck
(Max. girder
space)
* ∆ (in) Deck
(Final)
∆ (in)
diaphragm
∆ (in) Barrier
+railing+medi
an
∆ (in) DW
(Min. girder
space)
∆ (in) DW
(Max. girder
space)
* ∆ (in)
DW
(Final)
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Transfer & development length of the tendons.
Per AASHTO the stress in strands increase linearly from zero to f_pe, within transfer length region.
When the strands reach f_pe, the stress will increase linearly within development length region
Transfer length l_t =60*db (in) 36
f_pi= f_pbt -Δf_pES (ksi) 183
fpe, from Girder calualtion, (ksi) 181
fps, from Girder calualtion, (ksi) 269
ҡ 1.6
Min l_d, (in) 143 eqv to 11.9 ft
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Divide the tendons into 3 groups, the first goup is bonded straight strands
The second and third groups are the debonded strands.
0, W 0.00 8 8 8 6 4 2 0 36 8 4
dv 5.00 8 8 8 6 4 2 0 36 8 4
0.1L 11.12 8 8 8 6 4 2 0 36 8 4
0.2L 22.24 10 10 10 8 4 2 0 36 8 4
0.3L 33.36 10 12 12 8 4 2 0 36 8 4
0.4L 44.48 10 12 12 8 4 2 0 36 8 4
0.5L 55.59 10 12 12 8 4 2 0 36 8 4
0.6L 66.71 10 12 12 8 4 2 0 36 8 4
0.7L 77.83 10 12 12 8 4 2 0 36 8 4
0.8L 88.95 10 10 10 8 4 2 0 36 8 4
0.9L 100.07 8 8 8 6 4 2 0 36 8 4
dv 106.19 8 8 8 6 4 2 0 36 8 4
L, E 111.19 8 8 8 6 4 2 0 36 8 4
No. Tendon at
12.75" From
Bot
No. Tendon at
14.75" From
Bot
Group 1 Fully
bonded #
tendons
Girder F
Length along
girder (ft)
No. Tendon
at 2.75"
From Bot
No. Tendon
at 10.75"
From Bot
No. Tendon
at 4.75" from
Bot
No. Tendon at
6.75" From Bot
No. Tendon
at 8.75" From
Bot
Group 2
partially
bonded #
tendons
Group 3
partially
bonded #
tendons
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Prestressing strand forces -Initial Prestressing Force @ Transfer
Positive sign--> updward ; negative sign--> downdward
0, W 0.00 45 0 0 353 0 0 0.00 0.00 0.00
dv 5.00 183 0 0 1431 0 0 0.67 0.14 0.05
0.1L 11.12 183 61 0 1431 106 0 1.40 0.29 0.11
0.2L 22.24 183 183 0 1431 318 0 2.48 0.51 0.20
0.3L 33.36 183 183 183 1431 318 159 3.26 0.68 0.26
0.4L 44.48 183 183 183 1431 318 159 3.73 0.77 0.30
0.5L 55.59 183 183 183 1431 318 159 3.88 0.80 0.31
0.6L 66.71 183 183 183 1431 318 159 3.73 0.77 0.30
0.7L 77.83 183 183 183 1431 318 159 3.26 0.68 0.26
0.8L 88.95 183 183 0 1431 318 0 2.48 0.51 0.20
0.9L 100.07 183 61 0 1431 106 0 1.40 0.29 0.11
dv 106.19 183 0 0 1431 0 0 0.67 0.14 0.05
L, E 111.19 45 0 0 353 0 0 0.00 0.00 0.00
Group 3
tendons (ksi)
Girder F
Length along
girder (ft) Group 1
tendons (kip)
Group 2
tendons
(kip)
Group 3
tendons (kip)
Group 1
tendons
(ksi)
Group 2
tendons (ksi)
Group 1
∆p/s,1 (in)
Group 2
∆p/s,2 (in)
Group 3
∆p/s,3 (in)
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
V, Volumn of girder (in^3/ft length ) 11100
S, surface area (in^2/ft length) 2976
Ks 0.965
Controlling, Ks 1
k_hc 1.08
H , % 60
k_f 0.65
k_td 1
t, maturity of concrete, (day) 40
t_i, age of concr. When loading (day) 1
Cr, creep factor 0.72
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
K M J T= J+K+M
0, W 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
dv 5.0 0.86 0.59 1.01 0.66 -0.33 -0.03 1.01 0.66
0.1L 11.1 1.80 1.21 2.08 1.32 -0.70 -0.06 2.08 1.32
0.2L 22.2 3.20 2.08 3.57 2.21 -1.27 -0.10 3.57 2.21
0.3L 33.4 4.20 2.67 4.58 2.75 -1.70 -0.13 4.58 2.75
0.4L 44.5 4.80 3.00 5.16 3.04 -1.97 -0.15 5.16 3.04
0.5L 55.6 5.00 3.11 5.35 3.10 -2.09 -0.16 5.35 3.10
0.6L 66.7 4.80 3.00 5.16 3.01 -2.00 -0.15 5.16 3.01
0.7L 77.8 4.20 2.67 4.58 2.71 -1.74 -0.13 4.58 2.71
0.8L 89.0 3.20 2.08 3.57 2.16 -1.32 -0.10 3.57 2.16
0.9L 100.1 1.80 1.21 2.08 1.28 -0.73 -0.06 2.08 1.28
dv 106.2 0.86 0.59 1.01 0.64 -0.35 -0.03 1.01 0.64
L, E 111.2 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
K M
0.00 0.00
0.33 0.03
0.70 0.06
1.27 0.10
1.70 0.13
1.97 0.15
2.09 0.16
2.00 0.15
1.74 0.13
1.32 0.10
0.73 0.06
0.35 0.03
0.00 0.00
Girder F
Length along
girder (ft)
∆ (in)
haunch+dec
k+diaphrag
m
∆ (in)
barrier+railing
+median
CiA, initial
camber
adjusted
creep, Ci*Cr
(in)
Cf, final
camber,
CiA+∆ DC (in)
Total initial
defelction
from
prestress
∆p/s (in)
Ci, initial
camber
∆p/s+ ∆ self
weight(in)
CiA, initial
camber
adjusted creep,
Ci*Cr (in)
Cf, final
camber,
CiA+∆ DC (in)
0.00
0.66
1.32
2.21
2.75
3.04 3.103.01
2.71
2.16
1.28
0.64
0.000.00
1.01
2.08
3.57
4.58
5.16
5.35
5.16
4.58
3.57
2.08
1.01
0.000.00
0.33
0.70
1.27
1.70
1.972.09
2.00
1.74
1.32
0.73
0.35
0.000.00 0.03 0.06 0.10 0.13 0.15 0.16 0.15 0.13 0.10 0.06 0.03 0.000.00
1.00
2.00
3.00
4.00
5.00
6.00
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Girder F Camber
T= J+K+M J K M
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Girder F For Drafting
0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L L
J 0.00 2.08 3.57 4.58 5.16 5.35 5.16 4.58 3.57 2.08 0.00
K 0.00 -0.70 -1.27 -1.70 -1.97 -2.09 -2.00 -1.74 -1.32 -0.73 0.00
M 0.00 -0.06 -0.10 -0.13 -0.15 -0.16 -0.15 -0.13 -0.10 -0.06 0.00
T 0.00 1.32 2.21 2.75 3.04 3.10 3.01 2.71 2.16 1.28 0.00
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Girder self weight (plf) 963
Concrete slab (plf) from previous table
Diaphramg (kip) from previous table
haunch (plf) 203
Barrier + railing (plf) from previous table
Median (plf) 300
E_ci (ksi) 4716
I_g (in^4) 373350
E_c (ksi) 5154
I_comp (in^4) 814836
* Adjusted distributed factors are applied to the final deflection, for the varied girder spacing.
0, W 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
dv 5.00 0.27 0.06 0.26 0.28 0.26 0.01 0.03 0.05 0.05 0.05
0.1L 11.08 0.58 0.12 0.54 0.58 0.54 0.02 0.06 0.10 0.10 0.10
0.2L 22.16 1.10 0.23 0.95 1.04 0.97 0.05 0.10 0.17 0.18 0.17
0.3L 33.24 1.51 0.32 1.25 1.36 1.28 0.07 0.13 0.22 0.24 0.23
0.4L 44.32 1.77 0.37 1.43 1.55 1.48 0.09 0.15 0.25 0.27 0.26
0.5L 55.40 1.85 0.39 1.49 1.62 1.55 0.12 0.16 0.26 0.28 0.27
0.6L 66.48 1.77 0.37 1.43 1.55 1.50 0.09 0.15 0.25 0.27 0.27
0.7L 77.56 1.51 0.32 1.25 1.36 1.33 0.07 0.13 0.22 0.24 0.23
0.8L 88.64 1.10 0.23 0.95 1.04 1.02 0.05 0.10 0.17 0.18 0.18
0.9L 99.72 0.58 0.12 0.54 0.58 0.58 0.02 0.06 0.10 0.10 0.10
dv 105.80 0.27 0.06 0.26 0.28 0.28 0.01 0.03 0.05 0.05 0.05
L, E 110.80 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Length along
girder (ft)
Girder G
Use E_ci Use E_c
∆ (in) self
weight
∆ (in)
haunch
∆ (in) Deck
(Min. girder
space)
∆ (in) Deck
(Max. girder
space)
* ∆ (in)
Deck (Final)
∆ (in)
diaphragm
∆ (in) Barrier
+railing+media
n
∆ (in) DW
(Min. girder
space)
∆ (in) DW
(Max. girder
space)
* ∆ (in)
DW
(Final)
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Transfer & development length of the tendons.
Per AASHTO the stress in strands increase linearly from zero to f_pe, within transfer length region.
When the strands reach f_pe, the stress will increase linearly within development length region
Transfer length l_t =60*db (in) 36
f_pi= f_pbt -Δf_pES (ksi) 183
fpe, from Girder calualtion, (ksi) 181
fps, from Girder calualtion, (ksi) 269
ҡ 1.6
Min l_d, (in) 143 eqv to 11.9 ft
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Divide the tendons into 3 groups, the first goup is bonded straight strands
The second and third groups are the debonded strands.
0, W 0.00 8 8 8 6 4 2 0 36 8 4
dv 5.00 8 8 8 6 4 2 0 36 8 4
0.1L 11.08 8 8 8 6 4 2 0 36 8 4
0.2L 22.16 10 10 10 8 4 2 0 36 8 4
0.3L 33.24 10 12 12 8 4 2 0 36 8 4
0.4L 44.32 10 12 12 8 4 2 0 36 8 4
0.5L 55.40 10 12 12 8 4 2 0 36 8 4
0.6L 66.48 10 12 12 8 4 2 0 36 8 4
0.7L 77.56 10 12 12 8 4 2 0 36 8 4
0.8L 88.64 10 10 10 8 4 2 0 36 8 4
0.9L 99.72 8 8 8 6 4 2 0 36 8 4
dv 105.80 8 8 8 6 4 2 0 36 8 4
L, E 110.80 8 8 8 6 4 2 0 36 8 4
Group 3
partially
bonded #
tendons
Girder G
Length along
girder (ft)
No.
Tendon at
2.75"
From Bot
No.
Tendon at
4.75" from
Bot
No. Tendon
at 6.75"
From Bot
No. Tendon
at 8.75" From
Bot
No. Tendon
at 10.75"
From Bot
No. Tendon
at 12.75"
From Bot
No. Tendon at
14.75" From
Bot
Group 1
Fully
bonded #
tendons
Group 2
partially
bonded #
tendons
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Prestressing strand forces -Initial Prestressing Force @ Transfer
Positive sign--> updward ; negative sign--> downdward
0, W 0.00 45 0 0 353 0 0 0.00 0.00 0.00
dv 5.00 183 0 0 1431 0 0 0.66 0.14 0.05
0.1L 11.08 183 61 0 1431 106 0 1.39 0.29 0.11
0.2L 22.16 183 183 0 1431 318 0 2.47 0.51 0.20
0.3L 33.24 183 183 183 1431 318 159 3.24 0.67 0.26
0.4L 44.32 183 183 183 1431 318 159 3.70 0.77 0.29
0.5L 55.40 183 183 183 1431 318 159 3.85 0.80 0.31
0.6L 66.48 183 183 183 1431 318 159 3.70 0.77 0.29
0.7L 77.56 183 183 183 1431 318 159 3.24 0.67 0.26
0.8L 88.64 183 183 0 1431 318 0 2.47 0.51 0.20
0.9L 99.72 183 61 0 1431 106 0 1.39 0.29 0.11
dv 105.80 183 0 0 1431 0 0 0.66 0.14 0.05
L, E 110.80 45 0 0 353 0 0 0.00 0.00 0.00
Group 1
tendons
(ksi)
Group 1 ∆p/s,1
(in)
Group 2
∆p/s,2 (in)
Group 3
∆p/s,3 (in)
Group 2
tendons
(ksi)
Group 3
tendons
(ksi)
Girder G
Length along
girder (ft) Group 1
tendons (kip)
Group 2
tendons
(kip)
Group 3
tendons
(kip)
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
V, Volumn of girder (in^3/ft length ) 11100
S, surface area (in^2/ft length) 2976
Ks 0.965
Controlling, Ks 1
k_hc 1.08
H , % 60
k_f 0.65
k_td 1
t, maturity of concrete, (day) 40
t_i, age of concr. When loading (day) 1
Cr, creep factor 0.72
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
K M J T= J+K+M
0, W 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
dv 5.0 0.85 0.59 1.01 0.66 -0.32 -0.03 1.01 0.66
0.1L 11.1 1.79 1.20 2.07 1.32 -0.69 -0.06 2.07 1.32
0.2L 22.2 3.17 2.07 3.56 2.21 -1.25 -0.10 3.56 2.21
0.3L 33.2 4.17 2.66 4.57 2.76 -1.67 -0.13 4.57 2.76
0.4L 44.3 4.76 2.99 5.15 3.05 -1.95 -0.15 5.15 3.05
0.5L 55.4 4.96 3.10 5.33 3.11 -2.06 -0.16 5.33 3.11
0.6L 66.5 4.76 2.99 5.15 3.02 -1.97 -0.15 5.15 3.02
0.7L 77.6 4.17 2.66 4.57 2.72 -1.72 -0.13 4.57 2.72
0.8L 88.6 3.17 2.07 3.56 2.16 -1.30 -0.10 3.56 2.16
0.9L 99.7 1.79 1.20 2.07 1.29 -0.72 -0.06 2.07 1.29
dv 105.8 0.85 0.59 1.01 0.64 -0.34 -0.03 1.01 0.64
L, E 110.8 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
K M
0.00 0.00
0.32 0.03
0.69 0.06
1.25 0.10
1.67 0.13
1.95 0.15
2.06 0.16
1.97 0.15
1.72 0.13
1.30 0.10
0.72 0.06
0.34 0.03
0.00 0.00
Total
initial
defelction
from
prestress
∆p/s (in)
Ci, initial
camber
∆p/s+ ∆
self
weight(in)
CiA, initial
camber
adjusted
creep, Ci*Cr
(in)
Cf, final
camber,
CiA+∆ DC (in)
Girder H
Length along
girder (ft)
∆ (in)
haunch+dec
k+diaphrag
m
∆ (in)
barrier+raili
ng+median
CiA, initial
camber
adjusted creep,
Ci*Cr (in)
Cf, final
camber,
CiA+∆ DC
(in)
0.00
0.66
1.32
2.21
2.76
3.05 3.113.02
2.72
2.16
1.29
0.64
0.000.00
1.01
2.07
3.56
4.57
5.15
5.33
5.15
4.57
3.56
2.07
1.01
0.000.00
0.32
0.69
1.25
1.67
1.952.06
1.97
1.72
1.30
0.72
0.34
0.000.00 0.03 0.06 0.10 0.13 0.15 0.16 0.15 0.13 0.10 0.06 0.03 0.000.00
1.00
2.00
3.00
4.00
5.00
6.00
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Girder G Camber
T= J+K+M J K M
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Girder G For Drafting
0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L L
J 0.00 2.07 3.56 4.57 5.15 5.33 5.15 4.57 3.56 2.07 0.00
K 0.00 -0.69 -1.25 -1.67 -1.95 -2.06 -1.97 -1.72 -1.30 -0.72 0.00
M 0.00 -0.06 -0.10 -0.13 -0.15 -0.16 -0.15 -0.13 -0.10 -0.06 0.00
T 0.00 1.32 2.21 2.76 3.05 3.11 3.02 2.72 2.16 1.29 0.00
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Girder self weight (plf) 963
Concrete slab (plf) from previous table
Diaphramg (kip) from previous table
haunch (plf) 203
Barrier + railing (plf) from previous table
Median (plf) 300
E_ci (ksi) 4716
I_g (in^4) 373350
E_c (ksi) 5154
I_comp (in^4) 814836
* Adjusted distributed factors are applied to the final deflection, for the varied girder spacing.
0, W 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
dv 5.00 0.26 0.06 0.25 0.26 0.25 0.01 0.03 0.04 0.04 0.04
0.1L 11.04 0.57 0.12 0.52 0.55 0.53 0.01 0.06 0.09 0.09 0.09
0.2L 22.08 1.09 0.23 0.93 0.97 0.94 0.02 0.10 0.16 0.16 0.16
0.3L 33.13 1.49 0.31 1.22 1.28 1.24 0.03 0.13 0.20 0.21 0.21
0.4L 44.17 1.74 0.37 1.40 1.46 1.42 0.05 0.15 0.23 0.24 0.24
0.5L 55.21 1.83 0.39 1.46 1.52 1.49 0.06 0.15 0.24 0.25 0.25
0.6L 66.25 1.74 0.37 1.40 1.46 1.44 0.05 0.15 0.23 0.24 0.24
0.7L 77.29 1.49 0.31 1.22 1.28 1.26 0.03 0.13 0.20 0.21 0.21
0.8L 88.33 1.09 0.23 0.93 0.97 0.97 0.02 0.10 0.16 0.16 0.16
0.9L 99.38 0.57 0.12 0.52 0.55 0.55 0.01 0.06 0.09 0.09 0.09
dv 105.42 0.26 0.06 0.25 0.26 0.26 0.01 0.03 0.04 0.04 0.04
L, E 110.42 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
Length along
girder (ft)
Girder H
Use E_ci Use E_c
∆ (in) self
weight ∆ (in) haunch
∆ (in) Deck
(Min. girder
space)
∆ (in) Deck
(Max. girder
space)
* ∆ (in) Deck
(Final)
∆ (in)
diaphragm
∆ (in) Barrier
+railing+media
n
∆ (in) DW
(Min. girder
space)
∆ (in) DW
(Max. girder
space)
* ∆ (in) DW
(Final)
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Transfer & development length of the tendons.
Per AASHTO the stress in strands increase linearly from zero to f_pe, within transfer length region.
When the strands reach f_pe, the stress will increase linearly within development length region
Transfer length l_t =60*db (in) 36
f_pi= f_pbt -Δf_pES (ksi) 183
fpe, from Girder calualtion, (ksi) 181
fps, from Girder calualtion, (ksi) 269
ҡ 1.6
Min l_d, (in) 143 eqv to 11.9 ft
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Divide the tendons into 3 groups, the first goup is bonded straight strands
The second and third groups are the debonded strands.
0, W 0.00 8 8 8 6 4 2 0 36 8 4
dv 5.00 8 8 8 6 4 2 0 36 8 4
0.1L 11.04 8 8 8 6 4 2 0 36 8 4
0.2L 22.08 10 10 10 8 4 2 0 36 8 4
0.3L 33.13 10 12 12 8 4 2 0 36 8 4
0.4L 44.17 10 12 12 8 4 2 0 36 8 4
0.5L 55.21 10 12 12 8 4 2 0 36 8 4
0.6L 66.25 10 12 12 8 4 2 0 36 8 4
0.7L 77.29 10 12 12 8 4 2 0 36 8 4
0.8L 88.33 10 10 10 8 4 2 0 36 8 4
0.9L 99.38 8 8 8 6 4 2 0 36 8 4
dv 105.42 8 8 8 6 4 2 0 36 8 4
L, E 110.42 8 8 8 6 4 2 0 36 8 4
Girder H
Length along
girder (ft) No. Tendon at
2.75" From Bot
No. Tendon at
4.75" from Bot
No. Tendon at
6.75" From
Bot
No. Tendon at
8.75" From Bot
Group 1 Fully
bonded #
tendons
Group 2
partially
bonded #
tendons
Group 3
partially
bonded #
tendons
No. Tendon at
10.75" From
Bot
No. Tendon
at 12.75"
From Bot
No. Tendon at
14.75" From
Bot
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Prestressing strand forces -Initial Prestressing Force @ Transfer
Positive sign--> updward ; negative sign--> downdward
0, W 0.00 45 0 0 353 0 0 0.00 0.00 0.00
dv 5.00 183 0 0 1431 0 0 0.67 0.14 0.05
0.1L 11.04 183 61 0 1431 106 0 1.39 0.29 0.11
0.2L 22.08 183 183 0 1431 318 0 2.47 0.51 0.19
0.3L 33.13 183 183 183 1431 318 159 3.24 0.67 0.26
0.4L 44.17 183 183 183 1431 318 159 3.70 0.76 0.29
0.5L 55.21 183 183 183 1431 318 159 3.85 0.79 0.30
0.6L 66.25 183 183 183 1431 318 159 3.70 0.76 0.29
0.7L 77.29 183 183 183 1431 318 159 3.24 0.67 0.26
0.8L 88.33 183 183 0 1431 318 0 2.47 0.51 0.19
0.9L 99.38 183 61 0 1431 106 0 1.39 0.29 0.11
dv 105.42 183 0 0 1431 0 0 0.67 0.14 0.05
L, E 110.42 45 0 0 353 0 0 0.00 0.00 0.00
Group 1
tendons (ksi)
Group 2
tendons (ksi)
Group 1 ∆p/s,1
(in)
Group 2 ∆p/s,2
(in)
Group 3 ∆p/s,3
(in)
Group 3
tendons (ksi)
Girder H
Length along
girder (ft)
Group 1
tendons (kip)
Group 2
tendons (kip)
Group 3
tendons
(kip)
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
V, Volumn of girder (in^3/ft length ) 11100
S, surface area (in^2/ft length) 2976
Ks 0.965
Controlling, Ks 1
k_hc 1.08
H , % 60
k_f 0.65
k_td 1
t, maturity of concrete, (day) 40
t_i, age of concr. When loading (day) 1
Cr, creep factor 0.72
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
K M J T= J+K+M
0, W 0.0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
dv 5.0 0.86 0.59 1.02 0.68 -0.31 -0.03 1.02 0.68
0.1L 11.0 1.78 1.21 2.08 1.36 -0.66 -0.06 2.08 1.36
0.2L 22.1 3.17 2.08 3.58 2.29 -1.19 -0.10 3.58 2.29
0.3L 33.1 4.16 2.67 4.59 2.87 -1.59 -0.13 4.59 2.87
0.4L 44.2 4.75 3.01 5.17 3.19 -1.84 -0.15 5.17 3.19
0.5L 55.2 4.95 3.12 5.36 3.28 -1.93 -0.15 5.36 3.28
0.6L 66.3 4.75 3.01 5.17 3.17 -1.85 -0.15 5.17 3.17
0.7L 77.3 4.16 2.67 4.59 2.85 -1.61 -0.13 4.59 2.85
0.8L 88.3 3.17 2.08 3.58 2.26 -1.22 -0.10 3.58 2.26
0.9L 99.4 1.78 1.21 2.08 1.34 -0.68 -0.06 2.08 1.34
dv 105.4 0.86 0.59 1.02 0.67 -0.32 -0.03 1.02 0.67
L, E 110.4 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
K M
0.00 0.00
0.31 0.03
0.66 0.06
1.19 0.10
1.59 0.13
1.84 0.15
1.93 0.15
1.85 0.15
1.61 0.13
1.22 0.10
0.68 0.06
0.32 0.03
0.00 0.00
Girder H
Length along
girder (ft)
∆ (in)
haunch+deck+
diaphragm
∆ (in)
barrier+raili
ng+median
CiA, initial
camber
adjusted creep,
Ci*Cr (in)
Cf, final
camber, CiA+∆
DC (in)
Total initial
defelction
from prestress
∆p/s (in)
Ci, initial
camber ∆p/s+ ∆
self weight(in)
CiA, initial
camber
adjusted
creep, Ci*Cr
(in)
Cf, final camber,
CiA+∆ DC (in)
0.00
0.68
1.36
2.29
2.87
3.193.28
3.17
2.85
2.26
1.34
0.67
0.000.00
1.02
2.08
3.58
4.59
5.17
5.36
5.17
4.59
3.58
2.08
1.02
0.000.00
0.31
0.66
1.19
1.59
1.841.93
1.85
1.61
1.22
0.68
0.32
0.000.00 0.03 0.06 0.10 0.13 0.15 0.15 0.15 0.13 0.10 0.06 0.03 0.000.00
1.00
2.00
3.00
4.00
5.00
6.00
0.0 20.0 40.0 60.0 80.0 100.0 120.0
Girder H Camber
T= J+K+M J K M
Project: Port of Stockton Fyffe Computed: JC Date: 5/2/20
Subject: Design Calculations Checked: CL Date: 5/17/20
Task: Girder Deflection & Camber Page: of:
Job #: NO:
Girder H For Drafting
0 0.1L 0.2L 0.3L 0.4L 0.5L 0.6L 0.7L 0.8L 0.9L L
J 0.00 2.08 3.58 4.59 5.17 5.36 5.17 4.59 3.58 2.08 0.00
K 0.00 -0.66 -1.19 -1.59 -1.84 -1.93 -1.85 -1.61 -1.22 -0.68 0.00
M 0.00 -0.06 -0.10 -0.13 -0.15 -0.15 -0.15 -0.13 -0.10 -0.06 0.00
T 0.00 1.36 2.29 2.87 3.19 3.28 3.17 2.85 2.26 1.34 0.00
3.2 Deck Design
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
3.2.1 Stay-in-Place (SIP) Panel with Cast-in-Place
(CIP) Deck Design
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Precast Prestressed Panel Design Checked: CL Date: 6/4/20
Task: Page: of:
Job #: NO:
References:
AASHTO & PCI Precast Panel Deck Design Examples
Stress: positive is compression; negative is tension
Barrier Type 836 Weight (plf), one side 600.00
DW, wearing surface weight (psf) 35.00
Concrete Density (pcf) 155.00
Precast Panel Thickness (in) 3.50
Total concrete deck thickness (in) 8.00
Total concrete deck weight (psf) 103.33
CIP concrete slab weight (psf) 58.13
S, Center to Center, Max Girder Spacing (ft) 10.05
S, TF edge to edge , Clear Girder Spacing (ft) 6.11
For the precast prestressed concerete panel:
f'ci at transfer (ksi) 6.40
f'c after 28 days (ksi) 8.00
E_ci (ksi) for panel @ transfer 4609.52
E_c (ksi) for panel @ service 5153.60
For the prestressing tendons in the panel:
f_pu, Ultimate stress, (ksi) 270.00
f_pi, initial pretensioning stress, (ksi) 202.50
f_py, yield strength, 0.9f_pu (ksi) 243.00
Es, Modulus of elasticity (ksi) 28500.00
Dimaeter of strands used (in) 0.375
A_t, area of one strand (in^2) 0.085
For the welded wire reinforcement in the panel:
fy (ksi) 60.00
Es, Modulus of elasticity (ksi) 29000.00
Top reinforcement clear cover (in) 2.50
Bot reinforcement clear cover (in) 1.00
Panel dimenion :
Length (ft), trans. Bridge direction 7.50
Width (ft), long. Bridge direction 6.89
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Precast Prestressed Panel Design Checked: CL Date: 6/4/20
Task: Page: of:
Job #: NO:
Construction load (applied to precast panel) (psf) 500.00
Moment due to Construction load (k-ft) 3.52
Live load:
Design truck HL 93 rear axle weight (kip) 32.00
P, Rear wheel weight HL-93 (lb) 16000.00
P, Rear wheel weight P-15 (lb) 27000.00
S, effective span length (ft), edge to edge dist+half W_tf(ft) 8.08
LL (lb-ft/ft) HL-93 5040.63
LL (lb-ft/ft) P_15 8506.05
L, length of portion of loaded span, eqv to S 8.08
IM, impact HL-93 0.33
IM, impact P-15 0.25
3.5"
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Precast Prestressed Panel Design Checked: CL Date: 6/4/20
Task: Page: of:
Job #: NO:
Moment from LL+IM (k-ft/ft) HL_93 5.36
Moment from LL+IM (k-ft/ft) P-15 8.51
Design the panel with 12in wide strip:
A, area of corss section of the panel (in^2/ft length ) 42.00
Sb, section modulus from bot. fiber Non-comp panel(in^3/ft) 24.50
St, section modulus from top. fiber Non-comp panel(in^3/ft) 24.50
9.49
For composite section properties:
Ec_CIP, for CIP slab (ksi) 4074.28
n, modular ratio of Ec_CIP/ E_c panel@service 0.79
Transformed width of 12" CIP slab (in) 9.49
1/2" wearing surface is considered to be an integral part of the 4.5" CIP slab
Conservatively use 4" of CIP slab for composite section
CIP slab thickness for comp. section (in) 4.00
A_CIP (in^2) 37.95
Ac, transformed composite section area (in^2) 79.95
Ybc, CG of comp section from Bot. of Panel (in) 3.53
Ytc, CG of comp section from top of CIP (in) 3.97
Ytg, CG of comp section to panel top (in) 0.03
I_c, comp. section moment of inertia (in^4) 373.81
S_bc, comp. section modulus from bot of panel (in^3) 105.90
S_tc=I_c/Y_tc/n, section modulus from top of CIP (in^3) 119.10
S_tg, comp. section moduls to the top fiber of panel (in^3) 12480.01
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Precast Prestressed Panel Design Checked: CL Date: 6/4/20
Task: Page: of:
Job #: NO:
For 1ft linear length of the block:
M_conc, bending moment due to deck (k-ft) 0.73
M_panel, bending moment due to deck (k-ft) 0.32
M_CIP, bending moment due to deck (k-ft) 0.41
Above is 1kip/ft uniformly distributed load applied to the transverse cross-section
Max. positive moment from above plot is (k-ft) 9.09
M_ws+, max positive moment from wearing surface (k-ft) 0.32
Above is the moment of 1kip applied at the end of cantilever to represent the barrier
Max positive moment from above plot is (k-ft) 0.00
M_b+, max positive moment from barrier (k-ft) 0.00
fb, stress @ bot. comp section @ serive (ksi) 1.00
6sqr(f'c) , allowable concrete tensile stress @ servive, σt 0.54
Ps, min = fb- σt (ksi) 0.46
Ps as force per panel width (kip/ftl) 19.45
Ps as force per panel (kipl) 134.08
Assume 15% of final loss to start the design
prestress force of Each 3/8" dia tendon (kip) 14.63
Tendon Spacing (in) 6.00 <--
Say design # of strands per panel 14 <--
Check the design :
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Precast Prestressed Panel Design Checked: CL Date: 6/4/20
Task: Page: of:
Job #: NO:
Find the prestress loss of the strands:
Humidity (same used for girder design ) 70.00 %
SH (ksi) 6.50
Assume 5% initially prestress loss, f_cir (ksi) 0.79
ES (ksi) 4.87
f_cds (ksi) -0.04
CR_c (ksi) 9.20
CR_s (ksi) 3.73
Loss at transfer:
Initial loss ratio: ES/f_pi 0.02 < 5% initial loss assumed
Assumption is conservative, so it is ok
Effective prestress @ transfer (ksi) 197.63
Total prestress force @ transfer (kip/panel) 234.44
Total prestress force @ transfer (kip/ft width) 34.00
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Precast Prestressed Panel Design Checked: CL Date: 6/4/20
Task: Page: of:
Job #: NO:
Total loss @ service
Final prestress loss (ksi) 24.30
f_se, effective prestress (ksi) 178.20
Prestress force @ service (kip/panel) 211.39
Prestress force @ service (kip/ft width ) 30.66
At transfer stress check
Allowable compressice stress, 0.6f'ci (ksi) 3.84
Allowable tensile stress (ksi) -0.20
At transfer, the panel only has self weight & prestress force:
f_top, top stress (ksi) 0.97 < 3.84 ok
f_bot, bottom stress (ksi) 0.65 < 3.84 ok
There are two more cases, that PS+Perm and all load combinations:
For PS+ permanent :
Allowable tensile stress 6*sqrt (f'c)(ksi) -0.54
Allowable compressice stress, 0.4f'ci (ksi) 3.20
For all load combination:
Allowable tensile stress 6*sqrt (f'c)(ksi) -0.54
Allowable compressice stress, 0.6f'ci (ksi) 4.80
For non-composite section, under PS+ deck wt+construction load
Construction load considered as LL, so use all load comb limits:
f_t, top stress (ksi) 0.90 < 4.8 ok
f_b, bottom stress (ksi) 0.56 < 4.8 ok
For composite section, under PS+ Permanent load (deck wt, WS, Barrier)
f_t, top stress (ksi) 1.12 < 3.20 ok
f_b, bottom stress (ksi) 0.34 < 3.20 ok
For composite section, under PS+ DL + (LL+IM)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Precast Prestressed Panel Design Checked: CL Date: 6/4/20
Task: Page: of:
Job #: NO:
f_t, top stress (ksi) HL-93 1.09 < 4.80 ok
f_b, bottom stress (ksi) HL-93 -0.27 less than -0.54 ok
Flexural strength of positive moment
Mu (kip-ft) 10.77 1.25DC+1.5 DW+1.75LL
Mu (kip-ft) 12.87
φ 1
As (in^2/ft) 0.17
d, dist from CG of strand to top of CIP (in) 5.75
ρ, ratio of pretensioning steel 0.00255
f'c of CIP concrete (ksi) Comp section 5.00
ϒ 0.28
ß1 (CIP concrete controls) 0.80
1.25DC+1.5 DW+1.35LL
(permit)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Precast Prestressed Panel Design Checked: CL Date: 6/4/20
Task: Page: of:
Job #: NO:
Initial f_su (ksi) 256.99
l_x, dist. From end of strand to CL of panel (ft) 3.75
D, nominal diameter of strand (in) 0.375
f_se, effective stress in strand after loss, (ksi) 178.20
Final f_su, check max limit (ksi) 238.80
φMn(k-ft) 18.25 > 12.87 ok
Check depth of the rectangular stress block:
a=As*fsu/(0.85f'c*b), (in) 0.81 < 4" CIP THK, ok
Ductility limit of the panel
ρ*f_su/f'c 0.12 < 0.29 ok
0.36 ß1 0.29
f_r, 0.75 SQRT(f'c) , modulus of rupture (ksi) 0.07
f_pe, compressive stress in Concr. Due to PS ONLY (ksi) 0.81
M_dnc, non-comp dead load moment (kip-ft) 0.73
M_cr, cracking moment (kip-ft) 5.32
1.2 M_cr (kip-ft) 6.39 < 18.25 ok
use welded wire mesh : 6x6 D4XD4 (in^2 /ft) 0.08
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Precast Prestressed Panel Design Checked: CL Date: 6/4/20
Task: Page: of:
Job #: NO:
Check the negative mement section: for LL to be max, take the location at 1st interior girder
Wheels are 4ft away from the barrier, so not beyonf the exterior girder.
Above is 1kip/ft uniformly distributed load applied to the transverse cross-section
At ext. girder moment from above plot is (k-ft) -15.28
M_ws-, max positive moment from wearing surface (k-ft) -0.53
Above is the moment of 1kip applied at the end of cantilever to represent the barrier
Max negative moment from above plot is (k-ft) -0.50
M_b-, max positive moment from barrier (k-ft) -0.30
M_LL+IM-, max negative moment from barrier (k-ft) -5.36
Mu, -, negative (k-ft) -10.64
No6 bar @ 6"
d, effective depth (in) 5.50
b (in) 12
φ 0.9
Rn = Mu- / φbd^2, (psi/ft) 390.74
m, = fy/(0.85f'c) 14.12
ρ 0.007
As, rebar (in^2) =ρ* (bd) 0.452
Use #6 @6" spacing <---
As, provided (in^2) 0.88
a= As*fy/(0.85f'c*b) 1.04
19.73 > 10.64 ok
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Precast Prestressed Panel Design Checked: CL Date: 6/4/20
Task: Page: of:
Job #: NO:
Maximum reinforcement
ρ_provided 0.013
ρ_b 0.034
ρ_max = 0.75*ρ_b 0.025 > 0.013 ok
Minimum reinforcement Neg. moment capacity
1.2 M_cr (kip-ft) 6.39 < 19.73 ok
Crack Control
dc, (in) 2.29
A (in^2) 18.3
z, (kip/in) 130
f_s (ksi) 37.44
f_s with limit (ksi) 36 (0.6fy)
Actural stress in reinforcement:
n= Es/Ec 7.12
ρ_provided 0.013
ρ_provided *n 0.09
k = sqrt( (ρ *n)^2+2*ρ *n)-ρ *n 0.35
j= (1-k/3) 0.88
fs= M_service /(j d As) 17.31 < 36 ok
3.2.2 Deck Overhang Design
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Design Calculations - Geometry Checked: CL Date: 6/4/20
Task: Deck Design Page: of:
Job #: # 6 bars NO:
Precast Panel Thickness (in) 3.50
Total concrete deck thickness (in) 8.00
Overhang Thickness (in) 8.50
Barrier Type 836 Weight (plf) 600.00
Barrier base width (in) 17.00
Wearing surface density (pcf) 35
Wearing surface Weight (plf) 2621
Raised Median 3'X8" weight (plf) 300
0
Max. Girder spacing (ft) 10.05
Top Cover of deck slab (in ) 2.125 AASHTO 5.12.3
Bottom cover of deck slab (in) 1 AASHTO 5.12.3
Rebar yield strength (ksi) 60
Concrete slab compressive stress (ksi) 5
Use equivalent strip method to find the moment demands of the concrete slab
For the portion with median, there is no LL; LL & median weight cannot occur simultaneously.
LL controls over median weight, so load comb. NOT include median weight
Strength I limit state control
DC1 Deck Self Weight w_DC1 (ksf) 0.10
DC2 Barrier weight w_DC2 (ksf) 0.42
DC3 Raised median w_DC3 (ksf) 0.00
DW Wearing surface w_DW (ksf) 0.04
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Design Calculations - Geometry Checked: CL Date: 6/4/20
Task: Deck Design Page: of:
Job #: # 6 bars NO:
Use above formula:
say c= 12
l (ft) 10.05
For positive& negative dead load moment:
M_DC1 (k-ft) 0.870
M_DC2 (k-ft) 3.565
M_DC3 (k-ft) 0.000
M_DW (k-ft) 0.295
Per AASHTO 4.6.2.1.6
Girder top flange width (in) 47.25
1/3 of top flange width (in) 15.75 > 15
15
Distance from the center of girder to design
section for neg moment (in)
Using the approximate method of deck analysis, live load effects may be determined by modeling the deck as a beam supported on the
girders. One or more axles may be placed side by side on the deck (representing axles from trucks in different traffic lanes) and move them
transversely across the deck to maximize the moments .
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Design Calculations - Geometry Checked: CL Date: 6/4/20
Task: Deck Design Page: of:
Job #: # 6 bars NO:
Use AASHTO Table A4-1 to find the max. live load moments per unit width (kip-ft/ft)
HL-93live load postive moment per unit width (k-ft/ft) 7.03
P-15 live load postive moment per unit width (k-ft/ft) 11.15 ( P15+IM0.25)
Strength I load combination 18.29 1.25DC+1.5DW+1.75LL
Strength II load combination 21.04 1.25DC+1.5DW+1.35LL(permit)
Maximum positive moment Mu+ (k-ft/ft) 21.04
Say #6 bar is used for reinforcement
#6 bar Diameter (in) 0.75
A_#6 (in^2) 0.44
de, effective depth from compression fiber to certroil of tensile force (in)
"= total depth -bottm cover -1/2bar dia 6.63
ø 0.90
k', say b=12" for 1ft wide section (k/in^2) 0.53
ρ 0.00952
As (in^2/in) 0.06304
Requireed # 6 bar spacing (in) 6.97998
Actual used spacing (in) 6 #6 bar transversely, @ bottom
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Design Calculations - Geometry Checked: CL Date: 6/4/20
Task: Deck Design Page: of:
Job #: # 6 bars NO:
Check for crack control per AASHTO 5.7.3.4-1
ϒ_e, class 1 exposure 1
dc, (in) 1.375
ß_s 1.2965
fss (use 0.6fy directly, conservative to do so) 36
700ϒ_e/(ß_s*fss)-2dc, (in) 12.25 > 6 " ✔
Check stress under service I load combination DC+DW+LL
Mu (k-ft/ft) 11.759
n=E_steel/E_CIP 7.12
Say that 4" wide of concrete section is used (eqv to spacing of #5)
Neutral axis of transformed section is y (in)
(Conc thk- top cover-y)*As*n= Concr width * y* (y/2)
As*n (in^2) 3.13
y, (in) 2.01
I_transformed (in^4) 63.03
Allowbale service stress (ksi) 36
σ_s, (service stress, ksi) My/I 22.84 < 36 ✔, stress is ok
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Design Calculations - Geometry Checked: CL Date: 6/4/20
Task: Deck Design Page: of:
Job #: # 6 bars NO:
Design For Negative moment @ interior girder
HL-93 live load negative moment per unit width (k-ft/ft) 4.71 Use Table A-4 AASHTO
P-15 live load negative moment per unit width (k-ft/ft) 7.47004
Mu, neg (strength I combination) , k-ft/ft 14.23
Mu, neg (strength II combination) , k-ft/ft 16.0696 Control
Say still use # 6 bar for top, transversely
de, effective depth from compression fiber to certroil of tensile force (in)
"= total depth -top cover -1/2bar dia 5.50
ø 0.90
k', say b=12" for 1ft wide section (k/in^2) 0.59
ρ 0.01064
As (in^2/in) 0.0585
Requireed # 6 bar spacing (in) 7.52157
Actual used spacing (in) 6 #6 bar transversely, @ top
Per previous calculation, crack control spacing should be ok, not repeat here.
Check service stress here:
Mu (k-ft/ft) 9.439
n=E_steel/E_CIP 7.12
Say that 4" wide of concrete section is used (eqv to spacing of #5)
Neutral axis of transformed section is y (in)
(Conc thk- top cover-y)*As*n= Concr width * y* (y/2)
As*n (in^2) 3.13
y, (in) 2.23
I_transformed (in^4) 93.44
σ_s, (service stress, ksi) My/I 11.41 << 36 ✔, stress is ok
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Design Calculations - Geometry Checked: CL Date: 6/4/20
Task: Deck Design @ Overhang Page: of:
Job #: NO:
Deck Overhang thickness (in) 8.50
Self Weight of Deck overhang region (lb/ft^2) 110
Barrier Type 836 Weight (plf) 600
Barrier base width (in) 17
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Design Calculations - Geometry Checked: CL Date: 6/4/20
Task: Deck Design @ Overhang Page: of:
Job #: NO:
Design Case 1: Check overhang for horizontal vehicular collision load
X, Design section of overhang (in) 8 inch away from interior base of barrier
Design section to CL of ext. girder (in) 19.625
Use general parapet values & dimensions from AASHTO rating TL -4:
(AASHTO)
AASHTO
The overhang is designed to resist an axial tension force from vehicular collision acting simultaneously with the collision + dead load
moment. This would be for extreme limit state design.
(Caltrans User Guide to
Bridge Standard Detail
Sheets Section 16)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Design Calculations - Geometry Checked: CL Date: 6/4/20
Task: Deck Design @ Overhang Page: of:
Job #: NO:
Parapet height (in) 36
Lc, length of parapet failure mechanism (in) 180
Lt, (in) 42
Mc/L (kip-ft/ft) 16.5 (Approximately, compred with other barriers)
R_w, Collision load capacity (kip) 93.40
a. At inside face of parapet
Design axial tensile force, R_w/(Lc+2H), (klf) 4.45
M_DL, slab k-ft/ft 0.17
M_DL, parapet, k-ft/ft 0.43
Mu, Design factored moment, k-ft/ft 17.24
Deck Overhang thickness (in) 8.50
Use #6 reinforcement bars @ overhang top
#6 bar Diameter (in) 0.75
A #6 (in^2) 0.44
d, overhang thk-top cover-half bar diameter, (in) 6.00 Say eqv to effective depth of section
Assume provided area of steel, (in^2/ft) 1.76
Say same spacing as the the rest of the slab 3 inch spacing
Tension in reinforcement (k/ft) 105.6
C, Compression in concrete (k/ft) 101.15
a= C/ (b*ß1* f'c), (in) 1.98
Mn, (k-ft /ft) 43.33
For extreme limit state, ø =1.0 This case not controls
ø Mn (k-ft/ft) 43.33 > 17.24 ok
c/de 0.39 < 0.42 steel yields before the conc. Crushing
b. At design section in the overhang
Say that effective length of collision, has 30 degrees of both sides spreading along the barrier length
Collision moment @ design section (k-ft/ft)
Mc/Lc *(Lc+2*0.577*X) 15.70
M_DL, Slab (k-ft/ft) 0.32
M_DL, parapet (k-ft/ft) 0.83
M_DW (k-ft/ft) 0.01
Mu, Design factored moment, k-ft/ft 17.14
Design axial tensile force, R_w/(Lc+2H+2*0.577X), (klf) 4.29
Assume req'd area of steel, (in^2/ft) 1.76
ø Mn (k-ft/ft) 43.33 > 17.14 ok
This case not controls
c. Check dead load + collision moments at design section in first span
Assumed distribution of the collision moment across the width of the deck
Dead load moment at design section due to dead loads on the overhang
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Design Calculations - Geometry Checked: CL Date: 6/4/20
Task: Deck Design @ Overhang Page: of:
Job #: NO:
Dead load moment at design section due to dead load on the first deck span
Collision moment @ exterior girder, M1 (k-ft/ft) 16.50
Collision moment @ 1st int. girder, M2 (k-ft/ft) 6.60
Per interpolation, total collision moment (k-ft/ft) 18.99
Using 30 degress angle distribtion:
Design collision moment (k-ft/ft) 14.57
M_DL, Slab (k-ft/ft) 0.90
M_DL, parapet (k-ft/ft) 1.81
M_DW (k-ft/ft) 0.10
Mu, Design factored moment, k-ft/ft 18.11
The dead load between the girder, creates much smaller moment at the design section, compared to the cantilever
segment deadload; therefore ignore such prior's moment to be conservative, because it is opposite direction.
