1 neesr project meeting 22/02/2008 modeling of bridge piers with shear-flexural interaction and...
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1NEESR Project Meeting
22/02/2008
Modeling of Bridge Piers with Shear-Flexural Interaction and Bridge System Response
Modeling of Bridge Piers with Shear-Flexural Interaction and Bridge System Response
Prof. Jian Zhang
Shi-Yu Xu
Prof. Jian Zhang
Shi-Yu Xu
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2 NEESR Project Meeting
Prototype Bridges
Structural Characteristics
FHWA Design Example #4Bridge #4
FHWA Design Example #8 Bridge #8
Mendocino Ave. OvercrossingBridge Mendocino (1963)
Span Length Three-span continuous Five-span continuous Uneven, four-span continuous
Total Length 320 ft long 500 ft long 302 ft long
Pier TypeTwo-column integral bent, monolithic at column top, pinned at base
Two-column integral bent, monolithic at column top and base
Single column variable height, monolithic at column top and base
Abutment Type
Seat Stub abutment with diaphragm Monolithic
Foundation Type Spread Footing Pile Group Pile Group
Expansion Joints
Expansion bearings & girder stops (shear keys)
Expansion bearings & girder stops Expansion bearings & girder stops
Force Resisting
Mechanism
[Longitudinal] intermediate bent columns & free longitudinal movement at abutments[Transverse] intermediate bent columns & abutments
[Longitudinal] intermediate bent columns and abutment backfill[Transverse] intermediate bent columns and abutment backfill
[Longitudinal] intermediate columns and abutment backfill[Transverse] intermediate columns and abutment backfill
Plan Geometry 30° skewed Straight Straight
Natural Period ~ 0.5 sec ~ 1.5 sec ~ 0.5 sec
Design Method Old design New design Old design
Three box girder concrete bridges are selected as prototype bridges for preliminary analysis.
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3 NEESR Project Meeting
Factors Affecting Bridge Response
Site Conditions
Soil-structure Interaction
Earthquake Characteristics
Ground Motion Selection
Structure Properties
Geometry (straight, skew or curved)
Stiffness, ductility, energy dissipation
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4 NEESR Project Meeting
k11
k44
k22
k55
k33
k66
ks
ky kθx
kz
Finite Element Bridge Models
fixed
k11
k44
k22
k55
k33
k66
kz (a) Bridge #4
(b) Bridge #8
(c) Bridge Mendocino
k11
k44
k22
k55
k33
k66
kykx
kz
kθx
XZ
Y
(d) Imaginary Bridge Mendocino with 30° skewed embankment & bent columns
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5 NEESR Project Meeting
Summary of Modeling Parameters
Interested Issue Question to Answer Model TypeTested Bridges
Bridge #4 Bridge #8 Mendocino
Effects of Input Ground Motion
How are seismic demands related to ground motion intensity?
Linear ● ●
Nonlinear ● ●
Effects of Vertical Acceleration
How does vertical acceleration change the bridge seismic demand?
Linear ● ●
Nonlinear ● ●
Effects of Nonlinearity
How does nonlinear behavior in columns affect the seismic demand of the bridges?
Linear v.s. Nonlinear ● ●
T/M ratio: Column type
What type of column design (bent column v.s. single column design) yields higher T/M ratio?
Bent ● ● ●
Single ●
T/M ratio: Skewness
Will skewed bents and/or abutments cause higher T/M ratio?
Straight ● ●
Skewed ● ●
T/M ratio: Stiffer column
What is the effect of a stiffer (short) column in the bridge systems?
One short column ●
T/M ratio:Pinned design @ Column base
Is pinned design at column bases advantageous in eliminating torsional demand on the columns?
Pinned w/ SSI ● ●
Fixed w/ SSI ● ●
Fixed w/o SSI ●
Effects of Axial-Shear- Flexural Interaction
How the interaction between combined loadings affects the capacity of bridges?
NonlinearABAQUS User Element
under development
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6 NEESR Project Meeting
Observations
Effect of PGA Linear Model : Response (A,D,SF,SM) increase almost
linearly with PGA. Non-linear Model : Response increase non-linearly with PGA.
Effect of Non-linearity Column forces (SF,SM) reduced by 5% ~ 60%. Non-linearity effects is more significant in strong earthquakes
than in small ones.
