post-tensioning design.pptx
TRANSCRIPT
Post-Tensioned Concrete Design
Brian SwartzUniversity of Hartford
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 2
Load Balancing (Equivalent Forces)
• Single Drape Point• Force required to hold prestressing strands in place:
PP θ
Pcosθθ
Psinθ
Pcosθ
Psinθ
2Psinθ
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 3
Load Balancing (Equivalent Forces)
• Single Drape Point• Force applied to the beam at transfer:
Pcosθθ
Psinθ
Pcosθ
Psinθ
2Psinθ
e
L
L
PeP
4sin2
PeL
LPe
FLM
4
4
4max
Internal moment due to equivalent force system equals P*e
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 4
Load Balancing (Equivalent Forces)
• Parabolic Profile
Pcosθ
θ
Psinθ
Pcosθ
Psinθ
e
L
L
P sin2
A
A
L
ParabolaTan
gent
to P
arab
ola
2
8sin2
L
Pe
L
P
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 5
Load Balancing (Equivalent Forces)
• Straight Profile with Eccentricity
PP
eM = P*e M = P*e
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 6
Load Balancing (Equivalent Forces)
Source: PTI Manual
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 7
Load Balancing (Equivalent Forces)
Source: Aalami (1990)
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 8
Load Balancing
• Rule of Thumb:– PT should balance ~70%-100% of structural dead
load
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 9
Indeterminate Structures
• “Primary” Effects
• Deflection due to “Primary” Effects
PP
eM = P*e M = P*e
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 10
Indeterminate Structures
• Deformation compatibility with supports– “Secondary” Reactions
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 11
Indeterminate StructuresPrimary Moment (P*e)
Secondary Moment
M = P*e M = P*e
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 12
Indeterminate Structures
Source: Aalami (1990)
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 13
Indeterminate Structures
Resultant Moment = Primary Moment + Secondary Moment
P*e
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 14
Exercise: Eq. Forces and Secondary Moments
Mprim = P*e1
Source: Lin and Burns, 1981
e1
Steel Centroid
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 15
Exercise: Eq. Forces and Secondary Moments
Mres
e1
P
Me res2
Center of Compression
Steel Centroid
Msec = Mres - Mprim
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 16
Secondary Moments as a “Load”
ACI 318-08
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 17
Flexural Analysis: Concrete Stress
• Concrete stress due to prestressing:
• Concrete stress due to loads:
I
Pey
A
Pf
P
Pe
P*e
I
Myf
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 18
Flexural Analysis: Steel StressUltimate Strength, fpu
Initial Prestress, fpo
Effective Prestress, fpe
Str
ess
in S
teel
Load on Beam
Girder Selfweight
Service Load
Cracking Load
Ultimate Load
Jacking, Elastic Shortening, and
Camber
Loss of Prestress
Bonded Tendons
Unbonded Tendons
Source: Lin and Burns, 1981
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 19
Bonded vs Unbonded
Source: PTI
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 20
Flexural Analysis: Steel Stress
• Steel stress due to loads (Bonded System)– Concrete Stress
– Concrete Strain
– Steel Strain
– Steel Stress
I
Myfc
IE
My
E
f
cc
cc
IE
My
ccs
I
Myn
IE
MyEEf
c
ssss
Strain Compatibility
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 21
Flexural Analysis: Steel Stress
• Steel stress due to loads (Bonded System)
Large steel strain/stress
Small steel strain/stress
Mo
men
t
Compatibility
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 22
Flexural Analysis: Steel Stress
• Steel stress due to loads (Unbonded System)
Large steel strain/stress
Small steel strain/stress
Mom
ent
SlipSlip
Average steel strain/stress
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 23
Flexural Analysis: Steel Stress
• Steel stress due to loads (Unbonded System)– Concrete Stress
– Concrete Strain (at any position)
– Concrete Strain (total over length of tendon)
I
Myfc
IE
My
E
f
cc
cc
L
x c
L
x
xc dxIE
xyxMd
00
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 24
Flexural Analysis: Steel Stress
• Steel stress due to loads (Unbonded System)– Steel strain (average of concrete strain)
– Steel stress
• Mild reinforcement required for crack control…
L
x cs dx
ILE
xyxM
L 0
L
x
L
x c
ssss dx
xI
xyxM
L
ndx
ILE
ExyxMEf
00
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 25
Flexural Analysis: Ultimate Capacity
22'
2''
adfA
adfAd
afAM tysppspssssn
Tp = Apsfps
CA’sf’s
Ts = Asfy
c ε’s
εt
εpeεp
εcu
Tp = Apsfps
f’s
Ts = Asfy
C
.85f’c
a/2
a
dt d’s dp
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 26
Flexural Analysis: Steel Stress at Ultimate
Reinforcing Steel
Prestressing Steelfpu
fps
fpy
fpe
fy
Strain
Str
ess
