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SUNY Buffalo
24 June 2008
SUNY Buffalo
24 June 2008
Seismic performance quantification of steel corrugated shear wall systemLaszlo Gergely Vigh, (Geri)Laszlo Gergely Vigh, (Geri)Visiting scholar, Stanford, CAAsst. Prof., Budapest University of Technology and Economics,Dept. Of Structural Engineering, Hungary
andProfessor Gregory Deierlein,Professor Eduardo Miranda,Abbie Liel (Stanford)Stephen Tipping (Tipping Mar + Associates)
Thanks are due to:The Thomas Cholnoky Foundation, Inc.
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Little background…
• Hard to work at Dept. of Structural Engineering
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Little background…
• Hard to work at Dept. of Structural Engineering
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Little background…
• Hard to work at Dept. of Structural Engineering
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Little background…
• Budapest University of Technology and Economics
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Source: www.bme.hu
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Little background…
• Budapest University of Technology and Economics
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Little background…
• Budapest University of Technology and Economics:
- 8 faculties and several innovation centers- Faculty of Civil Engineering :
• 10 departments
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• Dept. of Structural Engineering:•staffs: 57 (incl. appr. 25 of asst. prof – prof)•22 BSc, 16 MSc courses + optionals
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Little background…
• Dept. of Structural Engineering
1. Education2. Research – national research funds, and ‘selfish’
researches3. Industry & University
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3. Industry & University• R&D• Co-designer• Expert• Independent checks• Laboratory and site testing – Accredited laboratory
4. Student life…
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SUNY Buffalo
24 June 2008
SUNY Buffalo
24 June 2008
Seismic performance quantification of steel corrugated shear wall systemscorrugated shear wall systems
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Shear wall system
• corrugated sheet• boundary elements• screwed connection
Tipping Mar and Associates, Berkeley, CA
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Shear wall system
• corrugated sheet• boundary elements• screwed connection
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Seismic performance quantification by ATC-63
• performance quantification by cyclic testsor
• Applied Technology Council, Project 63• achieves primary life safety performance objective by
requiring an acceptably low probability of collapse• R, ΩΩΩΩ , C factors
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• R, ΩΩΩΩ0, Cd factors
1) idealized archetypical systems: realization, design (assume R)2) analytical model development and calibration3) nonlinear static (pushover) analysis ΩΩΩΩ0
4) nonlinear incremental dynamic analysis (IDA)5) fragility curves;
adjusted collapse margin ratio (ACMR) vs. acceptabl e ACMR↓
R, Cd
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Experimental results
• Stojadinovic et al. at UC Berkeley• 44 specimens
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Experimental results
• pinching hysteresis behavior
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Experimental results
• failure modes
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Experimental results
• failure modes
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Shear wall behavior –estimation of monotonic backbone curve
• challenge:- cyclic behavior is path-dependent- calibration to test results – we should know the monotonic behavior
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rigid
nonlin. spring
rigid lean
ing
colu
mn
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Shear wall behavior –estimation of monotonic backbone curve
• modelling technique
ANSYS
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ANSYSshell, beam &
spring elements
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Shear wall behavior –estimation of monotonic backbone curve
• single screw connection behavior
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Source: Dubina et al.
• literature• EC3• published experimental data
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Shear wall behavior –estimation of monotonic backbone curve
• single screw connection behavior
Screw characteristics
4000
5000
6000
7000
For
ce [k
N]
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0
1000
2000
3000
4000
0 1 2 3 4 5 6
Slip [mm]
For
ce [k
N]
elasto-plastic (no hardening)
mat. hard. - actual sigma-eps
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Shear wall behavior –estimation of monotonic backbone curve
• single screw connection behavior
Screw characteristics
4000
5000
6000
7000
For
ce [k
N]
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0
1000
2000
3000
4000
0 2 4 6 8 10 12 14 16 18 20
Slip [mm]
For
ce [k
N]
with drop
no drop
no drop, adjusted
0
20
40
60
80
100
120
0 25 50 75 100
Drift [mm]
Load
[kN
]test averageenvelope
adjusted FEMbackbone
FEM with rigidconnection
estimatedcapping point
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Shear wall behavior –estimation of monotonic backbone curve
• analysis of tested shear walls
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Shear wall behavior –estimation of monotonic backbone curve
• extension to longer walls
Group #14 - Wall length effect
500
600
all models include nonlinear screw
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0
100
200
300
400
0 20 40 60 80 100 120
Drift [mm]
Load
[kN
]
test, avg.
adjusted FEM
4 ft - eq. orthotropic
8 ft - eq. orthotropic
16 ft - eq. orthotropic
1
behavior and imperfection
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Model calibration
• OpenSees• Ibarra – Medina – Krawinkler model
Load
Mat. #2
Combined mat.