Effect of Vertical Ground Motion Only affect vertical response quantities. Incorrect Vertical responses increase almost linearly with maximum
vertical PGA. Tensile axial force is observed in columns during earthquakes. For bent column bridges, tensile axial force is observed in
columns in most of Bin 4 earthquakes; while axial force in the single column bridge seldom goes into tension side.
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7 NEESR Project Meeting
Observations (continued)
Effect of Column Type (Bent Column vs Single Column) on T/M ratio: Bent column design greatly reduce the Torsion/Moment ratio in colu
mns, if columns are the same in dimension and reinforcement. For bridges with bents, reducing the lateral stiffness/capacity of colu
mns will result in a higher T/M ratio. If bending capacity of columns is met in one of the horizontal directi
ons, torsion-moment interaction may become very significant.
Effect of Skewness on T/M ratio: Skewed bridges do NOT necessarily increase T/M ratio. (?)
Effect of Stiffer Column on T/M ratio: A relatively stiffer column in the bridges will introduce a higher level
of asymmetry into the system and thus results in higher T/M ratios.
Effect of Pinned Design at Column Base on T/M ratio: Pinned design at column bases greatly eliminates torsional demand.
Effect of Combined Actions Investigate Shear-Flexural Interaction first.
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8 NEESR Project Meeting
Model Verification – Specimen TP021
Input Displacement
Cross Section Side View
http://seismic.cv.titech.ac.jp/en/
Yoneda, Kawashima, and Shoji (2001)
Displacement
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9 NEESR Project Meeting
Experimental Program Overview
Column with large aspect ratio are controlled by flexural behavior; Column with small aspect ratio are controlled by shear behavior;
Aspect ratio 4≒ is about the ratio where moderate shear-flexural interaction can be observed.
HeightDiameter=
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10 NEESR Project Meeting
-60 -40 -20 0 20 40 60-150
-100
-50
0
50
100
150
Shear Displacement
She
ar F
orce
Hysteretic Loop
Analytical
Experimental
Spring includes both flexural and shear deformation.
Abaqus
Comparison with Exp. Result – TP021
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11NEESR Project Meeting
Model Verification – Specimen TP031 & TP032
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12NEESR Project Meeting
Experimental Program Overview
HeightDiameter=
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13NEESR Project Meeting
Comparison with Exp. Result – TP031 & TP032
Ozcebe and Saatcioglu’s model (1989) works fine with these two specimens under either compressive or tensile axial force, despite the transverse reinforcement ratio of the columns is as high as 0.79%.
-60 -40 -20 0 20 40 60-200
-150
-100
-50
0
50
100
150
200
Shear Displacement
She
ar F
orce
Hysteretic Loop
Analytical
Experimental
-80 -60 -40 -20 0 20 40 60 80
-100
-80
-60
-40
-20
0
20
40
60
80
100
Shear Displacement
She
ar F
orce
Hysteretic Loop
Analytical
Experimental
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14NEESR Project Meeting
Cyclic Loading: Abaqus UEL vs OpenSees
-60 -40 -20 0 20 40 60-150
-100
-50
0
50
100
150
displacement(mm)
shea
r (k
N)
Cyclic Pushover of TP-021, by OpenSees fiber section and ABAQUS user element