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 27
Flexural Analysis: Steel Stress at Ultimate
(most beams)
(most slabs)
ACI 318-08
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 28
Moment Redistribution
• Assumed bi-linear Moment-Curvature relationship
Mom
ent,
M
Curvature, θ
φMn
Moment-Curvature Exercise
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 29
Moment Redistribution: Neg M Hinges
L
Fix
ed
w
Fixe
d
24
2wL
12
2wL
12
2wL
0.4
0.4
n
n
M
M
Source: Bondy (2003)
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 30
Moment Redistribution: Neg M Hinges
L
Fix
ed
w
Fixed
-4.0
21
48
Lw
Additional load carried by effective simple-span
“Plastic Hinge” – Add’l curvature w/o taking more load
Source: Bondy (2003)
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 31
Moment Redistribution: Neg M Hinges
LF
ixe
d
w
Fixe
d
-4.0
+4.0
+2.67
-5.33
22
64
Lw
Additional plastic hinge (and failure) follows
Theoretical M-diagram if w2 is carried elastically
Source: Bondy (2003)
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 32
Moment Redistribution: Neg M Hinges
• If the design load is w2, the negative moment region can only carry 4/5.33 = 75% of its demand
• Therefore (1-4/5.33) = 25% of the demand must be “redistributed” to other sections
-4.0
+4.0
+2.67
-5.33
Source: Bondy (2003)
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 33
Moment Redistribution: Pos M Hinges
L
Fix
ed
w
Fixe
d
-3.0
+1.0+1.33
-2.67
Flexural capacity w1, plastic hinge
forms at midspan
w2, plastic hinge forms at end supports
Theoretical M-diagram if w2 is carried elastically
Source: Bondy (2003)
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 34
Moment Redistribution: Pos M Hinges
• If the design load is w2, the positive moment region can only carry 1/1.33 = 75% of its demand
• Therefore (1-1/1.33) = 25% of the demand must be “redistributed” to other sections
-3.0
+1.0+1.33
-2.67
Source: Bondy (2003)
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 35
Moment Redistribution: ACI 318-08
Source: ACI 318-08
Ductility
Re-analyze
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 36
Moment Redistribution
• Plastic hinges do not cause secondary moments to “disappear”
• Why is it important for post-tensioned structures?– Same “reinforcement” entire length– Continuous construction common
• Max effects from pattern loads
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 37
Moment Redistribution
DL
LL
Elastic M-diagram for load case yielding M+max
Redistributed M-diagram for load case yielding M+max
Elastic M-diagram for load case yielding M-max
Redistributed M-diagram for load case yielding M-max
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 38
Other Considerations
• Volume Change– Provide slip detail to prevent restraint cracks
• “Banded” Tendons for two-way slabs
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 39
Development Length
Ld ~ 0
Source: ASBI
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 40
Loss of Prestress
fpy
Strain
Str
ess
Jacking
fjack
fpu270 ksi
0.9*fpu = 243 ksi
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 41
Loss of Prestress
• Friction• Anchor Set• Elastic Shortening• Shrinkage• Creep• Relaxation
Specific to post-tensioning
Similar to pre-tensioning
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 42
Friction Loss
• Length effect – “wobble”• Curvature effect• Coefficient of Friction
• Monitor elongation in addition to pressure during jacking
• Overcoming Friction:– Over-tensioning (limited)– Jacking from “dead end”
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 43
Anchorage Set Loss
Concrete
Duct
Strand
Anchor cast in concrete
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 44
Anchorage Devices
STANDARD ANCHORSENCAPSULATEDANCHOR
WEDGES
ENCAPSULATEDANCHOR
Source: PTI
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 45
Anchorage Devices: Wedge
Source: PTI
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 46
Friction and Anchorage LossesJa
ckin
g S
tres
s 1
Anc
. Sea
ting
Loss
1
Jack
ing
Str
ess 2
Anc
. Sea
ting
Loss
2
Increased PT due to jacking2
Effect of live end jacking2
Jacking1 Jacking2
For
ce in
Ten
don
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 47
Elastic Shortening Losses
• Shortening of concrete compensated in jacking as the two occur simultaneously
• If only one strand (tendon) – no ES losses
• If multiple strands (tendons)– Tendons jacked early in the sequence will suffer
losses as subsequent tendons are stressed– The first strand stressed will suffer the most total
loss– The last strand jack has zero loss– Reasonable to take the average of first and last
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 48
Anchorage Zone Confinement
Source: PTI
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 49
Anchorage Zone Confinement
