Assessing Effectiveness of
Building Code Provisions
EQ: 11121, Sa: 2.86g
EQ: 11122, Sa: 2.32g
Greg Deierlein & Abbie Liel
Stanford University
Curt Haselton
Chico State University
… other contributors (PEER TA I & ATC 63)
PEER 2007 Annual Meeting
PBEE: Collapse (SAFETY) Assessment
Decision
Variable
DV: COLLAPSE
Damage
Measure
DM: Loss of Vertical Carrying
Capacity (LVCC)
Engineering
Demand
Parameter
Intensity
Measure
EDPs: Deformations & Forces
EDP: Interstory Drift Ratio
IM: Sa(T1) + Ground Motions
2
Illustration – 4 Story SMF Building
Office occupancy
Los Angeles Basin
Design Code: 2003 IBC /
2002 ACI / ASCE7-02
Perimeter Frame System
8 inch PT slab
Maximum considered EQ
demands:

Ss = 1.5g; S1 = 0.9g

Sa(2% in 50 yr) = 0.82g
Design V/W of 0.094g
Maximum inelastic design
drift of 1.9% (2% limit)
Typical Perimeter Frame Members
Beams: 32” to 40” deep
Columns: 24”x28” to 30”x40”
Governing Design Parameters
- Beams: minimum strength
- Column size: joint strength
- Column strength: SCWB
- Drift: just meets limit
3
Nonlinear Analysis & Calibration
EQ: 11122, Sa: 2.32g
1.5
Non-Deteriorated
Backbone
Normalized Moment (M/My)
1
0.5
0
-0.5
-1
-1.5
-8
-6
-4
-2
0
2
4
6
8
Chord Rotation (radians)
250
200
Experimental Results
Model Prediction
Shear Force (kN)
150
100
50
0
-50
-100
-150
-200
-250
-150
-100
-50
0
50
100
150
Column Top Horizontal Deflection (mm)
4
Incremental Dynamic Analysis – Collapse
4
3.5
Capacity Stats.:
Median = 2.2g
σLN = 0.36
3
(T=1.0s)[g]
2.5
Sa
Mediancol = 2.2g
1.5
σLN, col = 0.36g
g.m.
2
1
0.82g is 2% in 50 year motion
2% in 50
year = 0.5
0.82g
0
0
IDRcol = 7-12%
0.05
0.1
0.15
Maximum Interstory Drift Ratio
5
Simulation Results: Collapse Modes
EQ: 11151, Sa:
2.51g
EQ:
11021, Sa: 2.52g
11091, Sa: 2.19g
EQ: 11131, EQ:
Sa: 2.19g
EQ: 11121, Sa: 2.86g
EQ: 11122, Sa: 2.32g
EQ: 11152, Sa:EQ:
2.26g
11022, Sa: 2.12g
EQ:2.12g
11092, Sa: 3.06g
EQ: 11132, Sa:
EQ: 11141, Sa: 1.79g
4
40% of collapses
3.5
27% of collapses
(T=1.0s)[g]
2.5
Sa
3
1.5
2
g.m.
EQ: 11161, Sa: 0.66g
EQ: 11141, EQ:
Sa:
1.79g
Sa: 1.52g
17%11101,
of collapses
1
EQ: 11162, Sa: 0.72g
EQ: 11142, Sa:
EQ:1.32g
11102, Sa: 1.06g
12% of collapses
**Predicted by Static Pushover
0.5
0
0
0.05
0.1
0.15
Maximum Interstory Drift Ratio
Incremental
Dynamic Analysis
5% of collapses
2% of collapses
Collapse Fragility Curve
1
4
3.5
(T=1.0s)[g]
2.5
Sa
3
1.5
g.m.
2
1
0.5
0
0
0.05
0.1
Maximum Interstory Drift Ratio
Incremental
Dynamic Analysis
0.15
Cummulative Probability of Collapse
0.9
0.8
0.7
0.6
0.5
Median = 2.2g
0.4
sLN, Total = 0.36
0.3
0.2
Empirical CDF
Lognormal CDF (RTR Var.)
Lognormal CDF (RTR + Modeling Var.)
0.1
0
0
0.5
1
1.5
2
2.5
3
Sag.m.(T=1.0s) [g]
3.5
4
4.5
5
1.2
1.2
1.0
1.0
Normalized Moment (M/My)
Normalized Moment (M/My)
Uncertainty – Plastic Rotation Capacity
0.8
Mean (m) Plastic
Rotation Capacity
0.6
0.4
0.2
0.8
0.6
Reduced (m-s)
Plastic Rot. Cap.
Mean minus standard
deviation (lognormal)
for both plastic
rotation capacity and
post-capping stiffness
0.4
0.2
0.0
0.0
0.00
0.02
0.04
0.06
0.08
0.10
0.00
Total Chord Rotation (radians)
0.02
0.04
0.06
0.08
0.10
Total Chord Rotation (radians)
1.2
1.2
1
1
Sacomp(T=2.0s)[g]
Sacomp(T=2.0s)[g]
1.4
0.8
0.6
0.4
0.6
0.4
0.2
0.2
0
0
0.8
0.05
0.1
Maximum Interstory Drift Ratio
0.15
0
0
0.05
0.1
0.15
Maximum Interstory Drift Ratio
8
Correlation of Model Uncertainties
M, Column Base Moment
Type A: Parameters
within one element
1.5
1
0.5
0
-0.5
-1
-1.5
-8
-6
-4
-2
0
2
4
6
8
Θ, Chord Rotation
Type B: Between
parameters of
different elements
9
Collapse Capacity – with Modeling Uncert.
1
Median = 2.2g
Cummulative Probability of Collapse
0.9
sLN, RTR = 0.36
0.8
0.7
σLN, Total = 0.64 w/mod.
0.6
Margin 2.7x
0.5
0.4
0.3
P[collapse |Sa = 0.82g] = 5%
0.2
Empirical CDF
Lognormal CDF (RTR Var.)
Lognormal CDF (RTR + Modeling Var.)
0.1
5%
0
0
0.5
1
1.5
0.82g
2% in 50 yrs
2
2.5
3
Sag.m.(T=1.0s) [g]
3.5
4
4.5
5
Mean Annual Frequency of Collapse
1
Collapse
CDF
Cummulative Probability of Collapse
0.9
0.8
0.7
0.6
Collapse Performance
2.7
0.5