OpenSees force-based element (sampling freq=1/4)
ABAQUS UEL using OpenSees Pri-curve (sampling freq=1/5)
Primary Curve from OpenSees (reinf-steel + Popovics)Primary Curve from Response 2000
Column test data
OpenSees fails to capture:• Strength deterioration d
ue to cycles• Pinching behavior
UEL
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15NEESR Project Meeting
-60 -40 -20 0 20 40 60-150
-100
-50
0
50
100
150
displacement(mm)
shea
r (k
N)
Cyclic Pushover of TP-021, by ABAQUS user element & Slider-Plane
ABAQUS UEL using OpenSees Pri-curve (sampling freq=1/5)
ABAQUS UEL combined with rigid column and slider plane
Primary Curve from OpenSees (reinf-steel + Popovics)Primary Curve from Response 2000
Column test data
Validation of UEL + Rigid Column: Static Case
UEL
UEL
Deck
UEL
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16NEESR Project Meeting
Dynamic Verification: UNR Test - Column 9F1
Column Loading Motions
Column Details
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17NEESR Project Meeting
Column 9F1: Reinforcement & Test Setup
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18NEESR Project Meeting
Static Pushover Curve of Column 9F1
0 50 100 150 200 250 300 350 4000
50
100
150
displacement(mm)
shea
r (k
N)
Pushover Curves: Test vs OpenSees vs Response 2000
UNR Test: 9F1
OpenSees: 9F1 (80kips)Response 2K: 9F1 (80kips)
Response 2K + OpenSees
0 10 20 30 400
20
40
60
80
100
120
140
displacement(mm)
shea
r (k
N)
Response 2K: 9F1 (65kips)
Response 2K: 9F1 (80kips)Response 2K: 9F1 (116kips)
0 100 200 300 400 500 600 700 8000
50
100
150
displacement(mm)
shea
r (k
N)
Response 2K + OpenSees
Envelope of UNR Test
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19NEESR Project Meeting
Hysteretic Loop of Column 9F1: 0.33x
0 10 20 30 40-0.02
-0.01
0
0.01
0.02
disp
lace
men
t (m
)
Displacement time history of UNR test: 0.33 x El Centro
0 10 20 30 40-100
-50
0
50
100
time (sec)
shea
r (k
N)
Shear force time history of UNR test: 0.33 x El Centro
-0.02 -0.01 0 0.01 0.02-100
-50
0
50
100
shea
r (k
N)
Hysteretic loop of UNR test: 0.33 x El Centro
-0.2 0 0.2 0.4-100
-50
0
50
100
150Accumulated hysteretic loop
displacement (m)
shea
r (k
N)
UNR Test
ABAQUS UEL
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20NEESR Project Meeting
Hysteretic Loop of Column 9F1: 0.66x
0 10 20 30 40-0.04
-0.02
0
0.02
0.04
disp
lace
men
t (m
)
Displacement time history of UNR test: 0.66 x El Centro
0 10 20 30 40-200
-100
0
100
200
time (sec)
shea
r (k
N)
Shear force time history of UNR test: 0.66 x El Centro
-0.04 -0.02 0 0.02 0.04-200
-100
0
100
200
shea
r (k
N)
Hysteretic loop of UNR test: 0.66 x El Centro
-0.2 0 0.2 0.4-200
-100
0
100
200Accumulated hysteretic loop
displacement (m)
shea
r (k
N)
UNR Test
ABAQUS UEL
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21NEESR Project Meeting
Hysteretic Loop of Column 9F1: 1.00x
0 10 20 30 40-0.05
0
0.05
disp
lace
men
t (m
)
Displacement time history of UNR test: 1.00 x El Centro
0 10 20 30 40-200
-100
0
100
200
time (sec)
shea
r (k
N)
Shear force time history of UNR test: 1.00 x El Centro
-0.05 0 0.05-200
-100
0
100
200
shea
r (k
N)
Hysteretic loop of UNR test: 1.00 x El Centro
-0.2 0 0.2 0.4-200
-100
0
100
200Accumulated hysteretic loop
displacement (m)
shea
r (k
N)
UNR Test
ABAQUS UEL
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22NEESR Project Meeting