ø Mn (k-ft/ft) 43.33 > 18.11
This case controls
Design Case 2 Vertical collision force
For concrete parapets, the case of vertical collision never controls
Design Case 3 Check DL + LL
a. design section in the overhang
Wheel from the base of the barrier (in) 12
Wheel to CL of ext. girder (in) 15.625
Equivalent strip width for LL (in) 58.021
Mu, Strength I moment, k-ft/ft 6.14 1.25DC+1.5DW+1.75LL
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Design Calculations - Geometry Checked: CL Date: 6/4/20
Task: Deck Design @ Overhang Page: of:
Job #: NO:
Mu, Strength II moment, k-ft/ft 7.20 1.25DC+1.5DW+1.35LL(permit)
Mu, Design factored moment, k-ft/ft 7.20
For strength I limit state, ø =0.9
Assume req'd area of steel, (in^2/ft) 1.76
ø Mn (k-ft/ft) 39.00 > 7.20 ok
This case not controls
b. Check dead load + LL moments at design section in first span
Factored HL-93 M_LL (k-ft/ft) 8.38 (hand calc per lever rule)
Factored P-15 M_LL (k-ft/ft) 10.25 (hand calc per lever rule)
Controlling M_LL (k-ft/ft) 10.25
Equivalent strip width (in) 58.02
Mu, (k-ft/ft) 5.65
For strength I limit state, ø =0.9
Assume req'd area of steel, (in^2/ft) 1.76
ø Mn (k-ft/ft) 39.00 > 5.65 ok
This case not controls
Provided top reinforcement in the slab regions other than the overhang
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Design Calculations - Geometry Checked: CL Date: 6/4/20
Task: Deck Design @ Overhang Page: of:
Job #: NO:
6 inch spacing #6 bars @ top 0.88 in^2/ft > 0.6 in^2/ft ok
Cut-off length requirement:
15 times the bar diameter control, (in) 11.25 AASHTO 5.11.1.2.1
Req'd length past the CL of the ext. girder (in) 31.25
Development length : AASHTO 5.11.2
1.25*Ab*fy / sqrt (f'c), (in) 14.76
0.4*db*fy, (in) 18
(in) 12
Controlling length (in) 18.00
Correction factors:
Normal bars 1 AASHTO 5.11.2.1.2)
Development length (in) 18
Previously, design section is 13" away from CL of ext girder
length of bar past CL of Ext. girder: (in) 31
Compared with the cut-off length requirement:
The controlling length of the bar past CL of ext. grider 31 inch
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Design Calculations - Geometry Checked: CL Date: 6/4/20
Task: Deck Design of longitudinal reinforcement Page: of:
Job #: NO:
Longitudinal bottom reinforcement:
S (ft) 7.06
220 / sqrt (S)= 82.81 % > 67%
Controlling value is 67%
For deck is not under the median, transv. bot #6 @ 6 inch
Transverse bar (in^2/ft) 0.88
Req'd long. Bottom bar (in^2/ft) 0.59
For longitudinal reinforcement @bottom use #6 bars
Required Spacing (in) 8.96
Long. Direction #6 @ bottom @ spacing 9 inch
Top longitudinal reinforcement --> no specific requirement
Long. Direction #6 @Top @spacing 12 inch
4 Substructure Design
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
4.1 Abutment Pile Loading and Lateral Analysis
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
Project: Port of Stockton Fyffe Grade Separation Computed: CL Date: 4/20/20
Subject: Design Calculations - Abutment 1 Piles Checked: JC Date: 4/24/20
Task: Page: of:
Job #: NO:
CL of back wall to CL footing: -1.75 ft
CL of stem wall to CL footing: 0 ft
CL of bearing to CL footing: 0.00 ft
Top of fill
CL of Back
wall
CL of
Bearing
OG
CL of Footing
& Mid Pile
CL of
Leading Pile
CL of Trailing
Pile
Active Earth
Pressure
4' soil Surcharge for LL
Passive
Earth
Pressure
CL of Stem
wall
Top of roadway
Project: Port of Stockton Fyffe Grade Separation Computed: CL Date: 4/20/20
Subject: Design Calculations - Abutment 1 Piles Checked: JC Date: 4/24/20
Task: Page: of:
Job #: NO:
4' soil Surcharge for LLEdge of footing to face ofwall, back side: 4.75 ft
Edge of footing to face ofwall, front side: 4.75 ft
Top of fill to top of footing: 35.00 ft
Roadway thickness: 1.00 ft
Surcharge, assumed eq. height of soil: 4.00 ft
Lateral earth pressure, H: 40.00 ft
Triangle pressure height: 12.00 ft
Lateral earth pressure at top of fill: 125.0 psf
Rectangle pressure height: 28.00 ft
Lateral earth pressure: 300.0 psf
OG to bottom of footing: 8.50 ft
top Triangle pressure height, passive: 5.00 ft
top Lateral earth resistance, passive: 1,500.0 psf
lower Trapezoidal pressure height, passive: 2.50 ft
lower Lateral earth resistance, passive: 1,862.5 psf
LOADING
DC - Bearing Reaction, vertical: 1,155 kips
DW - Bearing Reaction, vertical: 148 kips
LL + IM - Bearing Reaction, vertical: 1 kips
BR - Bearing Reaction, Longitudinal: 15.3 kips
BR - Applied location to bottom of footing: 44.50 ft
FR - Bearing Reaction, Longitudinal: 7.7 kips
FR - Applied location to bottom of footing: 38.50 ft
DC - Abutment Retaining Wall: 1,165 kips
DC - Abutment Wing Walls: 163 kips
DC - Pile Cap: 671 kips
Fill Weight behind Abutment, on pile cap: 1,309 kips
to CL footing: -4.13 ft
Fill Weight under Bridge, on pile cap: 199 kips
to CL footing: 4.13 ft
Project: Port of Stockton Fyffe Grade Separation Computed: CL Date: 4/20/20
Subject: Design Calculations - Abutment 1 Piles Checked: JC Date: 4/24/20
Task: Page: of:
Job #: NO:
4' soil Surcharge for LLEH - Lateral Earth Pressure, active, Triangle: 107 kips
to bottom of footing: 35.50 ft
EH - Lateral Earth Pressure, active, Rectangle: 601 kips
to bottom of footing: 17.50 ft
Passive Earth Pressure, region 1: -269 kips
to bottom of footing: 4.17 ft
Passive Earth Pressure, region 2: -32 kips
to bottom of footing: 0.83 ft
Passive Earth Pressure, region 3: -269 kips
to bottom of footing: 1.25 ft
LOADING
TOTAL on Foundation
DC DW EV-1 EV-2 LL+IM BR EH Passive FR EQ
Vertical, P (kips) = 3,154 148 1,309 199 1 -- -- -- -- --
Lateral, V (kips) = -- -- -- -- -- 15 708 -569 8 --
Moment, M (kip-ft) = -1,221 0 -5,401 820 0 681 14,306 -1,481 295 --
Strength I Combination
Load factor, Max 1.25 1.50 1.35 1.35 1.75 1.75 1.50 -- 1.00 --
Load factor, Min 0.90 0.90 1.00 1.00 -- -- 0.90 0.90 -- --
SERVICE I
Pile Loads
Vertical, Max. p (kips) =
Vertical, Min. p (kips) =
Lateral, v (kips) =
STRENGTH I
Pile Loads
Vertical, Max. p (kips) =
Vertical, Min. p (kips) =
Lateral, v (kips) = 12 1 13
Transit TOTAL
1 -10 -9
236 10 246
Permanent
Permanent Transit TOTAL
154
3
7
1
160
4
60 -6 54
Project: Port of Stockton Fyffe Grade Separation Computed: CL Date: 4/20/20
Subject: Design Calculations - Abutment 2 Piles Checked: JC Date: 4/24/20
Task: Page: of:
Job #: NO:
CL of back wall to CL footing: -1.75 ft
CL of stem wall to CL footing: 0 ft
CL of bearing to CL footing: 0.00 ft
Top of fill
CL of Back wall
CL of
Bearing
OG
CL of Footing & Mid Pile
CL of
Leading Pile
CL of
Trailing Pile
Active
Earth
Pressure
4' soil Surcharge for LL
Passive
Earth
Pressure
CL of Stem
wall
Top of roadway
Project: Port of Stockton Fyffe Grade Separation Computed: CL Date: 4/20/20
Subject: Design Calculations - Abutment 2 Piles Checked: JC Date: 4/24/20
Task: Page: of:
Job #: NO:
4' soil Surcharge for LL
Edge of footing to face ofwall, back side: 4.75 ft
Edge of footing to face ofwall, front side: 4.75 ft
Top of fill to top of footing: 35.00 ft
Roadway thickness: 1.00 ft
Surcharge, assumed eq. height of soil: 4.00 ft
Lateral earth pressure, H: 40.00 ft
Triangle pressure height: 12.00 ft
Lateral earth pressure at top of fill: 125.0 psf
Rectangle pressure height: 28.00 ft
Lateral earth pressure: 300.0 psf
OG to bottom of footing: 8.50 ft
top Triangle pressure height, passive: 5.00 ft
top Lateral earth resistance, passive: 1,500.0 psf
lower Trapezoidal pressure height, passive: 2.50 ft
lower Lateral earth resistance, passive: 1,862.5 psf
LOADING
DC - Bearing Reaction, vertical: 1,155 kips
DW - Bearing Reaction, vertical: 148 kips
LL + IM - Bearing Reaction, vertical: 298 kips
BR - Bearing Reaction, Longitudinal: 30.6 kips
BR - Applied location to bottom of footing: 44.50 ft
FR - Bearing Reaction, Longitudinal: 15.3 kips
FR - Applied location to bottom of footing: 38.50 ft
DC - Abutment Retaining Wall: 1,272 kips
DC - Abutment Wing Walls: 163 kips
DC - Pile Cap: 712 kips
Fill Weight behind Abutment, on pile cap: 1,429 kips
to CL footing: -4.13 ft
Fill Weight under Bridge, on pile cap: 211 kips
to CL footing: 4.13 ft
EH - Lateral Earth Pressure, active, Triangle: 116 kips
to bottom of footing: 35.50 ft
EH - Lateral Earth Pressure, active, Rectangle: 657 kips
to bottom of footing: 17.50 ft
Project: Port of Stockton Fyffe Grade Separation Computed: CL Date: 4/20/20
Subject: Design Calculations - Abutment 2 Piles Checked: JC Date: 4/24/20
Task: Page: of:
Job #: NO:
4' soil Surcharge for LLPassive Earth Pressure, region 1: -293 kips
to bottom of footing: 4.17 ft
Passive Earth Pressure, region 2: -35 kips
to bottom of footing: 0.83 ft
Passive Earth Pressure, region 3: -293 kips
to bottom of footing: 1.25 ft
LOADING
TOTAL on Foundation
DC DW EV-1 EV-2 LL+IM BR EH Passive FR EQ
Vertical, P (kips) = 3,302 148 1,429 211 298 -- -- -- -- --
Lateral, V (kips) = -- -- -- -- -- 31 773 -622 15 --
Moment, M (kip-ft) = -1,221 0 -5,896 871 0 1,362 15,617 -1,617 589 --
Strength I Combination
Load factor, Max 1.25 1.50 1.35 1.35 1.75 1.75 1.50 -- 1.00 --
Load factor, Min 0.90 0.90 1.00 1.00 -- -- 0.90 0.90 -- --
SERVICE I
Pile Loads
Vertical, Max. p (kips) =
Vertical, Min. p (kips) =
Lateral, v (kips) =
STRENGTH I
Pile Loads
Vertical, Max. p (kips) =
Vertical, Min. p (kips) =
Lateral, v (kips) =
Permanent Transit TOTAL
145 17 163
54 -6 49
3 1 4
Permanent Transit TOTAL
224 28 251
-2 -12 -14
12 1 13
4.2 Abutment Footing Design
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/27/20
Subject: Design Calculations - Footings Checked: CL Date: 5/2/20
Task: Page: of:
Job #: NO:
Geometry
Abutment Wall Length (min, use Abutment 1) 95.17
Abutment Height, Total (ft) 35.00
Precast Square Concrete Pile Size (in) 14
Total Number of Piles 45
Number of Rows of Piles 3
Pile Spacing, Centerline to Centerline (alignment direction) (ft) 5.00
Pile Spacing, Centerline to Centerline (transverse to alignment) (ft) 5.50
Edge of Footing to Centerline of Leading Pile (Bridge side) (ft) 1.50
Edge of Footing to Centerline of Trailing Pile (Embankment side) (ft) 1.50
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/27/20
Subject: Design Calculations - Footings Checked: CL Date: 5/2/20
Task: Page: of:
Job #: NO:
Centerline of Stem Wall to Centerline of Leading Pile (ft) 5.00
Centerline of Stem Wall to Centerline of Trailing Pile (ft) 5.00
Centerline of Stem Wall to Centerline of Middle Row Pile (ft) 0.00
Pile Cap Thickness (ft) 3.50
Abutment Toe Critical Flexsual Section
Use the controling pile reaction for all the piles in calculation for conservativeness.
Factored P (kip) 251
Unfactored P (kip) 163
Dist. From leading pile to critical section (ft) 3
Factored moment along critical flexural section (kip-ft) 12257
Mu, factored moment per 1ft length of abutment (kip-ft/ft) 129
Mu_service moment per 1ft length of abutment (kip-ft/ft) 83
Design per 1ft length of the abutment
b, concrete design section (in) 12.00
Use # 9 bars
#9 bar diameter (in) 1.128
#9 bar area (in^2) 1.00
Use abutment 1's geometry for the calcualation, because considered the length & pile number,
abutment 1 has less of pile number per unit length of abutment.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/27/20
Subject: Design Calculations - Footings Checked: CL Date: 5/2/20
Task: Page: of:
Job #: NO:
fy, for rebar (ksi) 60
f'c, footing concrete (ksi) 4
fr = 0.24*sqrt(f'c) , (ksi) 0.48
I_g (in^4) 74088.00
Y_t (in) 21.00
M_cr = fr*I_g/Y_t (k-ft) 141.12
1.2 M_cr (k-ft) 169.34
1.33 Mu (k-ft) 171.30
Controlling design, the less of 1.2Mcr & 1.33Mu (k-ft) 169.34
Bottom reinforcement clear cover (in) 6.00
de, effective depth (in) 35.436
Ф 0.90
Rn = (1.2Mcr )/ (Ф b* de^2), ksi 0.15
ρ 0.0026
As = ρ*b*de , (in^2/ft length) 1.09
Number of #9 bar for 1ft 1.09
Max spacing (in) 11.045
Spacing of #9 bar used (in) 9.00
As_provided (in^2/ft) 1.33 > 1.09 min, ok
Check maximum reinforcement limits:
T=As* fy (kip) 80
a= T/(0.85*f'c *b), (in) 1.961
ß1 0.85
c = a/ ß1 , (in) 2.31
c /de 0.07 < 0.42, ok
Check Crack Control:
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/27/20
Subject: Design Calculations - Footings Checked: CL Date: 5/2/20
Task: Page: of:
Job #: NO:
dc (in) 6.564
h (in) 42
ß_s 1.265
ϒ_e, class 1 1
f_ss (ksi) 0.80
Max spacing limit from above (in) 681.2 This is NOT control
AASHTO
5.10.8 Max spacing (in)
12 > 9.00 ok
To find the f_ss, tensile stress under service:
E_s, rebar (ksi) 29,000
E_c, (ksi) 3,644
n= E_s,rebar/ E_c 7.96
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/27/20
Subject: Design Calculations - Footings Checked: CL Date: 5/2/20
Task: Page: of:
Job #: NO:
k 0.182
k* de, (in) 6.46
y= de - k* de (in) 28.97
I_trans, (In^4) 9986.9
fss = n*M_serv *y /I_trans (ksi) 0.80
Design the top reinforcement for footing:
P, factored pile reaction (kip) -14
P_service pile reaction (kip) 49
Moment arm for above pile reaction (ft) 3
The negative pile reaction shown above will create very small negative moment.
Mu, factored moment per 1ft length of abutment (kip-ft/ft) -6.963
Use # 7 bars @ footing top reinforcement
#7 bar diameter (in) 0.875
#7 bar area (in^2) 0.60
Using spacing of 9" , with 3" cover
A_s provided (in^2 /ft) 0.8
Check maximum reinforcement limits:
The moment is very small here, so the provided bar should be sufficient for the
min. reinforcement requiremnet.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/27/20
Subject: Design Calculations - Footings Checked: CL Date: 5/2/20
Task: Page: of:
Job #: NO:
T=As* fy (kip) 48
a= T/(0.85*f'c *b), (in) 1.18
ß1 0.85
c = a/ ß1 , (in) 1.384
de, effective depth (in) 38.563
c /de 0.036 < 0.42, ok
Design for shear
For Concrete's shear resistance
ß 2
bv (in) 12
The crack control requirement should be satisfied because fss stress will be very small caused by
the moment.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/27/20
Subject: Design Calculations - Footings Checked: CL Date: 5/2/20
Task: Page: of:
Job #: NO:
dv, (in) 34.5
Vc (kip) 52.26
Ф 0.9
ФVn (kip) 47.04
Vu(kip/ft length of abutment ) 39.63 < 47.04 ok
Check the punching shear for section without shear reinforcement
0.5 dv (in) 17.23
Pile critical region, length (in) 48.46
Pile critical region, width (in) 42.23
bo, perimeter (in) 181
ßc 1
0.126*sqrt(f'c)*bo*dv (kip) 1575
(0.063+0.126/ßc)sqrt(f'c)bo*dv (kip) 2160
Vn (kip) 1575 >> 251 ok
4.3 Abutment Stem Wall Design
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/27/20
Subject: Design Calculations - Stem Wall Checked: CL Date: 5/2/20
Task: Page: of:
Job #: NO:
References: AASHTO & LRFD Steel Girder Superstructure Design Example from FHWA
f'c, abutment concrete (ksi) 4
CL of back wall to CL footing: (ft) -1.75
CL of stem wall to CL footing: (ft) 0
CL of bearing to CL footing:(ft) 0
Edge of footing to face ofwall, back side (ft): 4.75
Edge of footing to face ofwall, front side: (ft) 4.75
Back wall height (ft) 7.5
Stem wall height (ft) 28.00
Stem wall thickness (ft) 3.50
Stem wall length (in bridge transv. Direction), ft 71.6
Use #9 bars or #11 bars for back wall & stem wall design
fy, for rebar (ksi) 60
#9 bar diameter (in) 1.128#9 bar area (in^2) 1.00
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/27/20
Subject: Design Calculations - Stem Wall Checked: CL Date: 5/2/20
Task: Page: of:
Job #: NO:
Loading Condition of the back wall:
For braking force from vehicles
Braking force for 2-lane (kip) in bridge long. 36.0
R_BR per 1ft length of back wall (kip) 0.50
Moment arm to based of back wall (ft) 28.00
For self weight of wall:
R_DLback per 1ft length of back wall (kip) 1.16
Moment arm to CL stem wall (ft) 1.25
R_DLstem per 1ft length of back wall (kip) 15.19
Moment arm to CL stem wall (ft) 0.00
R_DC from superstructure 1ft of back wall (kip) 14.75
Moment arm to CL stem wall (ft) 0.00
R_DW from superstructure 1ft of back wall (kip) 2.07
Moment arm to CL stem wall (ft) 0.00
For horizontal earth pressure:
R_EH per 1ft length of back wall (kip) 5.56
Moment arm to based of back wall (ft) 15.95
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/27/20
Subject: Design Calculations - Stem Wall Checked: CL Date: 5/2/20
Task: Page: of:
Job #: NO:
For live load surcharge:
Surcharge eqv height of soil (ft) 4.00 from Geotech
Live load surcharge eqv pressure (psf) 125 from Geotech
R_LS per 1ft length of back wall (kip) 4.44
Moment arm to based of stem wall (ft) 17.75
For loads due to temperature : say moderate climate
ϵ, Concrete thermal expansion (1/F) 0.000006
t, assumed concrete setting temperature(F) 45.00
For expansion:
∆_rise (F) = max temp -set temp 35.00
∆_exp = ϵ*∆t*L_span, (in) 0.29
∆_drop (F) = set temp- min temp 35.00
∆_contr = ϵ*∆t*L_span, (in) 0.29
Bearing pads properties:
Bearing pads Area (in^2) 360.00
G, Shear modulus (ksi) 0.10
h_rt, elastomer thickness (in) 3.00
Load due to temp change /bearing (kip) 3.42
Hu per 1ft length of back wall (kip) 0.38
Moment arm to based of stem wall (ft) 28.00
For LL from vehicles
End reaction for One lane +IM 42.56
(Lane load +(LL+IM))*Multipresence factor (kip) 146.88
R_LL per 1ft length of back wall (kip) 2.05
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/27/20
Subject: Design Calculations - Stem Wall Checked: CL Date: 5/2/20
Task: Page: of:
Job #: NO:
Wind load to transverse bridge direction acts different axis from loads above
Thus, NOT inlcude wind loads in the load combination
Factored M: 1.25DC+1.5 DW+1.75BR+1.5 EH+1.75LS+0.5 TU (controlling)
Mu (k-ft) 302.57
Unfactored moment :
M_serv (K-ft) 193.62
Factored shear force @ base of stem wall 1.5EH+1.75LS+1.75 BR+0.5TU
Vu (kip) 17.17
Factored vertical force @ base of stem wall 1.25DC+1.5 DW+ 1.75LL
F_v (kip) 45.58
Minimum reinforcement
fr = 0.24*sqrt(f'c) , (ksi) 0.48
I_g (in^4) 74088
Y_t (in) 21
M_cr = fr*I_g/Y_t (k-ft) 141.12
1.2 M_cr (k-ft) 169.34
1.33 Mu (k-ft) 402.42
Controlling moment for reinforcement (k-ft) 169.34
Use #9 Bars with 2.0" cover <---
de = wall thk-cover-0.5 bar dia (in) 39.44
Ф 0.90
Rn = (1.2Mcr )/ (Ф b* de^2), ksi 0.121
ρ 0.0021
As = ρ*b*de , (in^2/ft length) 0.972
Use #9 Bars with 9 inch Spacing <---
As_provided (in^2/ft) 1.33 > 0.97
ρ_e, As_provided /(b* de) 0.00282
Check the maximum reinforcement limit:
T= As_provided * fy (kip) 80
a= T/(0.85*f'c *b), (in) 1.96
ß1 0.85
c = a/ ß1 , (in) 2.31
c /de 0.058 < 0.42 say ok
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/27/20
Subject: Design Calculations - Stem Wall Checked: CL Date: 5/2/20
Task: Page: of:
Job #: NO:
Check crack control
dc (in) 3.06
h (in) 42
ß_s 1.11
ϒ_e, class 1 1
f_ss (ksi) 36.00 Controlling check
Max spacing limit from above (in) 11.35 > 9inch Spacing
AASHTO
5.10.8
To find the f_ss, tensile stress under service:
E_s, rebar (ksi) 29,000
E_c, (ksi) 3,644
n= E_s,rebar/ E_c 7.96
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/27/20
Subject: Design Calculations - Stem Wall Checked: CL Date: 5/2/20
Task: Page: of:
Job #: NO:
k 0.191
k* de, (in) 7.51
I_trans, (In^4) 12509.34
y= de - k* de (in) 31.92
fss = n*M_serv *y /I_trans (ksi) 47.18
Design for shear:
For Concrete's shear resistance
ß 2
bv (in) 12
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/27/20
Subject: Design Calculations - Stem Wall Checked: CL Date: 5/2/20
Task: Page: of:
Job #: NO:
dv, (in) 38.46
Vc (kip) 39.87
Ф 0.90
ФVc (kip) 35.88 > 17.17 Vu, ok
Shrinkage and temperature reinforcement:
b, (in) 12
h (in) 42
1.30bh/2/(b+h)/fy 0.101
Min, As /(Ab/fy)) 0.11
As_min (in^2/ft) 0.11
#6bar for each face of back wall 12 inch spacing <---
As_provided (in^2/ft) 0.44 > 0.11 ok
4.4 Abutment Backwall Design
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/27/20
Subject: Design Calculations - Back Wall Checked: CL Date: 5/2/20
Task: Page: of:
Job #: NO:
References: AASHTO & LRFD Steel Girder Superstructure Design Example from FHWA
f'c, abutment concrete (ksi) 4
CL of back wall to CL footing: (ft) -1.75
CL of stem wall to CL footing: (ft) 0
CL of bearing to CL footing:(ft) 0
Edge of footing to face ofwall, back side (ft): 4.75
Edge of footing to face ofwall, front side: (ft) 4.75
Back wall height (ft) 7.5
Back wall thickness (ft) 1
Back wall length (in bridge transv. Direction), ft 71.6
Use #9 bars or # 6 bars for back wall & stem wall design
fy, for rebar (ksi) 60
#5 bar diameter (in) 0.625#5 bar area (in^2) 0.31
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/27/20
Subject: Design Calculations - Back Wall Checked: CL Date: 5/2/20
Task: Page: of:
Job #: NO:
Loading Condition of the back wall:
For braking force from vehicles
Braking force for 2-lane (kip) in bridge long. 36.0
R_BR per 1ft length of back wall (kip) 0.50
Moment arm to CL back wall (ft) 0.00
For self weight of back wall:
R_DL per 1ft length of back wall (kip) 1.16
Moment arm to CL back wall (ft) 0.00
For horizontal earth pressure:
R_EH per 1ft length of back wall (kip) 0.66
Moment arm to based of back wall (ft) 2.50
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/27/20
Subject: Design Calculations - Back Wall Checked: CL Date: 5/2/20
Task: Page: of:
Job #: NO:
For live load surcharge:
Surcharge eqv height of soil (ft) 4.00 from Geotech
Live load surcharge eqv pressure (psf) 125 from Geotech
R_LS per 1ft length of back wall (kip) 0.94
Moment arm to based of back wall (ft) 3.75
For LL from vehicles
End reaction for One lane +IM 43
(Lane load +(LL+IM))*Multipresence factor (kip) 147
R_LL per 1ft length of back wall (kip) 2.05
Factored ultimate moment: 1.25DC+1.75BR+1.5 EH+1.75LS (controlling comb)
Mu (k-ft) 8.61
Unfactored moment :
M_serv (K-ft) 5.16
Factored shear force @ base of back wall 1.5EH+1.75LS +1.75 BR
Vu (kip) 3.50
Factored vertical force @ base of back wall 1.25DC+1.75LL
F_v (kip) 5.04
Minimum reinforcement
fr = 0.24*sqrt(f'c) , (ksi) 0.48
I_g (in^4) 1728
Y_t (in) 6
M_cr = fr*I_g/Y_t (k-ft) 11.52
1.2 M_cr (k-ft) 13.82
1.33 Mu (k-ft) 11.46
Controlling moment for reinforcement (k-ft) 11.46
Use #6 Bars with 2.0" cover <---
de = wall thk-cover-0.5 bar dia (in) 9.69
Ф 0.90
Rn = (1.33Mu)/ (Ф b* de^2), ksi 0.136
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/27/20
Subject: Design Calculations - Back Wall Checked: CL Date: 5/2/20
Task: Page: of:
Job #: NO:
ρ 0.0023
As = ρ*b*de , (in^2/ft length) 0.268
Use #5 Bars with 9 inch Spacing <---
As_provided (in^2/ft) 0.41 > 0.27
ρ_e, As_provided /(b* de) 0.00356
Check the maximum reinforcement limit:
T= As_provided * fy (kip) 24.8
a= T/(0.85*f'c *b), (in) 0.61
ß1 0.85
c = a/ ß1 , (in) 0.72
c /de 0.074 < 0.42 say ok
Check crack control
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/27/20
Subject: Design Calculations - Back Wall Checked: CL Date: 5/2/20
Task: Page: of:
Job #: NO:
dc (in) 2.81
h (in) 12
ß_s 1.44
ϒ_e, class 1 1
f_ss (ksi) 36.00
Max spacing limit from above (in) 7.90 > 9inch Spacing
AASHTO
5.10.8
To find the f_ss, tensile stress under service:
E_s, rebar (ksi) 29,000
E_c, (ksi) 3,644
n= E_s,rebar/ E_c 7.96
k 0.211
k* de, (in) 2.05
I_trans, (In^4) 226.33
y= de - k* de (in) 7.64
fss = n*M_serv *y /I_trans (ksi)
Design for shear:
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/27/20
Subject: Design Calculations - Back Wall Checked: CL Date: 5/2/20
Task: Page: of:
Job #: NO:
For Concrete's shear resistance
ß 2
bv (in) 12
dv, (in) 9.38
Vc (kip) 14.23
Ф 0.90
ФVc (kip) 12.81 > 3.50 Vu, ok
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 4/27/20
Subject: Design Calculations - Back Wall Checked: CL Date: 5/2/20
Task: Page: of:
Job #: NO:
Shrinkage and temperature reinforcement:
b, (in) 12
h (in) 12
1.30bh/2/(b+h)/fy 0.065
Min, As /(Ab/fy)) 0.11
As_min (in^2/ft) 0.264
#5 bar for each face of back wall @ 12 inch spacing <---
As_provided (in^2/ft) 0.31 > 0.264 ok
4.5 Abutment Joint Width
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Design Calculations Checked: CL Date: 6/11/20
Task: Joint Movement Calculations Page: of:
Job #: NO:
Bearing pads proerpties from MathCAD:
L (in) 14
W (in) 24
Area (in^2) 336
Total Beraing Pad Thickness (in) 3.45
Elastomer thickness (in) 3
Shear Modulus (ksi) 0.1
For Abutment 1 & 2:
Temperature Extremes: (F)
Maximum temperature: (F) 110.00
Minimum temperature: (F) 23.00
Temperature Range: (F) 87.00
ϵ, Concrete thermal expansion (1/F) 0.000006
Thermal Movement (inch/100ft) 0.63
Anticipated shortening for pretensioned concrete (inch/100ft) 0.12
Movement factor (inch/100ft) 0.75
Contribution Length (ft) 113.19
Calculated Movement (inch) 0.84
Movement Rating (MR), inch 1.00
Type of Seal Type B Seal (neoprene compression seal)
4.6 Abutment Seat Width Design
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Design Calculations Checked: CL Date: 6/11/20
Task: Abumtent seat width design Page: of:
Job #: NO:
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 6/1/20
Subject: Design Calculations Checked: CL Date: 6/11/20
Task: Abumtent seat width design Page: of:
Job #: NO:
With 15kip shear force applied to each pile:
North Abutment pile displacmenet (in) 0.75
1 North Abutment number of piles: 45
South Abutment pile displacmenet (in) 0.5
2 SouthAbutment number of piles: 51
Total stiffness from the piles (kip/ft) 29160
weight of the superstructure (kip) 2606
weight of the substructure (kip) 3821
Total weight of the structure above piles (kip) 4689
g (ft/sec^2) 32.2
m (lb-mass) 145637
Bridge period natural T (sec) 0.44
Structural acceleration from plan (g) 0.64
EQ force (kip) 3001
∆_EQ (in) 1.24
MR+∆_EQ + L (in) 16.24
Ds (in) 63.13
Min N_A (in) 30
bridge skew angle θ (degrees) 31
N_A/ cos θ (in) 35
4.7 Wingwall Design
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 5/20/20
Subject: Design Calculations - Wing Wall Checked: CL Date: 5/25/20
Task: Page: of:
Job #: NO:
It can be obserced from plot above, that the wing walls are contrained one side with the
abutments, and the other end is free of contraint. The soil pressure of the wall is from
geotech info shown below.
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 5/20/20
Subject: Design Calculations - Wing Wall Checked: CL Date: 5/25/20
Task: Page: of:
Job #: NO:
wall thickness (in) 18
cantilever strip width (in) 30
length of cantilever wall strip (ft) 15
Horiz. Soil pressure (include surcharge) (psf) 170
Moment from Soil pressure for cantilever strip (kip-ft) 19.125
Factored ultimate moment: 1.25DC+1.75BR+1.5 EH+1.75LS (controlling comb)
The soil pressue value shown includes both soil horizontal pressure and live load surcharge
Use 1.75 facotor to be more conservative
Mu (kip-ft) 33.469
M_service (kip-ft) 19.125
Vu (kip) 4.46
To simplify the problem, it is conservative to treat the soil pressure along the entire wall
length the same 170psf. Then the wall can be treated as a cantilever beam, with 1ft widt
(when taking 1ft dpee strip of the wall)
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 5/20/20
Subject: Design Calculations - Wing Wall Checked: CL Date: 5/25/20
Task: Page: of:
Job #: NO:
Minimum reinforcement
fr = 0.24*sqrt(f'c) , (ksi) 0.48
I_g (in^4) 1728
Y_t (in) 9
M_cr = fr*I_g/Y_t (k-ft) 7.68
1.2 M_cr (k-ft) 9.216
1.33 Mu (k-ft) 44.513
Controlling moment for reinforcement (k-ft) 9.216
Horizontal rebars @ interior side of wingwall:
# 6 bar is used. A_bar (in^2) 0.44
Spacing (in) 9
de = wall thk-cover-0.5 bar dia (in) 15.5
Ф 0.9
Rn = (1.2Mcr)/ (Ф b* de^2), ksi 0.017
f'c, wingwall concrete (ksi) 4
fy, for rebar (ksi) 60
ρ 0.0003
As_req = ρ*b*de , (in^2/ft length) 0.1325
As_provided( in^2) 0.33 > 0.132 ok
ρ_provided 0.0007
Check the maximum reinforcement limit:
T= As_provided * fy (kip) 19.8
a= T/(0.85*f'c *b), (in) 0.1941
ß1 0.85
c = a/ ß1 , (in) 0.2284
c /de 0.0147 < 0.42 say ok
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 5/20/20
Subject: Design Calculations - Wing Wall Checked: CL Date: 5/25/20
Task: Page: of:
Job #: NO:
Check crack control
dc (in) 2.50
h (in) 18
ß_s 1.23
ϒ_e, class 1 1
f_ss (ksi) 36.00
Max spacing limit from above (in) 10.80 > 9inch, ok
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 5/20/20
Subject: Design Calculations - Wing Wall Checked: CL Date: 5/25/20
Task: Page: of:
Job #: NO:
To find the f_ss, tensile stress under service:
E_s, rebar (ksi) 29,000
E_c, (ksi) 3,644
n= E_s,rebar/ E_c 8
k 0.10
k* de, (in) 1.5621
I_trans, (In^4) 525.41
y= de - k* de (in) 13.938
fss = n*M_serv *y /I_trans (ksi) 48.45
For Concrete's shear resistance
ß 2
bv (in) 12
dv, (in) 21.6
Vc (kip) 32.8
Ф 0.9
ФVc (kip) 29.5 > 4.5 ok
Project: Port of Stockton Fyffe Grade Separation Computed: JC Date: 5/20/20
Subject: Design Calculations - Wing Wall Checked: CL Date: 5/25/20
Task: Page: of:
Job #: NO:
Shrinkage and temperature reinforcement:
b, (in) 12
h (in) 12
1.30bh/2/(b+h)/fy 0.065
Min, As /(Ab/fy)) 0.11
Rebars arrangments as following:
Horizontally Interior side of the wall #6 @ 9", As_provided (in^2/ft)
0.33 > 0.11 ok
Horizontally exterior side of the wall #6 @ 9", As_provided (in^2/ft)
0.33 > 0.11 ok
Vertically both sides of the wall #5 @ 18", As_provided (in^2/ft)
0.21 > 0.11 ok
4.8 Bearing Design
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
Project: Fyffe Grade Separation Computed: JC Date: 4/20/2020
Subject: Bearing Design Checked: CL Date: 4/20/2020
Ma n y S o lu t io n sS M
Task: Abut 1: Bearing Pad - Method A Page: of:
Job #: No:
O NE CO MP ANY
Design Specifications:
1. AASHTO LRFD Bridge Design Specifications, 8th Edition with 2019 CA Ammendments
2. ITD LRFD Bridge Design Manual.
3. PCI Design Handbook, Precast & Prestressed Concrete, 5th ed.
Worksheet Summary:
Check girder bearing pads at Abut 1 per Method A specifications. See local calculation for
superstructure loads.
Design Criteria:
Bridge Properties:
η 1.0:= Importance factor
Wdia_Abut 58 kip⋅:= Abutment diaphragm weight Nb 8:= Number of bearings
αc 6 106−⋅:= Concrete coeff. of thermal
expansion
SF 1.33:= Shear factor (see PC girder calcs)
Bearing Pad Properties:
L 14 in⋅:= Length of pad (parallel to
girder longitudinal axis)
ni 5:= Number of interior layers
W 24 in⋅:= Width of pad (perpendicular to
girder longitudinal axis)
hs 0.0747 in⋅:= Steel laminate thickness
(14 ga. plate)
Gmin 130 psi⋅:= Shear modulus range hr_I 0.5 in⋅ hs+:= CL to CL height of interior layers
Gmax 200 psi⋅:=
Hardness 60:= Hardness (durometer) hr_E 0.25 in⋅hs
2+:= CL to CL height of exterior layers
hri hr_I hs−:= Thickness of interior elastomeric layers Check hri3
16in⋅,
"ok"⋅= hri 0.5 in⋅=
hre hr_E 0.5 hs⋅−:= Thickness of exterior elastomeric layers Check hre1
8in⋅,
"ok"⋅= hre 0.25 in⋅=
hrt ni hri⋅ 2 hre⋅+:= Total elastomeric thickness hrt 3 in⋅=
htot ni hr_I⋅ 2 hr_E⋅+:= Total bearing pad thickness Check 6 in⋅ htot, ( ) "ok"⋅= htot 3.448 in⋅=
Area L W⋅:= Pad area Area 336 in2⋅=
SiArea
2 hri⋅ L W+( )⋅:= Shape factor for interior layer AASHTO Eqn. 14.7.5.1-1 Si 8.842=
SeArea
2 hre⋅ L W+( )⋅:= Shape factor for exterior layer Se 17.684=
Fyffe_Bearing_Pad_Method_A.xmcd 1 of 6
Project: Fyffe Grade Separation Computed: JC Date: 4/20/2020
Subject: Bearing Design Checked: CL Date: 4/20/2020
Ma n y S o lu t io n sS M
Task: Abut 1: Bearing Pad - Method A Page: of:
Job #: No:
O NE CO MP ANY
Reactions:
DLDC 436 533+ 88+ 98+( ) kip⋅:= Superstructure DC from Spreadsheet DLDC 1155 kip⋅=
DLDW 148 kip⋅:= Superstructure DW from Spreadsheet DLDW 148 kip⋅=
DLdia_ABUT Wdia_Abut:= DLdia_ABUT 58 kip⋅=
PS0 kip⋅Nb
:= Secondary post-tensioning PS 0 kip⋅=
DLDLDC DLDW+ DLdia_ABUT+ PS+( )
Nb
:=DL 170.1 kip⋅=
LL
1
1.33124 0.75⋅ 0.64
113.16
2⋅−
⋅ 0.64113.16
2⋅+
Nb⋅ kip SF⋅
Nb
:= LL 104.9 kip⋅=
HL-93 Live load, from Spreadsheet (without impact)bTL DL LL+( ):=
TL 275.1 kip⋅=Expansion/Contraction:
Le1
2113.16ft( )⋅:= Total tributary bridge length Le 56.6 ft⋅=
εES 0:= Elastic shortening
strain
Use maximum strain due to long term creep and shrinkage
calculated per CALTRANS memo to designers (7-1, pg. 6)
or creep and shrinkage calculated in girder design
εLT0.01 ft⋅100 ft⋅
:= εLT 0.0001=
Per AASHTO Table 3.12.2.1-1 Procedure A, the temperature range is 10F - 80F for
concrete structures for moderate climates
∆temp_rise 35:= ∆temp_fall 35:=
εtemp αc ∆temp_rise ∆temp_fall+( )⋅:= Range of thermal movement strain εtemp 0.00042=
∆s εES εLT+0.75
0.5εtemp+
Le⋅:= Total service load longitudinal movement
(AASHTO Art. 14.7.5.3.4)∆s 0.5 in⋅=
∆u η εES εLT+0.75
0.5εtemp+
⋅ Le⋅:= ∆u 0.5 in⋅=
Fyffe_Bearing_Pad_Method_A.xmcd 2 of 6
Project: Fyffe Grade Separation Computed: JC Date: 4/20/2020
Subject: Bearing Design Checked: CL Date: 4/20/2020
Ma n y S o lu t io n sS M
Task: Abut 1: Bearing Pad - Method A Page: of:
Job #: No:
O NE CO MP ANY
Project: Fyffe Grade Separation Computed: JC Date: 4/20/2020
Subject: Bearing Design Checked: CL Date: 4/20/2020
Ma n y S o lu t io n sS M
Task: Abut 1: Bearing Pad - Method A Page: of:
Job #: No:
O NE CO MP ANY
Project: Fyffe Grade Separation Computed: JC Date: 4/20/2020
Subject: Bearing Design Checked: CL Date: 4/20/2020
Ma n y S o lu t io n sS M
Task: Abut 1: Bearing Pad - Method A Page: of:
Job #: No:
O NE CO MP ANY
Rotations:
Cc 1.39:= Creep factor (from Spreadsheet )
θP_S 0 Cc⋅:= Rotation due to post-tensioning θP_S 0 rad⋅=
θDL 0.00435 0.00532+ 0.000240+( ) Cc⋅:= Rotation due to DC (from Spreadsheet) θDL 0.013775 rad⋅=
θSDL 0.00040 0.00068+( ) Cc⋅:= Rotation due to DW (from Spreadsheet) θSDL 0.001501 rad⋅=
θLL
0.00323
0
:= Rotation due to live loads
(from CSi Bridge model)
θLL
0.00323
0
rad⋅=
θPG 0.003:= Rotation due to profile grade θPG 0.003 rad⋅=
θcon 0.005:= Added rotation due to construction tolerances
(AASHTO Art. 14.4.2.1)
θcon 0.005 rad⋅=
θsp θP_S θDL+ θSDL+ θLL1
+ θPG+ θcon+:= Maximum positive service load rotation θsp 0.0265 rad⋅=
θsn θP_S θDL+ θSDL+ θLL2
+ θPG+ θcon−:= Maximum negative service load rotation θsn 0.0133 rad⋅=
θm max θsp θsn, ( ):= Design service load rotation θm 0.0265 rad⋅=
Compressive Stress (AASHTO 14.7.6.3.2):
σTL_allow min 1.25 ksi⋅ 1.25 Gmin⋅ Si⋅, ( ):= Allowable total service load compressive stress
(AASHTO Eqn. 14.7.6.3.2-4)
σTL_allow 1250 psi⋅=
σDL DL Area1−⋅:= Average compressive stress due to service dead load σDL 506 psi⋅=
σLL LL Area1−⋅:= Average compressive stress due to live load σLL 312 psi=
σTL TL Area1−⋅:= Average compressive stress due to total service load σTL 819 psi⋅=
Check σTL_allow σTL, ( ) "ok"⋅=
Compressive Deflection (AASHTO 14.7.6.3.3):
∆c_DL_max min 0.07 hrt⋅1
8in⋅,
:= Maximum instantaneous DL deflection
(0.07*hrt per Caltrans Memo to Designers 7-1)
∆c_DL_max 0.125 in⋅=
∆c_LT_max min 0.07 hrt⋅3
16in⋅,
:= Maximum long term deflection
3/16" min. per ITD BDM Art. 14.7.5
∆c_LT_max 0.187 in⋅=
∆c_LL_max1
8in⋅:= Maximum instantaneous LL+IM deflection
ITD BDM Art. 14.7.5 (Art. C14.7.5.3.3)
∆c_LL_max 0.125 in⋅=
Estimate strain in reinforced bearings based on durometer specific compressive strain eqn. (ITD BDM A14.2)
σDL 506 psi= Avg. dead load stress σTL 819 psi⋅= Avg. total load stress
Hardness 60= Si 8.8= Shape factor (interior layer)
Fyffe_Bearing_Pad_Method_A.xmcd 3 of 6
Project: Fyffe Grade Separation Computed: JC Date: 4/20/2020
Subject: Bearing Design Checked: CL Date: 4/20/2020
Ma n y S o lu t io n sS M
Task: Abut 1: Bearing Pad - Method A Page: of:
Job #: No:
O NE CO MP ANY
Strain parameters for Total Load deflection (TL); Dead Load deflection (DL); & Live Load deflection
(LL) (i, interior elastometric layer; e, exterior elastomeric layer):
c_x S σ, ( )
C 0.05 σ 600 psi⋅( )1−⋅
0.15
⋅←
x 0.65S 6
1−⋅( )1.0 0.0004 σTL⋅ psi1−⋅−
←
Hardness 70= S 6≤∧if
C 0.5 σ 1000 psi⋅( )1−⋅
0.5
⋅←
x 0.25S 12
1−⋅( )0.4
←
Hardness 70= S 6>∧if
C 0.065 σ 600 psi⋅( )1−⋅
0.15
⋅←
x 0.60S 6
1−⋅( )0.725
←
Hardness 60= S 6≤∧if
C 0.65 σ 1000 psi⋅( )1−⋅
0.5
⋅←
x 0.25S 12
1−⋅( )0.15
←
Hardness 60= S 6>∧if
C 0.10 σ 600 psi⋅( )1−⋅
0.15
⋅←
x 0.60S 6
1−⋅( )0.725
←
Hardness 50= S 6≤∧if
C 0.6 σ 1000 psi⋅( )1−⋅
0.5
⋅←
x 0.275S 6
1−⋅( )0.15
←
Hardness 50= S 6>∧if
C x( )T
return
:=Total load parameters
Ci_TL c_x Si σTL, ( )1:= Ci_TL 0.588=
xi_TL c_x Si σTL, ( )2:= xi_TL 0.266=
Ce_TL c_x Se σTL, ( )1:= Ci_TL 0.588=
xe_TL c_x Se σTL, ( )2:= xi_TL 0.266=
Dead load parameters
Ci_DL c_x Si σDL, ( )1:= Ci_DL 0.463=
xi_DL c_x Si σDL, ( )2:= xi_DL 0.266=
Ce_DL c_x Se σDL, ( )1:= Ce_DL 0.463=
xe_DL c_x Se σDL, ( )2:= xe_DL 0.23=
Live load parameters
Ci_LL c_x Si σLL, ( )1:= Ci_LL 0.363=
xi_LL c_x Si σLL, ( )2:= xi_LL 0.266=
Ce_LL c_x Se σLL, ( )1:= Ce_LL 0.363=
xe_LL c_x Se σLL, ( )2:= xe_LL 0.23=
ε C σ, x, ( ) C σ psi1−⋅( )x
⋅ 1001−⋅:= ITD BDM Art. A14.2
Instantaneous comp. strain of interior/ exterior
elastomeric layer(s) (Total load)
εi_TL ε Ci_TL σTL, xi_TL, ( ):= εi_TL 0.035=
εe_TL ε Ce_TL σTL, xe_TL, ( ):= εe_TL 0.028=
Instantaneous comp. strain of interior/ exterior
elastomeric layer(s) (Dead load)
εi_DL ε Ci_DL σDL, xi_DL, ( ):= εi_DL 0.024=
εe_DL ε Ce_DL σDL, xe_DL, ( ):= εe_DL 0.019=
Instantaneous comp. strain of interior/ exterior
elastomeric layer(s) (Live load)
εi_LL ε Ci_LL σLL, xi_LL, ( ):= εi_LL 0.01674=
εe_LL ε Ce_LL σLL, xe_LL, ( ):= εe_LL 0.01362=
Fyffe_Bearing_Pad_Method_A.xmcd 4 of 6
Project: Fyffe Grade Separation Computed: JC Date: 4/20/2020
Subject: Bearing Design Checked: CL Date: 4/20/2020
Ma n y S o lu t io n sS M
Task: Abut 1: Bearing Pad - Method A Page: of:
Job #: No:
O NE CO MP ANY
Compressive Deflection (AASHTO 14.7.5.3.6):
∆c_DL ni hri⋅ εi_DL⋅ 2 hre⋅ εe_DL⋅+:= Instantaneous deflection due to DL
(Eqn. 14.7.5.3.6-2)
∆c_DL 0.07 in⋅=
∆c_LL ni hri⋅ εi_LL⋅ 2 hre⋅ εe_LL⋅+:= Instantaneous deflection due to LL
(Eqn. 14.7.5.3.6-1)
∆c_LL 0.049 in⋅=
∆c_TL ni hri⋅ εi_TL⋅ 2 hre⋅ εe_TL⋅+:= Instantaneous deflection due to TL ∆c_TL 0.101 in⋅=
Creep∆ 39 %⋅:= Percentage of creep expected for deflections over 25 yrs
(25% for Hardness of 50, 35% for 60, 45% for 70)
∆c_LT ∆c_TL Creep∆ ∆c_DL⋅+:= Total long term deflection ∆c_LT 0.129 in⋅=
Long term total load check Check ∆c_LT_max ∆c_LT, ( ) "ok"⋅=CheckCheck
Instantaneous dead load check Check ∆c_DL_max ∆c_DL, ( ) "ok"⋅=CheckCheck
Instantaneous live load check Check ∆c_LL_max ∆c_LL, ( ) "ok"⋅=Check
Shear Deformation (AASHTO 14.7.6.3.4):
∆V_min 2 ∆s⋅:= Allowable shear deformation
Eqn. 14.7.6.3.4-1
hrt 3 in⋅= ∆V_min 0.991 in⋅=
Check hrt ∆V_min, ( ) "ok"⋅=Check
Stability (AASHTO 14.7.6.3.6):
hmaxmin L W, ( )
3:= Maximum bearing pad height htot 3.4 in⋅= hmax 4.7 in⋅=
Check hmax htot, ( ) "ok"⋅=Check
Reinforcement (AASHTO 14.7.5.3.5):
Fy 36 ksi⋅:= Yield stress of the weakest steel at the contact surface
∆FTH 24 ksi⋅:= Constant amplitude fatigue threshold, Category A,
AASHTO Table 6.6.1.2.5-3
3.0 hri⋅ σTL⋅
Fy
0.034 in⋅= Eqn. 14.7.5.3.7-1
hs_min max
3.0 hri⋅ σTL⋅
Fy
2.0 hri⋅ σLL( )⋅
∆FTH
:=2.0 hri⋅ σLL⋅
∆FTH
0.013 in⋅= Eqn. 14.7.5.3.7-2
Minimum shim thickness hs 0.1 in⋅= hs_min 0.034 in⋅=
Check hs hs_min, ( ) "ok"⋅=Check
Fyffe_Bearing_Pad_Method_A.xmcd 5 of 6
Project: Fyffe Grade Separation Computed: JC Date: 4/20/2020
Subject: Bearing Design Checked: CL Date: 4/20/2020
Ma ny S o lu t io n sS M
Task: Abut 1: Bearing Pad - Method A Page: of:
Job #: No:
ONE COMP ANY
Resistance to Deformation (Anchorage, AASHTO 14.7.6.4):
Hu
Gmax Area⋅ ∆u⋅
hrt
:= Design shear force due to the pad deformationDL
534 kip⋅= Hu 11.1 kip⋅=
DLmin 0.9 DLDC DLDW+ DLdia_ABUT+( )⋅ PS+ SF
Nb
⋅:= DLmin 203.6 kip⋅=
Anchorage "Not Needed" Hu 0.2 DL⋅≤( )if
"Needed" otherwise
:= Anchorage "Not Needed"=
Fyffe_Bearing_Pad_Method_A.xmcd 6 of 6
5 MSE Wall Design
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
UltraWall
Project: Fyffe
Location: Site Location
Designer: JC
Date: 5/13/2020
Section: 10ft Mirafi
Design Method: AASHTO_LRFD_2014
Design Unit: UltraBlock
Seismic Acc: 0.330
SOIL PARAMETERS φ coh γ
Reinforced Soil: 34 deg 50psf 125pcf
Retained Soil: 34 deg 100psf 125pcf
Foundation Soil: 34 deg 200psf 125pcf
Leveling Pad: Crushed Stone
GEOMETRY
Design Height: 8.00ft Live Load: 250psf
Wall Batter/Tilt: 0.00/ 9.50 deg Live Load Offset: 8.00ft
Embedment: 2.00ft Live Load Width: 39ft
Leveling Pad Depth: 1.00ft Dead Load: 100psf
Slope Angle: 0.0 deg Dead Load Offset: 0.0ft
Slope Length: 0.0ft Dead Load Width: 39ft
Slope Toe Offset: 0.0ft Leveling Pad Width: 3.46ft
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 1
RESULTS (Static / Seismic)
CDR Sliding: 6.34 (fnd) / [3.14 ] CDR Bearing: 16.62 / 22.44
Eccentricity (e/L): 0.02 / -0.04 Bearing: 1408; Srvc 1078 / Seis 1069
CDR Connection: 1.92
ID Ht Lngth Geogri Ta_tn Rc % TMax (Tatn*RF) CDR Ta_tn Ta_cn CDR Ta_cn CDR Tpo CDR Sldg
2 4.92 8.00 8XT 4034 [5850] 100 443 [575] 3631 [7020] 8.19 [10.35] 1196 [1436] 2.70 [3.37] 2.70 96.77
1 2.46 8.00 8XT 4034 [5850] 100 742 [575] 3631 [7020] 4.89 [8.00] 1424 [1709] 1.92 [2.40] 3.25 11.54
Column Descriptions:
Tr: Tension required (Ta*Reduction factors) [ppf]
EP(Pa): Earth pressures from closed form solution or trial wedge [ppf]
Rc %: percent coverage for geosynthetics
EP (Pa) internal active earth pressure [ppf ]
LL (Pql) earth pressure due to live load surcharge [ppf ]
DL (Pqd) earth pressure due to dead load surcharge [ppf ]
Tmax maximum earth pressure on geosynthetic layer [ppf ]
CDRstr 'Capacity/Demand Ratio (CDR)' on geogrid strength (Tr/Tmax)
Ta cn allowable tension capacity on the connection [ppf ]
CDR Pkcn, Capacity/Demand Ratio on the connection (Ta cn/Tmax)
CDR PO, Capacity/Demand Ratio on pullout (Ta pullout/(Tmax - LL)
CDR Sldg [fndn], Capacity/Demand Ratio on sliding on the reinforcement, CDR sliding on the foundation
soils
Grid Embed, depth of embedment beyond the theorectical failure plane. [ft ]
(PaC): reduction in load due to cohesion [ppf]
PaT: sum of all earth pressures [ppf]
%D/H: ratio of based depth to height (warning for narrow walls, < 35%)
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 2
DESIGN DATA
Load Factors for Design
AASHTO Table 3.4.1-1 & 3.4.1-2
Load Case Str_Max Str_Min Extreme Max Extreme Min Service
Str I Dead Load (DC) 1.25 0.90 1.00 1.00 1.00
Soil Load Driving (EH) 1.50 0.90 1.00 1.00 1.00
Str I Vert Earth Load (EV) 1.35 1.00 1.00 1.00 1.00
Dead Load Surcharge (ES) 1.50 0.75 1.00 1.00 1.00
Live Load (LL, PL, LS) 1.75 0.00 1.00 0.00 1.00
AASHTO Table 11.5.7-1 & Article 11.5.8
MSE Resistance Case Strength Extreme Service
Bearing Resistance (RFbr) 0.65 0.90 1.00
Sliding Soil to Soil (RFsl) 1.00 1.00 1.00
Sliding Soil to Reinforcement (RFslrf) 1.00 1.00 1.00
Tensile Resistance (RFten) 0.90 1.20 1.00
Pullout Resistance (RFpo) 0.90 1.20 1.00
Overturning Resistance (RFot) 0.60 1.00 1.00
AASHTO Table 10.5.5.2.2-1
Gravity Resistance Case Strength Extreme Service
Bearing Resistance (RFbr) 0.45 0.45 0.45
Cast-In-Place Concrete to Stone (RFsl_cip) 0.80 1.00 1.00
Precast Concrete to Stone (RFsl_c) 0.90 1.00 1.00
Stone to Soil (RFsl_s) 0.90 0.90 0.90
Passive EP (RFep) 0.50 0.90 0.90
Application of Load Factors
Group DC EV LS EH Probable Use
Strength I-a 0.90 1.00 1.75 1.50 BC/EC/SL
Strength I-b 1.25 1.35 1.75 1.50 BC (max. value)
Service I 1.00 1.00 1.00 1.00 Settlement
Notes: BC - Bearing Capacity; EC - Eccentricity; SL - Sliding
By Inspection:
• Strength I-a (minimum vertical loads and maximum horizontal loads) will govern for the case of sliding and
eccentricity (overturning); and
• For the case of bearing capacity, maximum vertical loads will govern and the factored loads must be
compared for Strength I-b and Strength IV.
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 3
NOTES ON DESIGN UNITS
The wall section is designed on a 'per unit width bases' (lb/ft/ft of wall or kN/m/meter of wall). In the calculations the
software shows lb/ft or kN/m, neglecting the unit width factor for simplicity.
The weights for the wall unit are shown as lbs / ft3 (kN / m3). For SRW design a 1 sf unit is typically 1 ft deep, 1.5 ft
wide and 8 inches tall (or 1 ft3). therefore a typical value of 120 pcf is shown. With larger units the unit weight will
vary with the size of the unit. Say we have 4 ft wide unit, 1.5 ft tall and 24 inches deep with a tapered shape (sides
narrow), built with 150 pcf concrete. We add up the concrete, the gravel fill and divide by the volume and the results
may come out to 140 pcf, as shown in the table. The units with more gravel may have lower effective unit weights
based on the calculations.
Hollow Units
Hollow units with gravel fill are treated differently in AASHTO. If the fill can fall out as the unit is lifted, then AASHTO
only allows 80% of the weight of the fill to be used for eccentricity (overturning calculations). In the properties page
for the units the weight of the concrete may be as low as 75 pcf. This is the effective unit weight of the concrete only
(e.g. the weight of the concrete divided by the volume of the unit). The density of the concrete maybe 150 pcf, but not
the effective weight including the volume of the void spaces used for gravel fill.
Rounding Errors
When doing hand calculations the values may vary from the values shown in the software. The program is designed
using double precision values (64 bit precision: 14 decimal places). Over several calculations the results may differ
from the single calculation the user is making, probably inputting one or two already rounded values.
Result Rounding
As noted above the software is based on double precision values. For example, using an NCMA design method an
allowable factor of safety of 1.5 the software may calculate a value of 1.49999999999999, since this is less than 1.5,
it would be false (NG), even though the results shown is 1.50 (results are rounded to 2 places on the screen). In the
design check we round to 2 decimal places to check against the suggested value (1.49999999999 rounds to 1.50).