Margin: Sa,collapse = 2.7 MCE

5% Probability of collapse
0.4
0.3
0.2
5%
0
0
under design MCE = 5%
Empirical CDF
Lognormal CDF (RTR Var.)
Lognormal CDF (RTR + Modeling Var.)
0.1
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Sag.m.(T=1.0s) [g]
MAF of Excedance (Poisson rate)
0.0020

0.0018
MAFcol = 1.0 x 10-4
(0.5% in 50 years)
0.0016
Hazard
Curve
0.0014
0.0012
0.0010
0.0008
0.0006
2/50
0.0004
0.0002
0.0000
0
0.5
1
1.5
2
2.5
3
3.5
Sa at First Mode Period (g)
4
4.5
5
The 2% in 50 year ground motion
Illustration:
 Site dominated by single
event (M 6.9, R 14 km) -return period of 200 years
(MAF 25% in 50 yr)
 Boore-Joyner (BJ)
attenuation function
 Sa (25/50) -- median of BJ.
At T=1 sec., Sa = 0.28g
 Sa (2/50) -- +1.5s of BJ.
At T=1 sec., Sa = 0.56g.
Mean Annual Freq. = (Probability of Sa > Sa*, given EQ) x (MAF of EQ)
Ground motion selection (+e effect)
1.6
BJF Prediction: Median
BJF Prediction: Median +/- 1.0 sigma
BJF Prediction: Median +/- 1.0 sigma
BJF Prediction: Median +/- 2.0 sigma
BJF Prediction: Median +/- 2.0 sigma
Observed Sa - Loma Prieta (ID 11022)
1.4
Sa
component
[g]
1.2
1
0.8
0.6
+1.7 e at T = 1.0 sec.
0.4
-0.3 e at T = 0.45 sec.
0.2
0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Period [seconds]
Consider the Loma Prieta (11022 record):
• Close match to characteristic event [M 6.9, R 14, Sa(T=1) = 0.65g]
• Epsilon: +1.7 at T=1 sec; -0.3 at T = 0.45 sec
• General trend for +epsilon records to peak at the +e periods and drop
off elsewhere
Effect of Spectral Shape (e) on collapse capacity
LN(Sa) = -0.3481 + 0.311e
0.5 Best-Fit:
p-value = 4.716e-010
1
0.8
P[collapse]
0
+e
col
1
LN[Sa (T =1.71s)]
serror = 0.331 (LN units)
-0.5
Observation
Outlier
Regression
5/95% CIs on Mean
-1
-2
-1
0
e(T 1=1.71s)
1
2
0.6
+e
0.4
0.2
0
0
Empirical CDF with no e adjustment
Lognormal CDF with no e adjustment
Lognormal CDF after e adjustment
0.5
1
1.5
2
2.5
Sa(T=1.71s) [g]
Structural System Inelastic Deformation Capacity and Fundamental Period
SSF
High Deformation
Capacity
Moderate Deformation
Capacity
Brittle
Seismic Region
T 1 < 0.6s
T 1 > 1.4s
T 1 < 0.6s
T 1 > 1.4s
T 1 < 0.6s
T 1 > 1.4s
California High Seismic Region
1.30
1.50
1.25
1.15
1.00
1.00
Other Regions of Continental U.S.
1.00
1.15
1.00
1.10
1.00
1.00
14
* Baker (2005) found that the use of ε is not appropriate for pulse-type ground motions, so SSF should be used when these motions are expected (i.e. R < 10km).
1967 and 2003 Design Comparisons
180 ft.
120 ft.
1967 Design
Space Frame
1967 UBC, Zone 4
Design V/W: 0.068 g
Member sizes