Hysteretic Loop of Column 9F1: 1.50x
0 10 20 30 40-0.1
-0.05
0
0.05
0.1
disp
lace
men
t (m
)
Displacement time history of UNR test: 1.50 x El Centro
0 10 20 30 40-200
-100
0
100
200
time (sec)
shea
r (k
N)
Shear force time history of UNR test: 1.50 x El Centro
-0.1 -0.05 0 0.05 0.1-200
-100
0
100
200
shea
r (k
N)
Hysteretic loop of UNR test: 1.50 x El Centro
-0.2 0 0.2 0.4-200
-100
0
100
200Accumulated hysteretic loop
displacement (m)
shea
r (k
N)
UNR Test
ABAQUS UEL
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23NEESR Project Meeting
Hysteretic Loop of Column 9F1: 2.00x
0 10 20 30 40-0.1
-0.05
0
0.05
0.1
disp
lace
men
t (m
)
Displacement time history of UNR test: 2.00 x El Centro
0 10 20 30 40-200
-100
0
100
200
time (sec)
shea
r (k
N)
Shear force time history of UNR test: 2.00 x El Centro
-0.1 -0.05 0 0.05 0.1-200
-100
0
100
200
shea
r (k
N)
Hysteretic loop of UNR test: 2.00 x El Centro
-0.2 0 0.2 0.4-200
-100
0
100
200Accumulated hysteretic loop
displacement (m)
shea
r (k
N)
UNR Test
ABAQUS UEL
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24NEESR Project Meeting
Hysteretic Loop of Column 9F1: 2.50x
0 10 20 30 40-0.1
-0.05
0
0.05
0.1
disp
lace
men
t (m
)
Displacement time history of UNR test: 2.50 x El Centro
0 10 20 30 40-200
-100
0
100
200
time (sec)
shea
r (k
N)
Shear force time history of UNR test: 2.50 x El Centro
-0.1 -0.05 0 0.05 0.1-200
-100
0
100
200
shea
r (k
N)
Hysteretic loop of UNR test: 2.50 x El Centro
-0.2 0 0.2 0.4-200
-100
0
100
200Accumulated hysteretic loop
displacement (m)
shea
r (k
N)
UNR Test
ABAQUS UEL
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25NEESR Project Meeting
Hysteretic Loop of Column 9F1: 3.00x
0 10 20 30 40-0.15
-0.1
-0.05
0
0.05
0.1
disp
lace
men
t (m
)
Displacement time history of UNR test: 3.00 x El Centro
0 10 20 30 40-200
-100
0
100
200
time (sec)
shea
r (k
N)
Shear force time history of UNR test: 3.00 x El Centro
-0.1 -0.05 0 0.05 0.1 0.15-200
-100
0
100
200
shea
r (k
N)
Hysteretic loop of UNR test: 3.00 x El Centro
-0.2 0 0.2 0.4-200
-100
0
100
200Accumulated hysteretic loop
displacement (m)
shea
r (k
N)
UNR Test
ABAQUS UEL
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26NEESR Project Meeting
Time Histories of Column 9F1: 3.50x
0 10 20 30 40-0.2
-0.1
0
0.1
0.2
disp
lace
men
t (m
)
Displacement time history of UNR test: 3.50 x El Centro
0 10 20 30 40-200
-100
0
100
200
time (sec)
shea
r (k
N)
Shear force time history of UNR test: 3.50 x El Centro
-0.1 0 0.1 0.2 0.3-200
-100
0
100
200
shea
r (k
N)
Hysteretic loop of UNR test: 3.50 x El Centro
-0.2 0 0.2 0.4-200
-100
0
100
200Accumulated hysteretic loop
displacement (m)
shea
r (k
N)
UNR Test
ABAQUS UEL
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27NEESR Project Meeting
Time Histories of Column 9F1: 4.00x
0 10 20 30 40-0.6
-0.4
-0.2
0
0.2
disp
lace
men
t (m
)
Displacement time history of UNR test: 4.00 x El Centro
0 10 20 30 40-200
-100
0
100
200
time (sec)
shea
r (k
N)
Shear force time history of UNR test: 4.00 x El Centro
-0.2 0 0.2 0.4 0.6-200
-100
0
100
200
shea
r (k
N)
Hysteretic loop of UNR test: 4.00 x El Centro
-0.2 0 0.2 0.4-200
-100
0
100
200Accumulated hysteretic loop
displacement (m)
shea
r (k
N)
UNR Test
ABAQUS UEL
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28NEESR Project Meeting
Hysteretic Loop of Column 9F1: 0.33x
0 10 20 30 40-0.02