Given the precision of the calculation, this will provide a safe design even though the 'absolute' value is less than the
minimum suggested.
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 4
GEOGRID REINFORCING
STRUCTURAL PROPERTIES: Mirafi
GEOGRID PROPERTIES
Name Tult RFcr RFd RFid Ci Cd Alpha Ltds
8XT 7400 1.45 1.15 1.10 0.80 0.80 0.80 4034
CONNECTION STRENGTHS
Geogrid Slope 1 Intercept 1 Peak Break Slope 2 Intercept 2 Max Normal Rup Conn Conn Creep Tlot (%) Tlot
5XT 18.00 536 1571 3.00 964 2361 False 1.45 100 4700
8XT 19.00 946 4834 3.00 2357 7745 False 1.45 100 7400
10XT 22.00 1464 -1 0.00 0 4999 False 1.45 100 9500
20XT 26.00 1825 4746 0.00 4140 6936 False 1.45 100 13705
SHEAR STRENGTHS
Slope 0 deg
Intercept 3500psf
CONNECTION CREEP
In AASHTO design methods a mechanical connector may rupture the reinforcing, thus a creep reduction
factor would be applied. If no test data is available, the creep reduction factor for the reinforcing would be applied.If a
frictional connection is used, then a creep reduction factor would not be applied and a factor of 1.0 is applicable.
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 5
CALCULATION RESULTS
OVERVIEW
Calculates stability assuming the wall is a rigid body. Forces and moments are calculated about the base and
center of the wall. The base block width is used in the calculations. The concrete units and granular fill over the blocks
are used as resisting forces.
EARTH PRESSURES
The method of analysis uses the Coulomb Earth Pressure equation (below) to calculate active earth
pressures. Wall friction is assumed to act at the back of the wall face. The component of earth pressure is assumed to
act perpendicular to the boundary surface. The effective delta angle is delta minus the wall batter at the back face
(assumed to be vertical). If the slope breaks within the failure zone, a trial wedge method of analysis is used.
INTERNAL EARTH PRESSURES
Effective internal Delta angle delta = 0.0 deg
Coefficient of active earth pressure ka =0.282
Internal failure plane ρ = 61.0 deg
EXTERNAL EARTH PRESSURES
Effective Delta angle (delta = β delta =0.0 deg
Coefficient of active earth pressure ka =0.276
Effective Face Angle Face Alpha =0.00 deg
External failure plane ρ = 57.0 deg
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 6
W0: leveling pad W6: Rectangle zone in broken back
W1: facing units W7: Live load over the mass
W2: soil wedge behind the face (base of top block to bottom) W8: Dead load over the mass
W3: rectangular area in MSE area W9: Force Pa
W4: the wedge at the back of the mass W10: Surcharge load Paq
W5: slope area over the mass W11: Dead Load Surcharge Paqd
X-Len: is measured from the center of the base (+) Driving, (-) Resisting.
Name Factor γ Force (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 1.00 3384 -- 1.97 -- 6659 --
Soil(W2) 1.00 669 -- 0.48 -- 320 --
Soil(W3) 1.00 3930 -- -2.04 -- -- -7998
DL(W8) 1.00 434 -- 0.00 -- -- 0
Pa_h 1.00 -- 683 -- 2.67 1820 --
Sum (V, H) 1.00 8418 683 Sum Mom 8799.92 -7998
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 7
FORCES AND MOMENTS FACTORED FOR Str I-a
UltraWall increases all driving forces and reduces the resisting forces by the factors shown for Str I.
FACTORED LOADS: Str Ia
Name FactorMax γ FactorMin γ ForceSldg (V) ForceEcc (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 1.25 0.90 3046 3046 -- 1.97 -- 5994 --
Soil(W2) 1.35 1.00 669 669 -- 0.48 -- 320 --
Soil(W3) 1.35 1.00 3930 3930 -- -2.04 -- -- -7998
DL(W8) 1.50 0.75 434 434 -- 0.00 -- -- 0
Pa_h 1.50 0.90 -- -- 1024 -- 2.67 2730 --
Pa_v 1.50 0.90 0 0 -- -4.45 -- -- 0
Sum (V, H) 7971 7971 1024 Sum Mom 9044 -7998
FORCES AND MOMENTS FACTORED FOR Str I-b
UltraWall increase resisting loads and increases driving loads by the factors shown for Str I-b.
FACTORED LOADS: Str Ib
Name Factor γ Force (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 1.25 4230 -- 1.97 -- 8324 --
Soil(W2) 1.35 904 -- 0.48 -- 432 --
Soil(W3) 1.35 5305 -- -2.04 -- -- -10797
DL(W8) 1.50 651 -- 0.00 -- -- 0
Pa_h 1.50 -- 1024 -- 2.67 2730 --
Pa_v 1.50 0 -- -4.45 -- -- 0
Sum (V, H) 1.00 11091 1024 Sum Mom 11487 -10797
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 8
BASE SLIDING
Sliding at the base is checked at the foundation soil and a check in the reinforced fill zone.
W1(DCr) + W2(EVr) + W3(EVr) + W8(ESr)
(3384 * 0.90) + (669 * 1.00) + (3930 * 1.00) + (434 * 0.75)
N =7971ppf
Resisting force in the Reinforced Zone = (N tan(slope) + c B) x RFsl
(7971 tan(34.0) + 50.0 * 8) * 1 Rf1 =5776
Resisting force in the Foundation Zone = (N tan(slope) + c B) x RFsl
(7971 tan(34.0) + 200.0 * 8) * 1 Rf2 =6976
Driving force is the horizontal component of Pah(EHd)
(683 * 1.50)
Df =1024
CDR = Rf1 / Df CDR =6.34
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 9
SLIDING ON REINFORCING
Sliding along the reinforcing is checked at each layer within the reinforced zone.
Sliding resistance is calculated by taking the normal load on the reinforcing, N, times the tangent of the
friction angle of the reinforced soils , φ, times a reduction factor for sliding, Rsl.
Sliding along the reinforcing includes shearing through the face panel. The shear resistance of the face
panel is included as a resisting force, RF_face.
N = Normal load on the geogrid layer. = 3369
(N * tan(34.00) * Cd) + RF_face
(3369 * tan(34.00) * 0.80 ) + 3500 RF = 5318
The driving forces is the active earth pressure plus any surcharge loads behind the reinforced zone.
Pah_ext(EHd)
where:
z = depth to reinforcing from the surface at the end of the reinforcing. [5.54]
EHd = Load factor for Earth Pressure driving [EHd = 1.50]
Pah = 1/2 x γ z^2 x ka x cos(δ) [542.10]
Pah_ext, Pqh_ext, etc. could be from a closed from solution (Coulomb/Rankine) or from a trial wedge
solution.
DF = (542 x 1.50) DF = 461
CDR sliding = RF / DF CDR = 11.54
The table below shows a summary of the forces and reactions.
Elevation[ft] Name[ft] z ext[ft] N[ppf] % Coverage Friction Angle[deg] F_Resisting Pah(EHd) Pqh(LLd) Pqdh(DLd) PqMnDOT(LLd) F_Driving CDR_sl
4.92 8XT 3.08 1940 100.0 34.00 4547 250 0 130 0 47 96.77
2.46 8XT 5.54 3369 100.0 34.00 5318 813 0 235 0 461 11.54
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 10
ECCENTRICITY AND BEARING
Eccentricity is the calculation of the distance of the resultant force away from the centroid of mass. This
measure is an indication of the overturning of the mass. In rigid concrete structures, the limit to eccentricity is L/4 (the
middle half of the base). UltraWall uses an allowable eccentricity of e/L per the AASHTO LRFD guidelines.
Eccentricity is still used as a guide to design in some design methods. Eccentricity is based on case S1a (minimum
resisting forces, maximum driving forces. Bearing is based on case S1b (maximum resisting forces, maximum driving
forces).
UltraWall calculates three eccentricities:
1) S1a: Maximum eccentricity (overturning) where it uses the maximum driving forces combined
with the minimum resisting forces (see overturning).
2) S1b Maximum bearing where it uses the maximum driving forces combined with the maximum
resisting forces.
3) Service: Maximum bearing where it uses the actual driving forces combined with the actual
resisting forces in Service loading.
Calculation of Eccentricity for maximum bearing (S1b)
Moments resisting = + M3(EVd)
+ (-7998 * 1.35)
Mr =-10797ft-lbs
Moments driving = M1(DCr) + M2(EVd) + Pah(EHd)
+ (6659 * 1.25) + (320 * 1.35) + (1820 * 1.50)
Mo = 11487ft-lbs
e = (SumMr + SumMo)/SumV [ if e < 0, then e = 0 ]
e = (-10797 + 11487.0) /11090.5 e =0.062
Calculation of Bearing Pressures
Qal = (c*Nc + q*Nq + 0.5*gamma*(B')*Ng) * RFbrg
where:
Nc =42.16
Nq =29.44
Ng =41.06
c =200.00psf
RFbrg =0.65
q =250psf [embedment x gamma]
B' = B - 2e =7.88ft
Calculate Allowable Bearing, Qal Qal =23403psf
Applied Bearing Pressures (Sigma) (SumV)/B' =1408psf
Calculated CDR for bearing Qal/sigma =16.62
Design Sum Vert Mo Mr e Qal Sigma CDR
Strength I-b 11091 11487 -10797 0.062 23403 1408 16.62
Service 8418 8800 -7998 0.095 35835 1078 33.25
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 11
Elevation[ft] Name Ta*RF[ppf] Tas*RF[ppf] Coverage Ratio % Tmax[ppf] TSmax[ppf] CDR Str CDRs Str
4.92 8XT 3631 7020 100 443 678 8.19 10.35
2.46 8XT 3631 7020 100 742 877 4.89 8.00
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 12
PULLOUT CALCULATIONS
Pullout is the amount of resistance of the reinforcing has to a pullout failure based on the Tmax applied and
the depth of embedement (resistance). In an AASHTO design, the failure plane is fixed at the Rankine failure plane
angle, 45 + phi/2. All failure planes begin at the tail. of the facing units.
Failure Plane Angle = 62.0 Deg
F* = 0.67 x tan( φ ) [AASHTO 11.10.6.3.2]
F* = 0.67 x tan( 34) = 0.45
α = 0.80 [AASHTO Table 11.10.6.3.2-1]
RFpo = 0.90
Pullout = 2 x N x F* x α x Coverage x RFpo
Pullout = 2 x 1837 x 0.45 x 0.80 x 1.00 x 0.90 = 1195.31
Pullout is the calculated value or the Tult of the geogrid, whichever is less.
NOTE: The pullout capacity is limited by the LTDS of the reinforcing layer, not the ultimate pullout capacity calculated.
TABLE OF RESULTS
Elevation[ft] Normal[lbf] F* Alpha % Coverage Tmax[ppf] Le[ft] La[ft] Pullout_[Pr][ppf] CDR PO
4.92 1837 0.45 0.80 100 443 3.78 4.22 1195 2.70
2.46 3710 0.45 0.80 100 742 4.68 3.32 2414 3.25
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 13
CONNECTION CALCULATIONS
Connection is the amount of resistance of the reinforcing has to a pullout failure from the facing units based
on the Tmax applied and the normal load on the units. In an AASHTO LRFD design, creep on the connection may be
applied for frictional and mechanical connections.
Connection Capacity = [N tan(slope) + intercept] / RFcr
RFcr can be a value obtained from long-term testing or by default could be the creep reduction factor of the
geogrid reinforcing.
Base friction is used to reduce the tension in the bottom layer of reinforcing. The force in the bottom layer is
the tension from half way to the reinforcing layer above to the halfway to the foundation level below.
Base Friction = Base Shear x RFsliding
Base Shear = 3384 x tan( atan(0.80 x tan(40 )) + 0
2272 x 0.90 BF = 2045ppf
BF utilized to reduce bottom tension = 356ppf
CRu = Ultimate connection strength [1692 x tan( 19.00) + 946 = 1528.65 ]
CRru = CRu / TLot [1528.65/7400.00 = 0.21]
RFcrcn = 1.45 [Connection creep if tested, otherwise geogrid creep factor]
[if connection creep is set to 'false', RFcrcn = 1]
CRcr = CRru / RFcrcn [0.21 / 1.00 = 0.21]
Tac = Tult x CRcr / RFd * RFten [ 7400 x 0.21 / 1.15 x 0.90 = 1196.34]
TABLE OF RESULTS
Elev[ft] Name[ft] Tmax[ppf] Ttotal[ppf] Rc % RFcn_cr N[ppf] Avail_CN[ppf] CDR cn CDR cns
4.92 8XT 443 426 100 1.00 1692 1196 2.70 3.37
2.46 8XT 742 712 100 1.00 2538 1424 1.92 2.40
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 14
SEISMIC CALCULATIONS
The loads considered under seismic loading are primarily inertial loadings. The wave passes the structure
putting the mass into motion and then the mass will try to continue in the direction of the initial wave. In the
calculations you see the one dynamic earth pressure from the wedge of the soil behind the reinforced mass, and then
all the other forces come from inertia calculations of the face put into motion and then trying to be held in place.
In AASHTO LRFD, external stability is calculated based on 100% of Pae and 50% of Pir and then
50% of Pae and 100% of Pir. The values labelled Pae are 100% Pae/50% Pir; labels Pir are 50% Pae/100% Pir.
Design Acceleration A = 0.330
Displacment (d) d = 3.3in
Design Acceleration Coefficient Displacment Based (empirically)
Kh = A/2 = kh(ext) = 0.165
Vertical Acceleration kv =0.000
SEISMIC THRUST
EXTERNAL Kae
Kae Kae =0.384
Pae = 0.5*gamma*(H)^2*D_Kae Pae =435ppf
Pae_h/2 = Pae*cos(delta)/2 Pae_h/2 =217ppf
Pae_v/2 = Pae*sin(delta)/2 Pae_v/2 =0ppf
INERTIA FORCES OF THE STRUCTURE
Face (Pif) = (W0 + W1)*kh(int) = 3384 * 0.165 Pif =558ppf
Mass (Pir) = (W)*kh(int) = 3339 * 0.165 Pir =551ppf
Slope (Pis) = (W)*kh(int) = 0 * 0.165 Pis =0ppf
Dead Load(Pidl) = (DL)*kh(int) = 0 * 0.165 Pidl =0ppf
TABLE OF RESULTS FOR SEISMIC REACTIONS
Name Force (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 3384 -- 2.03 -- -- 6878
Soil(W2) 669 -- 3.52 -- -- 2357
Soil(W3) 3930 -- 6.04 -- -- 23717
DL(W8) 434 -- 5.83 -- -- 2531
Pa_h -- 683 -- 2.67 1820 --
Pir -- 551 -- 4.00 2204 --
Pif -- 558 -- 4.00 2234 --
Pae_h/2 -- 435 -- 4.00 870 --
Sum V / H 8417.64 2009.42 Sum Mom 7127.56 35482.65
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 15
UltraWall
Project: Fyffe
Location: Site Location
Designer: JC
Date: 5/13/2020
Section: 10ft Stratagrid
Design Method: AASHTO_LRFD_2014
Design Unit: UltraBlock
Seismic Acc: 0.330
SOIL PARAMETERS φ coh γ
Reinforced Soil: 34 deg 50psf 125pcf
Retained Soil: 34 deg 100psf 125pcf
Foundation Soil: 34 deg 200psf 125pcf
Leveling Pad: Crushed Stone
GEOMETRY
Design Height: 8.00ft Live Load: 250psf
Wall Batter/Tilt: 0.00/ 9.50 deg Live Load Offset: 8.00ft
Embedment: 2.00ft Live Load Width: 39ft
Leveling Pad Depth: 1.00ft Dead Load: 100psf
Slope Angle: 0.0 deg Dead Load Offset: 0.0ft
Slope Length: 0.0ft Dead Load Width: 39ft
Slope Toe Offset: 0.0ft Leveling Pad Width: 3.46ft
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 1
RESULTS (Static / Seismic)
CDR Sliding: 6.34 (fnd) / [3.14 ] CDR Bearing: 16.62 / 22.44
Eccentricity (e/L): 0.02 / -0.04 Bearing: 1408; Srvc 1078 / Seis 1069
CDR Connection: 1.70
ID Ht Lngth Geogri Ta_tn Rc % TMax (Tatn*RF) CDR Ta_tn Ta_cn CDR Ta_cn CDR Tpo CDR Sldg
2 4.92 8.00 SG500 3122 [4839] 100 443 [601] 2810 [5807] 6.34 [8.25] 1157 [1388] 2.61 [3.26] 2.70 100.00
1 2.46 8.00 SG500 3122 [4839] 100 742 [601] 2810 [5807] 3.79 [6.43] 1262 [1515] 1.70 [2.13] 3.25 [1.38] 27.82 [9.50]
Column Descriptions:
Tr: Tension required (Ta*Reduction factors) [ppf]
EP(Pa): Earth pressures from closed form solution or trial wedge [ppf]
Rc %: percent coverage for geosynthetics
EP (Pa) internal active earth pressure [ppf ]
LL (Pql) earth pressure due to live load surcharge [ppf ]
DL (Pqd) earth pressure due to dead load surcharge [ppf ]
Tmax maximum earth pressure on geosynthetic layer [ppf ]
CDRstr 'Capacity/Demand Ratio (CDR)' on geogrid strength (Tr/Tmax)
Ta cn allowable tension capacity on the connection [ppf ]
CDR Pkcn, Capacity/Demand Ratio on the connection (Ta cn/Tmax)
CDR PO, Capacity/Demand Ratio on pullout (Ta pullout/(Tmax - LL)
CDR Sldg [fndn], Capacity/Demand Ratio on sliding on the reinforcement, CDR sliding on the foundation
soils
Grid Embed, depth of embedment beyond the theorectical failure plane. [ft ]
(PaC): reduction in load due to cohesion [ppf]
PaT: sum of all earth pressures [ppf]
%D/H: ratio of based depth to height (warning for narrow walls, < 35%)
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 2
DESIGN DATA
Load Factors for Design
AASHTO Table 3.4.1-1 & 3.4.1-2
Load Case Str_Max Str_Min Extreme Max Extreme Min Service
Str I Dead Load (DC) 1.25 0.90 1.00 1.00 1.00
Soil Load Driving (EH) 1.50 0.90 1.00 1.00 1.00
Str I Vert Earth Load (EV) 1.35 1.00 1.00 1.00 1.00
Dead Load Surcharge (ES) 1.50 0.75 1.00 1.00 1.00
Live Load (LL, PL, LS) 1.75 0.00 1.00 0.00 1.00
AASHTO Table 11.5.7-1 & Article 11.5.8
MSE Resistance Case Strength Extreme Service
Bearing Resistance (RFbr) 0.65 0.90 1.00
Sliding Soil to Soil (RFsl) 1.00 1.00 1.00
Sliding Soil to Reinforcement (RFslrf) 1.00 1.00 1.00
Tensile Resistance (RFten) 0.90 1.20 1.00
Pullout Resistance (RFpo) 0.90 1.20 1.00
Overturning Resistance (RFot) 0.60 1.00 1.00
AASHTO Table 10.5.5.2.2-1
Gravity Resistance Case Strength Extreme Service
Bearing Resistance (RFbr) 0.45 0.45 0.45
Cast-In-Place Concrete to Stone (RFsl_cip) 0.80 1.00 1.00
Precast Concrete to Stone (RFsl_c) 0.90 1.00 1.00
Stone to Soil (RFsl_s) 0.90 0.90 0.90
Passive EP (RFep) 0.50 0.90 0.90
Application of Load Factors
Group DC EV LS EH Probable Use
Strength I-a 0.90 1.00 1.75 1.50 BC/EC/SL
Strength I-b 1.25 1.35 1.75 1.50 BC (max. value)
Service I 1.00 1.00 1.00 1.00 Settlement
Notes: BC - Bearing Capacity; EC - Eccentricity; SL - Sliding
By Inspection:
• Strength I-a (minimum vertical loads and maximum horizontal loads) will govern for the case of sliding and
eccentricity (overturning); and
• For the case of bearing capacity, maximum vertical loads will govern and the factored loads must be
compared for Strength I-b and Strength IV.
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 3
NOTES ON DESIGN UNITS
The wall section is designed on a 'per unit width bases' (lb/ft/ft of wall or kN/m/meter of wall). In the calculations the
software shows lb/ft or kN/m, neglecting the unit width factor for simplicity.
The weights for the wall unit are shown as lbs / ft3 (kN / m3). For SRW design a 1 sf unit is typically 1 ft deep, 1.5 ft
wide and 8 inches tall (or 1 ft3). therefore a typical value of 120 pcf is shown. With larger units the unit weight will
vary with the size of the unit. Say we have 4 ft wide unit, 1.5 ft tall and 24 inches deep with a tapered shape (sides
narrow), built with 150 pcf concrete. We add up the concrete, the gravel fill and divide by the volume and the results
may come out to 140 pcf, as shown in the table. The units with more gravel may have lower effective unit weights
based on the calculations.
Hollow Units
Hollow units with gravel fill are treated differently in AASHTO. If the fill can fall out as the unit is lifted, then AASHTO
only allows 80% of the weight of the fill to be used for eccentricity (overturning calculations). In the properties page
for the units the weight of the concrete may be as low as 75 pcf. This is the effective unit weight of the concrete only
(e.g. the weight of the concrete divided by the volume of the unit). The density of the concrete maybe 150 pcf, but not
the effective weight including the volume of the void spaces used for gravel fill.
Rounding Errors
When doing hand calculations the values may vary from the values shown in the software. The program is designed
using double precision values (64 bit precision: 14 decimal places). Over several calculations the results may differ
from the single calculation the user is making, probably inputting one or two already rounded values.
Result Rounding
As noted above the software is based on double precision values. For example, using an NCMA design method an
allowable factor of safety of 1.5 the software may calculate a value of 1.49999999999999, since this is less than 1.5,
it would be false (NG), even though the results shown is 1.50 (results are rounded to 2 places on the screen). In the
design check we round to 2 decimal places to check against the suggested value (1.49999999999 rounds to 1.50).
Given the precision of the calculation, this will provide a safe design even though the 'absolute' value is less than the
minimum suggested.
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 4
GEOGRID REINFORCING
STRUCTURAL PROPERTIES: Stratagrid
GEOGRID PROPERTIES
Name Tult RFcr RFd RFid Ci Cd Alpha Ltds
SG500 6400 1.55 1.15 1.15 0.80 0.80 0.80 3122
CONNECTION STRENGTHS
Geogrid Slope 1 Intercept 1 Peak Break Slope 2 Intercept 2 Max Normal Rup Conn Conn Creep Tlot (%) Tlot
SG500 29.00 688 1899 3.00 1641 7655 False 1.55 110 7040
SG550 46.00 670 2190 4.00 2785 7650 False 1.55 110 8965
SG600 46.00 670 2190 4.00 2785 7850 False 1.55 110 10010
SG700 37.00 643 -1 0.00 0 3100 False 1.55 100 11800
SHEAR STRENGTHS
Slope 0 deg
Intercept 11000psf
CONNECTION CREEP
In AASHTO design methods a mechanical connector may rupture the reinforcing, thus a creep reduction
factor would be applied. If no test data is available, the creep reduction factor for the reinforcing would be applied.If a
frictional connection is used, then a creep reduction factor would not be applied and a factor of 1.0 is applicable.
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 5
CALCULATION RESULTS
OVERVIEW
Calculates stability assuming the wall is a rigid body. Forces and moments are calculated about the base and
center of the wall. The base block width is used in the calculations. The concrete units and granular fill over the blocks
are used as resisting forces.
EARTH PRESSURES
The method of analysis uses the Coulomb Earth Pressure equation (below) to calculate active earth
pressures. Wall friction is assumed to act at the back of the wall face. The component of earth pressure is assumed to
act perpendicular to the boundary surface. The effective delta angle is delta minus the wall batter at the back face
(assumed to be vertical). If the slope breaks within the failure zone, a trial wedge method of analysis is used.
INTERNAL EARTH PRESSURES
Effective internal Delta angle delta = 0.0 deg
Coefficient of active earth pressure ka =0.282
Internal failure plane ρ = 61.0 deg
EXTERNAL EARTH PRESSURES
Effective Delta angle (delta = β delta =0.0 deg
Coefficient of active earth pressure ka =0.276
Effective Face Angle Face Alpha =0.00 deg
External failure plane ρ = 57.0 deg
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 6
W0: leveling pad W6: Rectangle zone in broken back
W1: facing units W7: Live load over the mass
W2: soil wedge behind the face (base of top block to bottom) W8: Dead load over the mass
W3: rectangular area in MSE area W9: Force Pa
W4: the wedge at the back of the mass W10: Surcharge load Paq
W5: slope area over the mass W11: Dead Load Surcharge Paqd
X-Len: is measured from the center of the base (+) Driving, (-) Resisting.
Name Factor γ Force (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 1.00 3384 -- 1.97 -- 6659 --
Soil(W2) 1.00 669 -- 0.48 -- 320 --
Soil(W3) 1.00 3930 -- -2.04 -- -- -7998
DL(W8) 1.00 434 -- 0.00 -- -- 0
Pa_h 1.00 -- 683 -- 2.67 1820 --
Sum (V, H) 1.00 8418 683 Sum Mom 8799.92 -7998
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 7
FORCES AND MOMENTS FACTORED FOR Str I-a
UltraWall increases all driving forces and reduces the resisting forces by the factors shown for Str I.
FACTORED LOADS: Str Ia
Name FactorMax γ FactorMin γ ForceSldg (V) ForceEcc (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 1.25 0.90 3046 3046 -- 1.97 -- 5994 --
Soil(W2) 1.35 1.00 669 669 -- 0.48 -- 320 --
Soil(W3) 1.35 1.00 3930 3930 -- -2.04 -- -- -7998
DL(W8) 1.50 0.75 434 434 -- 0.00 -- -- 0
Pa_h 1.50 0.90 -- -- 1024 -- 2.67 2730 --
Pa_v 1.50 0.90 0 0 -- -4.45 -- -- 0
Sum (V, H) 7971 7971 1024 Sum Mom 9044 -7998
FORCES AND MOMENTS FACTORED FOR Str I-b
UltraWall increase resisting loads and increases driving loads by the factors shown for Str I-b.
FACTORED LOADS: Str Ib
Name Factor γ Force (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 1.25 4230 -- 1.97 -- 8324 --
Soil(W2) 1.35 904 -- 0.48 -- 432 --
Soil(W3) 1.35 5305 -- -2.04 -- -- -10797
DL(W8) 1.50 651 -- 0.00 -- -- 0
Pa_h 1.50 -- 1024 -- 2.67 2730 --
Pa_v 1.50 0 -- -4.45 -- -- 0
Sum (V, H) 1.00 11091 1024 Sum Mom 11487 -10797
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 8
BASE SLIDING
Sliding at the base is checked at the foundation soil and a check in the reinforced fill zone.
W1(DCr) + W2(EVr) + W3(EVr) + W8(ESr)
(3384 * 0.90) + (669 * 1.00) + (3930 * 1.00) + (434 * 0.75)
N =7971ppf
Resisting force in the Reinforced Zone = (N tan(slope) + c B) x RFsl
(7971 tan(34.0) + 50.0 * 8) * 1 Rf1 =5776
Resisting force in the Foundation Zone = (N tan(slope) + c B) x RFsl
(7971 tan(34.0) + 200.0 * 8) * 1 Rf2 =6976
Driving force is the horizontal component of Pah(EHd)
(683 * 1.50)
Df =1024
CDR = Rf1 / Df CDR =6.34
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 9
SLIDING ON REINFORCING
Sliding along the reinforcing is checked at each layer within the reinforced zone.
Sliding resistance is calculated by taking the normal load on the reinforcing, N, times the tangent of the
friction angle of the reinforced soils , φ, times a reduction factor for sliding, Rsl.
Sliding along the reinforcing includes shearing through the face panel. The shear resistance of the face
panel is included as a resisting force, RF_face.
N = Normal load on the geogrid layer. = 3369
(N * tan(34.00) * Cd) + RF_face
(3369 * tan(34.00) * 0.80 ) + 11000 RF = 12818
The driving forces is the active earth pressure plus any surcharge loads behind the reinforced zone.
Pah_ext(EHd)
where:
z = depth to reinforcing from the surface at the end of the reinforcing. [5.54]
EHd = Load factor for Earth Pressure driving [EHd = 1.50]
Pah = 1/2 x γ z^2 x ka x cos(δ) [542.10]
Pah_ext, Pqh_ext, etc. could be from a closed from solution (Coulomb/Rankine) or from a trial wedge
solution.
DF = (542 x 1.50) DF = 461
CDR sliding = RF / DF CDR = 27.82
The table below shows a summary of the forces and reactions.
Elevation[ft] Name[ft] z ext[ft] N[ppf] % Coverage Friction Angle[deg] F_Resisting Pah(EHd) Pqh(LLd) Pqdh(DLd) PqMnDOT(LLd) F_Driving CDR_sl
4.92 SG500 3.08 1940 100.0 34.00 12047 250 0 130 0 47 100.00
2.46 SG500 5.54 3369 100.0 34.00 12818 813 0 235 0 461 27.82
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 10
ECCENTRICITY AND BEARING
Eccentricity is the calculation of the distance of the resultant force away from the centroid of mass. This
measure is an indication of the overturning of the mass. In rigid concrete structures, the limit to eccentricity is L/4 (the
middle half of the base). UltraWall uses an allowable eccentricity of e/L per the AASHTO LRFD guidelines.
Eccentricity is still used as a guide to design in some design methods. Eccentricity is based on case S1a (minimum
resisting forces, maximum driving forces. Bearing is based on case S1b (maximum resisting forces, maximum driving
forces).
UltraWall calculates three eccentricities:
1) S1a: Maximum eccentricity (overturning) where it uses the maximum driving forces combined
with the minimum resisting forces (see overturning).
2) S1b Maximum bearing where it uses the maximum driving forces combined with the maximum
resisting forces.
3) Service: Maximum bearing where it uses the actual driving forces combined with the actual
resisting forces in Service loading.
Calculation of Eccentricity for maximum bearing (S1b)
Moments resisting = + M3(EVd)
+ (-7998 * 1.35)
Mr =-10797ft-lbs
Moments driving = M1(DCr) + M2(EVd) + Pah(EHd)
+ (6659 * 1.25) + (320 * 1.35) + (1820 * 1.50)
Mo = 11487ft-lbs
e = (SumMr + SumMo)/SumV [ if e < 0, then e = 0 ]
e = (-10797 + 11487.0) /11090.5 e =0.062
Calculation of Bearing Pressures
Qal = (c*Nc + q*Nq + 0.5*gamma*(B')*Ng) * RFbrg
where:
Nc =42.16
Nq =29.44
Ng =41.06
c =200.00psf
RFbrg =0.65
q =250psf [embedment x gamma]
B' = B - 2e =7.88ft
Calculate Allowable Bearing, Qal Qal =23403psf
Applied Bearing Pressures (Sigma) (SumV)/B' =1408psf
Calculated CDR for bearing Qal/sigma =16.62
Design Sum Vert Mo Mr e Qal Sigma CDR
Strength I-b 11091 11487 -10797 0.062 23403 1408 16.62
Service 8418 8800 -7998 0.095 35835 1078 33.25
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 11
Elevation[ft] Name Ta*RF[ppf] Tas*RF[ppf] Coverage Ratio % Tmax[ppf] TSmax[ppf] CDR Str CDRs Str
4.92 SG500 2810 5807 100 443 704 6.34 8.25
2.46 SG500 2810 5807 100 742 903 3.79 6.43
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 12
PULLOUT CALCULATIONS
Pullout is the amount of resistance of the reinforcing has to a pullout failure based on the Tmax applied and
the depth of embedement (resistance). In an AASHTO design, the failure plane is fixed at the Rankine failure plane
angle, 45 + phi/2. All failure planes begin at the tail. of the facing units.
Failure Plane Angle = 62.0 Deg
F* = 0.67 x tan( φ ) [AASHTO 11.10.6.3.2]
F* = 0.67 x tan( 34) = 0.45
α = 0.80 [AASHTO Table 11.10.6.3.2-1]
RFpo = 0.90
Pullout = 2 x N x F* x α x Coverage x RFpo
Pullout = 2 x 1837 x 0.45 x 0.80 x 1.00 x 0.90 = 1195.31
Pullout is the calculated value or the Tult of the geogrid, whichever is less.
NOTE: The pullout capacity is limited by the LTDS of the reinforcing layer, not the ultimate pullout capacity calculated.
TABLE OF RESULTS
Elevation[ft] Normal[lbf] F* Alpha % Coverage Tmax[ppf] Le[ft] La[ft] Pullout_[Pr][ppf] CDR PO
4.92 1837 0.45 0.80 100 443 3.78 4.22 1195 2.70
2.46 3710 0.45 0.80 100 742 4.68 3.32 2414 3.25
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 13
CONNECTION CALCULATIONS
Connection is the amount of resistance of the reinforcing has to a pullout failure from the facing units based
on the Tmax applied and the normal load on the units. In an AASHTO LRFD design, creep on the connection may be
applied for frictional and mechanical connections.
Connection Capacity = [N tan(slope) + intercept] / RFcr
RFcr can be a value obtained from long-term testing or by default could be the creep reduction factor of the
geogrid reinforcing.
Base friction is used to reduce the tension in the bottom layer of reinforcing. The force in the bottom layer is
the tension from half way to the reinforcing layer above to the halfway to the foundation level below.
Base Friction = Base Shear x RFsliding
Base Shear = 3384 x tan( atan(0.80 x tan(40 )) + 0
2272 x 0.90 BF = 2045ppf
BF utilized to reduce bottom tension = 356ppf
CRu = Ultimate connection strength [1692 x tan( 29.00) + 688 = 1625.98 ]
CRru = CRu / TLot [1625.98/7040.00 = 0.23]
RFcrcn = 1.55 [Connection creep if tested, otherwise geogrid creep factor]
[if connection creep is set to 'false', RFcrcn = 1]
CRcr = CRru / RFcrcn [0.23 / 1.00 = 0.23]
Tac = Tult x CRcr / RFd * RFten [ 6400 x 0.23 / 1.15 x 0.90 = 1156.82]
TABLE OF RESULTS
Elev[ft] Name[ft] Tmax[ppf] Ttotal[ppf] Rc % RFcn_cr N[ppf] Avail_CN[ppf] CDR cn CDR cns
4.92 SG500 443 426 100 1.00 1692 1157 2.61 3.26
2.46 SG500 742 712 100 1.00 2538 1262 1.70 2.13
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 14
SEISMIC CALCULATIONS
The loads considered under seismic loading are primarily inertial loadings. The wave passes the structure
putting the mass into motion and then the mass will try to continue in the direction of the initial wave. In the
calculations you see the one dynamic earth pressure from the wedge of the soil behind the reinforced mass, and then
all the other forces come from inertia calculations of the face put into motion and then trying to be held in place.
In AASHTO LRFD, external stability is calculated based on 100% of Pae and 50% of Pir and then
50% of Pae and 100% of Pir. The values labelled Pae are 100% Pae/50% Pir; labels Pir are 50% Pae/100% Pir.
Design Acceleration A = 0.330
Displacment (d) d = 3.3in
Design Acceleration Coefficient Displacment Based (empirically)
Kh = A/2 = kh(ext) = 0.165
Vertical Acceleration kv =0.000
SEISMIC THRUST
EXTERNAL Kae
Kae Kae =0.384
Pae = 0.5*gamma*(H)^2*D_Kae Pae =435ppf
Pae_h/2 = Pae*cos(delta)/2 Pae_h/2 =217ppf
Pae_v/2 = Pae*sin(delta)/2 Pae_v/2 =0ppf
INERTIA FORCES OF THE STRUCTURE
Face (Pif) = (W0 + W1)*kh(int) = 3384 * 0.165 Pif =558ppf
Mass (Pir) = (W)*kh(int) = 3339 * 0.165 Pir =551ppf
Slope (Pis) = (W)*kh(int) = 0 * 0.165 Pis =0ppf
Dead Load(Pidl) = (DL)*kh(int) = 0 * 0.165 Pidl =0ppf
TABLE OF RESULTS FOR SEISMIC REACTIONS
Name Force (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 3384 -- 2.03 -- -- 6878
Soil(W2) 669 -- 3.52 -- -- 2357
Soil(W3) 3930 -- 6.04 -- -- 23717
DL(W8) 434 -- 5.83 -- -- 2531
Pa_h -- 683 -- 2.67 1820 --
Pir -- 551 -- 4.00 2204 --
Pif -- 558 -- 4.00 2234 --
Pae_h/2 -- 435 -- 4.00 870 --
Sum V / H 8417.64 2009.42 Sum Mom 7127.56 35482.65
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 15
UltraWall
Project: Fyffe
Location: Site Location
Designer: JC
Date: 5/13/2020
Section: 15ft Mirafi
Design Method: AASHTO_LRFD_2014
Design Unit: UltraBlock
Seismic Acc: 0.330
SOIL PARAMETERS φ coh γ
Reinforced Soil: 34 deg 50psf 125pcf
Retained Soil: 34 deg 100psf 125pcf
Foundation Soil: 34 deg 200psf 125pcf
Leveling Pad: Crushed Stone
GEOMETRY
Design Height: 13.00ft Live Load: 250psf
Wall Batter/Tilt: 0.00/ 9.50 deg Live Load Offset: 8.00ft
Embedment: 2.00ft Live Load Width: 39ft
Leveling Pad Depth: 1.00ft Dead Load: 100psf
Slope Angle: 0.0 deg Dead Load Offset: 0.0ft
Slope Length: 0.0ft Dead Load Width: 39ft
Slope Toe Offset: 0.0ft Leveling Pad Width: 3.46ft
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 1
RESULTS (Static / Seismic)
CDR Sliding: 3.04 (fnd) / [2.31 ] CDR Bearing: 11.60 / 17.62
Eccentricity (e/L): 0.07 / -0.10 Bearing: 2273; Srvc 1698 / Seis 1716
CDR Connection: 1.43
ID Ht Lngth Geogri Ta_tn Rc % TMax (Tatn*RF) CDR Ta_tn Ta_cn CDR Ta_cn CDR Tpo CDR Sldg
4 9.8310.50 8XT 4034 [5850] 100 461 [558] 3631 [7020] 7.88 [10.59] 1196 [1436] 2.60 [3.24] 3.14 22.52
3 7.3810.50 8XT 4034 [5850] 100 764 [558] 3631 [7020] 4.75 [8.08] 1424 [1709] 1.86 [2.33] 3.69 6.63 [3.10]
2 4.9210.50 8XT 4034 [5850] 100 1051 [558] 3631 [7020] 3.45 [7.12] 1652 [1983] 1.57 [1.97] 3.45 3.79 [2.43]
1 2.4610.50 8XT 4034 [5850] 100 1319 [558] 3631 [7020] 2.75 [6.41] 1880 [2256] 1.43 [1.78] 2.75 2.62 [1.97]
Column Descriptions:
Tr: Tension required (Ta*Reduction factors) [ppf]
EP(Pa): Earth pressures from closed form solution or trial wedge [ppf]
Rc %: percent coverage for geosynthetics
EP (Pa) internal active earth pressure [ppf ]
LL (Pql) earth pressure due to live load surcharge [ppf ]
DL (Pqd) earth pressure due to dead load surcharge [ppf ]
Tmax maximum earth pressure on geosynthetic layer [ppf ]
CDRstr 'Capacity/Demand Ratio (CDR)' on geogrid strength (Tr/Tmax)
Ta cn allowable tension capacity on the connection [ppf ]
CDR Pkcn, Capacity/Demand Ratio on the connection (Ta cn/Tmax)
CDR PO, Capacity/Demand Ratio on pullout (Ta pullout/(Tmax - LL)
CDR Sldg [fndn], Capacity/Demand Ratio on sliding on the reinforcement, CDR sliding on the foundation
soils
Grid Embed, depth of embedment beyond the theorectical failure plane. [ft ]
(PaC): reduction in load due to cohesion [ppf]
PaT: sum of all earth pressures [ppf]
%D/H: ratio of based depth to height (warning for narrow walls, < 35%)
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 2
DESIGN DATA
Load Factors for Design
AASHTO Table 3.4.1-1 & 3.4.1-2
Load Case Str_Max Str_Min Extreme Max Extreme Min Service
Str I Dead Load (DC) 1.25 0.90 1.00 1.00 1.00
Soil Load Driving (EH) 1.50 0.90 1.00 1.00 1.00
Str I Vert Earth Load (EV) 1.35 1.00 1.00 1.00 1.00
Dead Load Surcharge (ES) 1.50 0.75 1.00 1.00 1.00
Live Load (LL, PL, LS) 1.75 0.00 1.00 0.00 1.00
AASHTO Table 11.5.7-1 & Article 11.5.8
MSE Resistance Case Strength Extreme Service
Bearing Resistance (RFbr) 0.65 0.90 1.00
Sliding Soil to Soil (RFsl) 1.00 1.00 1.00
Sliding Soil to Reinforcement (RFslrf) 1.00 1.00 1.00
Tensile Resistance (RFten) 0.90 1.20 1.00
Pullout Resistance (RFpo) 0.90 1.20 1.00
Overturning Resistance (RFot) 0.60 1.00 1.00
AASHTO Table 10.5.5.2.2-1
Gravity Resistance Case Strength Extreme Service
Bearing Resistance (RFbr) 0.45 0.45 0.45
Cast-In-Place Concrete to Stone (RFsl_cip) 0.80 1.00 1.00
Precast Concrete to Stone (RFsl_c) 0.90 1.00 1.00
Stone to Soil (RFsl_s) 0.90 0.90 0.90
Passive EP (RFep) 0.50 0.90 0.90
Application of Load Factors
Group DC EV LS EH Probable Use
Strength I-a 0.90 1.00 1.75 1.50 BC/EC/SL
Strength I-b 1.25 1.35 1.75 1.50 BC (max. value)
Service I 1.00 1.00 1.00 1.00 Settlement
Notes: BC - Bearing Capacity; EC - Eccentricity; SL - Sliding
By Inspection:
• Strength I-a (minimum vertical loads and maximum horizontal loads) will govern for the case of sliding and
eccentricity (overturning); and
• For the case of bearing capacity, maximum vertical loads will govern and the factored loads must be
compared for Strength I-b and Strength IV.
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 3
NOTES ON DESIGN UNITS
The wall section is designed on a 'per unit width bases' (lb/ft/ft of wall or kN/m/meter of wall). In the calculations the
software shows lb/ft or kN/m, neglecting the unit width factor for simplicity.
The weights for the wall unit are shown as lbs / ft3 (kN / m3). For SRW design a 1 sf unit is typically 1 ft deep, 1.5 ft
wide and 8 inches tall (or 1 ft3). therefore a typical value of 120 pcf is shown. With larger units the unit weight will
vary with the size of the unit. Say we have 4 ft wide unit, 1.5 ft tall and 24 inches deep with a tapered shape (sides
narrow), built with 150 pcf concrete. We add up the concrete, the gravel fill and divide by the volume and the results
may come out to 140 pcf, as shown in the table. The units with more gravel may have lower effective unit weights
based on the calculations.
Hollow Units
Hollow units with gravel fill are treated differently in AASHTO. If the fill can fall out as the unit is lifted, then AASHTO
only allows 80% of the weight of the fill to be used for eccentricity (overturning calculations). In the properties page
for the units the weight of the concrete may be as low as 75 pcf. This is the effective unit weight of the concrete only
(e.g. the weight of the concrete divided by the volume of the unit). The density of the concrete maybe 150 pcf, but not
the effective weight including the volume of the void spaces used for gravel fill.
Rounding Errors
When doing hand calculations the values may vary from the values shown in the software. The program is designed
using double precision values (64 bit precision: 14 decimal places). Over several calculations the results may differ
from the single calculation the user is making, probably inputting one or two already rounded values.
Result Rounding
As noted above the software is based on double precision values. For example, using an NCMA design method an
allowable factor of safety of 1.5 the software may calculate a value of 1.49999999999999, since this is less than 1.5,
it would be false (NG), even though the results shown is 1.50 (results are rounded to 2 places on the screen). In the
design check we round to 2 decimal places to check against the suggested value (1.49999999999 rounds to 1.50).
Given the precision of the calculation, this will provide a safe design even though the 'absolute' value is less than the
minimum suggested.
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 4
GEOGRID REINFORCING
STRUCTURAL PROPERTIES: Mirafi
GEOGRID PROPERTIES
Name Tult RFcr RFd RFid Ci Cd Alpha Ltds
8XT 7400 1.45 1.15 1.10 0.80 0.80 0.80 4034
CONNECTION STRENGTHS
Geogrid Slope 1 Intercept 1 Peak Break Slope 2 Intercept 2 Max Normal Rup Conn Conn Creep Tlot (%) Tlot
5XT 18.00 536 1571 3.00 964 2361 False 1.45 100 4700
8XT 19.00 946 4834 3.00 2357 7745 False 1.45 100 7400
10XT 22.00 1464 -1 0.00 0 4999 False 1.45 100 9500
20XT 26.00 1825 4746 0.00 4140 6936 False 1.45 100 13705
SHEAR STRENGTHS
Slope 0 deg
Intercept 3500psf
CONNECTION CREEP
In AASHTO design methods a mechanical connector may rupture the reinforcing, thus a creep reduction
factor would be applied. If no test data is available, the creep reduction factor for the reinforcing would be applied.If a
frictional connection is used, then a creep reduction factor would not be applied and a factor of 1.0 is applicable.
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 5
CALCULATION RESULTS
OVERVIEW
Calculates stability assuming the wall is a rigid body. Forces and moments are calculated about the base and
center of the wall. The base block width is used in the calculations. The concrete units and granular fill over the blocks
are used as resisting forces.
EARTH PRESSURES
The method of analysis uses the Coulomb Earth Pressure equation (below) to calculate active earth
pressures. Wall friction is assumed to act at the back of the wall face. The component of earth pressure is assumed to
act perpendicular to the boundary surface. The effective delta angle is delta minus the wall batter at the back face
(assumed to be vertical). If the slope breaks within the failure zone, a trial wedge method of analysis is used.
INTERNAL EARTH PRESSURES
Effective internal Delta angle delta = 0.0 deg
Coefficient of active earth pressure ka =0.283
Internal failure plane ρ = 62.0 deg
EXTERNAL EARTH PRESSURES
Effective Delta angle (delta = β delta =0.0 deg
Coefficient of active earth pressure ka =0.282
Effective Face Angle Face Alpha =0.00 deg
External failure plane ρ = 61.0 deg
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 6
W0: leveling pad W6: Rectangle zone in broken back
W1: facing units W7: Live load over the mass
W2: soil wedge behind the face (base of top block to bottom) W8: Dead load over the mass
W3: rectangular area in MSE area W9: Force Pa
W4: the wedge at the back of the mass W10: Surcharge load Paq
W5: slope area over the mass W11: Dead Load Surcharge Paqd
X-Len: is measured from the center of the base (+) Driving, (-) Resisting.
Name Factor γ Force (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 1.00 5076 -- 2.81 -- 14246 --
Soil(W2) 1.00 1768 -- 1.18 -- 2085 --
Soil(W3) 1.00 9111 -- -2.45 -- -- -22291
DL(W8) 1.00 602 -- 0.00 -- -- 0
Pa_h 1.00 -- 2292 -- 4.33 9933 --
Pq_h 1.00 -- 342 -- 6.50 2222 --
Sum (V, H) 1.00 16557 2634 Sum Mom 28486.88 -22291
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 7
FORCES AND MOMENTS FACTORED FOR Str I-a
UltraWall increases all driving forces and reduces the resisting forces by the factors shown for Str I.
FACTORED LOADS: Str Ia
Name FactorMax γ FactorMin γ ForceSldg (V) ForceEcc (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 1.25 0.90 4569 4569 -- 2.81 -- 12822 --
Soil(W2) 1.35 1.00 1768 1768 -- 1.18 -- 2085 --
Soil(W3) 1.35 1.00 9111 9111 -- -2.45 -- -- -22291
DL(W8) 1.50 0.75 602 602 -- 0.00 -- -- 0
Pa_h 1.50 0.90 -- -- 3439 -- 4.33 14900 --
Pa_v 1.50 0.90 0 0 -- -5.98 -- -- 0
Pq_h 1.75 0.00 -- 598 598 -- 6.50 3888 --
Pq_v 1.75 0.00 0 0 -- -5.25 -- -- 0
Sum (V, H) 15899 15899 4037 Sum Mom 33695 -22291
FORCES AND MOMENTS FACTORED FOR Str I-b
UltraWall increase resisting loads and increases driving loads by the factors shown for Str I-b.
FACTORED LOADS: Str Ib
Name Factor γ Force (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 1.25 6346 -- 2.81 -- 17808 --
Soil(W2) 1.35 2386 -- 1.18 -- 2815 --
Soil(W3) 1.35 12301 -- -2.45 -- -- -30093
DL(W8) 1.50 903 -- 0.00 -- -- 0
Pa_h 1.50 -- 3439 -- 4.33 14900 --
Pa_v 1.50 0 -- -5.98 -- -- 0
Pq_h 1.75 -- 598 -- 6.50 3888 --
Pq_v 1.75 0 -- -5.25 -- -- 0
Sum (V, H) 1.00 21935 4037 Sum Mom 39411 -30093
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 8
BASE SLIDING
Sliding at the base is checked at the foundation soil and a check in the reinforced fill zone.
W1(DCr) + W2(EVr) + W3(EVr) + W8(ESr)
(5076 * 0.90) + (1768 * 1.00) + (9111 * 1.00) + (602 * 0.75)
N =15899ppf
Resisting force in the Reinforced Zone = (N tan(slope) + c B) x RFsl
(15899 tan(34.0) + 50.0 * 11) * 1 Rf1 =11249
Resisting force in the Foundation Zone = (N tan(slope) + c B) x RFsl
(15899 tan(34.0) + 200.0 * 11) * 1 Rf2 =12824
Driving force is the horizontal component of Pah(EHd) + Pqh(LLd)
(2292 * 1.50) + (342 * 1.75)
Df =4037
CDR = Rf1 / Df CDR =3.04
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 9
SLIDING ON REINFORCING
Sliding along the reinforcing is checked at each layer within the reinforced zone.
Sliding resistance is calculated by taking the normal load on the reinforcing, N, times the tangent of the
friction angle of the reinforced soils , φ, times a reduction factor for sliding, Rsl.
Sliding along the reinforcing includes shearing through the face panel. The shear resistance of the face
panel is included as a resisting force, RF_face.
N = Normal load on the geogrid layer. = 9002
(N * tan(34.00) * Cd) + RF_face
(9002 * tan(34.00) * 0.80 ) + 3500 RF = 8358
The driving forces is the active earth pressure plus any surcharge loads behind the reinforced zone.
Pah_ext(EHd) + Pqh_ext(LLd)
where:
z = depth to reinforcing from the surface at the end of the reinforcing. [10.54]
EHd = Load factor for Earth Pressure driving [EHd = 1.50]
Pah = 1/2 x γ z^2 x ka x cos(δ) [1961.63]
Pah_ext, Pqh_ext, etc. could be from a closed from solution (Coulomb/Rankine) or from a trial wedge
solution.
DF = (1962 x 1.50) + (529 * 1.75 DF = 3187
CDR sliding = RF / DF CDR = 2.62
The table below shows a summary of the forces and reactions.
Elevation[ft] Name[ft] z ext[ft] N[ppf] % Coverage Friction Angle[deg] F_Resisting Pah(EHd) Pqh(LLd) Pqdh(DLd) PqMnDOT(LLd) F_Driving CDR_sl
9.83 8XT 3.17 2776 100.0 34.00 4998 226 223 114 0 222 22.52
7.38 8XT 5.63 4725 100.0 34.00 6050 825 460 235 0 912 6.63
4.92 8XT 8.08 6800 100.0 34.00 7169 1725 696 341 0 1894 3.79
2.46 8XT 10.54 9002 100.0 34.00 8358 2942 926 447 0 3187 2.62
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 10
ECCENTRICITY AND BEARING
Eccentricity is the calculation of the distance of the resultant force away from the centroid of mass. This
measure is an indication of the overturning of the mass. In rigid concrete structures, the limit to eccentricity is L/4 (the
middle half of the base). UltraWall uses an allowable eccentricity of e/L per the AASHTO LRFD guidelines.
Eccentricity is still used as a guide to design in some design methods. Eccentricity is based on case S1a (minimum
resisting forces, maximum driving forces. Bearing is based on case S1b (maximum resisting forces, maximum driving
forces).
