Structural Response of Bent Caps in Reinforced Concrete Box- Girder Bridges · Structural Response of Bent Caps in Reinforced Concrete Box- Girder Bridges. Mohamed A. Moustafa, PhD,

Western Bridge Engineers Seminar, Reno, NV, Sep. 9-11, 2015

Structural Response of Bent Caps in Reinforced Concrete Box-Girder

BridgesMohamed A. Moustafa, PhD, PE

University of Nevada, Reno

Khalid M. Mosalam, PhD, PEUniversity of California, Berkeley

Sponsor:

Courtesy of Hamid Saadatmanesh, Simpson Strong-Tie

Jyi Lu Brigde, Chi-Chi, Taiwan 1999 Bent caps damage in past events• e.g. San Fernando 1971, Whittier 1987,

Chi-Chi 1999

Post-event repair is not feasible • $$$ + long down time

Why accurate bent cap response important?• Modeling and analysis • Optimized design (new bridges)• Retrofit design (old bridges)

2

Bent Cap Response

Motivation

?

Integral Bent Cap BeamRC Box-girder

Bridge

Problem Statement1. What is box-girder slab contribution to bent cap?

strain-based effective slab width approach

2. How can bent cap capacity accurately estimated? slab reinforcement inclusion

3. Could column over-design migrate damage to bent cap? informed retrofit decisions

3

Stage 1: Pre-test analyses:• FE analyses of prototype bridge• FE analyses of test specimen

Stage 2: Experimental program (2 large-scale specimens):• Quasi-static testing of SP1 (as-built & repaired)• Hybrid Simulation testing of SP2 (retrofitted)

Stage 3: Post-test analyses:• FE model calibration/parametric study• Design implications

4

Methodology

420'126' 168' 126'

30'6' 6'-9"

Elevation View

Prototype BridgeAdopted from Caltrans Academy Bridge

(Typical RC box-girder bridge in CA)

Soffit Slab (inverted)

Deck Slab (inverted)

Test specimen subassemblage

10'

6' 27'

66'89'-10"

918"

814"

30'

2'-11"

5'1'

11'

Cross-Section

5

Specimen Design & Test Setup

3D schematic of Test Setup

Design acc. to AASHTO, Caltrans SDC, and ACI-318

Two Specimens tested in an inverted position at UC Berkeley Structures Laboratory

Gravity & lateral loads applied at the column top

1/4 scale

6

Column16 #6 longitudinal bars

#3 spiral at 2-1/2 in.

Cap beam

8 #5 negative reinforcement

8 #5 positive reinforcement

#3 stirrups 4 branches at 5 in. spacing

Box-girder

#3 in transverse dir. at 4 in. spacing

#3 in longitudinal dir. at 2-1/2 in. spacing

#3 single branch tie at 4 in. spacing

Summary of specimen reinforcement

2'-6"

8'-6"

1'-6"

11'-738"

1'-2"

1'-4"

3' 3'

1'-4"

2 116"

1'-6"

2'

1'-838"

8'-6"

2'

6'-6"

1'-7 516"

1'

9"

2 516"

1'

1'-5"

5"

5"

7'-6"

Ø9" hole

3'-138"

1'-2"

Elevation Side View

6.7 m2.6 m

3.5 m

22'

7

Prototype Model

Pre-test FEA: OpenSees

Summary of critical GMs causing bent cap beam failure

GM Earthquake Year Magnitude Station#1 Nahanni- Canada 1985 6.76 Site 1#2 Loma Prieta 1989 6.93 LGPC#3 Northridge-01 1994 6.69 Rinaldi#4 Kobe- Japan 1995 6.90 Takarazuka#5 Chi-Chi- Taiwan 1999 7.62 TCU068

Objectives:

• Choose GMs with most severe effect on bent cap beam

• Select final GMs for loading protocol Prelim. nonlinear time history analysis of

prototype w/ & w/o vl. excitation

> 80 ground motions (GMs) from PEER NGA database (Criteria: Magnitude > 6 & Distance to fault < 20 km)

Beam Section 2

-10 -8 -6 -4 -2 0 2

x 10-4

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5x 10

5

Curvature [1/inch]

Mom

ent [

kip-

inch

]

-10 -8 -6 -4 -2 0 2

x 10-4

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5x 10

5

Curvature [1/inch]