Fy 2
Fu
αH2
αH = αH2
0
40
80
120
-80 -40 0 40 80Load
[kN
]
Fmax
βpFmax
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Drift, δδδδ
Mat. #1
δy 1 δy 2 δm
Fy 1residual
αC
αH1 = 0-120
-80
-40
-80 -40 0 40 80
Drift [mm]
Load
[kN
]
δp
αpδp
-120
-80
-40
0
40
80
120
-150 -100 -50 0 50 100 150
Drift [mm]
Load
[kN
]
γA γS
γK
γD
-100
-80
-60
-40
-20
0
20
40
60
80
100
-150 -100 -50 0 50 100 150
Drift [mm]
Load
[kN
]
#29 (group #14)
#26 (group #8)
#18 (group #1)
group #14 test avg.
group #8 test avg.
group #1 test avg.
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Model calibration
• calibration: GA
encoding: sequence e.g.: possible values of
γ A = [10 15 … 240 250]1xN
alleles for γ A : 1..N
variables:
α C , α p , β p , γ A , γ S , γ D , γ K
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popu
latio
n si
ze:
20 selection: roulette wheel
crossover :simple (4)
arithmetic (4)heuristic (4)
mutation:multi-non-uniform (8)
alleles for γ A : 1..N
(i.e. based on the sequence number of the possible values)encoding for a chromosome:
[2 4 12 1 55 8 8]elitism
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Model calibration
• final – uniform – model
0
5
10
15
20
25
Load
[kN
]
Spec #18
-50
0
50
100
Load
[kN
]
Spec #42
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-200 -100 0 100 200-25
-20
-15
-10
-5
Drift [mm]
Load
[kN
]
-200 -100 0 100 200-60
-40
-20
0
20
40
60
Drift [mm]
Load
[kN
]
Spec #44
-200 -100 0 100 200-100
Drift [mm]
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0
5
10
15
20
25
Load
[kN
]
Spec #18
-50
0
50
100
Load
[kN
]
Spec #42
Model calibration
• final – uniform – model
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-200 -100 0 100 200-25
-20
-15
-10
-5
Drift [mm]
Load
[kN
]
-200 -100 0 100 200-60
-40
-20
0
20
40
60
Drift [mm]
Load
[kN
]
Spec #44
-200 -100 0 100 200-100
Drift [mm]
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Building archetypes
• Archetype definitions• building function, configurations• number of stories• seismic zone
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Building archetypes
• Archetype definitions R = 4 High seismic (SDC Dmax)
SS = 1.5, S1 = 0.9 (SDS = 1.0, SD1 = 0.6)
Afloorseismic weight
Appr. period
Upper limit of period
SMT
(at Ta)Cs
Design base shear
wall length
[sqft] [psf] [s] [s] [g] [-] [kip] [ft]
1 1 Commercial 1600 30 0.112 0.16 1.50 0.25 12 12
5 2 Commercial 1600 30 0.19 0.27 1.50 0.25 24 24
Archetype Story # Function
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9 3 Commercial 1600 30 0.26 0.36 1.50 0.25 36 20
2 1 1&2 Family 500 10 0.112 0.16 1.50 0.25 1.25 8
6 2 1&2 Family 500 10 0.19 0.27 1.50 0.25 2.5 8
10 3 Multi-Family 500 30 0.26 0.36 1.50 0.25 11.25 12
13 4 Multi-Family 500 30 0.32 0.45 1.50 0.25 15 16
15 5 Multi-Family 500 30 0.38 0.53 1.50 0.25 18.75 20
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Building archetypes
• seismic design− based on assumed R− simplified proc: equivalent static loading
EQ loading demand, Vu
wall type Vnom VASD VLRFD
Story [kip] [lbs] [plf] (group#) [plf] [plf] [plf]
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[kip] [lbs] [plf] (group#) [plf] [plf] [plf]
R 6250 312 1 1173 469 657
4 11250 563 1 1173 469 657
3 15000 750 25 1505 602 843
2 17500 875 7 1836 734 1028
1
6250 lbs
1250
2500
3750
5000
18750 937 7 1836 734 1028