UltraWall calculates three eccentricities:
1) S1a: Maximum eccentricity (overturning) where it uses the maximum driving forces combined
with the minimum resisting forces (see overturning).
2) S1b Maximum bearing where it uses the maximum driving forces combined with the maximum
resisting forces.
3) Service: Maximum bearing where it uses the actual driving forces combined with the actual
resisting forces in Service loading.
Calculation of Eccentricity for maximum bearing (S1b)
Moments resisting = + M3(EVd)
+ (-22291 * 1.35)
Mr =-30093ft-lbs
Moments driving = M1(DCr) + M2(EVd) + Pah(EHd) + Pqh(LLd)
+ (14246 * 1.25) + (2085 * 1.35) + (9933 * 1.50) + (2222 * 1.75)
Mo = 39411ft-lbs
e = (SumMr + SumMo)/SumV [ if e < 0, then e = 0 ]
e = (-30093 + 39411.3) /21935.1 e =0.425
Calculation of Bearing Pressures
Qal = (c*Nc + q*Nq + 0.5*gamma*(B')*Ng) * RFbrg
where:
Nc =42.16
Nq =29.44
Ng =41.06
c =200.00psf
RFbrg =0.65
q =250psf [embedment x gamma]
B' = B - 2e =9.65ft
Calculate Allowable Bearing, Qal Qal =26364psf
Applied Bearing Pressures (Sigma) (SumV)/B' =2273psf
Calculated CDR for bearing Qal/sigma =11.60
Design Sum Vert Mo Mr e Qal Sigma CDR
Strength I-b 21935 39411 -30093 0.425 26364 2273 11.60
Service 16557 28487 -22291 0.374 40820 1698 24.04
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 11
Elevation[ft] Name Ta*RF[ppf] Tas*RF[ppf] Coverage Ratio % Tmax[ppf] TSmax[ppf] CDR Str CDRs Str
9.83 8XT 3631 7020 100 461 663 7.88 10.59
7.38 8XT 3631 7020 100 764 869 4.75 8.08
4.92 8XT 3631 7020 100 1051 986 3.45 7.12
2.46 8XT 3631 7020 100 1319 1095 2.75 6.41
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 12
PULLOUT CALCULATIONS
Pullout is the amount of resistance of the reinforcing has to a pullout failure based on the Tmax applied and
the depth of embedement (resistance). In an AASHTO design, the failure plane is fixed at the Rankine failure plane
angle, 45 + phi/2. All failure planes begin at the tail. of the facing units.
Failure Plane Angle = 62.0 Deg
F* = 0.67 x tan( φ ) [AASHTO 11.10.6.3.2]
F* = 0.67 x tan( 34) = 0.45
α = 0.80 [AASHTO Table 11.10.6.3.2-1]
RFpo = 0.90
Pullout = 2 x N x F* x α x Coverage x RFpo
Pullout = 2 x 2228 x 0.45 x 0.80 x 1.00 x 0.90 = 1449.58
Pullout is the calculated value or the Tult of the geogrid, whichever is less.
NOTE: The pullout capacity is limited by the LTDS of the reinforcing layer, not the ultimate pullout capacity calculated.
TABLE OF RESULTS
Elevation[ft] Normal[lbf] F* Alpha % Coverage Tmax[ppf] Le[ft] La[ft] Pullout_[Pr][ppf] CDR PO
9.83 2228 0.45 0.80 100 461 4.49 6.01 1450 3.14
7.38 4327 0.45 0.80 100 764 5.39 5.11 2816 3.69
4.92 6978 0.45 0.80 100 1051 6.28 4.22 3631 3.45
2.46 10104 0.45 0.80 100 1319 7.18 3.32 3631 2.75
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 13
CONNECTION CALCULATIONS
Connection is the amount of resistance of the reinforcing has to a pullout failure from the facing units based
on the Tmax applied and the normal load on the units. In an AASHTO LRFD design, creep on the connection may be
applied for frictional and mechanical connections.
Connection Capacity = [N tan(slope) + intercept] / RFcr
RFcr can be a value obtained from long-term testing or by default could be the creep reduction factor of the
geogrid reinforcing.
Base friction is used to reduce the tension in the bottom layer of reinforcing. The force in the bottom layer is
the tension from half way to the reinforcing layer above to the halfway to the foundation level below.
Base Friction = Base Shear x RFsliding
Base Shear = 5076 x tan( atan(0.80 x tan(40 )) + 0
3408 x 0.90 BF = 3067ppf
BF utilized to reduce bottom tension = 573ppf
CRu = Ultimate connection strength [1692 x tan( 19.00) + 946 = 1528.65 ]
CRru = CRu / TLot [1528.65/7400.00 = 0.21]
RFcrcn = 1.45 [Connection creep if tested, otherwise geogrid creep factor]
[if connection creep is set to 'false', RFcrcn = 1]
CRcr = CRru / RFcrcn [0.21 / 1.00 = 0.21]
Tac = Tult x CRcr / RFd * RFten [ 7400 x 0.21 / 1.15 x 0.90 = 1196.34]
TABLE OF RESULTS
Elev[ft] Name[ft] Tmax[ppf] Ttotal[ppf] Rc % RFcn_cr N[ppf] Avail_CN[ppf] CDR cn CDR cns
9.83 8XT 461 443 100 1.00 1692 1196 2.60 3.24
7.38 8XT 764 733 100 1.00 2538 1424 1.86 2.33
4.92 8XT 1051 1008 100 1.00 3384 1652 1.57 1.97
2.46 8XT 1319 1265 100 1.00 4230 1880 1.43 1.78
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 14
SEISMIC CALCULATIONS
The loads considered under seismic loading are primarily inertial loadings. The wave passes the structure
putting the mass into motion and then the mass will try to continue in the direction of the initial wave. In the
calculations you see the one dynamic earth pressure from the wedge of the soil behind the reinforced mass, and then
all the other forces come from inertia calculations of the face put into motion and then trying to be held in place.
In AASHTO LRFD, external stability is calculated based on 100% of Pae and 50% of Pir and then
50% of Pae and 100% of Pir. The values labelled Pae are 100% Pae/50% Pir; labels Pir are 50% Pae/100% Pir.
Design Acceleration A = 0.330
Displacment (d) d = 3.3in
Design Acceleration Coefficient Displacment Based (empirically)
Kh = A/2 = kh(ext) = 0.165
Vertical Acceleration kv =0.000
SEISMIC THRUST
EXTERNAL Kae
Kae Kae =0.384
Pae = 0.5*gamma*(H)^2*D_Kae Pae =1077ppf
Pae_h/2 = Pae*cos(delta)/2 Pae_h/2 =538ppf
Pae_v/2 = Pae*sin(delta)/2 Pae_v/2 =0ppf
INERTIA FORCES OF THE STRUCTURE
Face (Pif) = (W0 + W1)*kh(int) = 5076 * 0.165 Pif =838ppf
Mass (Pir) = (W)*kh(int) = 7586 * 0.165 Pir =1252ppf
Slope (Pis) = (W)*kh(int) = 0 * 0.165 Pis =0ppf
Dead Load(Pidl) = (DL)*kh(int) = 0 * 0.165 Pidl =0ppf
TABLE OF RESULTS FOR SEISMIC REACTIONS
Name Force (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 5076 -- 2.44 -- -- 12405
Soil(W2) 1768 -- 4.07 -- -- 7194
Soil(W3) 9111 -- 7.70 -- -- 70126
DL(W8) 602 -- 7.49 -- -- 4508
Pa_h -- 2292 -- 4.33 9933 --
Pq_h -- 342 -- 6.50 2222 --
Pir -- 1252 -- 6.50 8136 --
Pif -- 838 -- 6.50 5445 --
Pae_h/2 -- 1077 -- 6.50 3500 --
Sum V / H 16557.36 4920.09 Sum Mom 29235.44 94233.87
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 15
UltraWall
Project: Fyffe
Location: Site Location
Designer: JC
Date: 5/13/2020
Section: 15ft Stratagrid
Design Method: AASHTO_LRFD_2014
Design Unit: UltraBlock
Seismic Acc: 0.330
SOIL PARAMETERS φ coh γ
Reinforced Soil: 34 deg 50psf 125pcf
Retained Soil: 34 deg 100psf 125pcf
Foundation Soil: 34 deg 200psf 125pcf
Leveling Pad: Crushed Stone
GEOMETRY
Design Height: 13.00ft Live Load: 250psf
Wall Batter/Tilt: 0.00/ 9.50 deg Live Load Offset: 8.00ft
Embedment: 2.00ft Live Load Width: 39ft
Leveling Pad Depth: 1.00ft Dead Load: 100psf
Slope Angle: 0.0 deg Dead Load Offset: 0.0ft
Slope Length: 0.0ft Dead Load Width: 39ft
Slope Toe Offset: 0.0ft Leveling Pad Width: 3.46ft
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 1
RESULTS (Static / Seismic)
CDR Sliding: 3.04 (fnd) / [2.31 ] CDR Bearing: 11.60 / 17.62
Eccentricity (e/L): 0.07 / -0.10 Bearing: 2273; Srvc 1698 / Seis 1716
CDR Connection: 1.00
ID Ht Lngth Geogri Ta_tn Rc % TMax (Tatn*RF) CDR Ta_tn Ta_cn CDR Ta_cn CDR Tpo CDR Sldg
4 9.8310.50 SG500 3122 [4839] 100 461 [583] 2810 [5807] 6.10 [8.44] 1157 [1388] 2.51 [3.14] 3.14 56.32
3 7.3810.50 SG500 3122 [4839] 100 764 [583] 2810 [5807] 3.68 [6.50] 1262 [1515] 1.65 [2.07] 3.68 14.85 [6.95]
2 4.9210.50 SG500 3122 [4839] 100 1051 [583] 2810 [5807] 2.67 [5.74] 1294 [1552] 1.23 [1.54] 2.67 7.75 [4.96]
1 2.4610.50 SG500 3122 [4839] 100 1319 [583] 2810 [5807] 2.13 [5.19] 1325 [1590] 1.00 [1.26] 2.13 4.98 [3.73]
Column Descriptions:
Tr: Tension required (Ta*Reduction factors) [ppf]
EP(Pa): Earth pressures from closed form solution or trial wedge [ppf]
Rc %: percent coverage for geosynthetics
EP (Pa) internal active earth pressure [ppf ]
LL (Pql) earth pressure due to live load surcharge [ppf ]
DL (Pqd) earth pressure due to dead load surcharge [ppf ]
Tmax maximum earth pressure on geosynthetic layer [ppf ]
CDRstr 'Capacity/Demand Ratio (CDR)' on geogrid strength (Tr/Tmax)
Ta cn allowable tension capacity on the connection [ppf ]
CDR Pkcn, Capacity/Demand Ratio on the connection (Ta cn/Tmax)
CDR PO, Capacity/Demand Ratio on pullout (Ta pullout/(Tmax - LL)
CDR Sldg [fndn], Capacity/Demand Ratio on sliding on the reinforcement, CDR sliding on the foundation
soils
Grid Embed, depth of embedment beyond the theorectical failure plane. [ft ]
(PaC): reduction in load due to cohesion [ppf]
PaT: sum of all earth pressures [ppf]
%D/H: ratio of based depth to height (warning for narrow walls, < 35%)
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 2
DESIGN DATA
Load Factors for Design
AASHTO Table 3.4.1-1 & 3.4.1-2
Load Case Str_Max Str_Min Extreme Max Extreme Min Service
Str I Dead Load (DC) 1.25 0.90 1.00 1.00 1.00
Soil Load Driving (EH) 1.50 0.90 1.00 1.00 1.00
Str I Vert Earth Load (EV) 1.35 1.00 1.00 1.00 1.00
Dead Load Surcharge (ES) 1.50 0.75 1.00 1.00 1.00
Live Load (LL, PL, LS) 1.75 0.00 1.00 0.00 1.00
AASHTO Table 11.5.7-1 & Article 11.5.8
MSE Resistance Case Strength Extreme Service
Bearing Resistance (RFbr) 0.65 0.90 1.00
Sliding Soil to Soil (RFsl) 1.00 1.00 1.00
Sliding Soil to Reinforcement (RFslrf) 1.00 1.00 1.00
Tensile Resistance (RFten) 0.90 1.20 1.00
Pullout Resistance (RFpo) 0.90 1.20 1.00
Overturning Resistance (RFot) 0.60 1.00 1.00
AASHTO Table 10.5.5.2.2-1
Gravity Resistance Case Strength Extreme Service
Bearing Resistance (RFbr) 0.45 0.45 0.45
Cast-In-Place Concrete to Stone (RFsl_cip) 0.80 1.00 1.00
Precast Concrete to Stone (RFsl_c) 0.90 1.00 1.00
Stone to Soil (RFsl_s) 0.90 0.90 0.90
Passive EP (RFep) 0.50 0.90 0.90
Application of Load Factors
Group DC EV LS EH Probable Use
Strength I-a 0.90 1.00 1.75 1.50 BC/EC/SL
Strength I-b 1.25 1.35 1.75 1.50 BC (max. value)
Service I 1.00 1.00 1.00 1.00 Settlement
Notes: BC - Bearing Capacity; EC - Eccentricity; SL - Sliding
By Inspection:
• Strength I-a (minimum vertical loads and maximum horizontal loads) will govern for the case of sliding and
eccentricity (overturning); and
• For the case of bearing capacity, maximum vertical loads will govern and the factored loads must be
compared for Strength I-b and Strength IV.
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 3
NOTES ON DESIGN UNITS
The wall section is designed on a 'per unit width bases' (lb/ft/ft of wall or kN/m/meter of wall). In the calculations the
software shows lb/ft or kN/m, neglecting the unit width factor for simplicity.
The weights for the wall unit are shown as lbs / ft3 (kN / m3). For SRW design a 1 sf unit is typically 1 ft deep, 1.5 ft
wide and 8 inches tall (or 1 ft3). therefore a typical value of 120 pcf is shown. With larger units the unit weight will
vary with the size of the unit. Say we have 4 ft wide unit, 1.5 ft tall and 24 inches deep with a tapered shape (sides
narrow), built with 150 pcf concrete. We add up the concrete, the gravel fill and divide by the volume and the results
may come out to 140 pcf, as shown in the table. The units with more gravel may have lower effective unit weights
based on the calculations.
Hollow Units
Hollow units with gravel fill are treated differently in AASHTO. If the fill can fall out as the unit is lifted, then AASHTO
only allows 80% of the weight of the fill to be used for eccentricity (overturning calculations). In the properties page
for the units the weight of the concrete may be as low as 75 pcf. This is the effective unit weight of the concrete only
(e.g. the weight of the concrete divided by the volume of the unit). The density of the concrete maybe 150 pcf, but not
the effective weight including the volume of the void spaces used for gravel fill.
Rounding Errors
When doing hand calculations the values may vary from the values shown in the software. The program is designed
using double precision values (64 bit precision: 14 decimal places). Over several calculations the results may differ
from the single calculation the user is making, probably inputting one or two already rounded values.
Result Rounding
As noted above the software is based on double precision values. For example, using an NCMA design method an
allowable factor of safety of 1.5 the software may calculate a value of 1.49999999999999, since this is less than 1.5,
it would be false (NG), even though the results shown is 1.50 (results are rounded to 2 places on the screen). In the
design check we round to 2 decimal places to check against the suggested value (1.49999999999 rounds to 1.50).
Given the precision of the calculation, this will provide a safe design even though the 'absolute' value is less than the
minimum suggested.
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 4
GEOGRID REINFORCING
STRUCTURAL PROPERTIES: Stratagrid
GEOGRID PROPERTIES
Name Tult RFcr RFd RFid Ci Cd Alpha Ltds
SG500 6400 1.55 1.15 1.15 0.80 0.80 0.80 3122
CONNECTION STRENGTHS
Geogrid Slope 1 Intercept 1 Peak Break Slope 2 Intercept 2 Max Normal Rup Conn Conn Creep Tlot (%) Tlot
SG500 29.00 688 1899 3.00 1641 7655 False 1.55 110 7040
SG550 46.00 670 2190 4.00 2785 7650 False 1.55 110 8965
SG600 46.00 670 2190 4.00 2785 7850 False 1.55 110 10010
SG700 37.00 643 -1 0.00 0 3100 False 1.55 100 11800
SHEAR STRENGTHS
Slope 0 deg
Intercept 11000psf
CONNECTION CREEP
In AASHTO design methods a mechanical connector may rupture the reinforcing, thus a creep reduction
factor would be applied. If no test data is available, the creep reduction factor for the reinforcing would be applied.If a
frictional connection is used, then a creep reduction factor would not be applied and a factor of 1.0 is applicable.
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 5
CALCULATION RESULTS
OVERVIEW
Calculates stability assuming the wall is a rigid body. Forces and moments are calculated about the base and
center of the wall. The base block width is used in the calculations. The concrete units and granular fill over the blocks
are used as resisting forces.
EARTH PRESSURES
The method of analysis uses the Coulomb Earth Pressure equation (below) to calculate active earth
pressures. Wall friction is assumed to act at the back of the wall face. The component of earth pressure is assumed to
act perpendicular to the boundary surface. The effective delta angle is delta minus the wall batter at the back face
(assumed to be vertical). If the slope breaks within the failure zone, a trial wedge method of analysis is used.
INTERNAL EARTH PRESSURES
Effective internal Delta angle delta = 0.0 deg
Coefficient of active earth pressure ka =0.283
Internal failure plane ρ = 62.0 deg
EXTERNAL EARTH PRESSURES
Effective Delta angle (delta = β delta =0.0 deg
Coefficient of active earth pressure ka =0.282
Effective Face Angle Face Alpha =0.00 deg
External failure plane ρ = 61.0 deg
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 6
W0: leveling pad W6: Rectangle zone in broken back
W1: facing units W7: Live load over the mass
W2: soil wedge behind the face (base of top block to bottom) W8: Dead load over the mass
W3: rectangular area in MSE area W9: Force Pa
W4: the wedge at the back of the mass W10: Surcharge load Paq
W5: slope area over the mass W11: Dead Load Surcharge Paqd
X-Len: is measured from the center of the base (+) Driving, (-) Resisting.
Name Factor γ Force (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 1.00 5076 -- 2.81 -- 14246 --
Soil(W2) 1.00 1768 -- 1.18 -- 2085 --
Soil(W3) 1.00 9111 -- -2.45 -- -- -22291
DL(W8) 1.00 602 -- 0.00 -- -- 0
Pa_h 1.00 -- 2292 -- 4.33 9933 --
Pq_h 1.00 -- 342 -- 6.50 2222 --
Sum (V, H) 1.00 16557 2634 Sum Mom 28486.88 -22291
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 7
FORCES AND MOMENTS FACTORED FOR Str I-a
UltraWall increases all driving forces and reduces the resisting forces by the factors shown for Str I.
FACTORED LOADS: Str Ia
Name FactorMax γ FactorMin γ ForceSldg (V) ForceEcc (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 1.25 0.90 4569 4569 -- 2.81 -- 12822 --
Soil(W2) 1.35 1.00 1768 1768 -- 1.18 -- 2085 --
Soil(W3) 1.35 1.00 9111 9111 -- -2.45 -- -- -22291
DL(W8) 1.50 0.75 602 602 -- 0.00 -- -- 0
Pa_h 1.50 0.90 -- -- 3439 -- 4.33 14900 --
Pa_v 1.50 0.90 0 0 -- -5.98 -- -- 0
Pq_h 1.75 0.00 -- 598 598 -- 6.50 3888 --
Pq_v 1.75 0.00 0 0 -- -5.25 -- -- 0
Sum (V, H) 15899 15899 4037 Sum Mom 33695 -22291
FORCES AND MOMENTS FACTORED FOR Str I-b
UltraWall increase resisting loads and increases driving loads by the factors shown for Str I-b.
FACTORED LOADS: Str Ib
Name Factor γ Force (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 1.25 6346 -- 2.81 -- 17808 --
Soil(W2) 1.35 2386 -- 1.18 -- 2815 --
Soil(W3) 1.35 12301 -- -2.45 -- -- -30093
DL(W8) 1.50 903 -- 0.00 -- -- 0
Pa_h 1.50 -- 3439 -- 4.33 14900 --
Pa_v 1.50 0 -- -5.98 -- -- 0
Pq_h 1.75 -- 598 -- 6.50 3888 --
Pq_v 1.75 0 -- -5.25 -- -- 0
Sum (V, H) 1.00 21935 4037 Sum Mom 39411 -30093
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 8
BASE SLIDING
Sliding at the base is checked at the foundation soil and a check in the reinforced fill zone.
W1(DCr) + W2(EVr) + W3(EVr) + W8(ESr)
(5076 * 0.90) + (1768 * 1.00) + (9111 * 1.00) + (602 * 0.75)
N =15899ppf
Resisting force in the Reinforced Zone = (N tan(slope) + c B) x RFsl
(15899 tan(34.0) + 50.0 * 11) * 1 Rf1 =11249
Resisting force in the Foundation Zone = (N tan(slope) + c B) x RFsl
(15899 tan(34.0) + 200.0 * 11) * 1 Rf2 =12824
Driving force is the horizontal component of Pah(EHd) + Pqh(LLd)
(2292 * 1.50) + (342 * 1.75)
Df =4037
CDR = Rf1 / Df CDR =3.04
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 9
SLIDING ON REINFORCING
Sliding along the reinforcing is checked at each layer within the reinforced zone.
Sliding resistance is calculated by taking the normal load on the reinforcing, N, times the tangent of the
friction angle of the reinforced soils , φ, times a reduction factor for sliding, Rsl.
Sliding along the reinforcing includes shearing through the face panel. The shear resistance of the face
panel is included as a resisting force, RF_face.
N = Normal load on the geogrid layer. = 9002
(N * tan(34.00) * Cd) + RF_face
(9002 * tan(34.00) * 0.80 ) + 11000 RF = 15858
The driving forces is the active earth pressure plus any surcharge loads behind the reinforced zone.
Pah_ext(EHd) + Pqh_ext(LLd)
where:
z = depth to reinforcing from the surface at the end of the reinforcing. [10.54]
EHd = Load factor for Earth Pressure driving [EHd = 1.50]
Pah = 1/2 x γ z^2 x ka x cos(δ) [1961.63]
Pah_ext, Pqh_ext, etc. could be from a closed from solution (Coulomb/Rankine) or from a trial wedge
solution.
DF = (1962 x 1.50) + (529 * 1.75 DF = 3187
CDR sliding = RF / DF CDR = 4.98
The table below shows a summary of the forces and reactions.
Elevation[ft] Name[ft] z ext[ft] N[ppf] % Coverage Friction Angle[deg] F_Resisting Pah(EHd) Pqh(LLd) Pqdh(DLd) PqMnDOT(LLd) F_Driving CDR_sl
9.83 SG500 3.17 2776 100.0 34.00 12498 226 223 114 0 222 56.32
7.38 SG500 5.63 4725 100.0 34.00 13550 825 460 235 0 912 14.85
4.92 SG500 8.08 6800 100.0 34.00 14669 1725 696 341 0 1894 7.75
2.46 SG500 10.54 9002 100.0 34.00 15858 2942 926 447 0 3187 4.98
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 10
ECCENTRICITY AND BEARING
Eccentricity is the calculation of the distance of the resultant force away from the centroid of mass. This
measure is an indication of the overturning of the mass. In rigid concrete structures, the limit to eccentricity is L/4 (the
middle half of the base). UltraWall uses an allowable eccentricity of e/L per the AASHTO LRFD guidelines.
Eccentricity is still used as a guide to design in some design methods. Eccentricity is based on case S1a (minimum
resisting forces, maximum driving forces. Bearing is based on case S1b (maximum resisting forces, maximum driving
forces).
UltraWall calculates three eccentricities:
1) S1a: Maximum eccentricity (overturning) where it uses the maximum driving forces combined
with the minimum resisting forces (see overturning).
2) S1b Maximum bearing where it uses the maximum driving forces combined with the maximum
resisting forces.
3) Service: Maximum bearing where it uses the actual driving forces combined with the actual
resisting forces in Service loading.
Calculation of Eccentricity for maximum bearing (S1b)
Moments resisting = + M3(EVd)
+ (-22291 * 1.35)
Mr =-30093ft-lbs
Moments driving = M1(DCr) + M2(EVd) + Pah(EHd) + Pqh(LLd)
+ (14246 * 1.25) + (2085 * 1.35) + (9933 * 1.50) + (2222 * 1.75)
Mo = 39411ft-lbs
e = (SumMr + SumMo)/SumV [ if e < 0, then e = 0 ]
e = (-30093 + 39411.3) /21935.1 e =0.425
Calculation of Bearing Pressures
Qal = (c*Nc + q*Nq + 0.5*gamma*(B')*Ng) * RFbrg
where:
Nc =42.16
Nq =29.44
Ng =41.06
c =200.00psf
RFbrg =0.65
q =250psf [embedment x gamma]
B' = B - 2e =9.65ft
Calculate Allowable Bearing, Qal Qal =26364psf
Applied Bearing Pressures (Sigma) (SumV)/B' =2273psf
Calculated CDR for bearing Qal/sigma =11.60
Design Sum Vert Mo Mr e Qal Sigma CDR
Strength I-b 21935 39411 -30093 0.425 26364 2273 11.60
Service 16557 28487 -22291 0.374 40820 1698 24.04
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 11
Elevation[ft] Name Ta*RF[ppf] Tas*RF[ppf] Coverage Ratio % Tmax[ppf] TSmax[ppf] CDR Str CDRs Str
9.83 SG500 2810 5807 100 461 688 6.10 8.44
7.38 SG500 2810 5807 100 764 894 3.68 6.50
4.92 SG500 2810 5807 100 1051 1011 2.67 5.74
2.46 SG500 2810 5807 100 1319 1120 2.13 5.19
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 12
PULLOUT CALCULATIONS
Pullout is the amount of resistance of the reinforcing has to a pullout failure based on the Tmax applied and
the depth of embedement (resistance). In an AASHTO design, the failure plane is fixed at the Rankine failure plane
angle, 45 + phi/2. All failure planes begin at the tail. of the facing units.
Failure Plane Angle = 62.0 Deg
F* = 0.67 x tan( φ ) [AASHTO 11.10.6.3.2]
F* = 0.67 x tan( 34) = 0.45
α = 0.80 [AASHTO Table 11.10.6.3.2-1]
RFpo = 0.90
Pullout = 2 x N x F* x α x Coverage x RFpo
Pullout = 2 x 2228 x 0.45 x 0.80 x 1.00 x 0.90 = 1449.58
Pullout is the calculated value or the Tult of the geogrid, whichever is less.
NOTE: The pullout capacity is limited by the LTDS of the reinforcing layer, not the ultimate pullout capacity calculated.
TABLE OF RESULTS
Elevation[ft] Normal[lbf] F* Alpha % Coverage Tmax[ppf] Le[ft] La[ft] Pullout_[Pr][ppf] CDR PO
9.83 2228 0.45 0.80 100 461 4.49 6.01 1450 3.14
7.38 4327 0.45 0.80 100 764 5.39 5.11 2810 3.68
4.92 6978 0.45 0.80 100 1051 6.28 4.22 2810 2.67
2.46 10104 0.45 0.80 100 1319 7.18 3.32 2810 2.13
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 13
CONNECTION CALCULATIONS
Connection is the amount of resistance of the reinforcing has to a pullout failure from the facing units based
on the Tmax applied and the normal load on the units. In an AASHTO LRFD design, creep on the connection may be
applied for frictional and mechanical connections.
Connection Capacity = [N tan(slope) + intercept] / RFcr
RFcr can be a value obtained from long-term testing or by default could be the creep reduction factor of the
geogrid reinforcing.
Base friction is used to reduce the tension in the bottom layer of reinforcing. The force in the bottom layer is
the tension from half way to the reinforcing layer above to the halfway to the foundation level below.
Base Friction = Base Shear x RFsliding
Base Shear = 5076 x tan( atan(0.80 x tan(40 )) + 0
3408 x 0.90 BF = 3067ppf
BF utilized to reduce bottom tension = 573ppf
CRu = Ultimate connection strength [1692 x tan( 29.00) + 688 = 1625.98 ]
CRru = CRu / TLot [1625.98/7040.00 = 0.23]
RFcrcn = 1.55 [Connection creep if tested, otherwise geogrid creep factor]
[if connection creep is set to 'false', RFcrcn = 1]
CRcr = CRru / RFcrcn [0.23 / 1.00 = 0.23]
Tac = Tult x CRcr / RFd * RFten [ 6400 x 0.23 / 1.15 x 0.90 = 1156.82]
TABLE OF RESULTS
Elev[ft] Name[ft] Tmax[ppf] Ttotal[ppf] Rc % RFcn_cr N[ppf] Avail_CN[ppf] CDR cn CDR cns
9.83 SG500 461 443 100 1.00 1692 1157 2.51 3.14
7.38 SG500 764 733 100 1.00 2538 1262 1.65 2.07
4.92 SG500 1051 1008 100 1.00 3384 1294 1.23 1.54
2.46 SG500 1319 1265 100 1.00 4230 1325 1.00 1.26
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 14
SEISMIC CALCULATIONS
The loads considered under seismic loading are primarily inertial loadings. The wave passes the structure
putting the mass into motion and then the mass will try to continue in the direction of the initial wave. In the
calculations you see the one dynamic earth pressure from the wedge of the soil behind the reinforced mass, and then
all the other forces come from inertia calculations of the face put into motion and then trying to be held in place.
In AASHTO LRFD, external stability is calculated based on 100% of Pae and 50% of Pir and then
50% of Pae and 100% of Pir. The values labelled Pae are 100% Pae/50% Pir; labels Pir are 50% Pae/100% Pir.
Design Acceleration A = 0.330
Displacment (d) d = 3.3in
Design Acceleration Coefficient Displacment Based (empirically)
Kh = A/2 = kh(ext) = 0.165
Vertical Acceleration kv =0.000
SEISMIC THRUST
EXTERNAL Kae
Kae Kae =0.384
Pae = 0.5*gamma*(H)^2*D_Kae Pae =1077ppf
Pae_h/2 = Pae*cos(delta)/2 Pae_h/2 =538ppf
Pae_v/2 = Pae*sin(delta)/2 Pae_v/2 =0ppf
INERTIA FORCES OF THE STRUCTURE
Face (Pif) = (W0 + W1)*kh(int) = 5076 * 0.165 Pif =838ppf
Mass (Pir) = (W)*kh(int) = 7586 * 0.165 Pir =1252ppf
Slope (Pis) = (W)*kh(int) = 0 * 0.165 Pis =0ppf
Dead Load(Pidl) = (DL)*kh(int) = 0 * 0.165 Pidl =0ppf
TABLE OF RESULTS FOR SEISMIC REACTIONS
Name Force (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 5076 -- 2.44 -- -- 12405
Soil(W2) 1768 -- 4.07 -- -- 7194
Soil(W3) 9111 -- 7.70 -- -- 70126
DL(W8) 602 -- 7.49 -- -- 4508
Pa_h -- 2292 -- 4.33 9933 --
Pq_h -- 342 -- 6.50 2222 --
Pir -- 1252 -- 6.50 8136 --
Pif -- 838 -- 6.50 5445 --
Pae_h/2 -- 1077 -- 6.50 3500 --
Sum V / H 16557.36 4920.09 Sum Mom 29235.44 94233.87
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 15
UltraWall
Project: Fyffe
Location: Site Location
Designer: JC
Date: 5/13/2020
Section: 20ft Mirafi
Design Method: AASHTO_LRFD_2014
Design Unit: UltraBlock
Seismic Acc: 0.330
SOIL PARAMETERS φ coh γ
Reinforced Soil: 34 deg 50psf 125pcf
Retained Soil: 34 deg 100psf 125pcf
Foundation Soil: 34 deg 200psf 125pcf
Leveling Pad: Crushed Stone
GEOMETRY
Design Height: 18.00ft Live Load: 250psf
Wall Batter/Tilt: 0.00/ 9.50 deg Live Load Offset: 8.00ft
Embedment: 2.00ft Live Load Width: 39ft
Leveling Pad Depth: 1.00ft Dead Load: 100psf
Slope Angle: 0.0 deg Dead Load Offset: 0.0ft
Slope Length: 0.0ft Dead Load Width: 39ft
Slope Toe Offset: 0.0ft Leveling Pad Width: 3.46ft
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 1
RESULTS (Static / Seismic)
CDR Sliding: 2.24 (fnd) / [1.99 ] CDR Bearing: 10.50 / 16.49
Eccentricity (e/L): 0.09 / -0.16 Bearing: 2926; Srvc 2138 / Seis 2190
CDR Connection: 1.10
ID Ht Lngth Geogri Ta_tn Rc % TMax (Tatn*RF) CDR Ta_tn Ta_cn CDR Ta_cn CDR Tpo CDR Sldg
6 14.7513.50 8XT 4034 [5850] 100 479 [551] 3631 [7020] 7.59 [10.67] 1196 [1436] 2.50 [3.12] 3.92 35.53
5 12.2913.50 8XT 4034 [5850] 100 774 [551] 3631 [7020] 4.69 [8.11] 1424 [1709] 1.84 [2.30] 4.51 5.85 [3.23]
4 9.83 13.50 8XT 4034 [5850] 100 1062 [551] 3631 [7020] 3.42 [7.14] 1652 [1983] 1.56 [1.95] 3.42 3.77 [2.62]
3 7.38 13.50 8XT 4034 [5850] 100 1350 [551] 3631 [7020] 2.69 [6.38] 1880 [2256] 1.39 [1.74] 2.69 2.77 [2.18]
2 4.92 13.50 8XT 4034 [5850] 100 1637 [551] 3631 [7020] 2.22 [5.77] 2053 [2463] 1.25 [1.57] 2.22 2.19 [1.86]
1 2.46 13.50 8XT 4034 [5850] 100 1896 [551] 3631 [7020] 1.91 [5.31] 2088 [2505] 1.10 [1.38] 1.91 1.82 [1.62]
Column Descriptions:
Tr: Tension required (Ta*Reduction factors) [ppf]
EP(Pa): Earth pressures from closed form solution or trial wedge [ppf]
Rc %: percent coverage for geosynthetics
EP (Pa) internal active earth pressure [ppf ]
LL (Pql) earth pressure due to live load surcharge [ppf ]
DL (Pqd) earth pressure due to dead load surcharge [ppf ]
Tmax maximum earth pressure on geosynthetic layer [ppf ]
CDRstr 'Capacity/Demand Ratio (CDR)' on geogrid strength (Tr/Tmax)
Ta cn allowable tension capacity on the connection [ppf ]
CDR Pkcn, Capacity/Demand Ratio on the connection (Ta cn/Tmax)
CDR PO, Capacity/Demand Ratio on pullout (Ta pullout/(Tmax - LL)
CDR Sldg [fndn], Capacity/Demand Ratio on sliding on the reinforcement, CDR sliding on the foundation
soils
Grid Embed, depth of embedment beyond the theorectical failure plane. [ft ]
(PaC): reduction in load due to cohesion [ppf]
PaT: sum of all earth pressures [ppf]
%D/H: ratio of based depth to height (warning for narrow walls, < 35%)
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 2
DESIGN DATA
Load Factors for Design
AASHTO Table 3.4.1-1 & 3.4.1-2
Load Case Str_Max Str_Min Extreme Max Extreme Min Service
Str I Dead Load (DC) 1.25 0.90 1.00 1.00 1.00
Soil Load Driving (EH) 1.50 0.90 1.00 1.00 1.00
Str I Vert Earth Load (EV) 1.35 1.00 1.00 1.00 1.00
Dead Load Surcharge (ES) 1.50 0.75 1.00 1.00 1.00
Live Load (LL, PL, LS) 1.75 0.00 1.00 0.00 1.00
AASHTO Table 11.5.7-1 & Article 11.5.8
MSE Resistance Case Strength Extreme Service
Bearing Resistance (RFbr) 0.65 0.90 1.00
Sliding Soil to Soil (RFsl) 1.00 1.00 1.00
Sliding Soil to Reinforcement (RFslrf) 1.00 1.00 1.00
Tensile Resistance (RFten) 0.90 1.20 1.00
Pullout Resistance (RFpo) 0.90 1.20 1.00
Overturning Resistance (RFot) 0.60 1.00 1.00
AASHTO Table 10.5.5.2.2-1
Gravity Resistance Case Strength Extreme Service
Bearing Resistance (RFbr) 0.45 0.45 0.45
Cast-In-Place Concrete to Stone (RFsl_cip) 0.80 1.00 1.00
Precast Concrete to Stone (RFsl_c) 0.90 1.00 1.00
Stone to Soil (RFsl_s) 0.90 0.90 0.90
Passive EP (RFep) 0.50 0.90 0.90
Application of Load Factors
Group DC EV LS EH Probable Use
Strength I-a 0.90 1.00 1.75 1.50 BC/EC/SL
Strength I-b 1.25 1.35 1.75 1.50 BC (max. value)
Service I 1.00 1.00 1.00 1.00 Settlement
Notes: BC - Bearing Capacity; EC - Eccentricity; SL - Sliding
By Inspection:
• Strength I-a (minimum vertical loads and maximum horizontal loads) will govern for the case of sliding and
eccentricity (overturning); and
• For the case of bearing capacity, maximum vertical loads will govern and the factored loads must be
compared for Strength I-b and Strength IV.
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 3
NOTES ON DESIGN UNITS
The wall section is designed on a 'per unit width bases' (lb/ft/ft of wall or kN/m/meter of wall). In the calculations the
software shows lb/ft or kN/m, neglecting the unit width factor for simplicity.
The weights for the wall unit are shown as lbs / ft3 (kN / m3). For SRW design a 1 sf unit is typically 1 ft deep, 1.5 ft
wide and 8 inches tall (or 1 ft3). therefore a typical value of 120 pcf is shown. With larger units the unit weight will
vary with the size of the unit. Say we have 4 ft wide unit, 1.5 ft tall and 24 inches deep with a tapered shape (sides
narrow), built with 150 pcf concrete. We add up the concrete, the gravel fill and divide by the volume and the results
may come out to 140 pcf, as shown in the table. The units with more gravel may have lower effective unit weights
based on the calculations.
Hollow Units
Hollow units with gravel fill are treated differently in AASHTO. If the fill can fall out as the unit is lifted, then AASHTO
only allows 80% of the weight of the fill to be used for eccentricity (overturning calculations). In the properties page
for the units the weight of the concrete may be as low as 75 pcf. This is the effective unit weight of the concrete only
(e.g. the weight of the concrete divided by the volume of the unit). The density of the concrete maybe 150 pcf, but not
the effective weight including the volume of the void spaces used for gravel fill.
Rounding Errors
When doing hand calculations the values may vary from the values shown in the software. The program is designed
using double precision values (64 bit precision: 14 decimal places). Over several calculations the results may differ
from the single calculation the user is making, probably inputting one or two already rounded values.
Result Rounding
As noted above the software is based on double precision values. For example, using an NCMA design method an
allowable factor of safety of 1.5 the software may calculate a value of 1.49999999999999, since this is less than 1.5,
it would be false (NG), even though the results shown is 1.50 (results are rounded to 2 places on the screen). In the
design check we round to 2 decimal places to check against the suggested value (1.49999999999 rounds to 1.50).
Given the precision of the calculation, this will provide a safe design even though the 'absolute' value is less than the
minimum suggested.
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 4
GEOGRID REINFORCING
STRUCTURAL PROPERTIES: Mirafi
GEOGRID PROPERTIES
Name Tult RFcr RFd RFid Ci Cd Alpha Ltds
8XT 7400 1.45 1.15 1.10 0.80 0.80 0.80 4034
CONNECTION STRENGTHS
Geogrid Slope 1 Intercept 1 Peak Break Slope 2 Intercept 2 Max Normal Rup Conn Conn Creep Tlot (%) Tlot
5XT 18.00 536 1571 3.00 964 2361 False 1.45 100 4700
8XT 19.00 946 4834 3.00 2357 7745 False 1.45 100 7400
10XT 22.00 1464 -1 0.00 0 4999 False 1.45 100 9500
20XT 26.00 1825 4746 0.00 4140 6936 False 1.45 100 13705
SHEAR STRENGTHS
Slope 0 deg
Intercept 3500psf
CONNECTION CREEP
In AASHTO design methods a mechanical connector may rupture the reinforcing, thus a creep reduction
factor would be applied. If no test data is available, the creep reduction factor for the reinforcing would be applied.If a
frictional connection is used, then a creep reduction factor would not be applied and a factor of 1.0 is applicable.
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 5
CALCULATION RESULTS
OVERVIEW
Calculates stability assuming the wall is a rigid body. Forces and moments are calculated about the base and
center of the wall. The base block width is used in the calculations. The concrete units and granular fill over the blocks
are used as resisting forces.
EARTH PRESSURES
The method of analysis uses the Coulomb Earth Pressure equation (below) to calculate active earth
pressures. Wall friction is assumed to act at the back of the wall face. The component of earth pressure is assumed to
act perpendicular to the boundary surface. The effective delta angle is delta minus the wall batter at the back face
(assumed to be vertical). If the slope breaks within the failure zone, a trial wedge method of analysis is used.
INTERNAL EARTH PRESSURES
Effective internal Delta angle delta = 0.0 deg
Coefficient of active earth pressure ka =0.283
Internal failure plane ρ = 62.0 deg
EXTERNAL EARTH PRESSURES
Effective Delta angle (delta = β delta =0.0 deg
Coefficient of active earth pressure ka =0.283
Effective Face Angle Face Alpha =0.00 deg
External failure plane ρ = 62.0 deg
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 6
W0: leveling pad W6: Rectangle zone in broken back
W1: facing units W7: Live load over the mass
W2: soil wedge behind the face (base of top block to bottom) W8: Dead load over the mass
W3: rectangular area in MSE area W9: Force Pa
W4: the wedge at the back of the mass W10: Surcharge load Paq
W5: slope area over the mass W11: Dead Load Surcharge Paqd
X-Len: is measured from the center of the base (+) Driving, (-) Resisting.
Name Factor γ Force (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 1.00 5076 -- 3.89 -- 19773 --
Soil(W2) 1.00 3389 -- 2.13 -- 7222 --
Soil(W3) 1.00 17515 -- -2.86 -- -- -50054
LL(W7) 1.00 49 -- -6.65 -- -- -325
DL(W8) 1.00 820 -- 0.00 -- -- 0
Pa_h 1.00 -- 4768 -- 6.00 28607 --
Pq_h 1.00 -- 824 -- 9.00 7416 --
Sum (V, H) 1.00 26848 5592 Sum Mom 63018.74 -50380
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 7
FORCES AND MOMENTS FACTORED FOR Str I-a
UltraWall increases all driving forces and reduces the resisting forces by the factors shown for Str I.
FACTORED LOADS: Str Ia
Name FactorMax γ FactorMin γ ForceSldg (V) ForceEcc (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 1.25 0.90 4569 4569 -- 3.89 -- 17795 --
Soil(W2) 1.35 1.00 3389 3389 -- 2.13 -- 7222 --
Soil(W3) 1.35 1.00 17515 17515 -- -2.86 -- -- -50054
LL(W7) 1.75 0.00 0 86 -- -6.65 -- -- --
DL(W8) 1.50 0.75 820 820 -- 0.00 -- -- 0
Pa_h 1.50 0.90 -- -- 7152 -- 6.00 42911 --
Pa_v 1.50 0.90 0 0 -- -7.75 -- -- 0
Pq_h 1.75 0.00 -- 1442 1442 -- 9.00 12978 --
Pq_v 1.75 0.00 0 0 -- -6.75 -- -- 0
Sum (V, H) 26087 26172 8594 Sum Mom 80907 -50054
FORCES AND MOMENTS FACTORED FOR Str I-b
UltraWall increase resisting loads and increases driving loads by the factors shown for Str I-b.
FACTORED LOADS: Str Ib
Name Factor γ Force (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 1.25 6346 -- 3.89 -- 24716 --
Soil(W2) 1.35 4575 -- 2.13 -- 9750 --
Soil(W3) 1.35 23645 -- -2.86 -- -- -67573
LL(W7) 1.75 86 -- -6.65 -- -- -570
DL(W8) 1.50 1229 -- 0.00 -- -- 0
Pa_h 1.50 -- 7152 -- 6.00 42911 --
Pa_v 1.50 0 -- -7.75 -- -- 0
Pq_h 1.75 -- 1442 -- 9.00 12978 --
Pq_v 1.75 0 -- -6.75 -- -- 0
Sum (V, H) 1.00 35880 8594 Sum Mom 90356 -68143
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 8
BASE SLIDING
Sliding at the base is checked at the foundation soil and a check in the reinforced fill zone.
W1(DCr) + W2(EVr) + W3(EVr) + W8(ESr)
(5076 * 0.90) + (3389 * 1.00) + (17515 * 1.00) + (820 * 0.75)
N =26087ppf
Resisting force in the Reinforced Zone = (N tan(slope) + c B) x RFsl
(26087 tan(34.0) + 50.0 * 14) * 1 Rf1 =18271
Resisting force in the Foundation Zone = (N tan(slope) + c B) x RFsl
(26087 tan(34.0) + 200.0 * 14) * 1 Rf2 =20296
Driving force is the horizontal component of Pah(EHd) + Pqh(LLd)
(4768 * 1.50) + (824 * 1.75)
Df =8594
CDR = Rf1 / Df CDR =2.24
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 9
SLIDING ON REINFORCING
Sliding along the reinforcing is checked at each layer within the reinforced zone.
Sliding resistance is calculated by taking the normal load on the reinforcing, N, times the tangent of the
friction angle of the reinforced soils , φ, times a reduction factor for sliding, Rsl.
Sliding along the reinforcing includes shearing through the face panel. The shear resistance of the face
panel is included as a resisting force, RF_face.
N = Normal load on the geogrid layer. = 18264
(N * tan(34.00) * Cd) + RF_face
(18264 * tan(34.00) * 0.80 ) + 3500 RF = 13355
The driving forces is the active earth pressure plus any surcharge loads behind the reinforced zone.
Pah_ext(EHd) + Pqh_ext(LLd)
where:
z = depth to reinforcing from the surface at the end of the reinforcing. [15.54]
EHd = Load factor for Earth Pressure driving [EHd = 1.50]
Pah = 1/2 x γ z^2 x ka x cos(δ) [4268.00]
Pah_ext, Pqh_ext, etc. could be from a closed from solution (Coulomb/Rankine) or from a trial wedge
solution.
DF = (4268 x 1.50) + (1098 * 1.75 DF = 7328
CDR sliding = RF / DF CDR = 1.82
The table below shows a summary of the forces and reactions.
Elevation[ft] Name[ft] z ext[ft] N[ppf] % Coverage Friction Angle[deg] F_Resisting Pah(EHd) Pqh(LLd) Pqdh(DLd) PqMnDOT(LLd) F_Driving CDR_sl
14.75 8XT 3.25 3888 100.0 34.00 5598 168 242 83 0 158 35.53
12.29 8XT 5.71 6510 100.0 34.00 7013 863 705 242 0 1199 5.85
9.83 8XT 8.17 9259 100.0 34.00 8496 1766 1009 346 0 2256 3.77
7.38 8XT 10.63 12134 100.0 34.00 10048 2989 1313 450 0 3626 2.77
4.92 8XT 13.08 15136 100.0 34.00 11667 4537 1618 555 0 5316 2.19
2.46 8XT 15.54 18264 100.0 34.00 13355 6402 1922 659 0 7328 1.82
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 10
ECCENTRICITY AND BEARING
Eccentricity is the calculation of the distance of the resultant force away from the centroid of mass. This
measure is an indication of the overturning of the mass. In rigid concrete structures, the limit to eccentricity is L/4 (the
middle half of the base). UltraWall uses an allowable eccentricity of e/L per the AASHTO LRFD guidelines.
Eccentricity is still used as a guide to design in some design methods. Eccentricity is based on case S1a (minimum
resisting forces, maximum driving forces. Bearing is based on case S1b (maximum resisting forces, maximum driving
forces).
UltraWall calculates three eccentricities:
1) S1a: Maximum eccentricity (overturning) where it uses the maximum driving forces combined
with the minimum resisting forces (see overturning).
2) S1b Maximum bearing where it uses the maximum driving forces combined with the maximum
resisting forces.
3) Service: Maximum bearing where it uses the actual driving forces combined with the actual
resisting forces in Service loading.
Calculation of Eccentricity for maximum bearing (S1b)
Moments resisting = + M3(EVd) + LL(LLd)
+ (-50054 * 1.35) + (-325 x 1.75)
Mr =-68143ft-lbs
Moments driving = M1(DCr) + M2(EVd) + Pah(EHd) + Pqh(LLd)
+ (19773 * 1.25) + (7222 * 1.35) + (28607 * 1.50) + (7416 * 1.75)
Mo = 90356ft-lbs
e = (SumMr + SumMo)/SumV [ if e < 0, then e = 0 ]
e = (-68143 + 90355.6) /35880.1 e =0.619
Calculation of Bearing Pressures
Qal = (c*Nc + q*Nq + 0.5*gamma*(B')*Ng) * RFbrg
where:
Nc =42.16
Nq =29.44
Ng =41.06
c =200.00psf
RFbrg =0.65
q =250psf [embedment x gamma]
B' = B - 2e =12.26ft
Calculate Allowable Bearing, Qal Qal =30721psf
Applied Bearing Pressures (Sigma) (SumV)/B' =2926psf
Calculated CDR for bearing Qal/sigma =10.50
Design Sum Vert Mo Mr e Qal Sigma CDR
Strength I-b 35880 90356 -68143 0.619 30721 2926 10.50
Service 26848 63019 -50380 0.471 48024 2138 22.46
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 11
Elevation[ft] Name Ta*RF[ppf] Tas*RF[ppf] Coverage Ratio % Tmax[ppf] TSmax[ppf] CDR Str CDRs Str
14.75 8XT 3631 7020 100 479 658 7.59 10.67
12.29 8XT 3631 7020 100 774 866 4.69 8.11
9.83 8XT 3631 7020 100 1062 983 3.42 7.14
7.38 8XT 3631 7020 100 1350 1100 2.69 6.38
4.92 8XT 3631 7020 100 1637 1217 2.22 5.77
2.46 8XT 3631 7020 100 1896 1323 1.91 5.31
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 12
PULLOUT CALCULATIONS
Pullout is the amount of resistance of the reinforcing has to a pullout failure based on the Tmax applied and
the depth of embedement (resistance). In an AASHTO design, the failure plane is fixed at the Rankine failure plane
angle, 45 + phi/2. All failure planes begin at the tail. of the facing units.
Failure Plane Angle = 62.0 Deg
F* = 0.67 x tan( φ ) [AASHTO 11.10.6.3.2]
F* = 0.67 x tan( 34) = 0.45
α = 0.80 [AASHTO Table 11.10.6.3.2-1]
RFpo = 0.90
Pullout = 2 x N x F* x α x Coverage x RFpo
Pullout = 2 x 2886 x 0.45 x 0.80 x 1.00 x 0.90 = 1878.19
Pullout is the calculated value or the Tult of the geogrid, whichever is less.
NOTE: The pullout capacity is limited by the LTDS of the reinforcing layer, not the ultimate pullout capacity calculated.
TABLE OF RESULTS
Elevation[ft] Normal[lbf] F* Alpha % Coverage Tmax[ppf] Le[ft] La[ft] Pullout_[Pr][ppf] CDR PO
14.75 2886 0.45 0.80 100 479 5.70 7.80 1878 3.92
12.29 5367 0.45 0.80 100 774 6.60 6.90 3492 4.51
9.83 8398 0.45 0.80 100 1062 7.49 6.01 3631 3.42
7.38 11979 0.45 0.80 100 1350 8.39 5.11 3631 2.69
4.92 16085 0.45 0.80 100 1637 9.28 4.22 3631 2.22
2.46 20637 0.45 0.80 100 1896 10.18 3.32 3631 1.91
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 13
CONNECTION CALCULATIONS
Connection is the amount of resistance of the reinforcing has to a pullout failure from the facing units based
on the Tmax applied and the normal load on the units. In an AASHTO LRFD design, creep on the connection may be
applied for frictional and mechanical connections.
Connection Capacity = [N tan(slope) + intercept] / RFcr
RFcr can be a value obtained from long-term testing or by default could be the creep reduction factor of the
geogrid reinforcing.
Base friction is used to reduce the tension in the bottom layer of reinforcing. The force in the bottom layer is
the tension from half way to the reinforcing layer above to the halfway to the foundation level below.