Mom

ent [

kip-

inch

]

w/o vertical

w/ vertical

Moment-curvature relationship

7

Objectives:

• Behavior & mode of failure• Setup design & instrumentation

Pushover Analysis

• Vertical & lateral direction• Different constant gravity load

(0% 23% column axial capacity) Time-history Analysis

Pre-test FEA: DIANA

Brick ElementConcrete Mesh

Concrete mesh using brick solid elements

Embedded Reinforcement Mesh

Reinforcement mesh

ft

fc

Concrete Material Model

Constant Compression

Linear Tension Softening

8

Total Strain-Based Crack

Model

0 5 10 15 20 25 30 35 40 450

50

100

200

250

300

350

150

Horizontal Force [kips]

Ver

tical

For

ce [k

ips]

Only Cap Beam fails (mode 3)

Onl

y Co

lum

n fa

ils (m

ode

1)

Both cap beam andcolumn fail (mode 2)

Satisfy SDC requirements

Do not satisfy SDC requirements

Gravity Load

Equivalent Vertical EQ

Pushover Analysis

Displacement Pushover

Constant Gravity Load

Pre-test FEA: DIANA

9Mode 2Mode 1 Mode 3

Experimental Program

10

Objectives:

• Global subassemblage behavior (force, disp., stiffness)

• Local Bent cap & column behavior (moment, curvature, strains)

• Box-girder behavior (effective slab width)

Test Set Status Type Direction Gravity Different Scale Runs

SP1-1 As-built Cyclic Bidirectional 5% 0.25µ, 0.35µ, 0.50µ, 0.70µ, 1.0µ

SP1-2 As-built Cyclic Bidirectional 10% 1.4µ, 2.0µ, 2.8µ, 4.0µ, 5.6µ, 8.0µ

SP1-3 Repaired Cyclic Bidirectional 10% 1.4µ, 2.0µ, 2.8µ, 4.0µ, 5.6µ

SP1-4 Repaired HS Trials Bidirectional 0% 20%, 50% Rinaldi Ground Motion (GM)

SP1-5 Repaired HS Trials Bidirectional 10% 50%, 80%, 100% Rinaldi GM

SP2-1 Retrofitted HS Bidirectional 10% 25%, 50%, 75%, 100% Rinaldi GM

SP2-2 Retrofitted HS Transverse 15% 125%, 150%, 175%, 200% Rinaldi GM

Two identical specimens Repair & Retrofit?

Final test Matrix

Cyclic Tests: As-built SP1

Cyclic Loading Test Setup

11

Transverse Loading

Bidirectional Cyclic Loading Protocol

0 50 100 150 200 250 300-10

-5

0

5

10

Time [minutes]D

ispl

acem

ent [

inch

]

Transverse LoadingLongitudinal Loading

0 50 100 150 200 250 3000

50

100

150

Time [minutes]

Gra

vity

Loa

d [k

ips] 5% Axial

capacity10% Axial capacity


12

Cross-loading adopted from FEMA 461

Longitudinal Loading


13

0 50 100 150 200 250 300-10

-5

0

5

10

Time [minutes]D

ispl

acem

ent [

inch

]

Transverse LoadingLongitudinal Loading

0 50 100 150 200 250 3000

50

100

150

Time [minutes]

Gra

vity

Loa

d [k

ips] 5% Axial

capacity10% Axial capacity

Cross-loading adopted from FEMA 461

Bidirectional Cyclic Loading Protocol

Crack Propagation, Cover Spalling & Rebar Rupture in Column Plastic Hinge Region


14

-10 -5 0 5 10-50

-40

-30

-20

-10

0

10

20

30

40

50

Displacement [inch]

Forc

e [k

ips]

Longitudinal Loading

-10 -5 0 5 10-50

-40

-30

-20

-10

0

10

20

30

40

50

Displacement [inch]

Forc

e [k

ips]

Transverse Loading

Subassemblage Force-Displacement Relationship


15

Global Behavior

• Yielding of rebars & hairline cracks • NO spalling or PH formation

0 1 2 3 4 5 6 7 8

x 10-4

-500

0

500

1000

1500

2000

2500

3000

3500

4000

4500

Curvature [1/inch]

Mom

ent [

kip-

inch

]

-0.01 -0.008 -0.006 -0.004 -0.002 0 0.002 0.004 0.006 0.008 0.01

-4000

-3000

-2000

-1000

0

1000

2000

3000

4000

Curvature [1/inch]