-0.01
0
0.01
0.02
disp
lace
men
t (m
)
Displacement time history of UNR test: 0.33 x El Centro
OpenSees
UNR Test
0 10 20 30 40-100
-50
0
50
100
time (sec)
shea
r (k
N)
Shear force time history of UNR test: 0.33 x El Centro
-0.02 -0.01 0 0.01 0.02-100
-50
0
50
100
shea
r (k
N)
Hysteretic loop of UNR test: 0.33 x El Centro
OpenSees
UNR Test
-0.1 0 0.1 0.2 0.3 0.4-100
-50
0
50
100
150
displacement (m)
shea
r (k
N)
Accumulated hysteretic loop: 0.33 x El Centro
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29NEESR Project Meeting
Hysteretic Loop of Column 9F1: 0.66x
0 10 20 30 40-0.04
-0.02
0
0.02
0.04
disp
lace
men
t (m
)
Displacement time history of UNR test: 0.66 x El Centro
OpenSees
UNR Test
0 10 20 30 40-200
-100
0
100
200
time (sec)
shea
r (k
N)
Shear force time history of UNR test: 0.66 x El Centro
-0.04 -0.02 0 0.02 0.04-200
-100
0
100
200
shea
r (k
N)
Hysteretic loop of UNR test: 0.66 x El Centro
OpenSees
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-0.1 0 0.1 0.2 0.3 0.4-200
-100
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displacement (m)
shea
r (k
N)
Accumulated hysteretic loop: 0.66 x El Centro
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30NEESR Project Meeting
Hysteretic Loop of Column 9F1: 1.00x
0 10 20 30 40-0.05
0
0.05
disp
lace
men
t (m
)
Displacement time history of UNR test: 1.00 x El Centro
OpenSees
UNR Test
0 10 20 30 40-200
-100
0
100
200
time (sec)
shea
r (k
N)
Shear force time history of UNR test: 1.00 x El Centro
-0.04 -0.02 0 0.02 0.04 0.06-200
-100
0
100
200
shea
r (k
N)
Hysteretic loop of UNR test: 1.00 x El Centro
OpenSees
UNR Test
-0.1 0 0.1 0.2 0.3 0.4-200
-100
0
100
200
displacement (m)
shea
r (k
N)
Accumulated hysteretic loop: 1.00 x El Centro
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31NEESR Project Meeting
Hysteretic Loop of Column 9F1: 1.50x
0 10 20 30 40-0.1
-0.05
0
0.05
0.1
disp
lace
men
t (m
)
Displacement time history of UNR test: 1.50 x El Centro
OpenSees
UNR Test
0 10 20 30 40-200
-100
0
100
200
time (sec)
shea
r (k
N)
Shear force time history of UNR test: 1.50 x El Centro
-0.05 0 0.05 0.1 0.15-200
-100
0
100
200
shea
r (k
N)
Hysteretic loop of UNR test: 1.50 x El Centro
OpenSees
UNR Test
-0.1 0 0.1 0.2 0.3 0.4-200
-100
0
100
200
displacement (m)
shea
r (k
N)
Accumulated hysteretic loop: 1.50 x El Centro
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32NEESR Project Meeting
Hysteretic Loop of Column 9F1: 2.00x
0 10 20 30 40-0.1
-0.05
0
0.05
0.1
disp
lace
men
t (m
)
Displacement time history of UNR test: 2.00 x El Centro
OpenSees
UNR Test
0 10 20 30 40-200
-100
0
100
200
time (sec)
shea
r (k
N)
Shear force time history of UNR test: 2.00 x El Centro
-0.1 -0.05 0 0.05 0.1-200
-100
0
100
200
shea
r (k
N)
Hysteretic loop of UNR test: 2.00 x El Centro
OpenSees
UNR Test
-0.1 0 0.1 0.2 0.3 0.4-200
-100
0
100
200
displacement (m)
shea
r (k
N)
Accumulated hysteretic loop: 2.00 x El Centro
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33NEESR Project Meeting
Hysteretic Loop of Column 9F1: 2.50x
0 10 20 30 40-0.1
-0.05
0
0.05
0.1
disp
lace
men
t (m
)
Displacement time history of UNR test: 2.50 x El Centro
OpenSees
UNR Test
0 10 20 30 40-200
-100
0
100
200
time (sec)
shea
r (k
N)
Shear force time history of UNR test: 2.50 x El Centro
-0.1 -0.05 0 0.05 0.1-200
-100
0
100
200
shea
r (k
N)
Hysteretic loop of UNR test: 2.50 x El Centro