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Analytical model
• 2D truss structure
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rigid
nonlin. spring
rigid lean
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colu
mn
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Pushover analysis
250
300Archetype #15
Vmax
Vmax
= 214 kN; Vdesign
= 84 kN
Ω0 = 2.57
δy = 60.7 mm; δ
u = 165.2 mm
µC
= 2.72
T = 0.526 s
Vmax
= 214 kN (roof displ. = 138 mm)
Archetype #15
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0 50 100 150 200 250 3000
50
100
150
200
Vdesign
Roof displacement [mm]
Bas
e sh
ear
forc
e [k
N]
Vmax
V60%
δy
V80%
δu
ΩΩΩΩ 0 = 2.57
T = 0.526 sSSF = 1.20
Pushover analysis
design base shear
0 6.1 m
(displ. factor x10)
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IDA analysis
0 5 10 15 20 25 30-0.5
0
0.5
1
Time [s]
ag [g
]
Ground acceleration
50
100
Drif
t [m
m]
Floor #1 interstory drift(displ. factor x10)
• each archetype• 44 EQ records• nonlin. dyn. analysis• max. interstory drift
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0
Time [s]
Drif
t [m
m]
0 5 10 15 20 25 30-50
0
50
Time [s]
Drif
t [m
m]
Floor #4 interstory drift
0 5 10 15 20 25 30-200
-100
0
100
200
Time [s]
d [m
m]
Roof displacement
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IDA analysisS
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IDA analysis
• each archetype• each record• scaled up to collapse
5
Archetype #15 1
Archetype #15
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0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 150
0.5
1
1.5
2
2.5
3
3.5
4
4.5
SMT = 1.5g (at T = 0.526s)
SCT,median = 2.93g
Interstory drift [%]
SC
T [g
]
0 1 2 3 4 5 60
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
SMT = 1.5g (at T = 0.526s)
SCT,median = 2.93g
CMR = 1.956σσσσx
2 = 0.96σσσσx = 0.98
SCT [g]
Pro
babi
lity
[-]
(adjusted) collapse margin ratio
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IDA analysis
• or…
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Discussion
• comparison to wooden shear wall
K01
r1·K01
r2·K0
1
KP
1F0
Force, F
40
80
120
Fmax
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r3·K0
1
r4·K01FI
Displacement, ∆
∆u
∆max = β·∆un
∆un
KP = K0·[(F0/K0)/∆max]α
F = (F0 + r1·K0 ·∆) ·[1 – exp(-
Fu + r2·K0 ·(∆ - ∆u), ∆ ≥ -120
-80
-40
0
-80 -40 0 40 80
Drift [mm]
Load
[kN
]
δp
αpδp
βpFmax
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Discussion
• comparison to wooden shear wall
5.0
6.0
7.0 a
t T
= 0
.19
sec
(g)
CMR = 2.15/1.50 = 1.43
0.26
4
4.5
5Archetype #5
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0.0
1.0
2.0
3.0
4.0
0 1 2 3 4 5 6 7 8 9 10Maximum Interstory Drift Ratio (%)
Med
ian
Sa
at T
= 0
.19
sec
(g)
SCT(T = 0.26 s) = 2.15 g
SMT(T = 0. 26 s) = 1.50 g
X 1.43
0.26
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 150
0.5
1
1.5
2
2.5
3
3.5
SMT = 1.5g (at T = 0.265s)
SCT,median = 3.05g
Interstory drift [%]S
CT [g
]
• in general, very similar results
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Further observations
• Effect of ‘scaling’ fundamental period
3
4
5
SCT,median = 2.43g [g]
Archetype #19
3
4
5
SCT,median = 2.93g
[g]
Archetype #19
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0 5 10 150
1
2
3
SMT = 1.2g (at T = 0.749s)
SCT,median = 2.43g
Interstory drift [%]
SC
T [g
]
0 5 10 150
1
2
3
SMT = 1.5g (at T = 0.495s)