Mom

ent [

kip-

inch

]

Bent Cap Beam Column

• Rupture of rebars• cover spalling & PH formation


16

Local Behavior

Moment-Curvature Relationship

Procedure for estimating effective width from strain distribution

-60 -40 -20 0 20 40 600

0.5

1

1.5

2

2.5x 10

-3

-60 -40 -20 0 20 40 600

0.5

1

1.5

2

2.5x 10

-3

-60 -40 -20 0 20 40 600

0.5

1

1.5

2

2.5x 10

-3

-60 -40 -20 0 20 40 600

0.5

1

1.5

2

2.5x 10

-3

B eff

A B

C D

Extend tails to zero

Calculate shaded area (A)

1) Beff =A / εminor

2) Beff =A / εmean

εmin orεmean

Experimental data

Beff


17

Effective Slab Width

Section B Section D

Combined Load

D

Strain Distribution & Effective Slab Width during TRANSVERSE Loading

-40 -30 -20 -10 0 10 20 30 400

2

4

6

8

10

12

14x 10

-3

Effective Width Disribution [inch]

Stra

in [i

nch/

inch

]

Drift = 1.4 % (µ = 1.00)Drift = 2.7 % (µ = 1.96)Drift = 5.3 % (µ = 3.84)Drift = 10.5 % (µ = 7.57)Steel fyCap Beam limits

-40 -30 -20 -10 0 10 20 30 400

2

4

6

8

10

12

14x 10

-3


Stra

in [i

nch/

inch

]

Drift = 1.4 % (µ = 1.00)Drift = 2.7 % (µ = 1.96)Drift = 5.3 % (µ = 3.84)Drift = 10.5 % (µ = 7.57)Steel fyCap Beam limits

Section B Section D

0.3 0.4 0.5 0.8 1.1 1.4 1.9 2.7 3.8 5.3 7.5 10.50

20

40

60

80

100

120

140

160

180

200

Drift Ratio [%]

Bef

f [inc

h]

Experimental Value (using εmean)

Experimental Value (using εmin)

Caltrans Value

0.3 0.4 0.5 0.8 1.1 1.4 1.9 2.7 3.8 5.3 7.5 10.50

20

40

60

80

100

120

140

160

180

200

Drift Ratio [%]

Bef

f [inc

h]

Experimental Value (using εmean)

Experimental Value (using εmin)

Caltrans Value

Section B Section D


18

Repair Procedure

Cyclic Tests: Repaired SP1

19

WHAT is Hybrid Simulation?

HS Tests: Background

Experimental Simulation

Analytical Simulation

TYPES?Slow Hybrid Simulation vs. Real-time Hybrid Simulation

20

+ Hybrid Simulation (HS)=

More convenient & feasible than shaking table tests Mass modeling Larger structures Observing the damage progression Modeling physical boundary conditions

HS Tests: Background

Shaking Table

VS.

Hybrid Model

u1m, Im

u2

WHY Hybrid Simulation?

21

Slow HS Test Components:

• Physical Substructure: specimen subassemblage

• Computational Substructure:MDOF mass & damping

How HS works?

Communication Loop?

Main components of HS system

Two Actuators(Two Experimental DOFs)

Two MTS 407 Controllers

PI Interface Software

OpenSees/OpenFresco Computational Platform

DAQ/ DSP Card

Ethernet Connection

USB Cable

Displacement

Force

Ope

nFre

sco

1st development:New setup in OpenFresco2nd development:

New PI Interface

22

1 1 1 1( )i i r i i+ + + ++ + =.. .

M U CU P U P

HS Tests: Hybrid System

Retrofit Procedure

23

HS Tests: Retrofitted SP2

HS Test In-progress

24


Retrofitted SP2 Damage after HS TestsBent cap concrete crushing in compression

25


Bent cap moment-curvature relationship

Retrofit increased overall SYSTEM capacity by ~25%

Increased demand from column + higher gravity (15%) bent cap failure

26


Force-displacement relationship (transverse)

As-built SP1 vs. Retrofitted SP2

Overall mean values for effective slab width from SP1 cyclic & SP2 HS tests

Cyclic Tests HS Tests0

20

40

60

80

100

120

Effe

ctiv

e W

idth

[inc

h]