OpenSees
UNR Test
-0.1 0 0.1 0.2 0.3 0.4-200
-100
0
100
200
displacement (m)
shea
r (k
N)
Accumulated hysteretic loop: 2.50 x El Centro
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34NEESR Project Meeting
Hysteretic Loop of Column 9F1: 3.00x
0 10 20 30 40-0.15
-0.1
-0.05
0
0.05
0.1
disp
lace
men
t (m
)
Displacement time history of UNR test: 3.00 x El Centro
OpenSees
UNR Test
0 10 20 30 40-200
-100
0
100
200
time (sec)
shea
r (k
N)
Shear force time history of UNR test: 3.00 x El Centro
-0.1 -0.05 0 0.05 0.1 0.15-200
-100
0
100
200
shea
r (k
N)
Hysteretic loop of UNR test: 3.00 x El Centro
OpenSees
UNR Test
-0.1 0 0.1 0.2 0.3 0.4-200
-100
0
100
200
displacement (m)
shea
r (k
N)
Accumulated hysteretic loop: 3.00 x El Centro
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35NEESR Project Meeting
Time Histories of Column 9F1: 3.50x
0 10 20 30 40-0.2
-0.1
0
0.1
0.2
disp
lace
men
t (m
)
Displacement time history of UNR test: 3.50 x El Centro
OpenSees
UNR Test
0 10 20 30 40-200
-100
0
100
200
time (sec)
shea
r (k
N)
Shear force time history of UNR test: 3.50 x El Centro
-0.1 0 0.1 0.2 0.3-200
-100
0
100
200
shea
r (k
N)
Hysteretic loop of UNR test: 3.50 x El Centro
OpenSees
UNR Test
-0.1 0 0.1 0.2 0.3 0.4-200
-100
0
100
200
displacement (m)
shea
r (k
N)
Accumulated hysteretic loop: 3.50 x El Centro
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36NEESR Project Meeting
Time Histories of Column 9F1: 4.00x
0 10 20 30 40-0.6
-0.4
-0.2
0
0.2
disp
lace
men
t (m
)
Displacement time history of UNR test: 4.00 x El Centro
OpenSees
UNR Test
0 10 20 30 40-200
-100
0
100
200
time (sec)
shea
r (k
N)
Shear force time history of UNR test: 4.00 x El Centro
-0.2 0 0.2 0.4 0.6-200
-100
0
100
200
shea
r (k
N)
Hysteretic loop of UNR test: 4.00 x El Centro
OpenSees
UNR Test
-0.1 0 0.1 0.2 0.3 0.4-200
-100
0
100
200
displacement (m)
shea
r (k
N)
Accumulated hysteretic loop: 4.00 x El Centro
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37NEESR Project Meeting
Hysteretic Loop of Column 9F1: 0.33x ~0.66x
-0.02 -0.01 0 0.01 0.02-100
-50
0
50
100
displacement (m)
shea
r (k
N)
Hysteretic loop of UNR test: 0.33 x El Centro
UNR Test
ZeusNL
-0.1 0 0.1 0.2 0.3 0.4 0.5-100
-50
0
50
100
150
displacement (m)
shea
r (k
N)
Accumulated hysteretic loop of UNR test: 0.33 x El Centro
-0.04 -0.02 0 0.02 0.04-200
-100
0
100
200
displacement (m)
shea
r (k
N)
Hysteretic loop of UNR test: 0.66 x El Centro
UNR Test
ZeusNL
-0.1 0 0.1 0.2 0.3 0.4 0.5-200
-100
0
100
200
displacement (m)
shea
r (k
N)
Accumulated hysteretic loop of UNR test: 0.66 x El Centro
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38NEESR Project Meeting
Hysteretic Loop of Column 9F1: 1.00x ~1.50x
-0.04 -0.02 0 0.02 0.04 0.06-200
-100
0
100
200
displacement (m)
shea
r (k
N)
Hysteretic loop of UNR test: 1.00 x El Centro
UNR Test
ZeusNL
-0.1 0 0.1 0.2 0.3 0.4 0.5-200
-100
0
100
200
displacement (m)
shea
r (k
N)
Accumulated hysteretic loop of UNR test: 1.00 x El Centro
-0.06 -0.04 -0.02 0 0.02 0.04 0.06-200
-100
0
100
200
displacement (m)
shea
r (k
N)
Hysteretic loop of UNR test: 1.50 x El Centro
UNR Test
ZeusNL
-0.1 0 0.1 0.2 0.3 0.4 0.5-200
-100
0
100
200
displacement (m)
shea
r (k
N)
Accumulated hysteretic loop of UNR test: 1.50 x El Centro
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39NEESR Project Meeting
Hysteretic Loop of Column 9F1: 2.00x~2.50x