Interstory drift [%]S
CT [g
]
a) scaled at Tupper = 0.749 s b) scaled at Tmodel = 0.495 s
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Further observations
• Effect of ‘scaling’ fundamental period
3
4
5
SCT,median = 2.45g [g]
Archetype #17
3
4
5
SCT,median = 2.98g
[g]
Archetype #17
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0 5 10 150
1
2 SMT = 1.49g (at T = 0.603s)
SCT,median = 2.45g
Interstory drift [%]
SC
T [g
]
0 5 10 150
1
2 SMT = 1.5g (at T = 0.423s)
Interstory drift [%]S
CT [g
]
a) scaled at Tupper = 0.604 s b) scaled at Tmodel = 0.423 s
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Further observations
• Model parameter sensitivity
• capping displ. 50 75 mmcapping slope -0.15 -0.05 +6%
• .ααααP 0.75 0.40
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• .ααααP 0.75 0.40ββββP 0.25 0.21 +8%
• adjusted initial stiffness +6%
• 1.4 x strength +30%
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Performance quantification
• check R = 4 High seismic (SDC Dmax)SS = 1.5, S1 = 0.9 (SDS = 1.0, SD1 = 0.6)
ΩΩΩΩ0 µµµµC SSFSMT
(Tupper )SFanchor ββββtot ŜCT CMR ACMR
[-] [-] [-] [g] [-] [-] [g] [-] [-]
1 1 Commercial 2.38 6.25 1.31 1.50 2.1 0.70 2.79 1.86 2.44 >
Archetype Story # Function
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5 2 Commercial 2.40 4.37 1.26 1.50 1.89 0.70 3.06 2.04 2.57 >
9 3 Commercial 2.39 3.36 1.22 1.50 1.98 0.70 2.88 1.92 2.34 >
Mean 2.45 >
2 1 1&2 Family 9.91 6.31 1.31 1.50 2.1 0.70 6.00 4.00 5.24 >
6 2 1&2 Family 4.91 4.95 1.27 1.50 1.89 0.70 4.63 3.09 3.92 >
10 3 Multi-Family 2.52 4.06 1.25 1.50 1.98 0.70 3.16 2.11 2.64 >
13 4 Multi-Family 2.56 3.00 1.20 1.50 2 0.70 2.94 1.96 2.35 >
15 5 Multi-Family 2.57 2.72 1.20 1.50 2.1 0.70 2.93 1.96 2.35 >
Mean 3.30 >
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Performance quantification
• even for taller buildingsR = 4 High seismic (SDC Dmax)
SS = 1.5, S1 = 0.9 (SDS = 1.0, SD1 = 0.6)
ΩΩΩΩ0 µµµµC SSFSMT
(Tupper )SFanchor ββββtot ŜCT
[-] [-] [-] [g] [-] [-] [g]
Archetype Story # Function
2 1 1&2 Family 9.91 6.31 1.31 1.50 2.1 0.70 6.00
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6 2 1&2 Family 4.91 4.95 1.27 1.50 1.89 0.70 4.63
10 3 Multi-Family 2.52 4.06 1.25 1.50 1.98 0.70 3.16
13 4 Multi-Family 2.56 3.00 1.20 1.50 2 0.70 2.94
15 5 Multi-Family 2.57 2.72 1.20 1.50 2.1 0.70 2.93
17 6 Multi-Family 2.57 2.48 1.22 1.49 2.49 0.70 2.45
18 7 Multi-Family 2.08 2.40 1.22 1.33 2.37 0.70 2.54
19 8 Multi-Family 2.34 2.34 1.22 1.20 2.46 0.70 2.43
21 10 Multi-Family 2.42 2.31 1.23 1.02 2.49 0.70 2.25
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Performance quantification
• R = 4 !
• results and component behavior are very similar to wooden shear wall – as good as wood
• R = 6 is in code for wooden shear wall• additional finishing, partition walls?
+
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• additional finishing, partition walls?
• short period bldgs!• ASD design strength derivation from test
• uncertainties in the monotonic backbone estimation
-
+/-
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Performance quantification
conventional R factor vs. ATC -63
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conventional R factor vs. ATC -63
?
Page 46
SUNY Buffalo
24 June 2008
SUNY Buffalo
24 June 2008
Thank you for your attention!
But don’t go anywhere…