Col. 20x20 to 24x24
Beam depth 20 to 26
No SCWB, no joint
check, non-conforming
ties
2003 Design
Perimeter Frame
2003 UBC/2002 ACI
Design V/W: 0.094 g
Member sizes


Col. 24x28 to 30x40
Beam depth 32 to 42
Fully conforming design
Comparison of 1967 vs. 2003 Designs
Total Structure Base Shear (kips)
3500
3000
2500
2000
1500
Vdesign,2003 = 1270 kips
Vdesign,1967 = 1190 kips
1000
500
2003 building
1967 building
0
0
Column Hinge Backbone Parameters
Qp,cap : 1967 = 0.02 rad (COV 50%)
2003 = 0.06 rad
Kc/Ke: 1967 = -0.22 (COV 60%)
2003 = -0.08
FEMA 356 Qp limits:
1967 = 0.006 rad
2003 = 0.015 rad
0.01
0.02
0.03 0.04 0.05
Roof Drift Ratio
0.06
0.07
0.08
Static Pushover Response
Wu : 1967 = 2.4
2003 = 2.7
Du: 1967 = 1.5% roof drift ratio
2003 = 5.0%
Incremental Dynamic Analysis – Sidesway Collapse
4
3.5
2.5
1.5
Median Sa = 2.2g
2
g.m.
Sa (T=1.0s) [g]
2
(T=1.0s)[g]
Incremental Dynamic Analysis, Controlling Component, 1967 Analysis Model
2.5
Sa
3
1.5
Median Sa = 1.0 g
1
col
0
g
=
1
0.5
0
0.5
0
0.05
0.1
IDR
3-6%
col =Interstory
Maximum
Drift Ratio
1967 Design
0.15
0
0
IDRcol = 7-12%
0.05
0.1
Maximum Interstory Drift Ratio
2003 Design
Strength: Median Sa = 1.0g, COV = 30%
Strength: Median Sa = 2.2g, COV = 36%
Deformation: IDRmax = 3 to 6%
Deformation: IDRmax = 7 to 12%
0.15
Simulated (sidesway) collapse fragility: 4-story building
FACTORS CONSIDERED
• Beams & Cols: flexure-shear
• B-C Joints: shear/bond
• Modeling Uncertainty
• Spectral Shape (e)
1
1967, 4-Story
2003, 4-Story
P[Collapse]
0.75
0.5
50%
1.0
Margins (mcollapse/MCE)
2.7
• 2003: 2.7
0.25
• 1967: 1.0
4%
0
0
1
2
3
4
Collapse Sa / MCE
5
6
P[C/MCE]
• 2003: 4%
• 1967: 50%
1967 Sidesway and Vertical Collapse (4-story)
P[C | IM
im]imP] [CPSIM
| IM
P[[CCDMDM| NC
| NC
]  SIM
P[ NC
| ]IM 
P[C| IM
[CSIM
| IMim
im]]  P
IM, IM
 im] Pim
[ NC
| IMSIM
 im
SIM ,SIM
Total Collapse
Probability
=
Sidesway Collapse
+
Probability at IMi
Probability of LVCC X Probability of No SS
(given drift ratio)
Collapse at IMi
1
P[Collapse]
1967, 4-story
1967, 4-story, incl. column shear failure
1967, 4-story, incl. col. loss of vertical capacity
Per Elwood/Moehle & Aslani/Miranda:
0.75
• Column Shear Failure:
Column IDR = 0.024 (mean)
0.5
• Column Axial Failure:
Column IDR = 0.056 (mean)
Shear failure reduces
median capacity by
about 15%
0.25
0
0
1
2
Collapse Sa / MCE
3
Recall – Sidesway collapse occurs
at peak drift ratios of 0.03 to 0.06.
4
RC Building Archetype Study
• Archetype Design Space & Parameters
