Instrumentation needs for PBEE
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Transcript Instrumentation needs for PBEE
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
| IMim
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
| IMim
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