Experimental Value (using ε

mean)

Experimental Value (using εmin

)

Average Bef f

using εmean

Average Bef f

using εmin

Bef f

using Caltrans Value

~13ts

~ 19ts

12ts

Strain distribution from transverse-only up to 200% (left) & bidirectional up to 100% (right) at Section B

-60 -40 -20 0 20 40 600

05

01

15

02


Drift = 2.4 % ( µ = 1.70)Drift = 2.1 % ( µ = 1.54)Drift = 2.2 % ( µ = 1.61)Drift = 3.9 % ( µ = 2.82)Drift = 6.0 % ( µ = 4.32)Steel fyCap Beam limits

-60 -40 -20 0 20 40 600

0.005

0.01

0.015

0.02

0.024


Stra

in [i

nch/

inch

]

Drift = 8.1 % ( µ = 5.82)Drift = 8.8 % ( µ = 6.35)Drift = 10.0 % ( µ = 7.19)Drift = 8.9 % ( µ = 6.41)Steel fyCap Beam limits

Section B Section D

Combined Load

D

27

HS Tests: Retrofitted SP2Effective Slab Width

Calibrate FE model

• using SP1 experiments

Extensive parametric study

• e.g. different beam designs

Section Analysis

Force-displacement relationship (transverse dir. )

0 100 200 300 400 4650

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

4772 kip-inch

Time [minute]

Mom

ent [

kip-in

]

0 100 200 300 400 4650

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

4769 kip-inch

Time [minute]

Mom

ent [

kip-in

]

DIANAExperiment

Bent cap beam moment history

Final FE Calibrated Model

28

Post-test FEA

Section Analysis

12ts

w/o slab rft. 4504

w/ slab rft. 5977

18ts

w/o slab rft. 4566

w/ slab rft. 6855

SP2 HS Tests 6535

Bent cap beam capacity [kip-in] using section analysis

Design example using

Academy Bridge Prototype

3 column design scenarios

(ρlong. ~ 1.4%, 2.6%, 3.5%)

3 configurations for bent cap

for capacity check:

• 12ts w/o slab rft

• 12ts w/ slab rft

• 18ts w/ slab rft

Column Cross-section

Diameter 6 ft 6 ft 6 ft

Long. Rft. 26 #14 26 #18 36 #18

Rft. Ratio 1.44% 2.56% 3.53%

Hoops #8 @ 5 in. #8 @ 5 in. #8 @ 5 in.

Ultimate Moment Mp

[kip-ft]14,510 21,140 26,200

Overstrength Moment Mo

[kip-ft]17,410 25,370 31,440

Cap Beam M+ve Demand

[kip-ft]14,970 21,820 27,040

Cap Beam M-ve Demand

[kip-ft]15,670 22,830 28,300

Amplified demands due to higher column capacity (design

requirements or retrofit decision)

29

Design Implications

0 0.005 0.01 0.0150

0.5

1

1.5

2

2.5

3x 10

4

Curvature [1/ft]

Mom

ent [

kip-

ft]

18ts with slab rft

12ts with slab rft

12ts without slab rft

Section analysis for moment-curvature (e.g. results of negative moment side)

Case Column Design

Moment Demand [kip-ft]

12ts w/o slab rft 12ts w/ slab rft 18ts w/ slab rft

CapacitySatisfy

Capacity Check?

CapacitySatisfy

Capacity Check?

CapacitySatisfy

Capacity Check?

1 1.44% 15,67020,270

YES26,170

YES28,460

YES2 2.58% 22,830 NO YES YES3 3.50% 28,300 NO NO YES

Caltrans & AASHTO Seismic Capacity Check Revised design required if NOT satisfied!

30

Design Implications

• 12ts code value conservative & revised effective slab width of 18ts recommended to account for box-girder contributions;

• Transverse deck & soffit slab reinforcement within effective width should be included in bent cap capacity estimation;

• Overdesigned column retrofit may migrate damage to bent cap and/or superstructure;

• Accurate bent cap effective width & capacity check crucial for economical design & informed repair/retrofit decisions.

31

Conclusions

32

Thank You! Questions?

Documents

Structural Response of Bent Caps in Reinforced Concrete Box- Girder Bridges · Structural Response of Bent Caps in Reinforced Concrete Box- Girder Bridges. Mohamed A. Moustafa, PhD,