-0.1 -0.05 0 0.05 0.1 0.15-200
-100
0
100
200
displacement (m)
shea
r (k
N)
Hysteretic loop of UNR test: 2.00 x El Centro
UNR Test
ZeusNL
-0.1 0 0.1 0.2 0.3 0.4 0.5-200
-100
0
100
200
displacement (m)
shea
r (k
N)
Accumulated hysteretic loop of UNR test: 2.00 x El Centro
-0.2 -0.1 0 0.1 0.2 0.3-200
-100
0
100
200
displacement (m)
shea
r (k
N)
Hysteretic loop of UNR test: 2.50 x El Centro
UNR Test
ZeusNL
-0.1 0 0.1 0.2 0.3 0.4 0.5-200
-100
0
100
200
displacement (m)
shea
r (k
N)
Accumulated hysteretic loop of UNR test: 2.50 x El Centro
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40NEESR Project Meeting
Hysteretic Loop of Column 9F1:3.00x ~3.50x
-0.1 0 0.1 0.2 0.3-200
-100
0
100
200
displacement (m)
shea
r (k
N)
Hysteretic loop of UNR test: 3.00 x El Centro
UNR Test
ZeusNL
-0.1 0 0.1 0.2 0.3 0.4 0.5-200
-100
0
100
200
displacement (m)
shea
r (k
N)
Accumulated hysteretic loop of UNR test: 3.00 x El Centro
-0.1 0 0.1 0.2 0.3 0.4-100
-50
0
50
100
150
displacement (m)
shea
r (k
N)
Hysteretic loop of UNR test: 3.50 x El Centro
UNR Test
ZeusNL
-0.1 0 0.1 0.2 0.3 0.4 0.5-200
-100
0
100
200
displacement (m)
shea
r (k
N)
Accumulated hysteretic loop of UNR test: 3.50 x El Centro
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41NEESR Project Meeting
Time Histories of Column 9F1: 4.00x
-0.5 0 0.5 1 1.5 2-500
0
500
1000
displacement (m)
shea
r (k
N)
Hysteretic loop of UNR test: 4.00 x El Centro
UNR Test
ZeusNL
-0.1 0 0.1 0.2 0.3 0.4 0.5-600
-400
-200
0
200
displacement (m)
shea
r (k
N)
Accumulated hysteretic loop of UNR test: 4.00 x El Centro
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42NEESR Project Meeting
Average Response Ratio of Bridge #8
Displacement Section Force Section Moment Reaction Force Reaction Moment Acceleration0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5Average Response Ratio: UEL / non-linear M- (Bridge #8 subjected to Bin4 earthquakes)
Section forces/moments are taken at the bottom elements of columns.
Reaction forces/moments are taken at the ground nodes beneath the FNDNs.
Accelerations are taken at the midspans of the deck.
1.35
1.76
1.28
0.87
2.25
0.76
1.511.44
1.75
0.40
4.67
0.77
1.30
0.910.80
0.97 0.98 1.03
longi.
verti.
trans.
UELNL M-φ
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43NEESR Project Meeting
Average Response Ratio of Mendocino Bridge UELNL M-φ
Displacement Section Force Section Moment Reaction Force Reaction Moment Acceleration0
0.5
1
1.5
2
2.5
3
3.5
4
4.5Average Response Ratio: UEL / non-linear M- (Mendocino Bridge subjected to Bin4 earthquakes)
Section forces/moments are taken at the bottom elements of columns.
Reaction forces/moments are taken at the ground nodes beneath the FNDNs.
Accelerations are taken at the midspans of the deck.
1.060.96
1.30
0.98 0.95
0.70
2.59
3.52
2.58
0.32
0.95
0.68
1.75
4.24
1.62
0.98 0.97
1.09
longi.
verti.
trans.
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44 NEESR Project Meeting44
Verification of the nonlinear UEL spring
Almost done. Incorporating the nonlinear spring into 3D FE
bridge models Mendocino Bridge & Bridge #8. Effects of non-linear shear-flexural interaction on
bridge responses Cause and effect of the significant increase in moment need to be clarified.
UEL to include Axial-Shear-Flexural Interaction Effects of axial load variation on bridge system
responses
Future Work: Update