Base Friction = Base Shear x RFsliding
Base Shear = 5076 x tan( atan(0.80 x tan(40 )) + 0
3408 x 0.90 BF = 3067ppf
BF utilized to reduce bottom tension = 790ppf
CRu = Ultimate connection strength [1692 x tan( 19.00) + 946 = 1528.65 ]
CRru = CRu / TLot [1528.65/7400.00 = 0.21]
RFcrcn = 1.45 [Connection creep if tested, otherwise geogrid creep factor]
[if connection creep is set to 'false', RFcrcn = 1]
CRcr = CRru / RFcrcn [0.21 / 1.00 = 0.21]
Tac = Tult x CRcr / RFd * RFten [ 7400 x 0.21 / 1.15 x 0.90 = 1196.34]
TABLE OF RESULTS
Elev[ft] Name[ft] Tmax[ppf] Ttotal[ppf] Rc % RFcn_cr N[ppf] Avail_CN[ppf] CDR cn CDR cns
14.75 8XT 479 460 100 1.00 1692 1196 2.50 3.12
12.29 8XT 774 742 100 1.00 2538 1424 1.84 2.30
9.83 8XT 1062 1018 100 1.00 3384 1652 1.56 1.95
7.38 8XT 1350 1295 100 1.00 4230 1880 1.39 1.74
4.92 8XT 1637 1569 100 1.00 5076 2053 1.25 1.57
2.46 8XT 1896 1818 100 1.00 5923 2088 1.10 1.38
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 14
SEISMIC CALCULATIONS
The loads considered under seismic loading are primarily inertial loadings. The wave passes the structure
putting the mass into motion and then the mass will try to continue in the direction of the initial wave. In the
calculations you see the one dynamic earth pressure from the wedge of the soil behind the reinforced mass, and then
all the other forces come from inertia calculations of the face put into motion and then trying to be held in place.
In AASHTO LRFD, external stability is calculated based on 100% of Pae and 50% of Pir and then
50% of Pae and 100% of Pir. The values labelled Pae are 100% Pae/50% Pir; labels Pir are 50% Pae/100% Pir.
Design Acceleration A = 0.330
Displacment (d) d = 3.3in
Design Acceleration Coefficient Displacment Based (empirically)
Kh = A/2 = kh(ext) = 0.165
Vertical Acceleration kv =0.000
SEISMIC THRUST
EXTERNAL Kae
Kae Kae =0.384
Pae = 0.5*gamma*(H)^2*D_Kae Pae =2059ppf
Pae_h/2 = Pae*cos(delta)/2 Pae_h/2 =1029ppf
Pae_v/2 = Pae*sin(delta)/2 Pae_v/2 =0ppf
INERTIA FORCES OF THE STRUCTURE
Face (Pif) = (W0 + W1)*kh(int) = 5076 * 0.165 Pif =838ppf
Mass (Pir) = (W)*kh(int) = 13495 * 0.165 Pir =2227ppf
Slope (Pis) = (W)*kh(int) = 0 * 0.165 Pis =0ppf
Dead Load(Pidl) = (DL)*kh(int) = 0 * 0.165 Pidl =0ppf
TABLE OF RESULTS FOR SEISMIC REACTIONS
Name Force (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 5076 -- 2.86 -- -- 14493
Soil(W2) 3389 -- 4.62 -- -- 15651
Soil(W3) 17515 -- 9.61 -- -- 168278
LL(W7) 49 -- 13.40 -- -- 656
DL(W8) 820 -- 9.40 -- -- 7706
Pa_h -- 4768 -- 6.00 28607 --
Pq_h -- 824 -- 9.00 7416 --
Pir -- 2227 -- 9.00 20040 --
Pif -- 838 -- 9.00 7539 --
Pae_h/2 -- 2059 -- 9.00 9264 --
Sum V / H 26799.41 8861.55 Sum Mom 72866.46 206784.5
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 15
UltraWall
Project: Fyffe
Location: Site Location
Designer: JC
Date: 5/13/2020
Section: 20ft Stratagrid
Design Method: AASHTO_LRFD_2014
Design Unit: UltraBlock
Seismic Acc: 0.330
SOIL PARAMETERS φ coh γ
Reinforced Soil: 34 deg 50psf 125pcf
Retained Soil: 34 deg 100psf 125pcf
Foundation Soil: 34 deg 200psf 125pcf
Leveling Pad: Crushed Stone
GEOMETRY
Design Height: 18.00ft Live Load: 250psf
Wall Batter/Tilt: 0.00/ 9.50 deg Live Load Offset: 8.00ft
Embedment: 2.00ft Live Load Width: 39ft
Leveling Pad Depth: 1.00ft Dead Load: 100psf
Slope Angle: 0.0 deg Dead Load Offset: 0.0ft
Slope Length: 0.0ft Dead Load Width: 39ft
Slope Toe Offset: 0.0ft Leveling Pad Width: 3.46ft
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 1
RESULTS (Static / Seismic)
CDR Sliding: 2.24 (fnd) / [1.99 ] CDR Bearing: 10.50 / 16.49
Eccentricity (e/L): 0.09 / -0.16 Bearing: 2926; Srvc 2138 / Seis 2190
CDR Connection: 1.20
ID Ht Lngth Geogri Ta_tn Rc % TMax (Tatn*RF) CDR Ta_tn Ta_cn CDR Ta_cn CDR Tpo CDR Sldg
6 14.7513.50 SG500 3122 [4839] 100 479 [576] 2810 [5807] 5.87 [8.50] 1157 [1388] 2.42 [3.02] 3.92 83.13
5 12.2913.50 SG500 3122 [4839] 100 774 [576] 2810 [5807] 3.63 [6.52] 1262 [1515] 1.63 [2.04] 3.63 12.10 [6.67]
4 9.83 13.50 SG500 3122 [4839] 100 1062 [576] 2810 [5807] 2.65 [5.76] 1294 [1552] 1.22 [1.52] 2.65 7.09 [4.92]
3 7.38 13.50 SG600 4439 [6881] 100 1350 [576] 3995 [8257] 2.96 [7.34] 2192 [2630] 1.62 [2.03] 2.96 4.56 [3.58]
2 4.92 13.50 SG600 4439 [6881] 100 1637 [576] 3995 [8257] 2.44 [6.65] 2234 [2681] 1.36 [1.71] 2.44 3.42 [2.89]
1 2.46 13.50 SG600 4439 [6881] 100 1896 [576] 3995 [8257] 2.11 [6.13] 2276 [2731] 1.20 [1.50] 2.11 2.71 [2.41]
Column Descriptions:
Tr: Tension required (Ta*Reduction factors) [ppf]
EP(Pa): Earth pressures from closed form solution or trial wedge [ppf]
Rc %: percent coverage for geosynthetics
EP (Pa) internal active earth pressure [ppf ]
LL (Pql) earth pressure due to live load surcharge [ppf ]
DL (Pqd) earth pressure due to dead load surcharge [ppf ]
Tmax maximum earth pressure on geosynthetic layer [ppf ]
CDRstr 'Capacity/Demand Ratio (CDR)' on geogrid strength (Tr/Tmax)
Ta cn allowable tension capacity on the connection [ppf ]
CDR Pkcn, Capacity/Demand Ratio on the connection (Ta cn/Tmax)
CDR PO, Capacity/Demand Ratio on pullout (Ta pullout/(Tmax - LL)
CDR Sldg [fndn], Capacity/Demand Ratio on sliding on the reinforcement, CDR sliding on the foundation
soils
Grid Embed, depth of embedment beyond the theorectical failure plane. [ft ]
(PaC): reduction in load due to cohesion [ppf]
PaT: sum of all earth pressures [ppf]
%D/H: ratio of based depth to height (warning for narrow walls, < 35%)
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 2
DESIGN DATA
Load Factors for Design
AASHTO Table 3.4.1-1 & 3.4.1-2
Load Case Str_Max Str_Min Extreme Max Extreme Min Service
Str I Dead Load (DC) 1.25 0.90 1.00 1.00 1.00
Soil Load Driving (EH) 1.50 0.90 1.00 1.00 1.00
Str I Vert Earth Load (EV) 1.35 1.00 1.00 1.00 1.00
Dead Load Surcharge (ES) 1.50 0.75 1.00 1.00 1.00
Live Load (LL, PL, LS) 1.75 0.00 1.00 0.00 1.00
AASHTO Table 11.5.7-1 & Article 11.5.8
MSE Resistance Case Strength Extreme Service
Bearing Resistance (RFbr) 0.65 0.90 1.00
Sliding Soil to Soil (RFsl) 1.00 1.00 1.00
Sliding Soil to Reinforcement (RFslrf) 1.00 1.00 1.00
Tensile Resistance (RFten) 0.90 1.20 1.00
Pullout Resistance (RFpo) 0.90 1.20 1.00
Overturning Resistance (RFot) 0.60 1.00 1.00
AASHTO Table 10.5.5.2.2-1
Gravity Resistance Case Strength Extreme Service
Bearing Resistance (RFbr) 0.45 0.45 0.45
Cast-In-Place Concrete to Stone (RFsl_cip) 0.80 1.00 1.00
Precast Concrete to Stone (RFsl_c) 0.90 1.00 1.00
Stone to Soil (RFsl_s) 0.90 0.90 0.90
Passive EP (RFep) 0.50 0.90 0.90
Application of Load Factors
Group DC EV LS EH Probable Use
Strength I-a 0.90 1.00 1.75 1.50 BC/EC/SL
Strength I-b 1.25 1.35 1.75 1.50 BC (max. value)
Service I 1.00 1.00 1.00 1.00 Settlement
Notes: BC - Bearing Capacity; EC - Eccentricity; SL - Sliding
By Inspection:
• Strength I-a (minimum vertical loads and maximum horizontal loads) will govern for the case of sliding and
eccentricity (overturning); and
• For the case of bearing capacity, maximum vertical loads will govern and the factored loads must be
compared for Strength I-b and Strength IV.
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 3
NOTES ON DESIGN UNITS
The wall section is designed on a 'per unit width bases' (lb/ft/ft of wall or kN/m/meter of wall). In the calculations the
software shows lb/ft or kN/m, neglecting the unit width factor for simplicity.
The weights for the wall unit are shown as lbs / ft3 (kN / m3). For SRW design a 1 sf unit is typically 1 ft deep, 1.5 ft
wide and 8 inches tall (or 1 ft3). therefore a typical value of 120 pcf is shown. With larger units the unit weight will
vary with the size of the unit. Say we have 4 ft wide unit, 1.5 ft tall and 24 inches deep with a tapered shape (sides
narrow), built with 150 pcf concrete. We add up the concrete, the gravel fill and divide by the volume and the results
may come out to 140 pcf, as shown in the table. The units with more gravel may have lower effective unit weights
based on the calculations.
Hollow Units
Hollow units with gravel fill are treated differently in AASHTO. If the fill can fall out as the unit is lifted, then AASHTO
only allows 80% of the weight of the fill to be used for eccentricity (overturning calculations). In the properties page
for the units the weight of the concrete may be as low as 75 pcf. This is the effective unit weight of the concrete only
(e.g. the weight of the concrete divided by the volume of the unit). The density of the concrete maybe 150 pcf, but not
the effective weight including the volume of the void spaces used for gravel fill.
Rounding Errors
When doing hand calculations the values may vary from the values shown in the software. The program is designed
using double precision values (64 bit precision: 14 decimal places). Over several calculations the results may differ
from the single calculation the user is making, probably inputting one or two already rounded values.
Result Rounding
As noted above the software is based on double precision values. For example, using an NCMA design method an
allowable factor of safety of 1.5 the software may calculate a value of 1.49999999999999, since this is less than 1.5,
it would be false (NG), even though the results shown is 1.50 (results are rounded to 2 places on the screen). In the
design check we round to 2 decimal places to check against the suggested value (1.49999999999 rounds to 1.50).
Given the precision of the calculation, this will provide a safe design even though the 'absolute' value is less than the
minimum suggested.
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 4
GEOGRID REINFORCING
STRUCTURAL PROPERTIES: Stratagrid
GEOGRID PROPERTIES
Name Tult RFcr RFd RFid Ci Cd Alpha Ltds
SG500 6400 1.55 1.15 1.15 0.80 0.80 0.80 3122
SG600 9100 1.55 1.15 1.15 0.80 0.80 0.80 4439
CONNECTION STRENGTHS
Geogrid Slope 1 Intercept 1 Peak Break Slope 2 Intercept 2 Max Normal Rup Conn Conn Creep Tlot (%) Tlot
SG500 29.00 688 1899 3.00 1641 7655 False 1.55 110 7040
SG550 46.00 670 2190 4.00 2785 7650 False 1.55 110 8965
SG600 46.00 670 2190 4.00 2785 7850 False 1.55 110 10010
SG700 37.00 643 -1 0.00 0 3100 False 1.55 100 11800
SHEAR STRENGTHS
Slope 0 deg
Intercept 11000psf
CONNECTION CREEP
In AASHTO design methods a mechanical connector may rupture the reinforcing, thus a creep reduction
factor would be applied. If no test data is available, the creep reduction factor for the reinforcing would be applied.If a
frictional connection is used, then a creep reduction factor would not be applied and a factor of 1.0 is applicable.
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 5
CALCULATION RESULTS
OVERVIEW
Calculates stability assuming the wall is a rigid body. Forces and moments are calculated about the base and
center of the wall. The base block width is used in the calculations. The concrete units and granular fill over the blocks
are used as resisting forces.
EARTH PRESSURES
The method of analysis uses the Coulomb Earth Pressure equation (below) to calculate active earth
pressures. Wall friction is assumed to act at the back of the wall face. The component of earth pressure is assumed to
act perpendicular to the boundary surface. The effective delta angle is delta minus the wall batter at the back face
(assumed to be vertical). If the slope breaks within the failure zone, a trial wedge method of analysis is used.
INTERNAL EARTH PRESSURES
Effective internal Delta angle delta = 0.0 deg
Coefficient of active earth pressure ka =0.283
Internal failure plane ρ = 62.0 deg
EXTERNAL EARTH PRESSURES
Effective Delta angle (delta = β delta =0.0 deg
Coefficient of active earth pressure ka =0.283
Effective Face Angle Face Alpha =0.00 deg
External failure plane ρ = 62.0 deg
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 6
W0: leveling pad W6: Rectangle zone in broken back
W1: facing units W7: Live load over the mass
W2: soil wedge behind the face (base of top block to bottom) W8: Dead load over the mass
W3: rectangular area in MSE area W9: Force Pa
W4: the wedge at the back of the mass W10: Surcharge load Paq
W5: slope area over the mass W11: Dead Load Surcharge Paqd
X-Len: is measured from the center of the base (+) Driving, (-) Resisting.
Name Factor γ Force (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 1.00 5076 -- 3.89 -- 19773 --
Soil(W2) 1.00 3389 -- 2.13 -- 7222 --
Soil(W3) 1.00 17515 -- -2.86 -- -- -50054
LL(W7) 1.00 49 -- -6.65 -- -- -325
DL(W8) 1.00 820 -- 0.00 -- -- 0
Pa_h 1.00 -- 4768 -- 6.00 28607 --
Pq_h 1.00 -- 824 -- 9.00 7416 --
Sum (V, H) 1.00 26848 5592 Sum Mom 63018.74 -50380
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 7
FORCES AND MOMENTS FACTORED FOR Str I-a
UltraWall increases all driving forces and reduces the resisting forces by the factors shown for Str I.
FACTORED LOADS: Str Ia
Name FactorMax γ FactorMin γ ForceSldg (V) ForceEcc (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 1.25 0.90 4569 4569 -- 3.89 -- 17795 --
Soil(W2) 1.35 1.00 3389 3389 -- 2.13 -- 7222 --
Soil(W3) 1.35 1.00 17515 17515 -- -2.86 -- -- -50054
LL(W7) 1.75 0.00 0 86 -- -6.65 -- -- --
DL(W8) 1.50 0.75 820 820 -- 0.00 -- -- 0
Pa_h 1.50 0.90 -- -- 7152 -- 6.00 42911 --
Pa_v 1.50 0.90 0 0 -- -7.75 -- -- 0
Pq_h 1.75 0.00 -- 1442 1442 -- 9.00 12978 --
Pq_v 1.75 0.00 0 0 -- -6.75 -- -- 0
Sum (V, H) 26087 26172 8594 Sum Mom 80907 -50054
FORCES AND MOMENTS FACTORED FOR Str I-b
UltraWall increase resisting loads and increases driving loads by the factors shown for Str I-b.
FACTORED LOADS: Str Ib
Name Factor γ Force (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 1.25 6346 -- 3.89 -- 24716 --
Soil(W2) 1.35 4575 -- 2.13 -- 9750 --
Soil(W3) 1.35 23645 -- -2.86 -- -- -67573
LL(W7) 1.75 86 -- -6.65 -- -- -570
DL(W8) 1.50 1229 -- 0.00 -- -- 0
Pa_h 1.50 -- 7152 -- 6.00 42911 --
Pa_v 1.50 0 -- -7.75 -- -- 0
Pq_h 1.75 -- 1442 -- 9.00 12978 --
Pq_v 1.75 0 -- -6.75 -- -- 0
Sum (V, H) 1.00 35880 8594 Sum Mom 90356 -68143
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 8
BASE SLIDING
Sliding at the base is checked at the foundation soil and a check in the reinforced fill zone.
W1(DCr) + W2(EVr) + W3(EVr) + W8(ESr)
(5076 * 0.90) + (3389 * 1.00) + (17515 * 1.00) + (820 * 0.75)
N =26087ppf
Resisting force in the Reinforced Zone = (N tan(slope) + c B) x RFsl
(26087 tan(34.0) + 50.0 * 14) * 1 Rf1 =18271
Resisting force in the Foundation Zone = (N tan(slope) + c B) x RFsl
(26087 tan(34.0) + 200.0 * 14) * 1 Rf2 =20296
Driving force is the horizontal component of Pah(EHd) + Pqh(LLd)
(4768 * 1.50) + (824 * 1.75)
Df =8594
CDR = Rf1 / Df CDR =2.24
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 9
SLIDING ON REINFORCING
Sliding along the reinforcing is checked at each layer within the reinforced zone.
Sliding resistance is calculated by taking the normal load on the reinforcing, N, times the tangent of the
friction angle of the reinforced soils , φ, times a reduction factor for sliding, Rsl.
Sliding along the reinforcing includes shearing through the face panel. The shear resistance of the face
panel is included as a resisting force, RF_face.
N = Normal load on the geogrid layer. = 18264
(N * tan(34.00) * Cd) + RF_face
(18264 * tan(34.00) * 0.80 ) + 10000 RF = 19855
The driving forces is the active earth pressure plus any surcharge loads behind the reinforced zone.
Pah_ext(EHd) + Pqh_ext(LLd)
where:
z = depth to reinforcing from the surface at the end of the reinforcing. [15.54]
EHd = Load factor for Earth Pressure driving [EHd = 1.50]
Pah = 1/2 x γ z^2 x ka x cos(δ) [4268.00]
Pah_ext, Pqh_ext, etc. could be from a closed from solution (Coulomb/Rankine) or from a trial wedge
solution.
DF = (4268 x 1.50) + (1098 * 1.75 DF = 7328
CDR sliding = RF / DF CDR = 2.71
The table below shows a summary of the forces and reactions.
Elevation[ft] Name[ft] z ext[ft] N[ppf] % Coverage Friction Angle[deg] F_Resisting Pah(EHd) Pqh(LLd) Pqdh(DLd) PqMnDOT(LLd) F_Driving CDR_sl
14.75 SG500 3.25 3888 100.0 34.00 13098 168 242 83 0 158 83.13
12.29 SG500 5.71 6510 100.0 34.00 14513 863 705 242 0 1199 12.10
9.83 SG500 8.17 9259 100.0 34.00 15996 1766 1009 346 0 2256 7.09
7.38 SG600 10.63 12134 100.0 34.00 16548 2989 1313 450 0 3626 4.56
4.92 SG600 13.08 15136 100.0 34.00 18167 4537 1618 555 0 5316 3.42
2.46 SG600 15.54 18264 100.0 34.00 19855 6402 1922 659 0 7328 2.71
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 10
ECCENTRICITY AND BEARING
Eccentricity is the calculation of the distance of the resultant force away from the centroid of mass. This
measure is an indication of the overturning of the mass. In rigid concrete structures, the limit to eccentricity is L/4 (the
middle half of the base). UltraWall uses an allowable eccentricity of e/L per the AASHTO LRFD guidelines.
Eccentricity is still used as a guide to design in some design methods. Eccentricity is based on case S1a (minimum
resisting forces, maximum driving forces. Bearing is based on case S1b (maximum resisting forces, maximum driving
forces).
UltraWall calculates three eccentricities:
1) S1a: Maximum eccentricity (overturning) where it uses the maximum driving forces combined
with the minimum resisting forces (see overturning).
2) S1b Maximum bearing where it uses the maximum driving forces combined with the maximum
resisting forces.
3) Service: Maximum bearing where it uses the actual driving forces combined with the actual
resisting forces in Service loading.
Calculation of Eccentricity for maximum bearing (S1b)
Moments resisting = + M3(EVd) + LL(LLd)
+ (-50054 * 1.35) + (-325 x 1.75)
Mr =-68143ft-lbs
Moments driving = M1(DCr) + M2(EVd) + Pah(EHd) + Pqh(LLd)
+ (19773 * 1.25) + (7222 * 1.35) + (28607 * 1.50) + (7416 * 1.75)
Mo = 90356ft-lbs
e = (SumMr + SumMo)/SumV [ if e < 0, then e = 0 ]
e = (-68143 + 90355.6) /35880.1 e =0.619
Calculation of Bearing Pressures
Qal = (c*Nc + q*Nq + 0.5*gamma*(B')*Ng) * RFbrg
where:
Nc =42.16
Nq =29.44
Ng =41.06
c =200.00psf
RFbrg =0.65
q =250psf [embedment x gamma]
B' = B - 2e =12.26ft
Calculate Allowable Bearing, Qal Qal =30721psf
Applied Bearing Pressures (Sigma) (SumV)/B' =2926psf
Calculated CDR for bearing Qal/sigma =10.50
Design Sum Vert Mo Mr e Qal Sigma CDR
Strength I-b 35880 90356 -68143 0.619 30721 2926 10.50
Service 26848 63019 -50380 0.471 48024 2138 22.46
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 11
Elevation[ft] Name Ta*RF[ppf] Tas*RF[ppf] Coverage Ratio % Tmax[ppf] TSmax[ppf] CDR Str CDRs Str
14.75 SG500 2810 5807 100 479 683 5.87 8.50
12.29 SG500 2810 5807 100 774 891 3.63 6.52
9.83 SG500 2810 5807 100 1062 1008 2.65 5.76
7.38 SG600 3995 8257 100 1350 1126 2.96 7.34
4.92 SG600 3995 8257 100 1637 1242 2.44 6.65
2.46 SG600 3995 8257 100 1896 1348 2.11 6.13
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 12
PULLOUT CALCULATIONS
Pullout is the amount of resistance of the reinforcing has to a pullout failure based on the Tmax applied and
the depth of embedement (resistance). In an AASHTO design, the failure plane is fixed at the Rankine failure plane
angle, 45 + phi/2. All failure planes begin at the tail. of the facing units.
Failure Plane Angle = 62.0 Deg
F* = 0.67 x tan( φ ) [AASHTO 11.10.6.3.2]
F* = 0.67 x tan( 34) = 0.45
α = 0.80 [AASHTO Table 11.10.6.3.2-1]
RFpo = 0.90
Pullout = 2 x N x F* x α x Coverage x RFpo
Pullout = 2 x 2886 x 0.45 x 0.80 x 1.00 x 0.90 = 1878.19
Pullout is the calculated value or the Tult of the geogrid, whichever is less.
NOTE: The pullout capacity is limited by the LTDS of the reinforcing layer, not the ultimate pullout capacity calculated.
TABLE OF RESULTS
Elevation[ft] Normal[lbf] F* Alpha % Coverage Tmax[ppf] Le[ft] La[ft] Pullout_[Pr][ppf] CDR PO
14.75 2886 0.45 0.80 100 479 5.70 7.80 1878 3.92
12.29 5367 0.45 0.80 100 774 6.60 6.90 2810 3.63
9.83 8398 0.45 0.80 100 1062 7.49 6.01 2810 2.65
7.38 11979 0.45 0.80 100 1350 8.39 5.11 3995 2.96
4.92 16085 0.45 0.80 100 1637 9.28 4.22 3995 2.44
2.46 20637 0.45 0.80 100 1896 10.18 3.32 3995 2.11
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 13
CONNECTION CALCULATIONS
Connection is the amount of resistance of the reinforcing has to a pullout failure from the facing units based
on the Tmax applied and the normal load on the units. In an AASHTO LRFD design, creep on the connection may be
applied for frictional and mechanical connections.
Connection Capacity = [N tan(slope) + intercept] / RFcr
RFcr can be a value obtained from long-term testing or by default could be the creep reduction factor of the
geogrid reinforcing.
Base friction is used to reduce the tension in the bottom layer of reinforcing. The force in the bottom layer is
the tension from half way to the reinforcing layer above to the halfway to the foundation level below.
Base Friction = Base Shear x RFsliding
Base Shear = 5076 x tan( atan(0.80 x tan(40 )) + 0
3408 x 0.90 BF = 3067ppf
BF utilized to reduce bottom tension = 790ppf
CRu = Ultimate connection strength [1692 x tan( 29.00) + 688 = 1625.98 ]
CRru = CRu / TLot [1625.98/7040.00 = 0.23]
RFcrcn = 1.55 [Connection creep if tested, otherwise geogrid creep factor]
[if connection creep is set to 'false', RFcrcn = 1]
CRcr = CRru / RFcrcn [0.23 / 1.00 = 0.23]
Tac = Tult x CRcr / RFd * RFten [ 6400 x 0.23 / 1.15 x 0.90 = 1156.82]
TABLE OF RESULTS
Elev[ft] Name[ft] Tmax[ppf] Ttotal[ppf] Rc % RFcn_cr N[ppf] Avail_CN[ppf] CDR cn CDR cns
14.75 SG500 479 460 100 1.00 1692 1157 2.42 3.02
12.29 SG500 774 742 100 1.00 2538 1262 1.63 2.04
9.83 SG500 1062 1018 100 1.00 3384 1294 1.22 1.52
7.38 SG600 1350 1294 100 1.00 4230 2192 1.62 2.03
4.92 SG600 1637 1569 100 1.00 5076 2234 1.36 1.71
2.46 SG600 1896 1818 100 1.00 5923 2276 1.20 1.50
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 14
SEISMIC CALCULATIONS
The loads considered under seismic loading are primarily inertial loadings. The wave passes the structure
putting the mass into motion and then the mass will try to continue in the direction of the initial wave. In the
calculations you see the one dynamic earth pressure from the wedge of the soil behind the reinforced mass, and then
all the other forces come from inertia calculations of the face put into motion and then trying to be held in place.
In AASHTO LRFD, external stability is calculated based on 100% of Pae and 50% of Pir and then
50% of Pae and 100% of Pir. The values labelled Pae are 100% Pae/50% Pir; labels Pir are 50% Pae/100% Pir.
Design Acceleration A = 0.330
Displacment (d) d = 3.3in
Design Acceleration Coefficient Displacment Based (empirically)
Kh = A/2 = kh(ext) = 0.165
Vertical Acceleration kv =0.000
SEISMIC THRUST
EXTERNAL Kae
Kae Kae =0.384
Pae = 0.5*gamma*(H)^2*D_Kae Pae =2059ppf
Pae_h/2 = Pae*cos(delta)/2 Pae_h/2 =1029ppf
Pae_v/2 = Pae*sin(delta)/2 Pae_v/2 =0ppf
INERTIA FORCES OF THE STRUCTURE
Face (Pif) = (W0 + W1)*kh(int) = 5076 * 0.165 Pif =838ppf
Mass (Pir) = (W)*kh(int) = 13495 * 0.165 Pir =2227ppf
Slope (Pis) = (W)*kh(int) = 0 * 0.165 Pis =0ppf
Dead Load(Pidl) = (DL)*kh(int) = 0 * 0.165 Pidl =0ppf
TABLE OF RESULTS FOR SEISMIC REACTIONS
Name Force (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 5076 -- 2.86 -- -- 14493
Soil(W2) 3389 -- 4.62 -- -- 15651
Soil(W3) 17515 -- 9.61 -- -- 168278
LL(W7) 49 -- 13.40 -- -- 656
DL(W8) 820 -- 9.40 -- -- 7706
Pa_h -- 4768 -- 6.00 28607 --
Pq_h -- 824 -- 9.00 7416 --
Pir -- 2227 -- 9.00 20040 --
Pif -- 838 -- 9.00 7539 --
Pae_h/2 -- 2059 -- 9.00 9264 --
Sum V / H 26799.41 8861.55 Sum Mom 72866.46 206784.5
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 15
UltraWall
Project: Fyffe
Location: Site Location
Designer: JC
Date: 5/13/2020
Section: Section 1
Design Method: AASHTO_LRFD_2014
Design Unit: UltraBlock
Seismic Acc: 0.330
SOIL PARAMETERS φ coh γ
Reinforced Soil: 34 deg 50psf 125pcf
Retained Soil: 34 deg 100psf 125pcf
Foundation Soil: 34 deg 200psf 125pcf
Leveling Pad: Crushed Stone
GEOMETRY
Design Height: 25.00ft Live Load: 250psf
Wall Batter/Tilt: 0.00/ 9.46 deg Live Load Offset: 8.00ft
Embedment: 2.00ft Live Load Width: 39ft
Leveling Pad Depth: 1.00ft Dead Load: 100psf
Slope Angle: 0.0 deg Dead Load Offset: 0.0ft
Slope Length: 0.0ft Dead Load Width: 39ft
Slope Toe Offset: 0.0ft Leveling Pad Width: 3.96ft
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 1
RESULTS (Static / Seismic)
CDR Sliding: 1.99 (fnd) / [1.85 ] CDR Bearing: 9.18 / 14.60
Eccentricity (e/L): 0.10 / -0.19 Bearing: 4007; Srvc 2902 / Seis 2974
CDR Connection: 1.11
ID Ht Lngth Geogri Ta_tn Rc % TMax (Tatn*RF) CDR Ta_tn Ta_cn CDR Ta_cn CDR Tpo CDR Sldg
9 22.1317.50 8XT 4034 [5850] 100 398 [619] 3631 [7020] 9.12 [9.80] 1196 [1436] 3.00 [3.75] 5.25 100.00
8 19.6717.50 8XT 4034 [5850] 100 616 [619] 3631 [7020] 5.90 [8.07] 1424 [1709] 2.31 [2.89] 5.90 9.20 [3.69]
7 17.2117.50 8XT 4034 [5850] 100 1018 [619] 3631 [7020] 3.57 [6.79] 1652 [1983] 1.62 [2.03] 3.57 4.74 [2.98]
6 14.7517.50 8XT 4034 [5850] 100 1306 [619] 3631 [7020] 2.78 [6.10] 1880 [2256] 1.44 [1.80] 2.78 3.49 [2.55]
5 12.2917.50 8XT 4034 [5850] 100 1595 [619] 3631 [7020] 2.28 [5.54] 2053 [2463] 1.29 [1.61] 2.28 2.76 [2.21]
4 9.83 17.50 8XT 4034 [5850] 100 1883 [619] 3631 [7020] 1.93 [5.07] 2088 [2505] 1.11 [1.39] 1.93 2.29 [1.95]
3 7.38 17.50 20XT 7472 [10834] 100 2171 [619] 6725 [13001] 3.10 [8.65] 3240 [3888] 1.49 [1.87] 3.10 1.97 [1.74]
2 4.92 17.50 20XT 7472 [10834] 100 2457 [619] 6725 [13001] 2.74 [8.03] 3240 [3888] 1.32 [1.65] 2.74 1.73 [1.57]
1 2.46 17.50 20XT 7472 [10834] 100 2704 [619] 6725 [13001] 2.49 [7.56] 3240 [3888] 1.20 [1.50] 2.49 1.54 [1.44]
Column Descriptions:
Tr: Tension required (Ta*Reduction factors) [ppf]
EP(Pa): Earth pressures from closed form solution or trial wedge [ppf]
Rc %: percent coverage for geosynthetics
EP (Pa) internal active earth pressure [ppf ]
LL (Pql) earth pressure due to live load surcharge [ppf ]
DL (Pqd) earth pressure due to dead load surcharge [ppf ]
Tmax maximum earth pressure on geosynthetic layer [ppf ]
CDRstr 'Capacity/Demand Ratio (CDR)' on geogrid strength (Tr/Tmax)
Ta cn allowable tension capacity on the connection [ppf ]
CDR Pkcn, Capacity/Demand Ratio on the connection (Ta cn/Tmax)
CDR PO, Capacity/Demand Ratio on pullout (Ta pullout/(Tmax - LL)
CDR Sldg [fndn], Capacity/Demand Ratio on sliding on the reinforcement, CDR sliding on the foundation
soils
Grid Embed, depth of embedment beyond the theorectical failure plane. [ft ]
(PaC): reduction in load due to cohesion [ppf]
PaT: sum of all earth pressures [ppf]
%D/H: ratio of based depth to height (warning for narrow walls, < 35%)
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 2
DESIGN DATA
Load Factors for Design
AASHTO Table 3.4.1-1 & 3.4.1-2
Load Case Str_Max Str_Min Extreme Max Extreme Min Service
Str I Dead Load (DC) 1.25 0.90 1.00 1.00 1.00
Soil Load Driving (EH) 1.50 0.90 1.00 1.00 1.00
Str I Vert Earth Load (EV) 1.35 1.00 1.00 1.00 1.00
Dead Load Surcharge (ES) 1.50 0.75 1.00 1.00 1.00
Live Load (LL, PL, LS) 1.75 0.00 1.00 0.00 1.00
AASHTO Table 11.5.7-1 & Article 11.5.8
MSE Resistance Case Strength Extreme Service
Bearing Resistance (RFbr) 0.65 0.90 1.00
Sliding Soil to Soil (RFsl) 1.00 1.00 1.00
Sliding Soil to Reinforcement (RFslrf) 1.00 1.00 1.00
Tensile Resistance (RFten) 0.90 1.20 1.00
Pullout Resistance (RFpo) 0.90 1.20 1.00
Overturning Resistance (RFot) 0.60 1.00 1.00
AASHTO Table 10.5.5.2.2-1
Gravity Resistance Case Strength Extreme Service
Bearing Resistance (RFbr) 0.45 0.45 0.45
Cast-In-Place Concrete to Stone (RFsl_cip) 0.80 1.00 1.00
Precast Concrete to Stone (RFsl_c) 0.90 1.00 1.00
Stone to Soil (RFsl_s) 0.90 0.90 0.90
Passive EP (RFep) 0.50 0.90 0.90
Application of Load Factors
Group DC EV LS EH Probable Use
Strength I-a 0.90 1.00 1.75 1.50 BC/EC/SL
Strength I-b 1.25 1.35 1.75 1.50 BC (max. value)
Service I 1.00 1.00 1.00 1.00 Settlement
Notes: BC - Bearing Capacity; EC - Eccentricity; SL - Sliding
By Inspection:
• Strength I-a (minimum vertical loads and maximum horizontal loads) will govern for the case of sliding and
eccentricity (overturning); and
• For the case of bearing capacity, maximum vertical loads will govern and the factored loads must be
compared for Strength I-b and Strength IV.
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 3
NOTES ON DESIGN UNITS
The wall section is designed on a 'per unit width bases' (lb/ft/ft of wall or kN/m/meter of wall). In the calculations the
software shows lb/ft or kN/m, neglecting the unit width factor for simplicity.
The weights for the wall unit are shown as lbs / ft3 (kN / m3). For SRW design a 1 sf unit is typically 1 ft deep, 1.5 ft
wide and 8 inches tall (or 1 ft3). therefore a typical value of 120 pcf is shown. With larger units the unit weight will
vary with the size of the unit. Say we have 4 ft wide unit, 1.5 ft tall and 24 inches deep with a tapered shape (sides
narrow), built with 150 pcf concrete. We add up the concrete, the gravel fill and divide by the volume and the results
may come out to 140 pcf, as shown in the table. The units with more gravel may have lower effective unit weights
based on the calculations.
Hollow Units
Hollow units with gravel fill are treated differently in AASHTO. If the fill can fall out as the unit is lifted, then AASHTO
only allows 80% of the weight of the fill to be used for eccentricity (overturning calculations). In the properties page
for the units the weight of the concrete may be as low as 75 pcf. This is the effective unit weight of the concrete only
(e.g. the weight of the concrete divided by the volume of the unit). The density of the concrete maybe 150 pcf, but not
the effective weight including the volume of the void spaces used for gravel fill.
Rounding Errors
When doing hand calculations the values may vary from the values shown in the software. The program is designed
using double precision values (64 bit precision: 14 decimal places). Over several calculations the results may differ
from the single calculation the user is making, probably inputting one or two already rounded values.
Result Rounding
As noted above the software is based on double precision values. For example, using an NCMA design method an
allowable factor of safety of 1.5 the software may calculate a value of 1.49999999999999, since this is less than 1.5,
it would be false (NG), even though the results shown is 1.50 (results are rounded to 2 places on the screen). In the
design check we round to 2 decimal places to check against the suggested value (1.49999999999 rounds to 1.50).
Given the precision of the calculation, this will provide a safe design even though the 'absolute' value is less than the
minimum suggested.
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 4
GEOGRID REINFORCING
STRUCTURAL PROPERTIES: Mirafi
GEOGRID PROPERTIES
Name Tult RFcr RFd RFid Ci Cd Alpha Ltds
8XT 7400 1.45 1.15 1.10 0.80 0.80 0.80 4034
20XT 13705 1.45 1.15 1.10 0.80 0.80 0.80 7472
CONNECTION STRENGTHS
Geogrid Slope 1 Intercept 1 Peak Break Slope 2 Intercept 2 Max Normal Rup Conn Conn Creep Tlot (%) Tlot
5XT 18.00 536 1571 3.00 964 2361 False 1.45 0 4700
8XT 19.00 946 4834 3.00 2357 7745 False 1.45 0 7400
10XT 22.00 1464 -1 0.00 0 4999 False 1.45 0 9500
20XT 26.00 1825 4746 0.00 4140 6936 False 1.45 0 13705
SHEAR STRENGTHS
Slope 0 deg
Intercept 3500psf
CONNECTION CREEP
In AASHTO design methods a mechanical connector may rupture the reinforcing, thus a creep reduction
factor would be applied. If no test data is available, the creep reduction factor for the reinforcing would be applied.If a
frictional connection is used, then a creep reduction factor would not be applied and a factor of 1.0 is applicable.
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 5
CALCULATION RESULTS
OVERVIEW
Calculates stability assuming the wall is a rigid body. Forces and moments are calculated about the base and
center of the wall. The base block width is used in the calculations. The concrete units and granular fill over the blocks
are used as resisting forces.
EARTH PRESSURES
The method of analysis uses the Coulomb Earth Pressure equation (below) to calculate active earth
pressures. Wall friction is assumed to act at the back of the wall face. The component of earth pressure is assumed to
act perpendicular to the boundary surface. The effective delta angle is delta minus the wall batter at the back face
(assumed to be vertical). If the slope breaks within the failure zone, a trial wedge method of analysis is used.
INTERNAL EARTH PRESSURES
Effective internal Delta angle delta = 0.0 deg
Coefficient of active earth pressure ka =0.280
Internal failure plane ρ = 59.0 deg
EXTERNAL EARTH PRESSURES
Effective Delta angle (delta = β delta =0.0 deg
Coefficient of active earth pressure ka =0.283
Effective Face Angle Face Alpha =0.00 deg
External failure plane ρ = 62.0 deg
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 6
W0: leveling pad W6: Rectangle zone in broken back
W1: facing units W7: Live load over the mass
W2: soil wedge behind the face (base of top block to bottom) W8: Dead load over the mass
W3: rectangular area in MSE area W9: Force Pa
W4: the wedge at the back of the mass W10: Surcharge load Paq
W5: slope area over the mass W11: Dead Load Surcharge Paqd
X-Len: is measured from the center of the base (+) Driving, (-) Resisting.
Name Factor γ Force (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 1.00 5923 -- 5.29 -- 31315 --
Soil(W2) 1.00 6509 -- 3.32 -- 21617 --
Soil(W3) 1.00 33029 -- -3.47 -- -- -114457
LL(W7) 1.00 745 -- -7.26 -- -- -5407
DL(W8) 1.00 1098 -- 0.00 -- -- 0
Pa_h 1.00 -- 9714 -- 8.33 80952 --
Pq_h 1.00 -- 1144 -- 12.50 14306 --
Sum (V, H) 1.00 47303 10859 Sum Mom 148190.42 -119864
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 7
FORCES AND MOMENTS FACTORED FOR Str I-a
UltraWall increases all driving forces and reduces the resisting forces by the factors shown for Str I.
FACTORED LOADS: Str Ia
Name FactorMax γ FactorMin γ ForceSldg (V) ForceEcc (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 1.25 0.90 5330 5330 -- 5.29 -- 28183 --
Soil(W2) 1.35 1.00 6509 6509 -- 3.32 -- 21617 --
Soil(W3) 1.35 1.00 33029 33029 -- -3.47 -- -- -114457
LL(W7) 1.75 0.00 0 1303 -- -7.26 -- -- --
DL(W8) 1.50 0.75 1098 1098 -- 0.00 -- -- 0
Pa_h 1.50 0.90 -- -- 14571 -- 8.33 121428 --
Pa_v 1.50 0.90 0 0 -- -10.14 -- -- 0
Pq_h 1.75 0.00 -- 2003 2003 -- 12.50 25036 --
Pq_v 1.75 0.00 0 0 -- -8.75 -- -- 0
Sum (V, H) 45691 46995 16574 Sum Mom 196265 -114457
FORCES AND MOMENTS FACTORED FOR Str I-b
UltraWall increase resisting loads and increases driving loads by the factors shown for Str I-b.
FACTORED LOADS: Str Ib
Name Factor γ Force (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 1.25 7403 -- 5.29 -- 39144 --
Soil(W2) 1.35 8787 -- 3.32 -- 29183 --
Soil(W3) 1.35 44589 -- -3.47 -- -- -154517
LL(W7) 1.75 1303 -- -7.26 -- -- -9462
DL(W8) 1.50 1647 -- 0.00 -- -- 0
Pa_h 1.50 -- 14571 -- 8.33 121428 --
Pa_v 1.50 0 -- -10.14 -- -- 0
Pq_h 1.75 -- 2003 -- 12.50 25036 --
Pq_v 1.75 0 -- -8.75 -- -- 0
Sum (V, H) 1.00 63729 16574 Sum Mom 214791 -163980
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 8
BASE SLIDING
Sliding at the base is checked at the foundation soil and a check in the reinforced fill zone.
W1(DCr) + W2(EVr) + W3(EVr) + W8(ESr)
(5923 * 0.90) + (6509 * 1.00) + (33029 * 1.00) + (1098 * 0.75)
N =45691ppf
Resisting force in the Reinforced Zone = (N tan(slope) + c B) x RFsl
(45691 tan(34.0) + 50.0 * 18) * 1 Rf1 =31694
Resisting force in the Foundation Zone = (N tan(slope) + c B) x RFsl
(45691 tan(34.0) + 200.0 * 18) * 1 Rf2 =34319
Driving force is the horizontal component of Pah(EHd) + Pqh(LLd)
(9714 * 1.50) + (1144 * 1.75)
Df =16574
CDR = Rf1 / Df CDR =1.99
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 9
SLIDING ON REINFORCING
Sliding along the reinforcing is checked at each layer within the reinforced zone.
Sliding resistance is calculated by taking the normal load on the reinforcing, N, times the tangent of the
friction angle of the reinforced soils , φ, times a reduction factor for sliding, Rsl.
Sliding along the reinforcing includes shearing through the face panel. The shear resistance of the face
panel is included as a resisting force, RF_face.
N = Normal load on the geogrid layer. = 35896
(N * tan(34.00) * Cd) + RF_face
(35896 * tan(34.00) * 0.80 ) + 3500 RF = 22870
The driving forces is the active earth pressure plus any surcharge loads behind the reinforced zone.
Pah_ext(EHd) + Pqh_ext(LLd)
where:
z = depth to reinforcing from the surface at the end of the reinforcing. [22.54]
EHd = Load factor for Earth Pressure driving [EHd = 1.50]
Pah = 1/2 x γ z^2 x ka x cos(δ) [8978.44]
Pah_ext, Pqh_ext, etc. could be from a closed from solution (Coulomb/Rankine) or from a trial wedge
solution.
DF = (8978 x 1.50) + (1593 * 1.75 DF = 14811
CDR sliding = RF / DF CDR = 1.54
The table below shows a summary of the forces and reactions.
Elevation[ft] Name[ft] z ext[ft] N[ppf] % Coverage Friction Angle[deg] F_Resisting Pah(EHd) Pqh(LLd) Pqdh(DLd) PqMnDOT(LLd) F_Driving CDR_sl
22.13 8XT 5.33 4708 100.0 34.00 6040 0 0 0 0 -576 100.00
19.67 8XT 5.33 8166 100.0 34.00 7906 660 578 198 0 860 9.20
17.21 8XT 7.79 11750 100.0 34.00 9840 1607 963 330 0 2075 4.74
14.75 8XT 10.25 15459 100.0 34.00 11842 2782 1267 434 0 3397 3.49
12.29 8XT 12.71 19295 100.0 34.00 13912 4276 1570 538 0 5039 2.76
9.83 8XT 15.17 23257 100.0 34.00 16049 6097 1876 643 0 7000 2.29
7.38 20XT 17.63 27344 100.0 34.00 18255 8233 2180 747 0 9284 1.97
4.92 20XT 20.08 31557 100.0 34.00 20528 10690 2484 852 0 11887 1.73
2.46 20XT 22.54 35896 100.0 34.00 22870 13468 2788 956 0 14811 1.54
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 10
ECCENTRICITY AND BEARING
Eccentricity is the calculation of the distance of the resultant force away from the centroid of mass. This
measure is an indication of the overturning of the mass. In rigid concrete structures, the limit to eccentricity is L/4 (the
middle half of the base). UltraWall uses an allowable eccentricity of e/L per the AASHTO LRFD guidelines.
Eccentricity is still used as a guide to design in some design methods. Eccentricity is based on case S1a (minimum
resisting forces, maximum driving forces. Bearing is based on case S1b (maximum resisting forces, maximum driving
forces).
UltraWall calculates three eccentricities:
1) S1a: Maximum eccentricity (overturning) where it uses the maximum driving forces combined
with the minimum resisting forces (see overturning).
2) S1b Maximum bearing where it uses the maximum driving forces combined with the maximum
resisting forces.
3) Service: Maximum bearing where it uses the actual driving forces combined with the actual
resisting forces in Service loading.
Calculation of Eccentricity for maximum bearing (S1b)
Moments resisting = + M3(EVd) + LL(LLd)
+ (-114457 * 1.35) + (-5407 x 1.75)
Mr =-163980ft-lbs
Moments driving = M1(DCr) + M2(EVd) + Pah(EHd) + Pqh(LLd)
+ (31315 * 1.25) + (21617 * 1.35) + (80952 * 1.50) + (14306 * 1.75)
Mo = 214791ft-lbs
e = (SumMr + SumMo)/SumV [ if e < 0, then e = 0 ]
e = (-163980 + 214790.8) /63729.3 e =0.797
Calculation of Bearing Pressures
Qal = (c*Nc + q*Nq + 0.5*gamma*(B')*Ng) * RFbrg
where:
Nc =42.16
Nq =29.44
Ng =41.06
c =200.00psf
RFbrg =0.65
q =250psf [embedment x gamma]
B' = B - 2e =15.91ft
Calculate Allowable Bearing, Qal Qal =36799psf
Applied Bearing Pressures (Sigma) (SumV)/B' =4007psf
Calculated CDR for bearing Qal/sigma =9.18
Design Sum Vert Mo Mr e Qal Sigma CDR
Strength I-b 63729 214791 -163980 0.797 36799 4007 9.18
Service 47303 148190 -119864 0.599 57632 2902 19.86
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 11
Elevation[ft] Name Ta*RF[ppf] Tas*RF[ppf] Coverage Ratio % Tmax[ppf] TSmax[ppf] CDR Str CDRs Str
22.13 8XT 3631 7020 100 398 716 9.12 9.80
19.67 8XT 3631 7020 100 616 869 5.90 8.07
17.21 8XT 3631 7020 100 1018 1033 3.57 6.79
14.75 8XT 3631 7020 100 1306 1150 2.78 6.10
12.29 8XT 3631 7020 100 1595 1268 2.28 5.54
9.83 8XT 3631 7020 100 1883 1385 1.93 5.07
7.38 20XT 6725 13001 100 2171 1502 3.10 8.65
4.92 20XT 6725 13001 100 2457 1619 2.74 8.03
2.46 20XT 6725 13001 100 2704 1719 2.49 7.56
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 12
PULLOUT CALCULATIONS
Pullout is the amount of resistance of the reinforcing has to a pullout failure based on the Tmax applied and
the depth of embedement (resistance). In an AASHTO design, the failure plane is fixed at the Rankine failure plane
angle, 45 + phi/2. All failure planes begin at the tail. of the facing units.
Failure Plane Angle = 62.0 Deg
F* = 0.67 x tan( φ ) [AASHTO 11.10.6.3.2]
F* = 0.67 x tan( 34) = 0.45
α = 0.80 [AASHTO Table 11.10.6.3.2-1]
RFpo = 0.90
Pullout = 2 x N x F* x α x Coverage x RFpo
Pullout = 2 x 3215 x 0.45 x 0.80 x 1.00 x 0.90 = 2091.90
Pullout is the calculated value or the Tult of the geogrid, whichever is less.
NOTE: The pullout capacity is limited by the LTDS of the reinforcing layer, not the ultimate pullout capacity calculated.
TABLE OF RESULTS
Elevation[ft] Normal[lbf] F* Alpha % Coverage Tmax[ppf] Le[ft] La[ft] Pullout_[Pr][ppf] CDR PO
22.13 3215 0.45 0.80 100 398 7.00 10.50 2092 5.25
19.67 6053 0.45 0.80 100 616 7.90 9.60 3631 5.90
17.21 9443 0.45 0.80 100 1018 8.79 8.71 3631 3.57
14.75 13384 0.45 0.80 100 1306 9.69 7.81 3631 2.78
12.29 17878 0.45 0.80 100 1595 10.59 6.91 3631 2.28
9.83 22922 0.45 0.80 100 1883 11.49 6.01 3631 1.93
7.38 28519 0.45 0.80 100 2171 12.38 5.12 6725 3.10
4.92 34518 0.45 0.80 100 2457 13.28 4.22 6725 2.74
2.46 41087 0.45 0.80 100 2704 14.18 3.32 6725 2.49
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 13
CONNECTION CALCULATIONS
Connection is the amount of resistance of the reinforcing has to a pullout failure from the facing units based
on the Tmax applied and the normal load on the units. In an AASHTO LRFD design, creep on the connection may be
applied for frictional and mechanical connections.
Connection Capacity = [N tan(slope) + intercept] / RFcr
RFcr can be a value obtained from long-term testing or by default could be the creep reduction factor of the
geogrid reinforcing.
Base friction is used to reduce the tension in the bottom layer of reinforcing. The force in the bottom layer is
the tension from half way to the reinforcing layer above to the halfway to the foundation level below.