Source: PTI
P
Anchorage Device
Local Zone
General Zone
NCHRP Report 356
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 50
Anchorage Zone Design: Local
Compression stress under anchorage bearing plate
Friction from bearing plate
Confining pressure produced by spiral
Shear forces transfer force into surrounding concrete reducing compression stress on confined core
Compression stresses at lower end of confined cylinder
Source: VSL
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 51
Anchorage Zone Design: General
Source: NCHRP Report 356
Strut and Tie Model
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 52
Grouted Post-Tensioned Systems
• Objectives in grouting:– Durability – corrosion protection– Structural bonded – “bonded” behavior
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 53
Grouting: Anchor Details
Source: PTI
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 54
Grouting
Grout In
Vent
Vent
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 55
Grouting: Materials
• Fluidity• Bleed• Segregation• Set Time• Strength• Permeability• Volume Change• Corrosion Protection
Source: Andrea Schokker
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 56
Grouting: Materials
• Must be easy to pump• Must have minimal bleeding
– “Thixotropic”Intermediate Lens
Bleed
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 57
Multistrand Stressing
Source: PTI
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 58
Monostrand Jacking
Source: PTI
Source: PTI
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 59
PT Advantages: Structural
• Increase span-to-depth ratio– Reduce floor thickness
• Dead Load• Story (building) height
– Increase span lengths• More usable space
• Connection of precast components
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 60
PT Advantages: Geometric Flexibility
Source: PTI
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 61
PT Advantages: Geometric Flexibility
Source: PTI
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 62
PT Advantages: Geometric Flexibility
Source: PTI
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 63
PT Advantages: Constructability
• Earlier stripping of formwork– Faster construction cycle
• Reduced need for re-shoring– Approx. weight of one floor “balanced” by post-
tensioning force• Schedule flexibility
– Earlier installation of non-structural components
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 64
PT Advantages: Serviceability
• Uncracked behavior– Reduced deflection (for the same thickness)– Durability
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 65
PT Applications: Buildings
Source: PTI
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 66
PT Applications: Slab on Grade
Source: PTI
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 67
PT Applications: Mat Foundations
Source: PTI
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 68
PT Applications: Industrial Floors
Source: PTI
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 69
PT Applications: Parking Structures
Source: PTI
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 70
PT Applications: Prestressed Ground Anchors
Source: PTI
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 71
PT Applications: Prestressed Ground Anchors
Source: PTI
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 72
PT Applications: Storage Structures
Source: PTI
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 73
PT Applications: Spliced Girder Bridges
Source: PTI
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 74
PT Applications: Segmental Bridges
Source: ASBI
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 75
PT Applications: Barrier Cable
Source: PTI
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 76
PT Applications: Retrofit & Strengthening
Source: Seneca Structural Engineering
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 77
Summary: Why teach post-tensioning?
• Reinforce basic mechanics in the curriculum• Do not treat as a separate concept from pre-
tensioning• Increasingly common in practice
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 78
Resources: PTI
Post-Tensioning Institute38800 Country Club Dr. Farmington Hills, MI 48331248-848-3180www.post-tensioning.org
04/18/2023 Developed by Brian Swartz for the PCA Professor’s Seminar 79
References
• Aalami, B.O. “Load Balancing: A Comprehensive Solution to Post-Tensioning.” ACI Structural Journal, V. 87, N.6, Nov-Dec 1990. pp 662-670.
• Bondy, K.B. “Moment Redistribution: Principles and Practice Using ACI 318-02.” PTI Journal, Jan 2003, pp 3-21.
• Post-Tensioning Institute. “Post-Tensioning Manual.” Sixth Edition. 2006.• Lin, T.Y. and Burns, N.H. “Design of Prestressed Concrete Structures .” Third Edition. John
Wiley and Sons. 1981.