heights & configurations
seismic design shears
3-Bay Multistory
Interior/Exterior Joints
Deterioration, P-D
Wtrib
Wlean
M
beam
column
beamcolumn joint
H1st-story
• Archetype Analysis Model
n-stories at H
capacity design/detailing
foundation
leaning
(P-D)
column
bay size
• Archetype Index Buildings
Heights: 1, 4, 8, 12, 20
Space & Perimeter
Space Frame
(Atrib/Atotal = 1.0)
Perimeter Frame
(Atrib/Atotal = 0.16)
Effects of Codes (’67 vs ’03) and Building Heights
1
P[Collapse]
0.75
1967:
8 – 12 – 4
stories
2003:
12 – 8 – 4
stories
0.5
1967, 4-Story
2003, 8-Story
Normalized
2003,Collapse
12-Story
Sidesway
1967, 8-Story
Fragilities
1967, 12-Story
2003, 4-Story
0.25
0
0
1
2
3
4
Collapse Sa / MCE
5
6
1967 Sidesway and Vertical Collapse: 8-story
P[C | IM
im]imP] [CPSIM
| IM
P[[CCDMDM| NC
| NC
]  SIM
P[ NC
| ]IM 
P[C| IM
[CSIM
| IMim
im]]  P
IM, IM
 im] Pim
[ NC
| IMSIM
 im
SIM ,SIM
Total Collapse
Probability
=
Sidesway Collapse
+
Probability at IMi
Probability of LVCC X Probability of No SS
(given drift ratio)
Collapse at IMi
1
From Elwood/Moehle & Aslani/Miranda:
• Column Shear Failure:
Column IDR = 0.022 (avg.)
= 0.014 (1st-story)
P[Collapse]
0.75
0.5
• Column Axial Failure:
Column IDR = 0.050 (avg)
= 0.025 (1st-story)
AXIAL collapse reduces
median by ~ 40%
0.25
0
0
1967, 8-story, w/shear
1967, 8-story, w/ LVCC
1967, 8-story
1
2
Collapse Sa / MCE
3
4
Sidesway collapse occurs at peak
(median) drift ratio of 0.038.
SUMMARY – Key Collapse Results
Simulated Sidesway Collapse Statistics
P[Collapse|MCE]
2003
1967
MAF (x10-4)
2003
1967
m-IDR,ult
2003
1967
4-Story
4%
50%
3
30
0.083
0.038
8-Story Space
7%
80%
5
150
0.068
0.038
12-Story Perimeter
14%
67%
11
100
0.053
0.035
5 to 12x
10 to 30x
Including Shear-to-Axial Column Failure for 1967 Designs:
• 4-story building: little change
• 8-story building: significant change (column IDR = 0.025)
MAF,collapse = 190 x 10-4 c/yr (35x rate of 2003 design)
Comments on Collapse Assessment
Accuracy of Assessment Procedure



stiffness/strength degrading models
characterization of ground hazard (spectral shape effect)
modeling uncertainties ..
Comparison of 1960-70’s versus modern frames




“regular” frames have 10 to 30x collapse risk
what about irregular frames?
validation & corroboration of results
appropriate level of safety?
Interpretations and Implications



communicating risks in consistent & meaningful ways
providing tools and engineering solutions (new buildings & retrofit)
action/implementation strategies