Base Friction = Base Shear x RFsliding
Base Shear = 5923 x tan( atan(0.80 x tan(40 )) + 0
3976 x 0.90 BF = 3578ppf
BF utilized to reduce bottom tension = 1128ppf
CRu = Ultimate connection strength [1692 x tan( 19.00) + 946 = 1528.65 ]
CRru = CRu / TLot [1528.65/7400.00 = 0.21]
RFcrcn = 1.45 [Connection creep if tested, otherwise geogrid creep factor]
[if connection creep is set to 'false', RFcrcn = 1]
CRcr = CRru / RFcrcn [0.21 / 1.00 = 0.21]
Tac = Tult x CRcr / RFd * RFten [ 7400 x 0.21 / 1.15 x 0.90 = 1196.34]
TABLE OF RESULTS
Elev[ft] Name[ft] Tmax[ppf] Ttotal[ppf] Rc % RFcn_cr N[ppf] Avail_CN[ppf] CDR cn CDR cns
22.13 8XT 398 383 100 1.00 1692 1196 3.00 3.75
19.67 8XT 616 590 100 1.00 2538 1424 2.31 2.89
17.21 8XT 1018 976 100 1.00 3384 1652 1.62 2.03
14.75 8XT 1306 1252 100 1.00 4230 1880 1.44 1.80
12.29 8XT 1595 1529 100 1.00 5076 2053 1.29 1.61
9.83 8XT 1883 1805 100 1.00 5923 2088 1.11 1.39
7.38 20XT 2171 2081 100 1.00 6769 3240 1.49 1.87
4.92 20XT 2457 2355 100 1.00 7615 3240 1.32 1.65
2.46 20XT 2704 2592 100 1.00 8461 3240 1.20 1.50
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 14
SEISMIC CALCULATIONS
The loads considered under seismic loading are primarily inertial loadings. The wave passes the structure
putting the mass into motion and then the mass will try to continue in the direction of the initial wave. In the
calculations you see the one dynamic earth pressure from the wedge of the soil behind the reinforced mass, and then
all the other forces come from inertia calculations of the face put into motion and then trying to be held in place.
In AASHTO LRFD, external stability is calculated based on 100% of Pae and 50% of Pir and then
50% of Pae and 100% of Pir. The values labelled Pae are 100% Pae/50% Pir; labels Pir are 50% Pae/100% Pir.
Design Acceleration A = 0.330
Displacment (d) d = 3.3in
Design Acceleration Coefficient Displacment Based (empirically)
Kh = A/2 = kh(ext) = 0.165
Vertical Acceleration kv =0.000
SEISMIC THRUST
EXTERNAL Kae
Kae Kae =0.384
Pae = 0.5*gamma*(H)^2*D_Kae Pae =3971ppf
Pae_h/2 = Pae*cos(delta)/2 Pae_h/2 =1986ppf
Pae_v/2 = Pae*sin(delta)/2 Pae_v/2 =0ppf
INERTIA FORCES OF THE STRUCTURE
Face (Pif) = (W0 + W1)*kh(int) = 5923 * 0.165 Pif =977ppf
Mass (Pir) = (W)*kh(int) = 24559 * 0.165 Pir =4052ppf
Slope (Pis) = (W)*kh(int) = 0 * 0.165 Pis =0ppf
Dead Load(Pidl) = (DL)*kh(int) = 0 * 0.165 Pidl =0ppf
TABLE OF RESULTS FOR SEISMIC REACTIONS
Name Force (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 5923 -- 3.46 -- -- 20507
Soil(W2) 6509 -- 5.43 -- -- 35335
Soil(W3) 33029 -- 12.22 -- -- 403461
LL(W7) 745 -- 16.01 -- -- 11923
DL(W8) 1098 -- 12.01 -- -- 13186
Pa_h -- 9714 -- 8.33 80952 --
Pq_h -- 1144 -- 12.50 14306 --
Pir -- 4052 -- 12.50 50653 --
Pif -- 977 -- 12.50 12215 --
Pae_h/2 -- 3971 -- 12.50 24821 --
Sum V / H 46558.22 16729.4 Sum Mom 182947.35 484412.85
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 15
UltraWall
Project: Fyffe
Location: Site Location
Designer: JC
Date: 5/13/2020
Section: 25ft Stratagrid
Design Method: AASHTO_LRFD_2014
Design Unit: UltraBlock
Seismic Acc: 0.330
SOIL PARAMETERS φ coh γ
Reinforced Soil: 34 deg 50psf 125pcf
Retained Soil: 34 deg 100psf 125pcf
Foundation Soil: 34 deg 200psf 125pcf
Leveling Pad: Crushed Stone
GEOMETRY
Design Height: 25.00ft Live Load: 250psf
Wall Batter/Tilt: 0.00/ 9.50 deg Live Load Offset: 8.00ft
Embedment: 2.00ft Live Load Width: 39ft
Leveling Pad Depth: 1.00ft Dead Load: 100psf
Slope Angle: 0.0 deg Dead Load Offset: 0.0ft
Slope Length: 0.0ft Dead Load Width: 39ft
Slope Toe Offset: 0.0ft Leveling Pad Width: 3.96ft
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 1
RESULTS (Static / Seismic)
CDR Sliding: 1.95 (fnd) / [1.83 ] CDR Bearing: 9.50 / 14.88
Eccentricity (e/L): 0.10 / -0.20 Bearing: 3899; Srvc 2817 / Seis 2890
CDR Connection: 0.97...NG
ID Ht Lngth Geogri Ta_tn Rc % TMax (Tatn*RF) CDR Ta_tn Ta_cn CDR Ta_cn CDR Tpo CDR Sldg
1122.1317.50 SG500 3122 [4839] 100 398 [513] 2810 [5807] 7.06 [9.52] 1157 [1388] 2.91 [3.63] 5.27 100.00
1019.6717.50 SG500 3122 [4839] 100 616 [513] 2810 [5807] 4.56 [7.61] 1262 [1515] 2.05 [2.57] 4.56 17.91 [7.69]
9 17.2117.50 SG500 3122 [4839] 100 1018 [513] 2810 [5807] 2.76 [6.27] 1294 [1552] 1.27 [1.59] 2.76 8.35 [5.48]
8 14.7517.50 SG500 3122 [4839] 100 1306 [513] 2810 [5807] 2.15 [5.56] 1325 [1590] 1.01 [1.27] 2.15 5.69 [4.28]
7 12.2917.50 SG600 4439 [6881] 100 1595 [513] 3995 [8257] 2.51 [7.11] 2234 [2681] 1.40 [1.75] 2.51 4.05 [3.31]
6 9.83 17.50 SG600 4439 [6881] 100 1883 [513] 3995 [8257] 2.12 [6.46] 2276 [2731] 1.21 [1.51] 2.12 3.22 [2.78]
5 7.38 17.50 SG600 4439 [6881] 100 2171 [513] 3995 [8257] 1.84 [5.91] 2318 [2782] 1.07 [1.34] 1.84 2.66 [2.39]
4 4.92 17.50 SG600 4439 [6881] 100 1816 [513] 3995 [8257] 2.20 [5.51] 2360 [2832] 1.30 [1.63] 2.20 2.27 [2.09]
3 3.69 17.50 SG500 3122 [4839] 100 1290 [513] 2810 [5807] 2.18 [3.72] 1451 [1742] 1.12 [1.41] 2.18 2.19 [2.05]
2 2.46 17.50 SG500 3122 [4839] 100 1352 [513] 2810 [5807] 2.08 [3.60] 1453 [1744] 1.07 [1.35] 2.08 2.05 [1.93]
1 1.23 17.50 SG500 3122 [4839] 100 1497 [513] 2810 [5807] 1.88 [3.41] 1453 [1744] 0.97 [1.21] [?] 1.97 1.92 [1.83]
Column Descriptions:
Tr: Tension required (Ta*Reduction factors) [ppf]
EP(Pa): Earth pressures from closed form solution or trial wedge [ppf]
Rc %: percent coverage for geosynthetics
EP (Pa) internal active earth pressure [ppf ]
LL (Pql) earth pressure due to live load surcharge [ppf ]
DL (Pqd) earth pressure due to dead load surcharge [ppf ]
Tmax maximum earth pressure on geosynthetic layer [ppf ]
CDRstr 'Capacity/Demand Ratio (CDR)' on geogrid strength (Tr/Tmax)
Ta cn allowable tension capacity on the connection [ppf ]
CDR Pkcn, Capacity/Demand Ratio on the connection (Ta cn/Tmax)
CDR PO, Capacity/Demand Ratio on pullout (Ta pullout/(Tmax - LL)
CDR Sldg [fndn], Capacity/Demand Ratio on sliding on the reinforcement, CDR sliding on the foundation
soils
Grid Embed, depth of embedment beyond the theorectical failure plane. [ft ]
(PaC): reduction in load due to cohesion [ppf]
PaT: sum of all earth pressures [ppf]
%D/H: ratio of based depth to height (warning for narrow walls, < 35%)
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 2
DESIGN DATA
Load Factors for Design
AASHTO Table 3.4.1-1 & 3.4.1-2
Load Case Str_Max Str_Min Extreme Max Extreme Min Service
Str I Dead Load (DC) 1.25 0.90 1.00 1.00 1.00
Soil Load Driving (EH) 1.50 0.90 1.00 1.00 1.00
Str I Vert Earth Load (EV) 1.35 1.00 1.00 1.00 1.00
Dead Load Surcharge (ES) 1.50 0.75 1.00 1.00 1.00
Live Load (LL, PL, LS) 1.75 0.00 1.00 0.00 1.00
AASHTO Table 11.5.7-1 & Article 11.5.8
MSE Resistance Case Strength Extreme Service
Bearing Resistance (RFbr) 0.65 0.90 1.00
Sliding Soil to Soil (RFsl) 1.00 1.00 1.00
Sliding Soil to Reinforcement (RFslrf) 1.00 1.00 1.00
Tensile Resistance (RFten) 0.90 1.20 1.00
Pullout Resistance (RFpo) 0.90 1.20 1.00
Overturning Resistance (RFot) 0.60 1.00 1.00
AASHTO Table 10.5.5.2.2-1
Gravity Resistance Case Strength Extreme Service
Bearing Resistance (RFbr) 0.45 0.45 0.45
Cast-In-Place Concrete to Stone (RFsl_cip) 0.80 1.00 1.00
Precast Concrete to Stone (RFsl_c) 0.90 1.00 1.00
Stone to Soil (RFsl_s) 0.90 0.90 0.90
Passive EP (RFep) 0.50 0.90 0.90
Application of Load Factors
Group DC EV LS EH Probable Use
Strength I-a 0.90 1.00 1.75 1.50 BC/EC/SL
Strength I-b 1.25 1.35 1.75 1.50 BC (max. value)
Service I 1.00 1.00 1.00 1.00 Settlement
Notes: BC - Bearing Capacity; EC - Eccentricity; SL - Sliding
By Inspection:
• Strength I-a (minimum vertical loads and maximum horizontal loads) will govern for the case of sliding and
eccentricity (overturning); and
• For the case of bearing capacity, maximum vertical loads will govern and the factored loads must be
compared for Strength I-b and Strength IV.
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 3
NOTES ON DESIGN UNITS
The wall section is designed on a 'per unit width bases' (lb/ft/ft of wall or kN/m/meter of wall). In the calculations the
software shows lb/ft or kN/m, neglecting the unit width factor for simplicity.
The weights for the wall unit are shown as lbs / ft3 (kN / m3). For SRW design a 1 sf unit is typically 1 ft deep, 1.5 ft
wide and 8 inches tall (or 1 ft3). therefore a typical value of 120 pcf is shown. With larger units the unit weight will
vary with the size of the unit. Say we have 4 ft wide unit, 1.5 ft tall and 24 inches deep with a tapered shape (sides
narrow), built with 150 pcf concrete. We add up the concrete, the gravel fill and divide by the volume and the results
may come out to 140 pcf, as shown in the table. The units with more gravel may have lower effective unit weights
based on the calculations.
Hollow Units
Hollow units with gravel fill are treated differently in AASHTO. If the fill can fall out as the unit is lifted, then AASHTO
only allows 80% of the weight of the fill to be used for eccentricity (overturning calculations). In the properties page
for the units the weight of the concrete may be as low as 75 pcf. This is the effective unit weight of the concrete only
(e.g. the weight of the concrete divided by the volume of the unit). The density of the concrete maybe 150 pcf, but not
the effective weight including the volume of the void spaces used for gravel fill.
Rounding Errors
When doing hand calculations the values may vary from the values shown in the software. The program is designed
using double precision values (64 bit precision: 14 decimal places). Over several calculations the results may differ
from the single calculation the user is making, probably inputting one or two already rounded values.
Result Rounding
As noted above the software is based on double precision values. For example, using an NCMA design method an
allowable factor of safety of 1.5 the software may calculate a value of 1.49999999999999, since this is less than 1.5,
it would be false (NG), even though the results shown is 1.50 (results are rounded to 2 places on the screen). In the
design check we round to 2 decimal places to check against the suggested value (1.49999999999 rounds to 1.50).
Given the precision of the calculation, this will provide a safe design even though the 'absolute' value is less than the
minimum suggested.
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 4
GEOGRID REINFORCING
STRUCTURAL PROPERTIES: Stratagrid
GEOGRID PROPERTIES
Name Tult RFcr RFd RFid Ci Cd Alpha Ltds
SG500 6400 1.55 1.15 1.15 0.80 0.80 0.80 3122
SG600 9100 1.55 1.15 1.15 0.80 0.80 0.80 4439
CONNECTION STRENGTHS
Geogrid Slope 1 Intercept 1 Peak Break Slope 2 Intercept 2 Max Normal Rup Conn Conn Creep Tlot (%) Tlot
SG500 29.00 688 1899 3.00 1641 7655 False 1.55 110 7040
SG550 46.00 670 2190 4.00 2785 7650 False 1.55 110 8965
SG600 46.00 670 2190 4.00 2785 7850 False 1.55 110 10010
SG700 37.00 643 -1 0.00 0 3100 False 1.55 100 11800
SHEAR STRENGTHS
Slope 0 deg
Intercept 11000psf
CONNECTION CREEP
In AASHTO design methods a mechanical connector may rupture the reinforcing, thus a creep reduction
factor would be applied. If no test data is available, the creep reduction factor for the reinforcing would be applied.If a
frictional connection is used, then a creep reduction factor would not be applied and a factor of 1.0 is applicable.
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 5
CALCULATION RESULTS
OVERVIEW
Calculates stability assuming the wall is a rigid body. Forces and moments are calculated about the base and
center of the wall. The base block width is used in the calculations. The concrete units and granular fill over the blocks
are used as resisting forces.
EARTH PRESSURES
The method of analysis uses the Coulomb Earth Pressure equation (below) to calculate active earth
pressures. Wall friction is assumed to act at the back of the wall face. The component of earth pressure is assumed to
act perpendicular to the boundary surface. The effective delta angle is delta minus the wall batter at the back face
(assumed to be vertical). If the slope breaks within the failure zone, a trial wedge method of analysis is used.
INTERNAL EARTH PRESSURES
Effective internal Delta angle delta = 0.0 deg
Coefficient of active earth pressure ka =0.280
Internal failure plane ρ = 59.0 deg
EXTERNAL EARTH PRESSURES
Effective Delta angle (delta = β delta =0.0 deg
Coefficient of active earth pressure ka =0.283
Effective Face Angle Face Alpha =0.00 deg
External failure plane ρ = 62.0 deg
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 6
W0: leveling pad W6: Rectangle zone in broken back
W1: facing units W7: Live load over the mass
W2: soil wedge behind the face (base of top block to bottom) W8: Dead load over the mass
W3: rectangular area in MSE area W9: Force Pa
W4: the wedge at the back of the mass W10: Surcharge load Paq
W5: slope area over the mass W11: Dead Load Surcharge Paqd
X-Len: is measured from the center of the base (+) Driving, (-) Resisting.
Name Factor γ Force (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 1.00 5076 -- 5.28 -- 26793 --
Soil(W2) 1.00 6537 -- 3.31 -- 21627 --
Soil(W3) 1.00 32969 -- -3.47 -- -- -114566
LL(W7) 1.00 740 -- -7.27 -- -- -5382
DL(W8) 1.00 1096 -- 0.00 -- -- 0
Pa_h 1.00 -- 9714 -- 8.33 80952 --
Pq_h 1.00 -- 1144 -- 12.50 14306 --
Sum (V, H) 1.00 46419 10859 Sum Mom 143678.87 -119948
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 7
FORCES AND MOMENTS FACTORED FOR Str I-a
UltraWall increases all driving forces and reduces the resisting forces by the factors shown for Str I.
FACTORED LOADS: Str Ia
Name FactorMax γ FactorMin γ ForceSldg (V) ForceEcc (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 1.25 0.90 4569 4569 -- 5.28 -- 24114 --
Soil(W2) 1.35 1.00 6537 6537 -- 3.31 -- 21627 --
Soil(W3) 1.35 1.00 32969 32969 -- -3.47 -- -- -114566
LL(W7) 1.75 0.00 0 1296 -- -7.27 -- -- --
DL(W8) 1.50 0.75 1096 1096 -- 0.00 -- -- 0
Pa_h 1.50 0.90 -- -- 14571 -- 8.33 121428 --
Pa_v 1.50 0.90 0 0 -- -10.14 -- -- 0
Pq_h 1.75 0.00 -- 2003 2003 -- 12.50 25036 --
Pq_v 1.75 0.00 0 0 -- -8.75 -- -- 0
Sum (V, H) 44897 46193 16574 Sum Mom 192205 -114566
FORCES AND MOMENTS FACTORED FOR Str I-b
UltraWall increase resisting loads and increases driving loads by the factors shown for Str I-b.
FACTORED LOADS: Str Ib
Name Factor γ Force (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 1.25 6346 -- 5.28 -- 33491 --
Soil(W2) 1.35 8825 -- 3.31 -- 29197 --
Soil(W3) 1.35 44508 -- -3.47 -- -- -154663
LL(W7) 1.75 1296 -- -7.27 -- -- -9419
DL(W8) 1.50 1644 -- 0.00 -- -- 0
Pa_h 1.50 -- 14571 -- 8.33 121428 --
Pa_v 1.50 0 -- -10.14 -- -- 0
Pq_h 1.75 -- 2003 -- 12.50 25036 --
Pq_v 1.75 0 -- -8.75 -- -- 0
Sum (V, H) 1.00 62619 16574 Sum Mom 209152 -164082
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 8
BASE SLIDING
Sliding at the base is checked at the foundation soil and a check in the reinforced fill zone.
W1(DCr) + W2(EVr) + W3(EVr) + W8(ESr)
(5076 * 0.90) + (6537 * 1.00) + (32969 * 1.00) + (1096 * 0.75)
N =44897ppf
Resisting force in the Reinforced Zone = (N tan(slope) + c B) x RFsl
(44897 tan(34.0) + 50.0 * 18) * 1 Rf1 =31158
Resisting force in the Foundation Zone = (N tan(slope) + c B) x RFsl
(44897 tan(34.0) + 200.0 * 18) * 1 Rf2 =33783
Driving force is the horizontal component of Pah(EHd) + Pqh(LLd)
(9714 * 1.50) + (1144 * 1.75)
Df =16574
CDR = Rf1 / Df CDR =1.95
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 9
SLIDING ON REINFORCING
Sliding along the reinforcing is checked at each layer within the reinforced zone.
Sliding resistance is calculated by taking the normal load on the reinforcing, N, times the tangent of the
friction angle of the reinforced soils , φ, times a reduction factor for sliding, Rsl.
Sliding along the reinforcing includes shearing through the face panel. The shear resistance of the face
panel is included as a resisting force, RF_face.
N = Normal load on the geogrid layer. = 38080
(N * tan(34.00) * Cd) + RF_face
(38080 * tan(34.00) * 0.80 ) + 11000 RF = 31548
The driving forces is the active earth pressure plus any surcharge loads behind the reinforced zone.
Pah_ext(EHd) + Pqh_ext(LLd)
where:
z = depth to reinforcing from the surface at the end of the reinforcing. [23.77]
EHd = Load factor for Earth Pressure driving [EHd = 1.50]
Pah = 1/2 x γ z^2 x ka x cos(δ) [9984.30]
Pah_ext, Pqh_ext, etc. could be from a closed from solution (Coulomb/Rankine) or from a trial wedge
solution.
DF = (9984 x 1.50) + (1680 * 1.75 DF = 16393
CDR sliding = RF / DF CDR = 1.92
The table below shows a summary of the forces and reactions.
Elevation[ft] Name[ft] z ext[ft] N[ppf] % Coverage Friction Angle[deg] F_Resisting Pah(EHd) Pqh(LLd) Pqdh(DLd) PqMnDOT(LLd) F_Driving CDR_sl
22.13 SG500 5.33 4700 100.0 34.00 13536 0 0 0 0 -576 100.00
19.67 SG500 5.33 8153 100.0 34.00 15399 660 578 198 0 860 17.91
17.21 SG500 7.79 11732 100.0 34.00 17331 1607 963 330 0 2075 8.35
14.75 SG500 10.25 15438 100.0 34.00 19331 2782 1267 434 0 3397 5.69
12.29 SG600 12.71 19271 100.0 34.00 20399 4276 1570 538 0 5039 4.05
9.83 SG600 15.17 23229 100.0 34.00 22535 6097 1876 643 0 7000 3.22
7.38 SG600 17.63 27314 100.0 34.00 24739 8233 2180 747 0 9284 2.66
4.92 SG600 20.08 31526 100.0 34.00 27012 10690 2484 852 0 11887 2.27
3.69 SG500 21.31 33679 100.0 34.00 29173 12039 2636 904 0 13309 2.19
2.46 SG500 22.54 35864 100.0 34.00 30352 13468 2788 956 0 14811 2.05
1.23 SG500 23.77 38080 100.0 34.00 31548 14976 2940 1008 0 16393 1.92
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 10
ECCENTRICITY AND BEARING
Eccentricity is the calculation of the distance of the resultant force away from the centroid of mass. This
measure is an indication of the overturning of the mass. In rigid concrete structures, the limit to eccentricity is L/4 (the
middle half of the base). UltraWall uses an allowable eccentricity of e/L per the AASHTO LRFD guidelines.
Eccentricity is still used as a guide to design in some design methods. Eccentricity is based on case S1a (minimum
resisting forces, maximum driving forces. Bearing is based on case S1b (maximum resisting forces, maximum driving
forces).
UltraWall calculates three eccentricities:
1) S1a: Maximum eccentricity (overturning) where it uses the maximum driving forces combined
with the minimum resisting forces (see overturning).
2) S1b Maximum bearing where it uses the maximum driving forces combined with the maximum
resisting forces.
3) Service: Maximum bearing where it uses the actual driving forces combined with the actual
resisting forces in Service loading.
Calculation of Eccentricity for maximum bearing (S1b)
Moments resisting = + M3(EVd) + LL(LLd)
+ (-114566 * 1.35) + (-5382 x 1.75)
Mr =-164082ft-lbs
Moments driving = M1(DCr) + M2(EVd) + Pah(EHd) + Pqh(LLd)
+ (26793 * 1.25) + (21627 * 1.35) + (80952 * 1.50) + (14306 * 1.75)
Mo = 209152ft-lbs
e = (SumMr + SumMo)/SumV [ if e < 0, then e = 0 ]
e = (-164082 + 209152.4) /62618.7 e =0.720
Calculation of Bearing Pressures
Qal = (c*Nc + q*Nq + 0.5*gamma*(B')*Ng) * RFbrg
where:
Nc =42.16
Nq =29.44
Ng =41.06
c =200.00psf
RFbrg =0.65
q =250psf [embedment x gamma]
B' = B - 2e =16.06ft
Calculate Allowable Bearing, Qal Qal =37058psf
Applied Bearing Pressures (Sigma) (SumV)/B' =3899psf
Calculated CDR for bearing Qal/sigma =9.50
Design Sum Vert Mo Mr e Qal Sigma CDR
Strength I-b 62619 209152 -164082 0.720 37058 3899 9.50
Service 46419 143679 -119948 0.511 58082 2817 20.62
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 11
Elevation[ft] Name Ta*RF[ppf] Tas*RF[ppf] Coverage Ratio % Tmax[ppf] TSmax[ppf] CDR Str CDRs Str
22.13 SG500 2810 5807 100 398 610 7.06 9.52
19.67 SG500 2810 5807 100 616 763 4.56 7.61
17.21 SG500 2810 5807 100 1018 927 2.76 6.27
14.75 SG500 2810 5807 100 1306 1044 2.15 5.56
12.29 SG600 3995 8257 100 1595 1161 2.51 7.11
9.83 SG600 3995 8257 100 1883 1279 2.12 6.46
7.38 SG600 3995 8257 100 2171 1396 1.84 5.91
4.92 SG600 3995 8257 100 1816 1498 2.20 5.51
3.69 SG500 2810 5807 100 1290 1562 2.18 3.72
2.46 SG500 2810 5807 100 1352 1613 2.08 3.60
1.23 SG500 2810 5807 100 1497 1705 1.88 3.41
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 12
PULLOUT CALCULATIONS
Pullout is the amount of resistance of the reinforcing has to a pullout failure based on the Tmax applied and
the depth of embedement (resistance). In an AASHTO design, the failure plane is fixed at the Rankine failure plane
angle, 45 + phi/2. All failure planes begin at the tail. of the facing units.
Failure Plane Angle = 62.0 Deg
F* = 0.67 x tan( φ ) [AASHTO 11.10.6.3.2]
F* = 0.67 x tan( 34) = 0.45
α = 0.80 [AASHTO Table 11.10.6.3.2-1]
RFpo = 0.90
Pullout = 2 x N x F* x α x Coverage x RFpo
Pullout = 2 x 3222 x 0.45 x 0.80 x 1.00 x 0.90 = 2096.73
Pullout is the calculated value or the Tult of the geogrid, whichever is less.
NOTE: The pullout capacity is limited by the LTDS of the reinforcing layer, not the ultimate pullout capacity calculated.
TABLE OF RESULTS
Elevation[ft] Normal[lbf] F* Alpha % Coverage Tmax[ppf] Le[ft] La[ft] Pullout_[Pr][ppf] CDR PO
22.13 3222 0.45 0.80 100 398 7.01 10.49 2097 5.27
19.67 6064 0.45 0.80 100 616 7.91 9.59 2810 4.56
17.21 9456 0.45 0.80 100 1018 8.81 8.69 2810 2.76
14.75 13399 0.45 0.80 100 1306 9.70 7.80 2810 2.15
12.29 17893 0.45 0.80 100 1595 10.60 6.90 3995 2.51
9.83 22937 0.45 0.80 100 1883 11.49 6.01 3995 2.12
7.38 28532 0.45 0.80 100 2171 12.39 5.11 3995 1.84
4.92 34527 0.45 0.80 100 1816 13.28 4.22 3995 2.20
3.69 37740 0.45 0.80 100 1290 13.73 3.77 2810 2.18
2.46 41091 0.45 0.80 100 1352 14.18 3.32 2810 2.08
1.23 44580 0.45 0.80 100 1497 14.63 2.87 2810 1.88
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 13
CONNECTION CALCULATIONS
Connection is the amount of resistance of the reinforcing has to a pullout failure from the facing units based
on the Tmax applied and the normal load on the units. In an AASHTO LRFD design, creep on the connection may be
applied for frictional and mechanical connections.
Connection Capacity = [N tan(slope) + intercept] / RFcr
RFcr can be a value obtained from long-term testing or by default could be the creep reduction factor of the
geogrid reinforcing.
Base friction is used to reduce the tension in the bottom layer of reinforcing. The force in the bottom layer is
the tension from half way to the reinforcing layer above to the halfway to the foundation level below.
Base Friction = Base Shear x RFsliding
Base Shear = 5076 x tan( atan(0.80 x tan(40 )) + 0
3408 x 0.90 BF = 3067ppf
BF utilized to reduce bottom tension = 571ppf
CRu = Ultimate connection strength [1692 x tan( 29.00) + 688 = 1625.98 ]
CRru = CRu / TLot [1625.98/7040.00 = 0.23]
RFcrcn = 1.55 [Connection creep if tested, otherwise geogrid creep factor]
[if connection creep is set to 'false', RFcrcn = 1]
CRcr = CRru / RFcrcn [0.23 / 1.00 = 0.23]
Tac = Tult x CRcr / RFd * RFten [ 6400 x 0.23 / 1.15 x 0.90 = 1156.82]
TABLE OF RESULTS
Elev[ft] Name[ft] Tmax[ppf] Ttotal[ppf] Rc % RFcn_cr N[ppf] Avail_CN[ppf] CDR cn CDR cns
22.13 SG500 398 382 100 1.00 1692 1157 2.91 3.63
19.67 SG500 616 590 100 1.00 2538 1262 2.05 2.57
17.21 SG500 1018 976 100 1.00 3384 1294 1.27 1.59
14.75 SG500 1306 1252 100 1.00 4230 1325 1.01 1.27
12.29 SG600 1595 1529 100 1.00 5076 2234 1.40 1.75
9.83 SG600 1883 1805 100 1.00 5923 2276 1.21 1.51
7.38 SG600 2171 2081 100 1.00 6769 2318 1.07 1.34
4.92 SG600 1816 1740 100 1.00 7615 2360 1.30 1.63
3.69 SG500 1290 1237 100 1.00 7615 1451 1.12 1.41
2.46 SG500 1352 1296 100 1.00 8461 1453 1.07 1.35
1.23 SG500 1497 1435 100 1.00 8461 1453 0.97 1.21
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 14
SEISMIC CALCULATIONS
The loads considered under seismic loading are primarily inertial loadings. The wave passes the structure
putting the mass into motion and then the mass will try to continue in the direction of the initial wave. In the
calculations you see the one dynamic earth pressure from the wedge of the soil behind the reinforced mass, and then
all the other forces come from inertia calculations of the face put into motion and then trying to be held in place.
In AASHTO LRFD, external stability is calculated based on 100% of Pae and 50% of Pir and then
50% of Pae and 100% of Pir. The values labelled Pae are 100% Pae/50% Pir; labels Pir are 50% Pae/100% Pir.
Design Acceleration A = 0.330
Displacment (d) d = 3.3in
Design Acceleration Coefficient Displacment Based (empirically)
Kh = A/2 = kh(ext) = 0.165
Vertical Acceleration kv =0.000
SEISMIC THRUST
EXTERNAL Kae
Kae Kae =0.384
Pae = 0.5*gamma*(H)^2*D_Kae Pae =3971ppf
Pae_h/2 = Pae*cos(delta)/2 Pae_h/2 =1986ppf
Pae_v/2 = Pae*sin(delta)/2 Pae_v/2 =0ppf
INERTIA FORCES OF THE STRUCTURE
Face (Pif) = (W0 + W1)*kh(int) = 5076 * 0.165 Pif =838ppf
Mass (Pir) = (W)*kh(int) = 24558 * 0.165 Pir =4052ppf
Slope (Pis) = (W)*kh(int) = 0 * 0.165 Pis =0ppf
Dead Load(Pidl) = (DL)*kh(int) = 0 * 0.165 Pidl =0ppf
TABLE OF RESULTS FOR SEISMIC REACTIONS
Name Force (V) Force (H) X-len Y-len Mo Mr
Face Blocks(W1) 5076 -- 3.47 -- -- 17626
Soil(W2) 6537 -- 5.44 -- -- 35570
Soil(W3) 32969 -- 12.22 -- -- 403046
LL(W7) 740 -- 16.02 -- -- 11860
DL(W8) 1096 -- 12.02 -- -- 13175
Pa_h -- 9714 -- 8.33 80952 --
Pq_h -- 1144 -- 12.50 14306 --
Pir -- 4052 -- 12.50 50652 --
Pif -- 838 -- 12.50 10470 --
Pae_h/2 -- 3971 -- 12.50 24821 --
Sum V / H 45678.67 16589.72 Sum Mom 181201.41 481277.36
Note: Calculations and quantities are for PRELIMINARY ANALYTICAL USE ONLY and MUST NOT be used for final
n or construction without the independent review, verification, and approval by a qualified professional engineer.
UltraWall 5.0.19345 15
6 Appendix
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
6.1 Appendix A Csi Models and Outputs
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
License #2010*1J2ULGRNHP9JJDE
Girder A Shown, other girders similar
Prepared by
HDR, Inc
Model Name: hl93 - Girder A.bdb
10 June 2020
hl93 - Girder A.bdb CSiBridge v20.2.1 - License #2010*1J2ULGRNHP9JJDE 10 June 2020
HDR, Inc Page 2 of 24
Table: Case - Moving Load 1 - Lane Assignments
Table: Case - Moving Load 1 - Lane Assignments
Case AssignNum VehClass ScaleFactor MinLoaded MaxLoaded NumLanes
hl93 1 HL-93K 1. 0 0 1
P15 1 P15 1. 0 0 1
Table: Case - Moving Load 2 - Lanes Loaded
Table: Case - Moving Load 2 - Lanes Loaded
Case AssignNum Lane
hl93 1 LANE1
P15 1 LANE1
Table: Case - Moving Load 3 - MultiLane Factors
Table: Case - Moving Load 3 - MultiLane Factors
Case NumberLanes
ScaleFactor
hl93 1 1.
P15 1 1.
Table: Connectivity - Frame
Table: Connectivity - Frame
Frame JointI JointJ Length
ft
2 1 3 11.32
3 3 4 11.32
4 4 5 11.32
5 5 6 11.32
6 6 7 11.32
7 7 8 11.32
8 8 9 11.32
9 9 10 11.32
10 10 11 11.32
11 11 2 11.32
Table: Coordinate Systems
Table: Coordinate Systems
Name Type X Y Z AboutZ AboutY AboutX
ft ft ft Degrees Degrees Degrees
GLOBAL Cartesian 0. 0. 0. 0. 0. 0.
hl93 - Girder A.bdb CSiBridge v20.2.1 - License #2010*1J2ULGRNHP9JJDE 10 June 2020
HDR, Inc Page 3 of 24
Table: Element Forces - Frames, Part 1 of 2
Table: Element Forces - Frames, Part 1 of 2
Frame Station OutputCase StepType StepLabel P V2 V3
ft Kip Kip Kip
2 0. hl93 Max 0. 0. 0.
2 1.8853 hl93 Max 0. 0.739 0.
2 3.7706 hl93 Max 0. 1.478 0.
2 5.6558 hl93 Max 0. 2.217 0.
2 5.6558 hl93 Max 0. 2.217 0.
2 7.5411 hl93 Max 0. 3.016 0.
2 9.4264 hl93 Max 0. 3.815 0.
2 11.3117 hl93 Max 0. 4.615 0.
2 11.3117 hl93 Max 0. 4.615 0.
2 11.32 hl93 Max 0. 4.796 0.
2 0. hl93 Min 0. -124.089 0.
2 1.8853 hl93 Min 0. -121.317 0.
2 3.7706 hl93 Min 0. -118.546 0.
2 5.6558 hl93 Min 0. -115.775 0.
2 5.6558 hl93 Min 0. -115.775 0.
2 7.5411 hl93 Min 0. -113.064 0.
2 9.4264 hl93 Min 0. -110.353 0.
2 11.3117 hl93 Min 0. -107.642 0.
2 11.3117 hl93 Min 0. -107.642 0.
2 11.32 hl93 Min 0. -101.224 0.
2 0. P15 Max 0. 0. 0.
2 1.8853 P15 Max 0. 1.124 0.
2 3.7706 P15 Max 0. 2.248 0.
2 5.6558 P15 Max 0. 3.373 0.
2 5.6558 P15 Max 0. 3.373 0.
2 7.5411 P15 Max 0. 4.497 0.
2 9.4264 P15 Max 0. 5.621 0.
2 11.3117 P15 Max 0. 6.745 0.
2 11.3117 P15 Max 0. 6.745 0.
2 11.32 P15 Max 0. 6.745 0.
2 0. P15 Min 0. -247.102 0.
2 1.8853 P15 Min 0. -239.324 0.
2 3.7706 P15 Min 0. -231.545 0.
2 5.6558 P15 Min 0. -223.767 0.
2 5.6558 P15 Min 0. -223.767 0.
2 7.5411 P15 Min 0. -217.022 0.
2 9.4264 P15 Min 0. -210.277 0.
2 11.3117 P15 Min 0. -203.532 0.
2 11.3117 P15 Min 0. -203.532 0.
2 11.32 P15 Min 0. -183.282 0.
3 0. hl93 Max 0. 4.796 0.
3 1.8839 hl93 Max 0. 5.968 0.
3 3.7678 hl93 Max 0. 7.14 0.
3 5.6517 hl93 Max 0. 8.312 0.
3 5.6517 hl93 Max 0. 8.312 0.
3 7.5383 hl93 Max 0. 9.942 0.
3 9.425 hl93 Max 0. 11.572 0.
3 11.3117 hl93 Max 0. 13.202 0.
3 11.3117 hl93 Max 0. 13.202 0.
3 11.32 hl93 Max 0. 13.564 0.
3 0. hl93 Min 0. -101.224 0.
3 1.8839 hl93 Min 0. -100.71 0.
3 3.7678 hl93 Min 0. -100.197 0.
hl93 - Girder A.bdb CSiBridge v20.2.1 - License #2010*1J2ULGRNHP9JJDE 10 June 2020
HDR, Inc Page 4 of 24
Table: Element Forces - Frames, Part 1 of 2
Frame Station OutputCase StepType StepLabel P V2 V3
ft Kip Kip Kip
3 5.6517 hl93 Min 0. -99.684 0.
3 5.6517 hl93 Min 0. -99.684 0.
3 7.5383 hl93 Min 0. -97.092 0.
3 9.425 hl93 Min 0. -94.5 0.
3 11.3117 hl93 Min 0. -91.907 0.
3 11.3117 hl93 Min 0. -91.907 0.
3 11.32 hl93 Min 0. -85.67 0.
3 0. P15 Max 0. 6.745 0.
3 1.8839 P15 Max 0. 7.87 0.
3 3.7678 P15 Max 0. 8.995 0.
3 5.6517 P15 Max 0. 10.12 0.
3 5.6517 P15 Max 0. 10.12 0.
3 7.5383 P15 Max 0. 12.166 0.
3 9.425 P15 Max 0. 14.211 0.
3 11.3117 P15 Max 0. 16.257 0.
3 11.3117 P15 Max 0. 16.257 0.
3 11.32 P15 Max 0. 16.257 0.
3 0. P15 Min 0. -183.282 0.
3 1.8839 P15 Min 0. -183.282 0.
3 3.7678 P15 Min 0. -183.282 0.
3 5.6517 P15 Min 0. -183.282 0.
3 5.6517 P15 Min 0. -183.282 0.
3 7.5383 P15 Min 0. -176.532 0.
3 9.425 P15 Min 0. -169.782 0.
3 11.3117 P15 Min 0. -163.032 0.
3 11.3117 P15 Min 0. -163.032 0.
3 11.32 P15 Min 0. -145.818 0.
4 0. hl93 Max 0. 13.564 0.
4 1.8839 hl93 Max 0. 15.143 0.
4 3.7678 hl93 Max 0. 16.722 0.
4 5.6517 hl93 Max 0. 18.3 0.
4 5.6517 hl93 Max 0. 18.3 0.
4 7.5383 hl93 Max 0. 20.228 0.
4 9.425 hl93 Max 0. 22.156 0.
4 11.3117 hl93 Max 0. 24.084 0.
4 11.3117 hl93 Max 0. 24.084 0.
4 11.32 hl93 Max 0. 24.627 0.
4 0. hl93 Min 0. -85.67 0.
4 1.8839 hl93 Min 0. -85.217 0.
4 3.7678 hl93 Min 0. -84.764 0.
4 5.6517 hl93 Min 0. -84.312 0.
4 5.6517 hl93 Min 0. -84.312 0.
4 7.5383 hl93 Min 0. -81.84 0.
4 9.425 hl93 Min 0. -79.369 0.
4 11.3117 hl93 Min 0. -76.897 0.
4 11.3117 hl93 Min 0. -76.897 0.
4 11.32 hl93 Min 0. -70.841 0.
4 0. P15 Max 0. 16.257 0.
4 1.8839 P15 Max 0. 18.507 0.
4 3.7678 P15 Max 0. 20.757 0.
4 5.6517 P15 Max 0. 23.007 0.
4 5.6517 P15 Max 0. 23.007 0.
4 7.5383 P15 Max 0. 25.257 0.
4 9.425 P15 Max 0. 27.507 0.
hl93 - Girder A.bdb CSiBridge v20.2.1 - License #2010*1J2ULGRNHP9JJDE 10 June 2020
HDR, Inc Page 5 of 24
Table: Element Forces - Frames, Part 1 of 2
Frame Station OutputCase StepType StepLabel P V2 V3
ft Kip Kip Kip
4 11.3117 P15 Max 0. 29.757 0.
4 11.3117 P15 Max 0. 29.757 0.
4 11.32 P15 Max 0. 29.757 0.
4 0. P15 Min 0. -145.818 0.
4 1.8839 P15 Min 0. -145.818 0.
4 3.7678 P15 Min 0. -145.818 0.
4 5.6517 P15 Min 0. -145.818 0.
4 5.6517 P15 Min 0. -145.818 0.
4 7.5383 P15 Min 0. -140.193 0.
4 9.425 P15 Min 0. -134.568 0.
4 11.3117 P15 Min 0. -128.943 0.
4 11.3117 P15 Min 0. -128.943 0.
4 11.32 P15 Min 0. -112.068 0.
5 0. hl93 Max 0. 24.627 0.
5 1.8839 hl93 Max 0. 26.435 0.
5 3.7678 hl93 Max 0. 28.242 0.
5 5.6517 hl93 Max 0. 30.049 0.
5 5.6517 hl93 Max 0. 30.049 0.
5 7.5383 hl93 Max 0. 32.098 0.
5 9.425 hl93 Max 0. 34.147 0.
5 11.3117 hl93 Max 0. 36.195 0.
5 11.3117 hl93 Max 0. 36.195 0.
5 11.32 hl93 Max 0. 36.92 0.
5 0. hl93 Min 0. -70.841 0.
5 1.8839 hl93 Min 0. -70.449 0.
5 3.7678 hl93 Min 0. -70.056 0.
5 5.6517 hl93 Min 0. -69.664 0.
5 5.6517 hl93 Min 0. -69.664 0.
5 7.5383 hl93 Min 0. -67.313 0.
5 9.425 hl93 Min 0. -64.962 0.
5 11.3117 hl93 Min 0. -62.611 0.
5 11.3117 hl93 Min 0. -62.611 0.
5 11.32 hl93 Min 0. -56.737 0.
5 0. P15 Max 0. 29.757 0.
5 1.8839 P15 Max 0. 32.725 0.
5 3.7678 P15 Max 0. 35.693 0.
5 5.6517 P15 Max 0. 38.66 0.
5 5.6517 P15 Max 0. 38.66 0.
5 7.5383 P15 Max 0. 42.035 0.
5 9.425 P15 Max 0. 45.41 0.
5 11.3117 P15 Max 0. 48.785 0.
5 11.3117 P15 Max 0. 48.785 0.
5 11.32 P15 Max 0. 48.785 0.
5 0. P15 Min 0. -112.068 0.
5 1.8839 P15 Min 0. -112.068 0.
5 3.7678 P15 Min 0. -112.068 0.
5 5.6517 P15 Min 0. -112.068 0.
5 5.6517 P15 Min 0. -112.068 0.
5 7.5383 P15 Min 0. -107.252 0.
5 9.425 P15 Min 0. -102.436 0.
5 11.3117 P15 Min 0. -97.621 0.
5 11.3117 P15 Min 0. -97.621 0.
5 11.32 P15 Min 0. -84.121 0.
6 0. hl93 Max 0. 36.92 0.
hl93 - Girder A.bdb CSiBridge v20.2.1 - License #2010*1J2ULGRNHP9JJDE 10 June 2020
HDR, Inc Page 6 of 24
Table: Element Forces - Frames, Part 1 of 2
Frame Station OutputCase StepType StepLabel P V2 V3
ft Kip Kip Kip
6 1.8839 hl93 Max 0. 38.787 0.
6 3.7678 hl93 Max 0. 40.655 0.
6 5.6517 hl93 Max 0. 42.523 0.
6 5.6517 hl93 Max 0. 42.523 0.
6 7.5383 hl93 Max 0. 44.692 0.
6 9.425 hl93 Max 0. 46.861 0.
6 11.3117 hl93 Max 0. 49.031 0.
6 11.3117 hl93 Max 0. 49.031 0.
6 11.32 hl93 Max 0. 49.936 0.
6 0. hl93 Min 0. -56.737 0.
6 1.8839 hl93 Min 0. -56.405 0.
6 3.7678 hl93 Min 0. -56.072 0.
6 5.6517 hl93 Min 0. -55.74 0.
6 5.6517 hl93 Min 0. -55.74 0.
6 7.5383 hl93 Min 0. -53.51 0.
6 9.425 hl93 Min 0. -51.28 0.
6 11.3117 hl93 Min 0. -49.05 0.
6 11.3117 hl93 Min 0. -49.05 0.
6 11.32 hl93 Min 0. -43.357 0.
6 0. P15 Max 0. 48.785 0.
6 1.8839 P15 Max 0. 52.16 0.
6 3.7678 P15 Max 0. 55.535 0.
6 5.6517 P15 Max 0. 58.91 0.
6 5.6517 P15 Max 0. 58.91 0.
6 7.5383 P15 Max 0. 62.801 0.
6 9.425 P15 Max 0. 66.691 0.
6 11.3117 P15 Max 0. 70.581 0.
6 11.3117 P15 Max 0. 70.581 0.
6 11.32 P15 Max 0. 70.581 0.
6 0. P15 Min 0. -84.121 0.
6 1.8839 P15 Min 0. -84.121 0.
6 3.7678 P15 Min 0. -84.121 0.
6 5.6517 P15 Min 0. -84.121 0.
6 5.6517 P15 Min 0. -84.121 0.
6 7.5383 P15 Min 0. -79.621 0.
6 9.425 P15 Min 0. -75.121 0.
6 11.3117 P15 Min 0. -70.621 0.
6 11.3117 P15 Min 0. -70.621 0.
6 11.32 P15 Min 0. -58.94 0.
7 0. hl93 Max 0. 49.936 0.
7 1.8839 hl93 Max 0. 51.864 0.
7 3.7678 hl93 Max 0. 53.792 0.
7 5.6517 hl93 Max 0. 55.72 0.
7 5.6517 hl93 Max 0. 55.72 0.
7 7.5383 hl93 Max 0. 58.011 0.
7 9.425 hl93 Max 0. 60.301 0.
7 11.3117 hl93 Max 0. 62.591 0.
7 11.3117 hl93 Max 0. 62.591 0.
7 11.32 hl93 Max 0. 63.678 0.
7 0. hl93 Min 0. -43.357 0.
7 1.8839 hl93 Min 0. -43.085 0.
7 3.7678 hl93 Min 0. -42.813 0.
7 5.6517 hl93 Min 0. -42.541 0.
7 5.6517 hl93 Min 0. -42.541 0.
hl93 - Girder A.bdb CSiBridge v20.2.1 - License #2010*1J2ULGRNHP9JJDE 10 June 2020
HDR, Inc Page 7 of 24
Table: Element Forces - Frames, Part 1 of 2
Frame Station OutputCase StepType StepLabel P V2 V3
ft Kip Kip Kip
7 7.5383 hl93 Min 0. -40.432 0.
7 9.425 hl93 Min 0. -38.323 0.
7 11.3117 hl93 Min 0. -36.214 0.
7 11.3117 hl93 Min 0. -36.214 0.
7 11.32 hl93 Min 0. -30.701 0.
7 0. P15 Max 0. 70.581 0.
7 1.8839 P15 Max 0. 75.081 0.
7 3.7678 P15 Max 0. 79.581 0.
7 5.6517 P15 Max 0. 84.081 0.
7 5.6517 P15 Max 0. 84.081 0.
7 7.5383 P15 Max 0. 88.581 0.
7 9.425 P15 Max 0. 93.081 0.
7 11.3117 P15 Max 0. 97.581 0.
7 11.3117 P15 Max 0. 97.581 0.
7 11.32 P15 Max 0. 97.581 0.
7 0. P15 Min 0. -58.94 0.
7 1.8839 P15 Min 0. -58.94 0.
7 3.7678 P15 Min 0. -58.94 0.
7 5.6517 P15 Min 0. -58.94 0.
7 5.6517 P15 Min 0. -58.94 0.
7 7.5383 P15 Min 0. -55.565 0.
7 9.425 P15 Min 0. -52.19 0.
7 11.3117 P15 Min 0. -48.815 0.
7 11.3117 P15 Min 0. -48.815 0.
7 11.32 P15 Min 0. -38.69 0.
8 0. hl93 Max 0. 63.678 0.
8 1.8839 hl93 Max 0. 65.666 0.
8 3.7678 hl93 Max 0. 67.654 0.
8 5.6517 hl93 Max 0. 69.643 0.
8 5.6517 hl93 Max 0. 69.643 0.
8 7.5383 hl93 Max 0. 72.054 0.
8 9.425 hl93 Max 0. 74.465 0.
8 11.3117 hl93 Max 0. 76.876 0.
8 11.3117 hl93 Max 0. 76.876 0.
8 11.32 hl93 Max 0. 78.143 0.
8 0. hl93 Min 0. -30.701 0.
8 1.8839 hl93 Min 0. -30.49 0.
8 3.7678 hl93 Min 0. -30.278 0.
8 5.6517 hl93 Min 0. -30.067 0.
8 5.6517 hl93 Min 0. -30.067 0.
8 7.5383 hl93 Min 0. -28.078 0.
8 9.425 hl93 Min 0. -26.09 0.
8 11.3117 hl93 Min 0. -24.101 0.
8 11.3117 hl93 Min 0. -24.101 0.
8 11.32 hl93 Min 0. -18.77 0.
8 0. P15 Max 0. 97.581 0.
8 1.8839 P15 Max 0. 102.393 0.
8 3.7678 P15 Max 0. 107.206 0.
8 5.6517 P15 Max 0. 112.018 0.
8 5.6517 P15 Max 0. 112.018 0.
8 7.5383 P15 Max 0. 117.643 0.
8 9.425 P15 Max 0. 123.268 0.
8 11.3117 P15 Max 0. 128.893 0.
8 11.3117 P15 Max 0. 128.893 0.
hl93 - Girder A.bdb CSiBridge v20.2.1 - License #2010*1J2ULGRNHP9JJDE 10 June 2020
HDR, Inc Page 8 of 24
Table: Element Forces - Frames, Part 1 of 2
Frame Station OutputCase StepType StepLabel P V2 V3
ft Kip Kip Kip
8 11.32 P15 Max 0. 128.893 0.
8 0. P15 Min 0. -38.69 0.
8 1.8839 P15 Min 0. -38.69 0.
8 3.7678 P15 Min 0. -38.69 0.
8 5.6517 P15 Min 0. -38.69 0.
8 5.6517 P15 Min 0. -38.69 0.
8 7.5383 P15 Min 0. -35.719 0.
8 9.425 P15 Min 0. -32.748 0.
8 11.3117 P15 Min 0. -29.777 0.
8 11.3117 P15 Min 0. -29.777 0.
8 11.32 P15 Min 0. -23.027 0.
9 0. hl93 Max 0. 78.143 0.
9 1.8839 hl93 Max 0. 80.192 0.
9 3.7678 hl93 Max 0. 82.241 0.
9 5.6517 hl93 Max 0. 84.29 0.
9 5.6517 hl93 Max 0. 84.29 0.
9 7.5383 hl93 Max 0. 86.821 0.
9 9.425 hl93 Max 0. 89.353 0.
9 11.3117 hl93 Max 0. 91.885 0.
9 11.3117 hl93 Max 0. 91.885 0.
9 11.32 hl93 Max 0. 93.333 0.
9 0. hl93 Min 0. -18.77 0.
9 1.8839 hl93 Min 0. -18.619 0.
9 3.7678 hl93 Min 0. -18.468 0.
9 5.6517 hl93 Min 0. -18.317 0.
9 5.6517 hl93 Min 0. -18.317 0.
9 7.5383 hl93 Min 0. -16.617 0.
9 9.425 hl93 Min 0. -14.917 0.
9 11.3117 hl93 Min 0. -13.217 0.
9 11.3117 hl93 Min 0. -13.217 0.
9 11.32 hl93 Min 0. -8.598 0.
9 0. P15 Max 0. 128.893 0.
9 1.8839 P15 Max 0. 134.518 0.
9 3.7678 P15 Max 0. 140.143 0.
9 5.6517 P15 Max 0. 145.768 0.
9 5.6517 P15 Max 0. 145.768 0.
9 7.5383 P15 Max 0. 151.503 0.
9 9.425 P15 Max 0. 157.237 0.
9 11.3117 P15 Max 0. 162.972 0.
9 11.3117 P15 Max 0. 162.972 0.
9 11.32 P15 Max 0. 162.972 0.
9 0. P15 Min 0. -23.027 0.
9 1.8839 P15 Min 0. -23.027 0.
9 3.7678 P15 Min 0. -23.027 0.
9 5.6517 P15 Min 0. -23.027 0.
9 5.6517 P15 Min 0. -23.027 0.
9 7.5383 P15 Min 0. -20.777 0.
9 9.425 P15 Min 0. -18.527 0.
9 11.3117 P15 Min 0. -16.277 0.
9 11.3117 P15 Min 0. -16.277 0.
