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
Cyclic Tests: As-built SP1
12
Cross-loading adopted from FEMA 461
Longitudinal Loading
Cyclic Tests: As-built SP1
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
Cyclic Tests: As-built SP1
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
Cyclic Tests: As-built SP1
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
Cyclic Tests: As-built SP1
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
Cyclic Tests: As-built SP1
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
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
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
Cyclic Tests: As-built SP1
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
HS Tests: Retrofitted SP2
Retrofitted SP2 Damage after HS TestsBent cap concrete crushing in compression
25
HS Tests: Retrofitted SP2
Bent cap moment-curvature relationship
Retrofit increased overall SYSTEM capacity by ~25%
Increased demand from column + higher gravity (15%) bent cap failure
26
HS Tests: Retrofitted SP2
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
Effective Width Disribution [inch]
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
Effective Width Disribution [inch]
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?