1 neesr project meeting 22/02/2008 modeling of bridge piers with shear-flexural interaction and...

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

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.


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


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


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


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.


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.


Model Verification – Specimen TP021

Input Displacement

Cross Section Side View

http://seismic.cv.titech.ac.jp/en/

Yoneda, Kawashima, and Shoji (2001)

Displacement


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=


-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


Model Verification – Specimen TP031 & TP032


Experimental Program Overview

HeightDiameter=


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


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


-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


Dynamic Verification: UNR Test - Column 9F1

Column Loading Motions

Column Details


Column 9F1: Reinforcement & Test Setup


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


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



0 10 20 30 40-0.04

-0.02

0

0.02

0.04

disp

lace

men

t (m

)


0 10 20 30 40-200

-100

0

100

200

time (sec)

shea

r (k

N)


-0.04 -0.02 0 0.02 0.04-200

-100

0

100

200

shea

r (k

N)


-0.2 0 0.2 0.4-200

-100

0

100


displacement (m)

shea

r (k

N)

UNR Test

ABAQUS UEL



0 10 20 30 40-0.05

0

0.05

disp

lace

men

t (m

)


0 10 20 30 40-200

-100

0

100

200

time (sec)

shea

r (k

N)


-0.05 0 0.05-200

-100

0

100

200

shea

r (k

N)


-0.2 0 0.2 0.4-200

-100

0

100


displacement (m)

shea

r (k

N)

UNR Test

ABAQUS UEL



0 10 20 30 40-0.1

-0.05

0

0.05

0.1

disp

lace

men

t (m

)


0 10 20 30 40-200

-100

0

100

200

time (sec)

shea

r (k

N)


-0.1 -0.05 0 0.05 0.1-200

-100

0

100

200

shea

r (k

N)


-0.2 0 0.2 0.4-200

-100

0

100


displacement (m)

shea

r (k

N)

UNR Test

ABAQUS UEL



0 10 20 30 40-0.15

-0.1

-0.05

0

0.05

0.1

disp

lace

men

t (m

)


0 10 20 30 40-200

-100

0

100

200

time (sec)

shea

r (k

N)


-0.1 -0.05 0 0.05 0.1 0.15-200

-100

0

100

200

shea

r (k

N)


-0.2 0 0.2 0.4-200

-100

0

100


displacement (m)

shea

r (k

N)

UNR Test

ABAQUS UEL


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

)


0 10 20 30 40-200

-100

0

100

200

time (sec)

shea

r (k

N)


-0.1 0 0.1 0.2 0.3-200

-100

0

100

200

shea

r (k

N)


-0.2 0 0.2 0.4-200

-100

0

100


displacement (m)

shea

r (k

N)

UNR Test

ABAQUS UEL



0 10 20 30 40-0.6

-0.4

-0.2

0

0.2

disp

lace

men

t (m

)


0 10 20 30 40-200

-100

0

100

200

time (sec)

shea

r (k

N)


-0.2 0 0.2 0.4 0.6-200

-100

0

100

200

shea

r (k

N)


-0.2 0 0.2 0.4-200

-100

0

100


displacement (m)

shea

r (k

N)

UNR Test

ABAQUS UEL



0 10 20 30 40-0.02

-0.01

0

0.01

0.02

disp

lace

men

t (m

)


OpenSees

UNR Test

0 10 20 30 40-100

-50

0

50

100

time (sec)

shea

r (k

N)


-0.02 -0.01 0 0.01 0.02-100

-50

0

50

100

shea

r (k

N)


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



0 10 20 30 40-0.04

-0.02

0

0.02

0.04

disp

lace

men

t (m

)


OpenSees

UNR Test

0 10 20 30 40-200

-100

0

100

200

time (sec)

shea

r (k

N)


-0.04 -0.02 0 0.02 0.04-200

-100

0

100

200

shea

r (k

N)


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)




0 10 20 30 40-0.05

0

0.05

disp

lace

men

t (m

)


OpenSees

UNR Test

0 10 20 30 40-200

-100

0

100

200

time (sec)

shea

r (k

N)


-0.04 -0.02 0 0.02 0.04 0.06-200

-100

0

100

200

shea

r (k

N)


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)




0 10 20 30 40-0.1

-0.05

0

0.05

0.1

disp

lace

men

t (m

)


OpenSees

UNR Test

0 10 20 30 40-200

-100

0

100

200

time (sec)

shea

r (k

N)


-0.05 0 0.05 0.1 0.15-200

-100

0

100

200

shea

r (k

N)


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)




0 10 20 30 40-0.1

-0.05

0

0.05

0.1

disp

lace

men

t (m

)


OpenSees

UNR Test

0 10 20 30 40-200

-100

0

100

200

time (sec)

shea

r (k

N)


-0.1 -0.05 0 0.05 0.1-200

-100

0

100

200

shea

r (k

N)


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)




0 10 20 30 40-0.15

-0.1

-0.05

0

0.05

0.1

disp

lace

men

t (m

)


OpenSees

UNR Test

0 10 20 30 40-200

-100

0

100

200

time (sec)

shea

r (k

N)


-0.1 -0.05 0 0.05 0.1 0.15-200

-100

0

100

200

shea

r (k

N)


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)




0 10 20 30 40-0.2

-0.1

0

0.1

0.2

disp

lace

men

t (m

)


OpenSees

UNR Test

0 10 20 30 40-200

-100

0

100

200

time (sec)

shea

r (k

N)


-0.1 0 0.1 0.2 0.3-200

-100

0

100

200

shea

r (k

N)


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)




0 10 20 30 40-0.6

-0.4

-0.2

0

0.2

disp

lace

men

t (m

)


OpenSees

UNR Test

0 10 20 30 40-200

-100

0

100

200

time (sec)

shea

r (k

N)


-0.2 0 0.2 0.4 0.6-200

-100

0

100

200

shea

r (k

N)


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)



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)


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)


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)



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)


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)


-0.06 -0.04 -0.02 0 0.02 0.04 0.06-200

-100

0

100

200

displacement (m)

shea

r (k

N)


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)



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)


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)


-0.2 -0.1 0 0.1 0.2 0.3-200

-100

0

100

200

displacement (m)

shea

r (k

N)


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)



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)


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)


-0.1 0 0.1 0.2 0.3 0.4-100

-50

0

50

100

150

displacement (m)

shea

r (k

N)


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)




-0.5 0 0.5 1 1.5 2-500

0

500

1000

displacement (m)

shea

r (k

N)


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)



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


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.

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

1 neesr project meeting 22/02/2008 modeling of bridge piers with shear-flexural interaction and...

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