9 11.32 P15 Min 0. -10.13 0.
10 0. hl93 Max 0. 93.333 0.
10 1.8839 hl93 Max 0. 95.443 0.
10 3.7678 hl93 Max 0. 97.552 0.
hl93 - Girder A.bdb CSiBridge v20.2.1 - License #2010*1J2ULGRNHP9JJDE 10 June 2020
HDR, Inc Page 9 of 24
Table: Element Forces - Frames, Part 1 of 2
Frame Station OutputCase StepType StepLabel P V2 V3
ft Kip Kip Kip
10 5.6517 hl93 Max 0. 99.661 0.
10 5.6517 hl93 Max 0. 99.661 0.
10 7.5383 hl93 Max 0. 102.313 0.
10 9.425 hl93 Max 0. 104.966 0.
10 11.3117 hl93 Max 0. 107.618 0.
10 11.3117 hl93 Max 0. 107.618 0.
10 11.32 hl93 Max 0. 109.249 0.
10 0. hl93 Min 0. -8.598 0.
10 1.8839 hl93 Min 0. -8.508 0.
10 3.7678 hl93 Min 0. -8.417 0.
10 5.6517 hl93 Min 0. -8.327 0.
10 5.6517 hl93 Min 0. -8.327 0.
10 7.5383 hl93 Min 0. -7.092 0.
10 9.425 hl93 Min 0. -5.857 0.
10 11.3117 hl93 Min 0. -4.622 0.
10 11.3117 hl93 Min 0. -4.622 0.
10 11.32 hl93 Min 0. -2.311 0.
10 0. P15 Max 0. 162.972 0.
10 1.8839 P15 Max 0. 169.722 0.
10 3.7678 P15 Max 0. 176.472 0.
10 5.6517 P15 Max 0. 183.222 0.
10 5.6517 P15 Max 0. 183.222 0.
10 7.5383 P15 Max 0. 189.972 0.
10 9.425 P15 Max 0. 196.722 0.
10 11.3117 P15 Max 0. 203.472 0.
10 11.3117 P15 Max 0. 203.472 0.
10 11.32 P15 Max 0. 203.472 0.
10 0. P15 Min 0. -10.13 0.
10 1.8839 P15 Min 0. -10.13 0.
10 3.7678 P15 Min 0. -10.13 0.
10 5.6517 P15 Min 0. -10.13 0.
10 5.6517 P15 Min 0. -10.13 0.
10 7.5383 P15 Min 0. -9.005 0.
10 9.425 P15 Min 0. -7.88 0.
10 11.3117 P15 Min 0. -6.755 0.
10 11.3117 P15 Min 0. -6.755 0.
10 11.32 P15 Min 0. -3.377 0.
11 0. hl93 Max 0. 109.249 0.
11 1.8853 hl93 Max 0. 111.42 0.
11 3.7706 hl93 Max 0. 113.592 0.
11 5.6558 hl93 Max 0. 115.763 0.
11 5.6558 hl93 Max 0. 115.763 0.
11 7.5439 hl93 Max 0. 118.538 0.
11 9.4319 hl93 Max 0. 121.313 0.
11 11.32 hl93 Max 0. 124.089 0.
11 0. hl93 Min 0. -2.311 0.
11 1.8853 hl93 Min 0. -2.281 0.
11 3.7706 hl93 Min 0. -2.25 0.
11 5.6558 hl93 Min 0. -2.22 0.
11 5.6558 hl93 Min 0. -2.22 0.
11 7.5439 hl93 Min 0. -1.48 0.
11 9.4319 hl93 Min 0. -0.74 0.
11 11.32 hl93 Min 0. 0. 0.
11 0. P15 Max 0. 203.472 0.
hl93 - Girder A.bdb CSiBridge v20.2.1 - License #2010*1J2ULGRNHP9JJDE 10 June 2020
HDR, Inc Page 10 of 24
Table: Element Forces - Frames, Part 1 of 2
Frame Station OutputCase StepType StepLabel P V2 V3
ft Kip Kip Kip
11 1.8853 P15 Max 0. 210.227 0.
11 3.7706 P15 Max 0. 216.982 0.
11 5.6558 P15 Max 0. 223.737 0.
11 5.6558 P15 Max 0. 223.737 0.
11 7.5439 P15 Max 0. 231.525 0.
11 9.4319 P15 Max 0. 239.314 0.
11 11.32 P15 Max 0. 247.102 0.
11 0. P15 Min 0. -3.377 0.
11 1.8853 P15 Min 0. -3.377 0.
11 3.7706 P15 Min 0. -3.377 0.
11 5.6558 P15 Min 0. -3.377 0.
11 5.6558 P15 Min 0. -3.377 0.
11 7.5439 P15 Min 0. -2.252 0.
11 9.4319 P15 Min 0. -1.126 0.
11 11.32 P15 Min 0. 0. 0.
Table: Element Forces - Frames, Part 2 of 2
Table: Element Forces - Frames, Part 2 of 2
Frame Station OutputCase StepType StepLabel T M2 M3
ft Kip-ft Kip-ft Kip-ft
2 0. hl93 Max 240.9359 0. 0.
2 1.8853 hl93 Max 235.6829 0. 221.5093
2 3.7706 hl93 Max 230.4298 0. 443.0186
2 5.6558 hl93 Max 225.1768 0. 664.5279
2 5.6558 hl93 Max 225.1768 0. 664.5279
2 7.5411 hl93 Max 220.1408 0. 861.1729
2 9.4264 hl93 Max 215.1047 0. 1057.8178
2 11.3117 hl93 Max 210.0687 0. 1254.4628
2 11.3117 hl93 Max 210.0687 0. 1254.4628
2 11.32 hl93 Max 197.8839 0. 1254.9871
2 0. hl93 Min -240.9359 0. 0.
2 1.8853 hl93 Min -235.6829 0. 0.
2 3.7706 hl93 Min -230.4298 0. 0.
2 5.6558 hl93 Min -225.1768 0. 0.
2 5.6558 hl93 Min -225.1768 0. 0.
2 7.5411 hl93 Min -220.1408 0. 0.
2 9.4264 hl93 Min -215.1047 0. 0.
2 11.3117 hl93 Min -210.0687 0. 0.
2 11.3117 hl93 Min -210.0687 0. 0.
2 11.32 hl93 Min -197.8839 0. 0.
2 0. P15 Max 494.2148 0. 0.
2 1.8853 P15 Max 478.6573 0. 421.8623
2 3.7706 P15 Max 463.0998 0. 843.7247
2 5.6558 P15 Max 447.5423 0. 1265.587
2 5.6558 P15 Max 447.5423 0. 1265.587
2 7.5411 P15 Max 434.052 0. 1611.1518
2 9.4264 P15 Max 420.5616 0. 1956.7166
2 11.3117 P15 Max 407.0713 0. 2302.2814
2 11.3117 P15 Max 407.0713 0. 2302.2814
2 11.32 P15 Max 366.5705 0. 2303.415
2 0. P15 Min -494.2148 0. 0.
2 1.8853 P15 Min -478.6573 0. 0.
hl93 - Girder A.bdb CSiBridge v20.2.1 - License #2010*1J2ULGRNHP9JJDE 10 June 2020
HDR, Inc Page 11 of 24
Table: Element Forces - Frames, Part 2 of 2
Frame Station OutputCase StepType StepLabel T M2 M3
ft Kip-ft Kip-ft Kip-ft
2 3.7706 P15 Min -463.0998 0. 0.
2 5.6558 P15 Min -447.5423 0. 0.
2 5.6558 P15 Min -447.5423 0. 0.
2 7.5411 P15 Min -434.052 0. 0.
2 9.4264 P15 Min -420.5616 0. 0.
2 11.3117 P15 Min -407.0713 0. 0.
2 11.3117 P15 Min -407.0713 0. 0.
2 11.32 P15 Min -366.5705 0. 0.
3 0. hl93 Max 197.8839 0. 1254.9871
3 1.8839 hl93 Max 197.1231 0. 1426.7103
3 3.7678 hl93 Max 196.3622 0. 1598.4336
3 5.6517 hl93 Max 195.6013 0. 1770.1569
3 5.6517 hl93 Max 195.6013 0. 1770.1569
3 7.5383 hl93 Max 190.9962 0. 1917.1539
3 9.425 hl93 Max 186.3911 0. 2064.151
3 11.3117 hl93 Max 181.786 0. 2211.148
3 11.3117 hl93 Max 181.786 0. 2211.148
3 11.32 hl93 Max 170.2532 0. 2211.5321
3 0. hl93 Min -197.8839 0. 0.
3 1.8839 hl93 Min -197.1231 0. 0.
3 3.7678 hl93 Min -196.3622 0. 0.
3 5.6517 hl93 Min -195.6013 0. 0.
3 5.6517 hl93 Min -195.6013 0. 0.
3 7.5383 hl93 Min -190.9962 0. 0.
3 9.425 hl93 Min -186.3911 0. 0.
3 11.3117 hl93 Min -181.786 0. 0.
3 11.3117 hl93 Min -181.786 0. 0.
3 11.32 hl93 Min -170.2532 0. 0.
3 0. P15 Max 366.5705 0. 2303.415
3 1.8839 P15 Max 366.5705 0. 2572.4746
3 3.7678 P15 Max 366.5705 0. 2841.5343
3 5.6517 P15 Max 366.5705 0. 3110.5939
3 5.6517 P15 Max 366.5705 0. 3110.5939
3 7.5383 P15 Max 354.9115 0. 3386.9991
3 9.425 P15 Max 343.2524 0. 3663.4042
3 11.3117 P15 Max 331.5934 0. 3939.8094
3 11.3117 P15 Max 331.5934 0. 3939.8094
3 11.32 P15 Max 303.9151 0. 3940.5825
3 0. P15 Min -366.5705 0. 0.
3 1.8839 P15 Min -366.5705 0. 0.
3 3.7678 P15 Min -366.5705 0. 0.
3 5.6517 P15 Min -366.5705 0. 0.
3 5.6517 P15 Min -366.5705 0. 0.
3 7.5383 P15 Min -354.9115 0. 0.
3 9.425 P15 Min -343.2524 0. 0.
3 11.3117 P15 Min -331.5934 0. 0.
3 11.3117 P15 Min -331.5934 0. 0.
3 11.32 P15 Min -303.9151 0. 0.
4 0. hl93 Max 170.2532 0. 2211.5321
4 1.8839 hl93 Max 169.7097 0. 2333.5001
4 3.7678 hl93 Max 169.1662 0. 2455.4681
4 5.6517 hl93 Max 168.6226 0. 2577.4362
4 5.6517 hl93 Max 168.6226 0. 2577.4362
4 7.5383 hl93 Max 164.4522 0. 2674.6313
hl93 - Girder A.bdb CSiBridge v20.2.1 - License #2010*1J2ULGRNHP9JJDE 10 June 2020
HDR, Inc Page 12 of 24
Table: Element Forces - Frames, Part 2 of 2
Frame Station OutputCase StepType StepLabel T M2 M3
ft Kip-ft Kip-ft Kip-ft
4 9.425 hl93 Max 160.2818 0. 2771.8263
4 11.3117 hl93 Max 156.1113 0. 2869.0214
4 11.3117 hl93 Max 156.1113 0. 2869.0214
4 11.32 hl93 Max 145.2306 0. 2869.2653
4 0. hl93 Min -170.2532 0. 0.
4 1.8839 hl93 Min -169.7097 0. 0.
4 3.7678 hl93 Min -169.1662 0. 0.
4 5.6517 hl93 Min -168.6226 0. 0.
4 5.6517 hl93 Min -168.6226 0. 0.
4 7.5383 hl93 Min -164.4522 0. 0.
4 9.425 hl93 Min -160.2818 0. 0.
4 11.3117 hl93 Min -156.1113 0. 0.
4 11.3117 hl93 Min -156.1113 0. 0.
4 11.32 hl93 Min -145.2306 0. 0.
4 0. P15 Max 303.9151 0. 3940.5825
4 1.8839 P15 Max 303.9151 0. 4175.8857
4 3.7678 P15 Max 303.9151 0. 4411.189
4 5.6517 P15 Max 303.9151 0. 4646.4922
4 5.6517 P15 Max 303.9151 0. 4646.4922
4 7.5383 P15 Max 294.9149 0. 4808.1997
4 9.425 P15 Max 285.9147 0. 4969.9072
4 11.3117 P15 Max 276.9145 0. 5131.6147
4 11.3117 P15 Max 276.9145 0. 5131.6147
4 11.32 P15 Max 254.2213 0. 5132.0475
4 0. P15 Min -303.9151 0. 0.
4 1.8839 P15 Min -303.9151 0. 0.
4 3.7678 P15 Min -303.9151 0. 0.
4 5.6517 P15 Min -303.9151 0. 0.
4 5.6517 P15 Min -303.9151 0. 0.
4 7.5383 P15 Min -294.9149 0. 0.
4 9.425 P15 Min -285.9147 0. 0.
4 11.3117 P15 Min -276.9145 0. 0.
4 11.3117 P15 Min -276.9145 0. 0.
4 11.32 P15 Min -254.2213 0. 0.
5 0. hl93 Max 145.2306 0. 2869.2653
5 1.8839 hl93 Max 144.9044 0. 2943.9498
5 3.7678 hl93 Max 144.5783 0. 3018.6343
5 5.6517 hl93 Max 144.2521 0. 3093.3188
5 5.6517 hl93 Max 144.2521 0. 3093.3188
5 7.5383 hl93 Max 140.5163 0. 3148.1599
5 9.425 hl93 Max 136.7806 0. 3203.001
5 11.3117 hl93 Max 133.0449 0. 3257.8422
5 11.3117 hl93 Max 133.0449 0. 3257.8422
5 11.32 hl93 Max 123.3168 0. 3257.8901
5 0. hl93 Min -145.2306 0. 0.
5 1.8839 hl93 Min -144.9044 0. 0.
5 3.7678 hl93 Min -144.5783 0. 0.
5 5.6517 hl93 Min -144.2521 0. 0.
5 5.6517 hl93 Min -144.2521 0. 0.
5 7.5383 hl93 Min -140.5163 0. 0.
5 9.425 hl93 Min -136.7806 0. 0.
5 11.3117 hl93 Min -133.0449 0. 0.
5 11.3117 hl93 Min -133.0449 0. 0.
5 11.32 hl93 Min -123.3168 0. 0.
hl93 - Girder A.bdb CSiBridge v20.2.1 - License #2010*1J2ULGRNHP9JJDE 10 June 2020
HDR, Inc Page 13 of 24
Table: Element Forces - Frames, Part 2 of 2
Frame Station OutputCase StepType StepLabel T M2 M3
ft Kip-ft Kip-ft Kip-ft
5 0. P15 Max 254.2213 0. 5132.0475
5 1.8839 P15 Max 254.2213 0. 5270.0274
5 3.7678 P15 Max 254.2213 0. 5408.0072
5 5.6517 P15 Max 254.2213 0. 5545.9871
5 5.6517 P15 Max 254.2213 0. 5545.9871
5 7.5383 P15 Max 249.0898 0. 5663.8691
5 9.425 P15 Max 243.9583 0. 5781.7511
5 11.3117 P15 Max 238.8268 0. 5899.6331
5 11.3117 P15 Max 238.8268 0. 5899.6331
5 11.32 P15 Max 225.3265 0. 5899.7025
5 0. P15 Min -254.2213 0. 0.
5 1.8839 P15 Min -254.2213 0. 0.
5 3.7678 P15 Min -254.2213 0. 0.
5 5.6517 P15 Min -254.2213 0. 0.
5 5.6517 P15 Min -254.2213 0. 0.
5 7.5383 P15 Min -249.0898 0. 0.
5 9.425 P15 Min -243.9583 0. 0.
5 11.3117 P15 Min -238.8268 0. 0.
5 11.3117 P15 Min -238.8268 0. 0.
5 11.32 P15 Min -225.3265 0. 0.
6 0. hl93 Max 123.3168 0. 3257.8901
6 1.8839 hl93 Max 123.208 0. 3287.8143
6 3.7678 hl93 Max 123.0992 0. 3317.7384
6 5.6517 hl93 Max 122.9903 0. 3347.6626
6 5.6517 hl93 Max 122.9903 0. 3347.6626
6 7.5383 hl93 Max 120.3986 0. 3352.7017
6 9.425 hl93 Max 117.8069 0. 3357.7409
6 11.3117 hl93 Max 115.2152 0. 3362.78
6 11.3117 hl93 Max 115.2152 0. 3362.78
6 11.32 hl93 Max 115.2022 0. 3362.6878
6 0. hl93 Min -123.3168 0. 0.
6 1.8839 hl93 Min -123.208 0. 0.
6 3.7678 hl93 Min -123.0992 0. 0.
6 5.6517 hl93 Min -122.9903 0. 0.
6 5.6517 hl93 Min -122.9903 0. 0.
6 7.5383 hl93 Min -120.3986 0. 0.
6 9.425 hl93 Min -117.8069 0. 0.
6 11.3117 hl93 Min -115.2152 0. 0.
6 11.3117 hl93 Min -115.2152 0. 0.
6 11.32 hl93 Min -115.2022 0. 0.
6 0. P15 Max 225.3265 0. 5899.7025
6 1.8839 P15 Max 225.3265 0. 5953.6569
6 3.7678 P15 Max 225.3265 0. 6007.6112
6 5.6517 P15 Max 225.3265 0. 6061.5656
6 5.6517 P15 Max 225.3265 0. 6061.5656
6 7.5383 P15 Max 221.8567 0. 6068.2936
6 9.425 P15 Max 218.3869 0. 6075.0217
6 11.3117 P15 Max 214.9171 0. 6081.7497
6 11.3117 P15 Max 214.9171 0. 6081.7497
6 11.32 P15 Max 214.8972 0. 6081.4687
6 0. P15 Min -225.3265 0. 0.
6 1.8839 P15 Min -225.3265 0. 0.
6 3.7678 P15 Min -225.3265 0. 0.
6 5.6517 P15 Min -225.3265 0. 0.
hl93 - Girder A.bdb CSiBridge v20.2.1 - License #2010*1J2ULGRNHP9JJDE 10 June 2020
HDR, Inc Page 14 of 24
Table: Element Forces - Frames, Part 2 of 2
Frame Station OutputCase StepType StepLabel T M2 M3
ft Kip-ft Kip-ft Kip-ft
6 5.6517 P15 Min -225.3265 0. 0.
6 7.5383 P15 Min -221.8567 0. 0.
6 9.425 P15 Min -218.3869 0. 0.
6 11.3117 P15 Min -214.9171 0. 0.
6 11.3117 P15 Min -214.9171 0. 0.
6 11.32 P15 Min -214.8972 0. 0.
7 0. hl93 Max 115.2022 0. 3362.6878
7 1.8839 hl93 Max 117.7903 0. 3357.7308
7 3.7678 hl93 Max 120.3784 0. 3352.7738
7 5.6517 hl93 Max 122.9665 0. 3347.8167
7 5.6517 hl93 Max 122.9665 0. 3347.8167
7 7.5383 hl93 Max 126.3153 0. 3317.9499
7 9.425 hl93 Max 129.664 0. 3288.0831
7 11.3117 hl93 Max 133.0128 0. 3258.2163
7 11.3117 hl93 Max 133.0128 0. 3258.2163
7 11.32 hl93 Max 133.6644 0. 3257.7837
7 0. hl93 Min -115.2022 0. 0.
7 1.8839 hl93 Min -117.7903 0. 0.
7 3.7678 hl93 Min -120.3784 0. 0.
7 5.6517 hl93 Min -122.9665 0. 0.
7 5.6517 hl93 Min -122.9665 0. 0.
7 7.5383 hl93 Min -126.3153 0. 0.
7 9.425 hl93 Min -129.664 0. 0.
7 11.3117 hl93 Min -133.0128 0. 0.
7 11.3117 hl93 Min -133.0128 0. 0.
7 11.32 hl93 Min -133.6644 0. 0.
7 0. P15 Max 214.8972 0. 6081.4687
7 1.8839 P15 Max 218.3604 0. 6074.8805
7 3.7678 P15 Max 221.8236 0. 6068.2922
7 5.6517 P15 Max 225.2867 0. 6061.7039
7 5.6517 P15 Max 225.2867 0. 6061.7039
7 7.5383 P15 Max 229.7868 0. 6007.9514
7 9.425 P15 Max 234.2869 0. 5954.1989
7 11.3117 P15 Max 238.787 0. 5900.4464
7 11.3117 P15 Max 238.787 0. 5900.4464
7 11.32 P15 Max 238.787 0. 5899.815
7 0. P15 Min -214.8972 0. 0.
7 1.8839 P15 Min -218.3604 0. 0.
7 3.7678 P15 Min -221.8236 0. 0.
7 5.6517 P15 Min -225.2867 0. 0.
7 5.6517 P15 Min -225.2867 0. 0.
7 7.5383 P15 Min -229.7868 0. 0.
7 9.425 P15 Min -234.2869 0. 0.
7 11.3117 P15 Min -238.787 0. 0.
7 11.3117 P15 Min -238.787 0. 0.
7 11.32 P15 Min -238.787 0. 0.
8 0. hl93 Max 133.6644 0. 3257.7837
8 1.8839 hl93 Max 137.1823 0. 3203.1601
8 3.7678 hl93 Max 140.7002 0. 3148.5365
8 5.6517 hl93 Max 144.2181 0. 3093.9129
8 5.6517 hl93 Max 144.2181 0. 3093.9129
8 7.5383 hl93 Max 148.1706 0. 3019.1985
8 9.425 hl93 Max 152.123 0. 2944.4841
8 11.3117 hl93 Max 156.0755 0. 2869.7697
hl93 - Girder A.bdb CSiBridge v20.2.1 - License #2010*1J2ULGRNHP9JJDE 10 June 2020
HDR, Inc Page 15 of 24
Table: Element Forces - Frames, Part 2 of 2
Frame Station OutputCase StepType StepLabel T M2 M3
ft Kip-ft Kip-ft Kip-ft
8 11.3117 hl93 Max 156.0755 0. 2869.7697
8 11.32 hl93 Max 157.3791 0. 2869.1412
8 0. hl93 Min -133.6644 0. 0.
8 1.8839 hl93 Min -137.1823 0. 0.
8 3.7678 hl93 Min -140.7002 0. 0.
8 5.6517 hl93 Min -144.2181 0. 0.
8 5.6517 hl93 Min -144.2181 0. 0.
8 7.5383 hl93 Min -148.1706 0. 0.
8 9.425 hl93 Min -152.123 0. 0.
8 11.3117 hl93 Min -156.0755 0. 0.
8 11.3117 hl93 Min -156.0755 0. 0.
8 11.32 hl93 Min -157.3791 0. 0.
8 0. P15 Max 238.787 0. 5899.815
8 1.8839 P15 Max 243.9119 0. 5782.2425
8 3.7678 P15 Max 249.0368 0. 5664.6699
8 5.6517 P15 Max 254.1617 0. 5547.0974
8 5.6517 P15 Max 254.1617 0. 5547.0974
8 7.5383 P15 Max 261.7195 0. 5408.9665
8 9.425 P15 Max 269.2772 0. 5270.8356
8 11.3117 P15 Max 276.835 0. 5132.7048
8 11.3117 P15 Max 276.835 0. 5132.7048
8 11.32 P15 Max 276.835 0. 5131.71
8 0. P15 Min -238.787 0. 0.
8 1.8839 P15 Min -243.9119 0. 0.
8 3.7678 P15 Min -249.0368 0. 0.
8 5.6517 P15 Min -254.1617 0. 0.
8 5.6517 P15 Min -254.1617 0. 0.
8 7.5383 P15 Min -261.7195 0. 0.
8 9.425 P15 Min -269.2772 0. 0.
8 11.3117 P15 Min -276.835 0. 0.
8 11.3117 P15 Min -276.835 0. 0.
8 11.32 P15 Min -276.835 0. 0.
9 0. hl93 Max 157.3791 0. 2869.1412
9 1.8839 hl93 Max 161.1143 0. 2772.2289
9 3.7678 hl93 Max 164.8496 0. 2675.3167
9 5.6517 hl93 Max 168.5848 0. 2578.4045
9 5.6517 hl93 Max 168.5848 0. 2578.4045
9 7.5383 hl93 Max 172.972 0. 2456.3817
9 9.425 hl93 Max 177.3591 0. 2334.359
9 11.3117 hl93 Max 181.7463 0. 2212.3363
9 11.3117 hl93 Max 181.7463 0. 2212.3363
9 11.32 hl93 Max 183.7019 0. 2211.5675
9 0. hl93 Min -157.3791 0. 0.
9 1.8839 hl93 Min -161.1143 0. 0.
9 3.7678 hl93 Min -164.8496 0. 0.
9 5.6517 hl93 Min -168.5848 0. 0.
9 5.6517 hl93 Min -168.5848 0. 0.
9 7.5383 hl93 Min -172.972 0. 0.
9 9.425 hl93 Min -177.3591 0. 0.
9 11.3117 hl93 Min -181.7463 0. 0.
9 11.3117 hl93 Min -181.7463 0. 0.
9 11.32 hl93 Min -183.7019 0. 0.
9 0. P15 Max 276.835 0. 5131.71
9 1.8839 P15 Max 285.8352 0. 4970.5591
hl93 - Girder A.bdb CSiBridge v20.2.1 - License #2010*1J2ULGRNHP9JJDE 10 June 2020
HDR, Inc Page 16 of 24
Table: Element Forces - Frames, Part 2 of 2
Frame Station OutputCase StepType StepLabel T M2 M3
ft Kip-ft Kip-ft Kip-ft
9 3.7678 P15 Max 294.8354 0. 4809.4082
9 5.6517 P15 Max 303.8356 0. 4648.2573
9 5.6517 P15 Max 303.8356 0. 4648.2573
9 7.5383 P15 Max 313.0551 0. 4412.8482
9 9.425 P15 Max 322.2746 0. 4177.4391
9 11.3117 P15 Max 331.494 0. 3942.03
9 11.3117 P15 Max 331.494 0. 3942.03
9 11.32 P15 Max 331.494 0. 3940.695
9 0. P15 Min -276.835 0. 0.
9 1.8839 P15 Min -285.8352 0. 0.
9 3.7678 P15 Min -294.8354 0. 0.
9 5.6517 P15 Min -303.8356 0. 0.
9 5.6517 P15 Min -303.8356 0. 0.
9 7.5383 P15 Min -313.0551 0. 0.
9 9.425 P15 Min -322.2746 0. 0.
9 11.3117 P15 Min -331.494 0. 0.
9 11.3117 P15 Min -331.494 0. 0.
9 11.32 P15 Min -331.494 0. 0.
10 0. hl93 Max 183.7019 0. 2211.5675
10 1.8839 hl93 Max 187.6545 0. 2064.9001
10 3.7678 hl93 Max 191.6071 0. 1918.2326
10 5.6517 hl93 Max 195.5597 0. 1771.5651
10 5.6517 hl93 Max 195.5597 0. 1771.5651
10 7.5383 hl93 Max 200.3815 0. 1599.7404
10 9.425 hl93 Max 205.2033 0. 1427.9157
10 11.3117 hl93 Max 210.0252 0. 1256.091
10 11.3117 hl93 Max 210.0252 0. 1256.091
10 11.32 hl93 Max 212.6347 0. 1255.1821
10 0. hl93 Min -183.7019 0. 0.
10 1.8839 hl93 Min -187.6545 0. 0.
10 3.7678 hl93 Min -191.6071 0. 0.
10 5.6517 hl93 Min -195.5597 0. 0.
10 5.6517 hl93 Min -195.5597 0. 0.
10 7.5383 hl93 Min -200.3815 0. 0.
10 9.425 hl93 Min -205.2033 0. 0.
10 11.3117 hl93 Min -210.0252 0. 0.
10 11.3117 hl93 Min -210.0252 0. 0.
10 11.32 hl93 Min -212.6347 0. 0.
10 0. P15 Max 331.494 0. 3940.695
10 1.8839 P15 Max 343.1464 0. 3664.6752
10 3.7678 P15 Max 354.7988 0. 3388.6554
10 5.6517 P15 Max 366.4512 0. 3112.6356
10 5.6517 P15 Max 366.4512 0. 3112.6356
10 7.5383 P15 Max 379.9515 0. 2843.4231
10 9.425 P15 Max 393.4518 0. 2574.2106
10 11.3117 P15 Max 406.952 0. 2304.9981
10 11.3117 P15 Max 406.952 0. 2304.9981
10 11.32 P15 Max 406.952 0. 2303.3025
10 0. P15 Min -331.494 0. 0.
10 1.8839 P15 Min -343.1464 0. 0.
10 3.7678 P15 Min -354.7988 0. 0.
10 5.6517 P15 Min -366.4512 0. 0.
10 5.6517 P15 Min -366.4512 0. 0.
10 7.5383 P15 Min -379.9515 0. 0.
hl93 - Girder A.bdb CSiBridge v20.2.1 - License #2010*1J2ULGRNHP9JJDE 10 June 2020
HDR, Inc Page 17 of 24
Table: Element Forces - Frames, Part 2 of 2
Frame Station OutputCase StepType StepLabel T M2 M3
ft Kip-ft Kip-ft Kip-ft
10 9.425 P15 Min -393.4518 0. 0.
10 11.3117 P15 Min -406.952 0. 0.
10 11.3117 P15 Min -406.952 0. 0.
10 11.32 P15 Min -406.952 0. 0.
11 0. hl93 Max 212.6347 0. 1255.1821
11 1.8853 hl93 Max 216.8078 0. 1058.6054
11 3.7706 hl93 Max 220.9809 0. 862.0287
11 5.6558 hl93 Max 225.154 0. 665.452
11 5.6558 hl93 Max 225.154 0. 665.452
11 7.5439 hl93 Max 230.4147 0. 443.6347
11 9.4319 hl93 Max 235.6753 0. 221.8173
11 11.32 hl93 Max 240.9359 0. 0.
11 0. hl93 Min -212.6347 0. 0.
11 1.8853 hl93 Min -216.8078 0. 0.
11 3.7706 hl93 Min -220.9809 0. 0.
11 5.6558 hl93 Min -225.154 0. 0.
11 5.6558 hl93 Min -225.154 0. 0.
11 7.5439 hl93 Min -230.4147 0. 0.
11 9.4319 hl93 Min -235.6753 0. 0.
11 11.32 hl93 Min -240.9359 0. 0.
11 0. P15 Max 406.952 0. 2303.3025
11 1.8853 P15 Max 420.4623 0. 1957.9626
11 3.7706 P15 Max 433.9725 0. 1612.6227
11 5.6558 P15 Max 447.4827 0. 1267.2829
11 5.6558 P15 Max 447.4827 0. 1267.2829
11 7.5439 P15 Max 463.0601 0. 844.8552
11 9.4319 P15 Max 478.6374 0. 422.4276
11 11.32 P15 Max 494.2148 0. 0.
11 0. P15 Min -406.952 0. 0.
11 1.8853 P15 Min -420.4623 0. 0.
11 3.7706 P15 Min -433.9725 0. 0.
11 5.6558 P15 Min -447.4827 0. 0.
11 5.6558 P15 Min -447.4827 0. 0.
11 7.5439 P15 Min -463.0601 0. 0.
11 9.4319 P15 Min -478.6374 0. 0.
11 11.32 P15 Min -494.2148 0. 0.
Table: Frame Design Procedures
Table: Frame Design Procedures
Frame DesignProc
2 No Design
3 No Design
4 No Design
5 No Design
6 No Design
7 No Design
8 No Design
9 No Design
10 No Design
11 No Design
hl93 - Girder A.bdb CSiBridge v20.2.1 - License #2010*1J2ULGRNHP9JJDE 10 June 2020
HDR, Inc Page 18 of 24
Table: Frame Load Transfer Options
Table: Frame Load Transfer Options
Frame Transfer
2 Yes
3 Yes
4 Yes
5 Yes
6 Yes
7 Yes
8 Yes
9 Yes
10 Yes
11 Yes
Table: Frame Section Assignments
Table: Frame Section Assignments
Frame AnalSect DesignSect MatProp
2 CA BT55 comp N.A. Default
3 CA BT55 comp N.A. Default
4 CA BT55 comp N.A. Default
5 CA BT55 comp N.A. Default
6 CA BT55 comp N.A. Default
7 CA BT55 comp N.A. Default
8 CA BT55 comp N.A. Default
9 CA BT55 comp N.A. Default
10 CA BT55 comp N.A. Default
11 CA BT55 comp N.A. Default
Table: Frame Section Properties 01 - General, Part 2 of 5
Table: Frame Section Properties 01 - General, Part 2 of 5
SectionName Area TorsConst I33 I22 I23 AS2 AS3
ft2 ft4 ft4 ft4 ft4 ft2 ft2
CA BT55 comp 6.4236 1.246786 18.004919 3.253521 0. 3.0574 5.3173
CA I36 3. 0.496726 3.038194 0.39728 0. 1.8054 2.7122
CA I42 3.2917 0.529817 4.600694 0.405551 0. 2.0272 2.9536
CA I48 3.5833 0.56293 6.577932 0.413821 0. 2.2635 3.1787
CA I54 3.875 0.596137 8.989198 0.422092 0. 2.5077 3.3918
CA I60 4.1667 0.630034 11.906829 0.430363 0. 2.7566 3.5959
CA I66 4.4583 0.66313 15.335648 0.438633 0. 3.0083 3.7931
FSEC1 0.0459 0.000011 0.007615 0.000382 0. 0.0208 0.022
hl93 - Girder A.bdb CSiBridge v20.2.1 - License #2010*1J2ULGRNHP9JJDE 10 June 2020
HDR, Inc Page 19 of 24
Table: Frame Section Properties 01 - General, Part 3 of 5
Table: Frame Section Properties 01 - General, Part 3 of 5
SectionName S33 S22 Z33 Z22 R33 R22
ft3 ft3 ft3 ft3 ft ft
CA BT55 comp 7.61169 1.652582 9.739402 3.400188 1.66667 0.72131
CA I36 1.928993 0.501827 2.733631 0.890625 1.00833 0.3639
CA I42 2.509491 0.512275 3.520089 0.93316 1.18333 0.35101
CA I48 3.13235 0.522722 4.379464 0.975694 1.35833 0.33983
CA I54 3.817824 0.533169 5.311756 1.018229 1.525 0.33004
CA I60 3.954225 0.543616 6.316964 1.060764 1.69167 0.32138
CA I66 5.349653 0.554063 7.395089 1.103299 1.85833 0.31366
FSEC1 0.01523 0.001836 0.017346 0.00285 0.4073 0.09128
Table: Frame Section Properties 01 - General, Part 4 of 5
Table: Frame Section Properties 01 - General, Part 4 of 5
SectionName EccV2 AMod A2Mod A3Mod JMod I2Mod I3Mod MMod
ft
CA BT55 comp 1. 1. 1. 1. 1. 2. 1.
CA I36 1. 1. 1. 1. 1. 1. 1.
CA I42 1. 1. 1. 1. 1. 1. 1.
CA I48 1. 1. 1. 1. 1. 1. 1.
CA I54 1. 1. 1. 1. 1. 1. 1.
CA I60 1. 1. 1. 1. 1. 1. 1.
CA I66 1. 1. 1. 1. 1. 1. 1.
FSEC1 1. 1. 1. 1. 1. 1. 1.
Table: Frame Section Properties 01 - General, Part 5 of 5
Table: Frame Section Properties 01 - General, Part
5 of 5
SectionName WMod
CA BT55 comp 1.
CA I36 1.
CA I42 1.
CA I48 1.
CA I54 1.
CA I60 1.
CA I66 1.
FSEC1 1.
Table: Joint Displacements, Part 1 of 2
Table: Joint Displacements, Part 1 of 2
Joint OutputCase StepType StepLabel U1 U2 U3 R1
ft ft ft Radians
1 hl93 Max 0. 0. 0. 0.
1 hl93 Min 0. 0. 0. 0.
1 P15 Max 0. 0. 0. 0.
1 P15 Min 0. 0. 0. 0.
2 hl93 Max 0. 0. 0. 0.
2 hl93 Min 0. 0. 0. 0.
hl93 - Girder A.bdb CSiBridge v20.2.1 - License #2010*1J2ULGRNHP9JJDE 10 June 2020
HDR, Inc Page 20 of 24
Table: Joint Displacements, Part 1 of 2
Joint OutputCase StepType StepLabel U1 U2 U3 R1
ft ft ft Radians
2 P15 Max 0. 0. 0. 0.
2 P15 Min 0. 0. 0. 0.
3 hl93 Max 0. 0. 0. 0.006319
3 hl93 Min 0. 0. -0.048899 -0.006319
3 P15 Max 0. 0. 0. 0.01195
3 P15 Min 0. 0. -0.097298 -0.01195
4 hl93 Max 0. 0. 0. 0.011133
4 hl93 Min 0. 0. -0.093033 -0.011133
4 P15 Max 0. 0. 0. 0.020443
4 P15 Min 0. 0. -0.183412 -0.020443
5 hl93 Max 0. 0. 0. 0.014438
5 hl93 Min 0. 0. -0.128171 -0.014438
5 P15 Max 0. 0. 0. 0.026624
5 P15 Min 0. 0. -0.250727 -0.026624
6 hl93 Max 0. 0. 0. 0.016391
6 hl93 Min 0. 0. -0.150988 -0.016391
6 P15 Max 0. 0. 0. 0.030607
6 P15 Min 0. 0. -0.293473 -0.030607
7 hl93 Max 0. 0. 0. 0.016913
7 hl93 Min 0. 0. -0.158622 -0.016913
7 P15 Max 0. 0. 0. 0.03155
7 P15 Min 0. 0. -0.307924 -0.03155
8 hl93 Max 0. 0. 0. 0.01639
8 hl93 Min 0. 0. -0.150987 -0.01639
8 P15 Max 0. 0. 0. 0.030607
8 P15 Min 0. 0. -0.293477 -0.030607
9 hl93 Max 0. 0. 0. 0.014438
9 hl93 Min 0. 0. -0.12817 -0.014438
9 P15 Max 0. 0. 0. 0.026622
9 P15 Min 0. 0. -0.250731 -0.026622
10 hl93 Max 0. 0. 0. 0.011133
10 hl93 Min 0. 0. -0.093033 -0.011133
10 P15 Max 0. 0. 0. 0.020444
10 P15 Min 0. 0. -0.183413 -0.020444
11 hl93 Max 0. 0. 0. 0.00632
11 hl93 Min 0. 0. -0.048899 -0.00632
11 P15 Max 0. 0. 0. 0.011949
11 P15 Min 0. 0. -0.097297 -0.011949
Table: Joint Displacements, Part 2 of 2
Filter: CaseType <> 'LinModal' And CaseType <> 'Combination'
Table: Joint Displacements, Part 2 of 2
Joint StepLabel R2 R3
Radians Radians
1 0.004298 0.
1 0. 0.
1 0.008545 0.
1 0. 0.
2 0. 0.
2 -0.004298 0.
2 0. 0.
hl93 - Girder A.bdb CSiBridge v20.2.1 - License #2010*1J2ULGRNHP9JJDE 10 June 2020
HDR, Inc Page 21 of 24
Table: Joint Displacements, Part 2 of 2
Joint StepLabel R2 R3
Radians Radians
2 -0.008545 0.
3 0.004088 0.
3 0. 0.
3 0.008055 0.
3 0. 0.
4 0.003489 0.
4 0. 0.
4 0.006756 0.
4 0. 0.
5 0.002579 0.
5 0. 0.
5 0.004838 0.
5 0. 0.
6 0.001467 0.
6 0. 0.
6 0.002534 0.
6 0. 0.
7 0.000414 0.
7 -0.000414 0.
7 0.000551 0.
7 -0.000551 0.
8 0. 0.
8 -0.001467 0.
8 0. 0.
8 -0.002534 0.
9 0. 0.
9 -0.002579 0.
9 0. 0.
9 -0.004838 0.
10 0. 0.
10 -0.003489 0.
10 0. 0.
10 -0.006756 0.
11 0. 0.
11 -0.004088 0.
11 0. 0.
11 -0.008055 0.
Table: Joint Pattern Definitions
Table: Joint Pattern Definitions
Pattern AutoBridge BridgeObj BridgePType
BridgeLPat
Default
hl93 - Girder A.bdb CSiBridge v20.2.1 - License #2010*1J2ULGRNHP9JJDE 10 June 2020
HDR, Inc Page 22 of 24
Table: Joint Reactions, Part 1 of 2
Filter: CaseType <> 'LinModal' And CaseType <> 'Combination'
Table: Joint Reactions, Part 1 of 2
Joint OutputCase StepType StepLabel F1 F2 F3 M1
Kip Kip Kip Kip-ft
1 hl93 Max 0. 0. 124.089 240.9359
1 hl93 Min 0. 0. 0. -240.9359
1 P15 Max 0. 0. 247.102 494.2148
1 P15 Min 0. 0. 0. -494.2148
2 hl93 Max 0. 0. 124.089 240.9359
2 hl93 Min 0. 0. 0. -240.9359
2 P15 Max 0. 0. 247.102 494.2148
2 P15 Min 0. 0. 0. -494.2148
Table: Joint Reactions, Part 2 of 2
Filter: CaseType <> 'LinModal' And CaseType <> 'Combination'
Table: Joint Reactions, Part 2 of 2
Joint StepLabel M2 M3
Kip-ft Kip-ft
1 0. 0.
1 0. 0.
1 0. 0.
1 0. 0.
2 0. 0.
2 0. 0.
2 0. 0.
2 0. 0.
Table: Joint Restraint Assignments
Table: Joint Restraint Assignments
Joint U1 U2 U3 R1 R2 R3
1 Yes Yes Yes Yes No Yes
2 No Yes Yes Yes No Yes
Table: Load Pattern Definitions
Table: Load Pattern Definitions
LoadPat DesignType SelfWtMult AutoLoad NotBasePat NotRatio NotDir
DEAD Dead 1.
hl93 Vehicle Live 0.
hl93 - Girder A.bdb CSiBridge v20.2.1 - License #2010*1J2ULGRNHP9JJDE 10 June 2020
HDR, Inc Page 23 of 24
Table: Material List 1 - By Object Type
Table: Material List 1 - By Object Type
ObjectType Material TotalWeight NumPieces
Kip
Frame Concrete 8ksi
112.709 10
Table: Material List 2 - By Section Property
Table: Material List 2 - By Section Property
Section ObjectType NumPieces TotalLength TotalWeight
ft Kip
CA BT55 comp Frame 10 113.2 112.709
Table: Material Properties 02 - Basic Mechanical Properties
Table: Material Properties 02 - Basic Mechanical Properties
Material UnitWeight UnitMass E1 G12 U12 A1
Kip/ft3 Kip-s2/ft4 Kip/ft2 Kip/ft2 1/F
4000Psi 1.5000E-01 4.6621E-03 519119.5 216299.79 0.2 5.5000E-06
A615Gr60 4.9000E-01 1.5230E-02 4176000. 6.5000E-06
A709Gr50 4.9000E-01 1.5230E-02 4176000. 1606153.85
0.3 6.5000E-06
A722Gr150TypII 4.9000E-01 1.5230E-02 4320000. 6.5000E-06
Concrete 8ksi 1.5500E-01 4.8175E-03 742118. 309215.83 0.2 5.5000E-06
Table: Material Properties 03b - Concrete Data
Table: Material Properties 03b - Concrete Data
Material Fc eFc FinalSlope EFact CreepFact ShrinkFact
Kip/ft2 Kip/ft2
4000Psi 576. 576. -0.1
Concrete 8ksi 1152. 1497.6 -0.1
Table: Multi-Step Moving Load 1 - General
Table: Multi-Step Moving Load 1 - General
LoadPat LoadDur LoadDisc
Sec Sec
hl93 10. 0.1
Table: Multi-Step Moving Load 2 - Vehicle Data
Table: Multi-Step Moving Load 2 - Vehicle Data
LoadPat Vehicle Lane Station StartTime Direction Speed FLLocation
ft Sec ft/sec
hl93 HL-93F LANE1 0. 0. Forward 1.
hl93 - Girder A.bdb CSiBridge v20.2.1 - License #2010*1J2ULGRNHP9JJDE 10 June 2020
HDR, Inc Page 24 of 24
Table: Objects And Elements - Joints
Table: Objects And Elements - Joints
JointElem JointObject GlobalX GlobalY GlobalZ
ft ft ft
1 1 -56.6 0. 0.
2 2 56.6 0. 0.
3 3 -45.28 0. 0.
4 4 -33.96 0. 0.
5 5 -22.64 0. 0.
6 6 -11.32 0. 0.
7 7 0. 0. 0.
8 8 11.32 0. 0.
9 9 22.64 0. 0.
10 10 33.96 0. 0.
11 11 45.28 0. 0.
6.2 Appendix B Lpile Analysis
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
6.2.1 North Abutment Piles
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
================================================================================
LPile for Windows, Version 2019-11.002
Analysis of Individual Piles and Drilled Shafts
Subjected to Lateral Loading Using the p-y Method
© 1985-2019 by Ensoft, Inc.
All Rights Reserved
================================================================================
This copy of LPile is being used by:
HDR inc
walnut creek
Serial Number of Security Device: 202613844
This copy of LPile is licensed for exclusive use by:
HDR, Various, Global License
Use of this program by any entity other than HDR, Various, Global License
is a violation of the software license agreement.
--------------------------------------------------------------------------------
Files Used for Analysis
--------------------------------------------------------------------------------
Path to file locations:
\Users\jchen\Documents\Fyffe\LPile\
Name of input data file:
NorthAbut LPile (USCS units).lp11
Name of output report file:
NorthAbut LPile (USCS units).lp11
Name of plot output file:
NorthAbut LPile (USCS units).lp11
Name of runtime message file:
NorthAbut LPile (USCS units).lp11
--------------------------------------------------------------------------------
Date and Time of Analysis
--------------------------------------------------------------------------------
Date: June 1, 2020 Time: 18:57:19
--------------------------------------------------------------------------------
Problem Title
--------------------------------------------------------------------------------
Project Name: Fyffe Grade Separation
Job Number:
Client: Port of Stockton
Engineer: JChen
Description:
--------------------------------------------------------------------------------
Program Options and Settings
--------------------------------------------------------------------------------
Computational Options:
- Conventional Analysis
Engineering Units Used for Data Input and Computations:
- US Customary System Units (pounds, feet, inches)
Analysis Control Options:
- Maximum number of iterations allowed = 500
- Deflection tolerance for convergence = 1.0000E-05 in
- Maximum allowable deflection = 100.0000 in
- Number of pile increments = 100
Loading Type and Number of Cycles of Loading:
- Static loading specified
- Use of p-y modification factors for p-y curves not selected
- Analysis uses layering correction (Method of Georgiadis)
- No distributed lateral loads are entered
- Loading by lateral soil movements acting on pile not selected
- Input of shear resistance at the pile tip not selected
- Input of moment resistance at the pile tip not selected
- Computation of pile-head foundation stiffness matrix not selected
- Push-over analysis of pile not selected
- Buckling analysis of pile not selected
Output Options:
- Output files use decimal points to denote decimal symbols.
- Values of pile-head deflection, bending moment, shear force, and
soil reaction are printed for full length of pile.
- Printing Increment (nodal spacing of output points) = 1
- No p-y curves to be computed and reported for user-specified depths
- Print using wide report formats
--------------------------------------------------------------------------------
Pile Structural Properties and Geometry
--------------------------------------------------------------------------------
Number of pile sections defined = 1
Total length of pile = 55.000 ft
Depth of ground surface below top of pile = 0.0000 ft
Pile diameters used for p-y curve computations are defined using 2 points.
p-y curves are computed using pile diameter values interpolated with depth over
the length of the pile. A summary of values of pile diameter vs. depth follows.
Depth Below Pile
Point Pile Head Diameter
No. feet inches
----- ------------- -------------
1 0.000 14.0000
2 55.000 14.0000
Input Structural Properties for Pile Sections:
----------------------------------------------
Pile Section No. 1:
Section 1 is an elastic pile
Cross-sectional shape = rectangular
Length of section = 55.000000 ft
Width of top of section = 14.000000 in
Width of bottom of section = 14.000000 in
Top Section Depth = 14.000000 in
Bottom Section Depth = 14.000000 in
Top Area = 196.000000 sq. in
Bottom Area = 196.000000 sq. in
Moment of Inertia at Top = 3201. in^4
Moment of Inertia at Bottom = 3201. in^4
Elastic Modulus = 4074281. psi
--------------------------------------------------------------------------------
Ground Slope and Pile Batter Angles
--------------------------------------------------------------------------------
Ground Slope Angle = 0.000 degrees
= 0.000 radians
Pile Batter Angle = 0.000 degrees
= 0.000 radians
--------------------------------------------------------------------------------
Soil and Rock Layering Information
--------------------------------------------------------------------------------
The soil profile is modelled using 11 layers
Layer 1 is soft clay, p-y criteria by Matlock, 1970
Distance from top of pile to top of layer = 0.0000 ft
Distance from top of pile to bottom of layer = 11.000000 ft
Effective unit weight at top of layer = 100.000000 pcf
Effective unit weight at bottom of layer = 100.000000 pcf
Undrained cohesion at top of layer = 700.000000 psf
Undrained cohesion at bottom of layer = 700.000000 psf
Epsilon-50 at top of layer = 0.010000
Epsilon-50 at bottom of layer = 0.010000
Layer 2 is sand, p-y criteria by Reese et al., 1974
Distance from top of pile to top of layer = 11.000000 ft
Distance from top of pile to bottom of layer = 21.000000 ft
Effective unit weight at top of layer = 46.000000 pcf
Effective unit weight at bottom of layer = 46.000000 pcf
Friction angle at top of layer = 32.000000 deg.
Friction angle at bottom of layer = 32.000000 deg.
Subgrade k at top of layer = 0.0000 pci
Subgrade k at bottom of layer = 0.0000 pci
NOTE: Default values for subgrade k will be computed for this layer.
Layer 3 is soft clay, p-y criteria by Matlock, 1970
Distance from top of pile to top of layer = 21.000000 ft
Distance from top of pile to bottom of layer = 28.000000 ft
Effective unit weight at top of layer = 67.000000 pcf
Effective unit weight at bottom of layer = 67.000000 pcf
Undrained cohesion at top of layer = 1000.000000 psf
Undrained cohesion at bottom of layer = 1000.000000 psf
Epsilon-50 at top of layer = 0.010000
Epsilon-50 at bottom of layer = 0.010000
Layer 4 is sand, p-y criteria by Reese et al., 1974
Distance from top of pile to top of layer = 28.000000 ft
Distance from top of pile to bottom of layer = 40.000000 ft
Effective unit weight at top of layer = 49.000000 pcf
Effective unit weight at bottom of layer = 49.000000 pcf
Friction angle at top of layer = 33.000000 deg.
Friction angle at bottom of layer = 33.000000 deg.
Subgrade k at top of layer = 65.000000 pci
Subgrade k at bottom of layer = 65.000000 pci
Layer 5 is stiff clay without free water
Distance from top of pile to top of layer = 40.000000 ft
Distance from top of pile to bottom of layer = 46.000000 ft
Effective unit weight at top of layer = 56.000000 pcf
Effective unit weight at bottom of layer = 56.000000 pcf
Undrained cohesion at top of layer = 1500. psf
Undrained cohesion at bottom of layer = 1500. psf
Epsilon-50 at top of layer = 0.007000
Epsilon-50 at bottom of layer = 0.007000
Layer 6 is sand, p-y criteria by Reese et al., 1974
Distance from top of pile to top of layer = 46.000000 ft
Distance from top of pile to bottom of layer = 57.000000 ft
Effective unit weight at top of layer = 56.000000 pcf
Effective unit weight at bottom of layer = 56.000000 pcf
Friction angle at top of layer = 34.000000 deg.
Friction angle at bottom of layer = 34.000000 deg.
Subgrade k at top of layer = 65.000000 pci
Subgrade k at bottom of layer = 65.000000 pci
Layer 7 is stiff clay without free water
Distance from top of pile to top of layer = 57.000000 ft
Distance from top of pile to bottom of layer = 61.000000 ft
Effective unit weight at top of layer = 56.000000 pcf
Effective unit weight at bottom of layer = 56.000000 pcf
Undrained cohesion at top of layer = 2000. psf
Undrained cohesion at bottom of layer = 2000. psf
Epsilon-50 at top of layer = 0.005000
Epsilon-50 at bottom of layer = 0.005000
Layer 8 is sand, p-y criteria by Reese et al., 1974
Distance from top of pile to top of layer = 61.000000 ft
Distance from top of pile to bottom of layer = 71.000000 ft
Effective unit weight at top of layer = 56.000000 pcf
Effective unit weight at bottom of layer = 56.000000 pcf
Friction angle at top of layer = 38.000000 deg.
Friction angle at bottom of layer = 38.000000 deg.
Subgrade k at top of layer = 75.000000 pci
Subgrade k at bottom of layer = 75.000000 pci
Layer 9 is stiff clay without free water
Distance from top of pile to top of layer = 71.000000 ft
Distance from top of pile to bottom of layer = 89.000000 ft
Effective unit weight at top of layer = 56.000000 pcf
Effective unit weight at bottom of layer = 56.000000 pcf
Undrained cohesion at top of layer = 3000. psf
Undrained cohesion at bottom of layer = 3000. psf
Epsilon-50 at top of layer = 0.005000
Epsilon-50 at bottom of layer = 0.005000
Layer 10 is stiff clay without free water
Distance from top of pile to top of layer = 89.000000 ft
Distance from top of pile to bottom of layer = 125.000000 ft
Effective unit weight at top of layer = 56.000000 pcf
Effective unit weight at bottom of layer = 56.000000 pcf
Undrained cohesion at top of layer = 5000. psf
Undrained cohesion at bottom of layer = 5000. psf
Epsilon-50 at top of layer = 0.004000
Epsilon-50 at bottom of layer = 0.004000
Layer 11 is stiff clay without free water
Distance from top of pile to top of layer = 125.000000 ft
Distance from top of pile to bottom of layer = 125.000000 ft
Effective unit weight at top of layer = 56.000000 pcf
Effective unit weight at bottom of layer = 56.000000 pcf
Undrained cohesion at top of layer = 5000. psf
Undrained cohesion at bottom of layer = 5000. psf
Epsilon-50 at top of layer = 0.004000
Epsilon-50 at bottom of layer = 0.004000
(Depth of the lowest soil layer extends 70.000 ft below the pile tip)
--------------------------------------------------------------------------------
Summary of Input Soil Properties
--------------------------------------------------------------------------------
Layer Soil Type Layer Effective Undrained Angle of
E50
Layer Name Depth Unit Wt. Cohesion Friction
or kpy
Num. (p-y Curve Type) ft pcf psf deg.
krm pci
----- ------------------- ---------- ---------- ---------- ----------
---------- ----------
1 Soft 0.00 100.0000 700.0000 --
0.01000 --
Clay 11.0000 100.0000 700.0000 --
0.01000 --
2 Sand 11.0000 46.0000 -- 32.0000
-- default
(Reese, et al.) 21.0000 46.0000 -- 32.0000
-- default
3 Soft 21.0000 67.0000 1000.0000 --
0.01000 --
Clay 28.0000 67.0000 1000.0000 --
0.01000 --
4 Sand 28.0000 49.0000 -- 33.0000
-- 65.0000
(Reese, et al.) 40.0000 49.0000 -- 33.0000
-- 65.0000
5 Stiff Clay 40.0000 56.0000 1500. --
0.00700 --
w/o Free Water 46.0000 56.0000 1500. --
0.00700 --
6 Sand 46.0000 56.0000 -- 34.0000
-- 65.0000
(Reese, et al.) 57.0000 56.0000 -- 34.0000
-- 65.0000
7 Stiff Clay 57.0000 56.0000 2000. --
0.00500 --
w/o Free Water 61.0000 56.0000 2000. --
0.00500 --
8 Sand 61.0000 56.0000 -- 38.0000
-- 75.0000
(Reese, et al.) 71.0000 56.0000 -- 38.0000
-- 75.0000
9 Stiff Clay 71.0000 56.0000 3000. --
0.00500 --
w/o Free Water 89.0000 56.0000 3000. --
0.00500 --
10 Stiff Clay 89.0000 56.0000 5000. --
0.00400 --
w/o Free Water 125.0000 56.0000 5000. --
0.00400 --
11 Stiff Clay 125.0000 56.0000 5000. --
0.00400 --
w/o Free Water 125.0000 56.0000 5000. --
0.00400 --
--------------------------------------------------------------------------------
Static Loading Type
--------------------------------------------------------------------------------
Static loading criteria were used when computing p-y curves for all analyses.
--------------------------------------------------------------------------------
Pile-head Loading and Pile-head Fixity Conditions
--------------------------------------------------------------------------------
Number of loads specified = 1
Load Load Condition Condition Axial Thrust
Compute Top y Run Analysis
No. Type 1 2 Force, lbs
vs. Pile Length
----- ---- -------------------- ----------------------- ----------------
--------------- ------------
1 1 V = 15000. lbs M = 0.0000 in-lbs 227000.
No Yes
V = shear force applied normal to pile axis
M = bending moment applied to pile head
y = lateral deflection normal to pile axis
S = pile slope relative to original pile batter angle
R = rotational stiffness applied to pile head
Values of top y vs. pile lengths can be computed only for load types with
specified shear loading (Load Types 1, 2, and 3).
Thrust force is assumed to be acting axially for all pile batter angles.
--------------------------------------------------------------------------------
Computations of Nominal Moment Capacity and Nonlinear Bending Stiffness
--------------------------------------------------------------------------------
Axial thrust force values were determined from pile-head loading conditions
Number of Pile Sections Analyzed = 1
Pile Section No. 1:
-------------------
Moment-curvature properties were derived from elastic section properties
--------------------------------------------------------------------------------
Layering Correction Equivalent Depths of Soil & Rock Layers
--------------------------------------------------------------------------------
Top of Equivalent
Layer Top Depth Same Layer Layer is F0 F1
Layer Below Below Type As Rock or Integral Integral
No. Pile Head Grnd Surf Layer is Below for Layer for Layer
ft ft Above Rock Layer lbs lbs
----- ---------- ---------- ---------- ---------- ---------- ----------
1 0.00 0.00 N.A. No 0.00 55125.
2 11.0000 8.4909 No No 55125. 345426.
3 21.0000 42.1249 No No 400551. 73500.
4 28.0000 20.0261 No No 474051. 1151359.
5 40.0000 107.4362 No No 1625410. 94500.
6 46.0000 33.9007 No No 1719910. 1402144.
7 57.0000 57.0000 No No 3122054. 0.00
8 61.0000 61.0000 No No 0.00 0.00
9 71.0000 71.0000 No No 0.00 0.00
10 89.0000 89.0000 No No 0.00 0.00
11 125.0000 125.0000 No No 0.00 N.A.
Notes: The F0 integral of Layer n+1 equals the sum of the F0 and F1 integrals
for Layer n. Layering correction equivalent depths are computed only
for soil types with both shallow-depth and deep-depth expressions for
peak lateral load transfer. These soil types are soft and stiff clays,
non-liquefied sands, and cemented c-phi soil.
--------------------------------------------------------------------------------
Computed Values of Pile Loading and Deflection
for Lateral Loading for Load Case Number 1
--------------------------------------------------------------------------------
Pile-head conditions are Shear and Moment (Loading Type 1)
Shear force at pile head = 15000.0 lbs
Applied moment at pile head = 0.0 in-lbs
Axial thrust load on pile head = 227000.0 lbs
Depth Deflect. Bending Shear Slope Total Bending Soil
Res. Soil Spr. Distrib.
X y Moment Force S Stress Stiffness p
Es*h Lat. Load
feet inches in-lbs lbs radians psi* in-lb^2
lb/inch lb/inch lb/inch
---------- ---------- ---------- ---------- ---------- ---------- ----------
---------- ---------- ----------
0.00 0.7309 2.66E-07 15000. -0.00784 1158. 1.30E+10
-130.4853 589.1072 0.00
0.5500 0.6792 107911. 14105. -0.00782 1394. 1.30E+10
-140.6678 1367. 0.00
1.1000 0.6277 209613. 13146. -0.00774 1616. 1.30E+10
-150.0184 1577. 0.00
1.6500 0.5770 304621. 12128. -0.00761 1824. 1.30E+10
-158.4985 1813. 0.00
2.2000 0.5273 392493. 11057. -0.00743 2016. 1.30E+10
-166.0713 2078. 0.00
2.7500 0.4790 472835. 9939. -0.00721 2192. 1.30E+10
-172.7014 2380. 0.00
3.3000 0.4321 545295. 8780. -0.00695 2350. 1.30E+10
-178.3547 2724. 0.00
3.8500 0.3872 609572. 7588. -0.00666 2491. 1.30E+10
-182.9980 3120. 0.00
4.4000 0.3442 665416. 6368. -0.00634 2613. 1.30E+10
-186.5992 3578. 0.00
4.9500 0.3035 712627. 5128. -0.00599 2716. 1.30E+10
-189.1265 4113. 0.00
5.5000 0.2651 751059. 3875. -0.00562 2800. 1.30E+10
-190.5481 4743. 0.00
6.0500 0.2293 780622. 2617. -0.00523 2865. 1.30E+10
-190.8316 5493. 0.00
6.6000 0.1961 801281. 1360. -0.00483 2910. 1.30E+10
-189.9428 6394. 0.00
7.1500 0.1655 813058. 113.5461 -0.00442 2936. 1.30E+10
-187.8446 7491. 0.00
7.7000 0.1377 816036. -1115. -0.00401 2942. 1.30E+10
-184.4939 8845. 0.00
8.2500 0.1125 810359. -2317. -0.00360 2930. 1.30E+10
-179.8391 10547. 0.00
8.8000 0.09013 796234. -3485. -0.00319 2899. 1.30E+10
-173.8131 12727. 0.00
9.3500 0.07038 773934. -4607. -0.00280 2850. 1.30E+10
-166.3232 15597. 0.00
9.9000 0.05322 743802. -5675. -0.00241 2785. 1.30E+10
-157.2319 19500. 0.00
10.4500 0.03853 706257. -6676. -0.00205 2702. 1.30E+10
-146.3176 25061. 0.00
11.0000 0.02621 661803. -7864. -0.00170 2605. 1.30E+10
-213.5861 53781. 0.00
11.5500 0.01610 607544. -9142. -0.00138 2487. 1.30E+10
-173.8023 71256. 0.00
12.1000 0.00801 545253. -10035. -0.00109 2350. 1.30E+10
-96.7308 79662. 0.00
12.6500 0.00175 478336. -10427. -8.28E-04 2204. 1.30E+10
-22.0968 83283. 0.00
13.2000 -0.00291 410093. -10374. -6.03E-04 2055. 1.30E+10
38.3749 86904. 0.00
13.7500 -0.00621 343211. -9966. -4.13E-04 1909. 1.30E+10
85.1810 90525. 0.00
14.3000 -0.00836 279779. -9291. -2.55E-04 1770. 1.30E+10
119.2534 94146. 0.00
14.8500 -0.00958 221329. -8430. -1.28E-04 1642. 1.30E+10
141.8438 97767. 0.00
15.4000 -0.01005 168891. -7452. -2.94E-05 1527. 1.30E+10
154.4127 101388. 0.00
15.9500 -0.00996 123051. -6419. 4.44E-05 1427. 1.30E+10
158.5301 105009. 0.00
16.5000 -0.00947 84023. -5382. 9.68E-05 1342. 1.30E+10
155.7872 108630. 0.00
17.0500 -0.00869 51718. -4380. 1.31E-04 1271. 1.30E+10
147.7245 112251. 0.00
17.6000 -0.00773 25808. -3445. 1.51E-04 1215. 1.30E+10
135.7742 115872. 0.00
18.1500 -0.00670 5793. -2597. 1.59E-04 1171. 1.30E+10
121.2188 119493. 0.00
18.7000 -0.00564 -8946. -1850. 1.58E-04 1178. 1.30E+10
105.1632 123114. 0.00
19.2500 -0.00461 -19098. -1311. 1.51E-04 1200. 1.30E+10
58.1730 83286. 0.00
19.8000 -0.00365 -26701. -962.6439 1.39E-04 1217. 1.30E+10
47.3229 85665. 0.00
20.3500 -0.00277 -32222. -684.4863 1.24E-04 1229. 1.30E+10
36.9673 88045. 0.00
20.9000 -0.00200 -36109. -471.8924 1.07E-04 1237. 1.30E+10
27.4551 90425. 0.00
21.4500 -0.00136 -38772. -154.4536 8.82E-05 1243. 1.30E+10
68.7384 334244. 0.00
22.0000 -8.40E-04 -38412. 265.7078 6.86E-05 1242. 1.30E+10
58.5832 460194. 0.00
22.5500 -4.51E-04 -35470. 616.1945 4.99E-05 1236. 1.30E+10
47.6249 696415. 0.00
23.1000 -1.81E-04 -30428. 889.2583 3.33E-05 1225. 1.30E+10
35.1217 1280923. 0.00
23.6500 -1.22E-05 -23832. 1052. 1.95E-05 1210. 1.30E+10
14.3271 7748172. 0.00
24.2000 7.70E-05 -16594. 1013. 9.31E-06 1194. 1.30E+10
-26.4001 2263846. 0.00
24.7500 1.11E-04 -10494. 827.1164 2.46E-06 1181. 1.30E+10
-29.8066 1776793. 0.00
25.3000 1.09E-04 -5683. 630.7708 -1.63E-06 1171. 1.30E+10
-29.6921 1790893. 0.00
25.8500 8.92E-05 -2162. 441.2659 -3.62E-06 1163. 1.30E+10
-27.7336 2053183. 0.00
26.4000 6.17E-05 152.1016 268.8020 -4.13E-06 1158. 1.30E+10
-24.5282 2625717. 0.00
26.9500 3.47E-05 1398. 121.0365 -3.74E-06 1161. 1.30E+10
-20.2493 3855272. 0.00
27.5000 1.23E-05 1761. 6.8061 -2.94E-06 1162. 1.30E+10
-14.3660 7679611. 0.00
28.0500 -4.09E-06 1497. -40.3063 -2.11E-06 1161. 1.30E+10
0.08952 144401. 0.00
28.6000 -1.55E-05 1235. -38.8675 -1.42E-06 1161. 1.30E+10
0.3465 147233. 0.00
29.1500 -2.28E-05 987.9424 -36.0100 -8.58E-07 1160. 1.30E+10
0.5194 150064. 0.00
29.7000 -2.69E-05 762.5007 -32.2425 -4.15E-07 1160. 1.30E+10
0.6222 152896. 0.00
30.2500 -2.83E-05 563.5854 -27.9835 -7.98E-08 1159. 1.30E+10
0.6684 155727. 0.00
30.8000 -2.79E-05 393.3581 -23.5648 1.62E-07 1159. 1.30E+10
0.6706 158558. 0.00
31.3500 -2.62E-05 252.0439 -19.2387 3.26E-07 1159. 1.30E+10
0.6403 161390. 0.00
31.9000 -2.36E-05 138.4312 -15.1865 4.24E-07 1158. 1.30E+10
0.5876 164221. 0.00
32.4500 -2.06E-05 50.3103 -11.5280 4.72E-07 1158. 1.30E+10
0.5210 167053. 0.00
33.0000 -1.74E-05 -15.1532 -8.3320 4.81E-07 1158. 1.30E+10
0.4475 169884. 0.00
33.5500 -1.42E-05 -61.1129 -5.6259 4.62E-07 1158. 1.30E+10
0.3725 172715. 0.00
34.1000 -1.13E-05 -90.7992 -3.4056 4.23E-07 1158. 1.30E+10
0.3003 175547. 0.00
34.6500 -8.65E-06 -107.3356 -1.6433 3.73E-07 1158. 1.30E+10
0.2337 178378. 0.00
35.2000 -6.36E-06 -113.6091 -0.2953 3.17E-07 1158. 1.30E+10
0.1748 181210. 0.00
35.7500 -4.46E-06 -112.1842 0.6919 2.60E-07 1158. 1.30E+10
0.1244 184041. 0.00
36.3000 -2.93E-06 -105.2560 1.3762 2.05E-07 1158. 1.30E+10
0.08300 186872. 0.00
36.8500 -1.75E-06 -94.6325 1.8165 1.55E-07 1158. 1.30E+10
0.05040 189704. 0.00
37.4000 -8.92E-07 -81.7418 2.0686 1.10E-07 1158. 1.30E+10
0.02601 192535. 0.00
37.9500 -3.03E-07 -67.6560 2.1840 7.21E-08 1158. 1.30E+10
0.00897 195367. 0.00
38.5000 6.00E-08 -53.1284 2.2077 4.15E-08 1158. 1.30E+10
-0.00180 198198. 0.00
39.0500 2.45E-07 -38.6391 2.1771 1.83E-08 1158. 1.30E+10
-0.00748 201029. 0.00
39.6000 3.02E-07 -24.4461 2.1216 2.36E-09 1158. 1.30E+10
-0.00932 203861. 0.00
40.1500 2.77E-07 -10.6408 1.6975 -6.52E-09 1158. 1.30E+10
-0.1192 2844155. 0.00
40.7000 2.16E-07 -2.0201 0.9971 -9.72E-09 1158. 1.30E+10
-0.09302 2844155. 0.00
41.2500 1.48E-07 2.5501 0.4792 -9.59E-09 1158. 1.30E+10
-0.06392 2844155. 0.00
41.8000 8.93E-08 4.3338 0.1412 -7.84E-09 1158. 1.30E+10
-0.03850 2844155. 0.00
42.3500 4.48E-08 4.4374 -0.04955 -5.62E-09 1158. 1.30E+10
-0.01931 2844155. 0.00
42.9000 1.51E-08 3.6967 -0.1347 -3.57E-09 1158. 1.30E+10
-0.00650 2844155. 0.00
43.4500 -2.28E-09 2.6699 -0.1529 -1.96E-09 1158. 1.30E+10
9.81E-04 2844155. 0.00
44.0000 -1.07E-08 1.6838 -0.1345 -8.54E-10 1158. 1.30E+10
0.00462 2844155. 0.00
44.5500 -1.35E-08 0.8977 -0.09993 -2.01E-10 1158. 1.30E+10
0.00584 2844155. 0.00
45.1000 -1.34E-08 0.3653 -0.06164 1.19E-10 1158. 1.30E+10
0.00576 2844155. 0.00
45.6500 -1.20E-08 0.08371 -0.02557 2.32E-10 1158. 1.30E+10
0.00516 2844155. 0.00
46.2000 -1.03E-08 0.02705 -0.00730 2.60E-10 1158. 1.30E+10
3.72E-04 237838. 0.00
46.7500 -8.55E-09 -0.01343 -0.00504 2.64E-10 1158. 1.30E+10
3.12E-04 240669. 0.00
47.3000 -6.83E-09 -0.04032 -0.00318 2.50E-10 1158. 1.30E+10
2.52E-04 243500. 0.00
47.8500 -5.25E-09 -0.05620 -0.00170 2.26E-10 1158. 1.30E+10
1.96E-04 246332. 0.00
48.4000 -3.86E-09 -0.06350 -5.77E-04 1.95E-10 1158. 1.30E+10
1.46E-04 249163. 0.00
48.9500 -2.67E-09 -0.06441 2.40E-04 1.63E-10 1158. 1.30E+10
1.02E-04 251995. 0.00
49.5000 -1.71E-09 -0.06082 7.94E-04 1.31E-10 1158. 1.30E+10
6.59E-05 254826. 0.00
50.0500 -9.41E-10 -0.05432 0.00113 1.02E-10 1158. 1.30E+10
3.67E-05 257657. 0.00
50.6000 -3.58E-10 -0.04618 0.00130 7.67E-11 1158. 1.30E+10
1.41E-05 260489. 0.00
51.1500 7.14E-11 -0.03739 0.00134 5.55E-11 1158. 1.30E+10
-2.85E-06 263320. 0.00
51.7000 3.76E-10 -0.02869 0.00128 3.88E-11 1158. 1.30E+10
-1.51E-05 266152. 0.00
52.2500 5.84E-10 -0.02063 0.00115 2.63E-11 1158. 1.30E+10
-2.38E-05 268983. 0.00
52.8000 7.23E-10 -0.01360 9.73E-04 1.77E-11 1158. 1.30E+10
-2.98E-05 271814. 0.00
53.3500 8.17E-10 -0.00785 7.62E-04 1.23E-11 1158. 1.30E+10
-3.40E-05 274646. 0.00
53.9000 8.85E-10 -0.00357 5.27E-04 9.37E-12 1158. 1.30E+10
-3.72E-05 277477. 0.00
54.4500 9.41E-10 -9.16E-04 2.73E-04 8.23E-12 1158. 1.30E+10
-4.00E-05 280309. 0.00
55.0000 9.94E-10 0.00 0.00 8.00E-12 1158. 1.30E+10
-4.26E-05 141570. 0.00
* The above values of total stress are combined axial and bending stresses.
Output Summary for Load Case No. 1:
Pile-head deflection = 0.73093916 inches
Computed slope at pile head = -0.00784471 radians
Maximum bending moment = 816036. inch-lbs
Maximum shear force = 15000. lbs
Depth of maximum bending moment = 7.70000000 feet below pile head
Depth of maximum shear force = 0.000000 feet below pile head
Number of iterations = 24
Number of zero deflection points = 6
--------------------------------------------------------------------------------
Summary of Pile-head Responses for Conventional Analyses
--------------------------------------------------------------------------------
Definitions of Pile-head Loading Conditions:
Load Type 1: Load 1 = Shear, V, lbs, and Load 2 = Moment, M, in-lbs
Load Type 2: Load 1 = Shear, V, lbs, and Load 2 = Slope, S, radians
Load Type 3: Load 1 = Shear, V, lbs, and Load 2 = Rot. Stiffness, R, in-lbs/rad.
Load Type 4: Load 1 = Top Deflection, y, inches, and Load 2 = Moment, M, in-lbs
Load Type 5: Load 1 = Top Deflection, y, inches, and Load 2 = Slope, S, radians
Load Load Load Axial Pile-head Pile-head Max
Shear Max Moment
Case Type Pile-head Type Pile-head Loading Deflection Rotation in
Pile in Pile
No. 1 Load 1 2 Load 2 lbs inches radians lbs
in-lbs
---- ----- ---------- ---------- ---------- ---------- ---------- ----------
---------- ----------
1 V, lb 15000. M, in-lb 0.00 227000. 0.7309 -0.00784
15000. 816036.
Maximum pile-head deflection = 0.7309391560 inches
Maximum pile-head rotation = -0.0078447071 radians = -0.449469 deg.
The analysis ended normally.
6.2.2 South Abutment Piles
Fyffe Grade Separation CLIENT: Port of Stockton
HDR Project Number: 10133899
Fyffe Bridge
================================================================================
LPile for Windows, Version 2019-11.002
Analysis of Individual Piles and Drilled Shafts
Subjected to Lateral Loading Using the p-y Method
© 1985-2019 by Ensoft, Inc.
All Rights Reserved
================================================================================
This copy of LPile is being used by:
HDR inc
walnut creek
Serial Number of Security Device: 202613844
This copy of LPile is licensed for exclusive use by:
HDR, Various, Global License
Use of this program by any entity other than HDR, Various, Global License
is a violation of the software license agreement.
--------------------------------------------------------------------------------
Files Used for Analysis
--------------------------------------------------------------------------------
Path to file locations:
\Users\jchen\Documents\Fyffe\LPile\
Name of input data file:
SouthAbut LPile (USCS units).lp11
Name of output report file:
SouthAbut LPile (USCS units).lp11
Name of plot output file:
SouthAbut LPile (USCS units).lp11
Name of runtime message file:
SouthAbut LPile (USCS units).lp11
--------------------------------------------------------------------------------
Date and Time of Analysis
--------------------------------------------------------------------------------
Date: June 1, 2020 Time: 18:58:35
--------------------------------------------------------------------------------
Problem Title
--------------------------------------------------------------------------------
Project Name: Fyffe Grade Separation
Job Number:
Client: Port of Stockton
Engineer: JChen
Description:
--------------------------------------------------------------------------------
Program Options and Settings
--------------------------------------------------------------------------------
Computational Options:
- Conventional Analysis
Engineering Units Used for Data Input and Computations:
- US Customary System Units (pounds, feet, inches)
Analysis Control Options:
- Maximum number of iterations allowed = 500
- Deflection tolerance for convergence = 1.0000E-05 in
- Maximum allowable deflection = 100.0000 in
- Number of pile increments = 100
Loading Type and Number of Cycles of Loading:
- Static loading specified
- Use of p-y modification factors for p-y curves not selected
- Analysis uses layering correction (Method of Georgiadis)
- No distributed lateral loads are entered
- Loading by lateral soil movements acting on pile not selected
- Input of shear resistance at the pile tip not selected
- Input of moment resistance at the pile tip not selected
- Computation of pile-head foundation stiffness matrix not selected
- Push-over analysis of pile not selected
- Buckling analysis of pile not selected
Output Options:
- Output files use decimal points to denote decimal symbols.
- Values of pile-head deflection, bending moment, shear force, and
soil reaction are printed for full length of pile.
- Printing Increment (nodal spacing of output points) = 1
- No p-y curves to be computed and reported for user-specified depths
- Print using wide report formats
--------------------------------------------------------------------------------
Pile Structural Properties and Geometry
--------------------------------------------------------------------------------
Number of pile sections defined = 1
Total length of pile = 55.000 ft
Depth of ground surface below top of pile = 0.0000 ft
Pile diameters used for p-y curve computations are defined using 2 points.
p-y curves are computed using pile diameter values interpolated with depth over
the length of the pile. A summary of values of pile diameter vs. depth follows.
Depth Below Pile
Point Pile Head Diameter
No. feet inches
----- ------------- -------------
1 0.000 14.0000
2 55.000 14.0000
Input Structural Properties for Pile Sections:
----------------------------------------------
Pile Section No. 1:
Section 1 is an elastic pile
Cross-sectional shape = rectangular
Length of section = 55.000000 ft
Width of top of section = 14.000000 in
Width of bottom of section = 14.000000 in
Top Section Depth = 14.000000 in
Bottom Section Depth = 14.000000 in
Top Area = 196.000000 sq. in
Bottom Area = 196.000000 sq. in
Moment of Inertia at Top = 3201. in^4
Moment of Inertia at Bottom = 3201. in^4
Elastic Modulus = 4074281. psi
--------------------------------------------------------------------------------
Ground Slope and Pile Batter Angles
--------------------------------------------------------------------------------
Ground Slope Angle = 0.000 degrees
= 0.000 radians
Pile Batter Angle = 0.000 degrees
= 0.000 radians
--------------------------------------------------------------------------------
Soil and Rock Layering Information
--------------------------------------------------------------------------------
The soil profile is modelled using 11 layers
Layer 1 is soft clay, p-y criteria by Matlock, 1970
Distance from top of pile to top of layer = 0.0000 ft
Distance from top of pile to bottom of layer = 10.000000 ft
Effective unit weight at top of layer = 100.000000 pcf
Effective unit weight at bottom of layer = 100.000000 pcf
Undrained cohesion at top of layer = 1000.000000 psf
Undrained cohesion at bottom of layer = 1000.000000 psf
Epsilon-50 at top of layer = 0.010000
Epsilon-50 at bottom of layer = 0.010000
Layer 2 is soft clay, p-y criteria by Matlock, 1970
Distance from top of pile to top of layer = 10.000000 ft
Distance from top of pile to bottom of layer = 17.000000 ft
Effective unit weight at top of layer = 38.000000 pcf
Effective unit weight at bottom of layer = 38.000000 pcf
Undrained cohesion at top of layer = 1000.000000 psf
Undrained cohesion at bottom of layer = 1000.000000 psf
Epsilon-50 at top of layer = 0.010000
Epsilon-50 at bottom of layer = 0.010000
Layer 3 is stiff clay without free water
Distance from top of pile to top of layer = 17.000000 ft
Distance from top of pile to bottom of layer = 26.000000 ft
Effective unit weight at top of layer = 46.000000 pcf
Effective unit weight at bottom of layer = 46.000000 pcf
Undrained cohesion at top of layer = 1500. psf
Undrained cohesion at bottom of layer = 1500. psf
Epsilon-50 at top of layer = 0.007000
Epsilon-50 at bottom of layer = 0.007000
Layer 4 is sand, p-y criteria by Reese et al., 1974
Distance from top of pile to top of layer = 26.000000 ft
Distance from top of pile to bottom of layer = 32.000000 ft
Effective unit weight at top of layer = 49.000000 pcf
Effective unit weight at bottom of layer = 49.000000 pcf
Friction angle at top of layer = 32.000000 deg.
Friction angle at bottom of layer = 32.000000 deg.
Subgrade k at top of layer = 62.000000 pci
Subgrade k at bottom of layer = 62.000000 pci
Layer 5 is stiff clay without free water
Distance from top of pile to top of layer = 32.000000 ft
Distance from top of pile to bottom of layer = 45.000000 ft
Effective unit weight at top of layer = 56.000000 pcf
Effective unit weight at bottom of layer = 56.000000 pcf
Undrained cohesion at top of layer = 1500. psf
Undrained cohesion at bottom of layer = 1500. psf
Epsilon-50 at top of layer = 0.007000
Epsilon-50 at bottom of layer = 0.007000
Layer 6 is sand, p-y criteria by Reese et al., 1974
Distance from top of pile to top of layer = 45.000000 ft
Distance from top of pile to bottom of layer = 50.000000 ft
Effective unit weight at top of layer = 56.000000 pcf
Effective unit weight at bottom of layer = 56.000000 pcf
Friction angle at top of layer = 36.000000 deg.
Friction angle at bottom of layer = 36.000000 deg.
Subgrade k at top of layer = 70.000000 pci
Subgrade k at bottom of layer = 70.000000 pci
Layer 7 is stiff clay without free water
Distance from top of pile to top of layer = 50.000000 ft
Distance from top of pile to bottom of layer = 64.000000 ft
Effective unit weight at top of layer = 56.000000 pcf
Effective unit weight at bottom of layer = 56.000000 pcf
Undrained cohesion at top of layer = 2000. psf
Undrained cohesion at bottom of layer = 2000. psf
Epsilon-50 at top of layer = 0.005000
Epsilon-50 at bottom of layer = 0.005000
Layer 8 is stiff clay without free water
Distance from top of pile to top of layer = 64.000000 ft
Distance from top of pile to bottom of layer = 74.000000 ft
Effective unit weight at top of layer = 56.000000 pcf
Effective unit weight at bottom of layer = 56.000000 pcf
Undrained cohesion at top of layer = 38.000000 psf
Undrained cohesion at bottom of layer = 38.000000 psf
Epsilon-50 at top of layer = 75.000000
Epsilon-50 at bottom of layer = 75.000000
Layer 9 is stiff clay without free water
Distance from top of pile to top of layer = 74.000000 ft
Distance from top of pile to bottom of layer = 94.000000 ft
Effective unit weight at top of layer = 56.000000 pcf
Effective unit weight at bottom of layer = 56.000000 pcf
Undrained cohesion at top of layer = 3000. psf
Undrained cohesion at bottom of layer = 3000. psf
Epsilon-50 at top of layer = 0.005000
Epsilon-50 at bottom of layer = 0.005000
Layer 10 is sand, p-y criteria by Reese et al., 1974
Distance from top of pile to top of layer = 94.000000 ft
Distance from top of pile to bottom of layer = 105.000000 ft
Effective unit weight at top of layer = 56.000000 pcf
Effective unit weight at bottom of layer = 56.000000 pcf
Friction angle at top of layer = 36.000000 deg.
Friction angle at bottom of layer = 36.000000 deg.
Subgrade k at top of layer = 70.000000 pci
Subgrade k at bottom of layer = 70.000000 pci
Layer 11 is stiff clay without free water
Distance from top of pile to top of layer = 105.000000 ft
Distance from top of pile to bottom of layer = 125.000000 ft
Effective unit weight at top of layer = 56.000000 pcf
Effective unit weight at bottom of layer = 56.000000 pcf
Undrained cohesion at top of layer = 5000. psf
Undrained cohesion at bottom of layer = 5000. psf
Epsilon-50 at top of layer = 0.004000
Epsilon-50 at bottom of layer = 0.004000
(Depth of the lowest soil layer extends 70.000 ft below the pile tip)
--------------------------------------------------------------------------------
Summary of Input Soil Properties
--------------------------------------------------------------------------------
Layer Soil Type Layer Effective Undrained Angle of
E50
Layer Name Depth Unit Wt. Cohesion Friction
or kpy
Num. (p-y Curve Type) ft pcf psf deg.
krm pci
----- ------------------- ---------- ---------- ---------- ----------
---------- ----------
1 Soft 0.00 100.0000 1000.0000 --
0.01000 --
Clay 10.0000 100.0000 1000.0000 --
0.01000 --
2 Soft 10.0000 38.0000 1000.0000 --
0.01000 --
Clay 17.0000 38.0000 1000.0000 --
0.01000 --
3 Stiff Clay 17.0000 46.0000 1500. --
0.00700 --
w/o Free Water 26.0000 46.0000 1500. --
0.00700 --
4 Sand 26.0000 49.0000 -- 32.0000
-- 62.0000
(Reese, et al.) 32.0000 49.0000 -- 32.0000
-- 62.0000
5 Stiff Clay 32.0000 56.0000 1500. --
0.00700 --
w/o Free Water 45.0000 56.0000 1500. --
0.00700 --
6 Sand 45.0000 56.0000 -- 36.0000
-- 70.0000
(Reese, et al.) 50.0000 56.0000 -- 36.0000
-- 70.0000
7 Stiff Clay 50.0000 56.0000 2000. --
0.00500 --
w/o Free Water 64.0000 56.0000 2000. --
0.00500 --
8 Stiff Clay 64.0000 56.0000 38.0000 --
75.0000 --
w/o Free Water 74.0000 56.0000 38.0000 --
75.0000 --
9 Stiff Clay 74.0000 56.0000 3000. --
0.00500 --
w/o Free Water 94.0000 56.0000 3000. --
0.00500 --
10 Sand 94.0000 56.0000 -- 36.0000
-- 70.0000
(Reese, et al.) 105.0000 56.0000 -- 36.0000
-- 70.0000
11 Stiff Clay 105.0000 56.0000 5000. --
0.00400 --
w/o Free Water 125.0000 56.0000 5000. --
0.00400 --
--------------------------------------------------------------------------------
Static Loading Type
--------------------------------------------------------------------------------
Static loading criteria were used when computing p-y curves for all analyses.
--------------------------------------------------------------------------------
Pile-head Loading and Pile-head Fixity Conditions
--------------------------------------------------------------------------------
Number of loads specified = 1
Load Load Condition Condition Axial Thrust
Compute Top y Run Analysis
No. Type 1 2 Force, lbs
vs. Pile Length
----- ---- -------------------- ----------------------- ----------------
--------------- ------------
1 1 V = 15000. lbs M = 0.0000 in-lbs 235000.
No Yes
V = shear force applied normal to pile axis
M = bending moment applied to pile head
y = lateral deflection normal to pile axis
S = pile slope relative to original pile batter angle
R = rotational stiffness applied to pile head
Values of top y vs. pile lengths can be computed only for load types with
specified shear loading (Load Types 1, 2, and 3).
Thrust force is assumed to be acting axially for all pile batter angles.
--------------------------------------------------------------------------------
Computations of Nominal Moment Capacity and Nonlinear Bending Stiffness
--------------------------------------------------------------------------------
Axial thrust force values were determined from pile-head loading conditions
Number of Pile Sections Analyzed = 1
Pile Section No. 1:
-------------------
Moment-curvature properties were derived from elastic section properties
--------------------------------------------------------------------------------
Layering Correction Equivalent Depths of Soil & Rock Layers
--------------------------------------------------------------------------------
Top of Equivalent
Layer Top Depth Same Layer Layer is F0 F1
Layer Below Below Type As Rock or Integral Integral
No. Pile Head Grnd Surf Layer is Below for Layer for Layer
ft ft Above Rock Layer lbs lbs
----- ---------- ---------- ---------- ---------- ---------- ----------
1 0.00 0.00 N.A. No 0.00 65833.
2 10.0000 10.0000 Yes No 65833. 72923.
3 17.0000 12.9921 No No 138757. 141671.
4 26.0000 17.8779 No No 280428. 356435.
5 32.0000 44.6938 No No 636863. 204750.
6 45.0000 23.8592 No No 841613. 624098.
7 50.0000 74.1589 No No 1465712. 105000.
8 64.0000 64.0000 No No 1570712. 0.00
9 74.0000 74.0000 No No 0.00 0.00
10 94.0000 94.0000 No No 0.00 0.00
11 105.0000 105.0000 No No 0.00 N.A.
Notes: The F0 integral of Layer n+1 equals the sum of the F0 and F1 integrals
for Layer n. Layering correction equivalent depths are computed only
for soil types with both shallow-depth and deep-depth expressions for
peak lateral load transfer. These soil types are soft and stiff clays,
non-liquefied sands, and cemented c-phi soil.
--------------------------------------------------------------------------------
Computed Values of Pile Loading and Deflection
for Lateral Loading for Load Case Number 1
--------------------------------------------------------------------------------
Pile-head conditions are Shear and Moment (Loading Type 1)
Shear force at pile head = 15000.0 lbs
Applied moment at pile head = 0.0 in-lbs
Axial thrust load on pile head = 235000.0 lbs
Depth Deflect. Bending Shear Slope Total Bending Soil
Res. Soil Spr. Distrib.
X y Moment Force S Stress Stiffness p
Es*h Lat. Load
feet inches in-lbs lbs radians psi* in-lb^2
lb/inch lb/inch lb/inch
---------- ---------- ---------- ---------- ---------- ---------- ----------
---------- ---------- ----------
0.00 0.4689 3.32E-07 15000. -0.00574 1199. 1.30E+10
-160.7669 1131. 0.00
0.5500 0.4310 104396. 13904. -0.00571 1427. 1.30E+10
-171.4658 2626. 0.00
1.1000 0.3935 201241. 12740. -0.00563 1639. 1.30E+10
-181.0350 3036. 0.00
1.6500 0.3567 290042. 11518. -0.00551 1833. 1.30E+10
-189.4210 3505. 0.00
2.2000 0.3208 370364. 10244. -0.00534 2009. 1.30E+10
-196.5730 4044. 0.00
2.7500 0.2862 441833. 8927. -0.00514 2165. 1.30E+10
-202.4426 4669. 0.00
3.3000 0.2530 504137. 7576. -0.00490 2301. 1.30E+10
-206.9837 5399. 0.00
3.8500 0.2215 557029. 6200. -0.00463 2417. 1.30E+10
-210.1517 6261. 0.00
4.4000 0.1919 600330. 4807. -0.00434 2512. 1.30E+10
-211.9031 7287. 0.00
4.9500 0.1643 633928. 3407. -0.00402 2585. 1.30E+10
-212.1945 8524. 0.00
5.5000 0.1388 657787. 2011. -0.00370 2637. 1.30E+10
-210.9814 10031. 0.00
6.0500 0.1155 671938. 627.5546 -0.00336 2668. 1.30E+10
-208.2159 11896. 0.00
6.6000 0.09446 676492. -732.2411 -0.00302 2678. 1.30E+10
-203.8434 14242. 0.00
7.1500 0.07567 671636. -2058. -0.00268 2668. 1.30E+10
-197.7973 17252. 0.00
7.7000 0.05912 657637. -3337. -0.00234 2637. 1.30E+10
-189.9887 21210. 0.00
8.2500 0.04476 634846. -4559. -0.00201 2587. 1.30E+10
-180.2892 26582. 0.00
8.8000 0.03253 603703. -5710. -0.00170 2519. 1.30E+10
-168.4943 34185. 0.00
9.3500 0.02231 564747. -6775. -0.00141 2434. 1.30E+10
-154.2456 45625. 0.00
9.9000 0.01398 518628. -7736. -0.00113 2333. 1.30E+10
-136.8282 64591. 0.00
10.4500 0.00738 466142. -8564. -8.82E-04 2218. 1.30E+10
-114.1312 102046. 0.00
11.0000 0.00234 408319. -9205. -6.61E-04 2092. 1.30E+10
-80.1948 226306. 0.00
11.5500 -0.00134 346682. -9244. -4.70E-04 1957. 1.30E+10
68.3709 336661. 0.00
12.1000 -0.00386 287752. -8697. -3.09E-04 1828. 1.30E+10
97.3636 166403. 0.00
12.6500 -0.00542 232836. -8016. -1.78E-04 1708. 1.30E+10
109.0388 132727. 0.00
13.2000 -0.00620 182488. -7280. -7.24E-05 1598. 1.30E+10
114.0578 121322. 0.00
13.7500 -0.00638 136965. -6524. 8.40E-06 1498. 1.30E+10
115.1130 119118. 0.00
14.3000 -0.00609 96348. -5770. 6.74E-05 1410. 1.30E+10
113.3794 122794. 0.00
14.8500 -0.00549 60595. -5034. 1.07E-04 1331. 1.30E+10
109.4908 131674. 0.00
15.4000 -0.00468 29564. -4330. 1.30E-04 1264. 1.30E+10
103.8282 146430. 0.00
15.9500 -0.00377 3032. -3669. 1.38E-04 1206. 1.30E+10
96.6335 169046. 0.00
16.5000 -0.00286 -19293. -3059. 1.34E-04 1241. 1.30E+10
88.0659 203535. 0.00
17.0500 -0.00200 -37767. -2118. 1.20E-04 1282. 1.30E+10
197.3037 650124. 0.00
17.6000 -0.00128 -47616. -884.7328 9.80E-05 1303. 1.30E+10
176.2815 911481. 0.00
18.1500 -7.09E-04 -49749. 199.1680 7.34E-05 1308. 1.30E+10
152.1733 1416742. 0.00
18.7000 -3.08E-04 -45215. 1109. 4.94E-05 1298. 1.30E+10
123.4877 2650293. 0.00
19.2500 -5.71E-05 -35266. 1598. 2.90E-05 1276. 1.30E+10
24.6207 2844155. 0.00
19.8000 7.55E-05 -24216. 1572. 1.40E-05 1252. 1.30E+10
-32.5254 2844155. 0.00
20.3500 1.27E-04 -14565. 1283. 4.15E-06 1231. 1.30E+10
-54.8198 2844155. 0.00
20.9000 1.30E-04 -7290. 917.0735 -1.38E-06 1215. 1.30E+10
-56.1525 2844155. 0.00
21.4500 1.09E-04 -2455. 576.6910 -3.84E-06 1204. 1.30E+10
-46.9937 2844155. 0.00
22.0000 7.96E-05 334.2620 308.4177 -4.38E-06 1200. 1.30E+10
-34.3012 2844155. 0.00
22.5500 5.13E-05 1629. 122.3270 -3.88E-06 1203. 1.30E+10
-22.0899 2844155. 0.00
23.1000 2.84E-05 1961. 9.0930 -2.97E-06 1203. 1.30E+10
-12.2235 2844155. 0.00
23.6500 1.20E-05 1759. -48.3364 -2.03E-06 1203. 1.30E+10
-5.1794 2844155. 0.00
24.2000 1.55E-06 1329. -67.6268 -1.25E-06 1202. 1.30E+10
-0.6662 2844155. 0.00
24.7500 -4.49E-06 869.8513 -63.4438 -6.94E-07 1201. 1.30E+10
1.9338 2844155. 0.00
25.3000 -7.62E-06 493.9761 -46.2316 -3.49E-07 1200. 1.30E+10
3.2820 2844155. 0.00
25.8500 -9.09E-06 260.6763 -22.4676 -1.58E-07 1200. 1.30E+10
3.9192 2844155. 0.00
26.4000 -9.70E-06 197.8937 -8.9053 -4.21E-08 1199. 1.30E+10
0.1906 129635. 0.00
26.9500 -9.65E-06 143.2575 -7.6378 4.42E-08 1199. 1.30E+10
0.1935 132335. 0.00
27.5000 -9.12E-06 96.9376 -6.3836 1.05E-07 1199. 1.30E+10
0.1866 135036. 0.00
28.0500 -8.26E-06 58.6688 -5.1987 1.44E-07 1199. 1.30E+10
0.1725 137737. 0.00
28.6000 -7.21E-06 27.8667 -4.1231 1.66E-07 1199. 1.30E+10
0.1535 140437. 0.00
29.1500 -6.07E-06 3.7288 -3.1822 1.74E-07 1199. 1.30E+10
0.1316 143138. 0.00
29.7000 -4.91E-06 -14.6782 -2.3895 1.71E-07 1199. 1.30E+10
0.1086 145839. 0.00
30.2500 -3.81E-06 -28.3446 -1.7486 1.61E-07 1199. 1.30E+10
0.08565 148540. 0.00
30.8000 -2.79E-06 -38.2576 -1.2547 1.44E-07 1199. 1.30E+10
0.06401 151240. 0.00
31.3500 -1.91E-06 -45.3525 -0.8966 1.23E-07 1199. 1.30E+10
0.04451 153941. 0.00
31.9000 -1.17E-06 -50.4730 -0.6577 9.84E-08 1199. 1.30E+10
0.02788 156642. 0.00
32.4500 -6.10E-07 -54.3392 0.3018 7.18E-08 1199. 1.30E+10
0.2629 2844155. 0.00
33.0000 -2.27E-07 -46.7125 1.4915 4.63E-08 1199. 1.30E+10
0.09765 2844155. 0.00
33.5500 7.84E-10 -34.7955 1.8126 2.56E-08 1199. 1.30E+10
-3.38E-04 2844155. 0.00
34.1000 1.12E-07 -22.8659 1.6523 1.11E-08 1199. 1.30E+10
-0.04825 2844155. 0.00
34.6500 1.47E-07 -13.0200 1.2843 1.98E-09 1199. 1.30E+10
-0.06325 2844155. 0.00
35.2000 1.38E-07 -5.9191 0.8792 -2.81E-09 1199. 1.30E+10
-0.05951 2844155. 0.00
35.7500 1.10E-07 -1.4059 0.5268 -4.66E-09 1199. 1.30E+10
-0.04726 2844155. 0.00
36.3000 7.65E-08 1.0497 0.2621 -4.75E-09 1199. 1.30E+10
-0.03298 2844155. 0.00
36.8500 4.69E-08 2.0680 0.08652 -3.97E-09 1199. 1.30E+10
-0.02021 2844155. 0.00
37.4000 2.42E-08 2.2041 -0.01457 -2.88E-09 1199. 1.30E+10
-0.01042 2844155. 0.00
37.9500 8.82E-09 1.8846 -0.06150 -1.85E-09 1199. 1.30E+10
-0.00380 2844155. 0.00
38.5000 -2.44E-10 1.3980 -0.07370 -1.02E-09 1199. 1.30E+10
1.05E-04 2844155. 0.00
39.0500 -4.64E-09 0.9149 -0.06676 -4.35E-10 1199. 1.30E+10
0.00200 2844155. 0.00
39.6000 -5.98E-09 0.5182 -0.05165 -7.22E-11 1199. 1.30E+10
0.00258 2844155. 0.00
40.1500 -5.59E-09 0.2334 -0.03518 1.18E-10 1199. 1.30E+10
0.00241 2844155. 0.00
40.7000 -4.43E-09 0.05341 -0.02093 1.90E-10 1199. 1.30E+10
0.00191 2844155. 0.00
41.2500 -3.08E-09 -0.04349 -0.01025 1.93E-10 1199. 1.30E+10
0.00133 2844155. 0.00
41.8000 -1.88E-09 -0.08252 -0.00320 1.61E-10 1199. 1.30E+10
8.10E-04 2844155. 0.00
42.3500 -9.54E-10 -0.08620 8.32E-04 1.18E-10 1199. 1.30E+10
4.11E-04 2844155. 0.00
42.9000 -3.17E-10 -0.07190 0.00264 7.84E-11 1199. 1.30E+10
1.36E-04 2844155. 0.00
43.4500 8.07E-11 -0.05160 0.00298 4.72E-11 1199. 1.30E+10
-3.48E-05 2844155. 0.00
44.0000 3.06E-10 -0.03278 0.00243 2.58E-11 1199. 1.30E+10
-1.32E-04 2844155. 0.00
44.5500 4.21E-10 -0.01966 0.00139 1.25E-11 1199. 1.30E+10
-1.82E-04 2844155. 0.00
45.1000 4.71E-10 -0.01445 7.33E-04 3.91E-12 1199. 1.30E+10
-1.79E-05 250034. 0.00
45.6500 4.73E-10 -0.01000 6.15E-04 -2.27E-12 1199. 1.30E+10
-1.81E-05 253084. 0.00
46.2000 4.41E-10 -0.00633 4.98E-04 -6.40E-12 1199. 1.30E+10
-1.71E-05 256133. 0.00
46.7500 3.89E-10 -0.00340 3.91E-04 -8.86E-12 1199. 1.30E+10
-1.53E-05 259182. 0.00
47.3000 3.24E-10 -0.00114 2.98E-04 -1.00E-11 1199. 1.30E+10
-1.29E-05 262231. 0.00
47.8500 2.56E-10 5.69E-04 2.22E-04 -1.02E-11 1199. 1.30E+10
-1.03E-05 265280. 0.00
48.4000 1.90E-10 0.00182 1.62E-04 -9.55E-12 1199. 1.30E+10
-7.74E-06 268330. 0.00
48.9500 1.30E-10 0.00274 1.19E-04 -8.39E-12 1199. 1.30E+10
-5.36E-06 271379. 0.00
49.5000 7.96E-11 0.00342 9.05E-05 -6.83E-12 1199. 1.30E+10
-3.31E-06 274428. 0.00
50.0500 4.02E-11 0.00396 -3.30E-06 -4.97E-12 1199. 1.30E+10
-2.51E-05 4125000. 0.00
50.6000 1.40E-11 0.00339 -1.15E-04 -3.11E-12 1199. 1.30E+10
-8.74E-06 4125000. 0.00
51.1500 0.00 0.00245 -1.42E-04 -1.63E-12 1199. 1.30E+10
5.45E-07 4125000. 0.00
51.7000 -7.55E-12 0.00152 -1.25E-04 0.00 1199. 1.30E+10
4.72E-06 4125000. 0.00
52.2500 -9.13E-12 8.05E-04 -9.02E-05 0.00 1199. 1.30E+10
5.71E-06 4125000. 0.00
52.8000 -8.03E-12 3.33E-04 -5.48E-05 0.00 1199. 1.30E+10
5.02E-06 4125000. 0.00
53.3500 -5.81E-12 8.02E-05 -2.63E-05 0.00 1199. 1.30E+10
3.63E-06 4125000. 0.00
53.9000 -3.32E-12 -1.50E-05 -7.47E-06 0.00 1199. 1.30E+10
2.08E-06 4125000. 0.00
54.4500 0.00 -1.96E-05 1.22E-06 0.00 1199. 1.30E+10
5.56E-07 4125000. 0.00
55.0000 1.48E-12 0.00 0.00 0.00 1199. 1.30E+10
-9.25E-07 2062500. 0.00
* The above values of total stress are combined axial and bending stresses.
Output Summary for Load Case No. 1:
Pile-head deflection = 0.46888973 inches
Computed slope at pile head = -0.00573659 radians
Maximum bending moment = 676492. inch-lbs
Maximum shear force = 15000. lbs
Depth of maximum bending moment = 6.60000000 feet below pile head
Depth of maximum shear force = 0.000000 feet below pile head
Number of iterations = 26
Number of zero deflection points = 8
--------------------------------------------------------------------------------
Summary of Pile-head Responses for Conventional Analyses
--------------------------------------------------------------------------------
Definitions of Pile-head Loading Conditions:
Load Type 1: Load 1 = Shear, V, lbs, and Load 2 = Moment, M, in-lbs
Load Type 2: Load 1 = Shear, V, lbs, and Load 2 = Slope, S, radians
Load Type 3: Load 1 = Shear, V, lbs, and Load 2 = Rot. Stiffness, R, in-lbs/rad.
Load Type 4: Load 1 = Top Deflection, y, inches, and Load 2 = Moment, M, in-lbs
Load Type 5: Load 1 = Top Deflection, y, inches, and Load 2 = Slope, S, radians
Load Load Load Axial Pile-head Pile-head Max
Shear Max Moment
Case Type Pile-head Type Pile-head Loading Deflection Rotation in
Pile in Pile
No. 1 Load 1 2 Load 2 lbs inches radians lbs
in-lbs
---- ----- ---------- ---------- ---------- ---------- ---------- ----------
---------- ----------
1 V, lb 15000. M, in-lb 0.00 235000. 0.4689 -0.00574
15000. 676492.
Maximum pile-head deflection = 0.4688897335 inches
Maximum pile-head rotation = -0.0057365858 radians = -0.328682 deg.
The analysis ended normally.