Utilization of the Conditional Mean Spectrum in risk and building code assessments

Utilization of the Conditional Mean Spectrum in risk and building code assessments, Jack Baker, WCEE 2024

1. Utilization of the Conditional Mean Spectrum
in risk and building code assessments
Thanks to former students Tamika J. Bassman, Ting Lin, Christophe Loth, Reagan Chandramohan
Thanks to colleagues Greg Deierlein, Curt Haselton, John Hooper,
Nicolas Luco, Peter Powers, Sanaz Rezaeian, KuanshiZhong
Jack W. Baker
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2. Ground motions for response history analysis
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Seismic sources
Ground motions
Target response
spectrum
Ground motions
Structural performance

3. Traditionally, the target is the Uniform Hazard Spectrum* (UHS)
J. Baker
30.05 0.1 0.5 1 3
Spectral Acceleration, SA [g]
10
-5
10
-4
10
-3
10
-2
10
-1
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SA(0.1 s)
SA(1 s)
SA(3 s) 0 1 2 3 4 5
Period, T [s]
0
0.5
1
1.5
2
S
p
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[
g
]
4.04x10
-4
exceedance rate UHS
2.1x10
-3
exceedance rate UHS
Example hazard curves for one site Uniform Hazard Spectra
*Sometimes slightly modified for idealized spectral shapes, risk targeting,…

4. Conditional mean values of spectral acceleration at all periods,
given the target Sa(1s) (“Conditional Mean Spectrum”)
J. Baker
4ln ( )|ln ( *) ln ln
( , , ) ( , *) ( *) ( )
i
Sa T Sa T Sa i i Sa i
M R T T T T T    

5. The CMS/UHS choice can have a significant impact on
response estimates sensitive to a range of excitation
frequencies
Collapse fragilities for a steel moment frame building
Chandramohan, Lin, Baker and Deierlein (2013). “Influence of
ground motion spectral shape and duration on seismic collapse
risk.”
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6. U.S. building codes give two ground motion selection options:
1.Use one uniform hazard spectrum (UHS)
2.Use two or more conditional mean spectra
(CMS)
›Ensure that their envelope is within 75% of the UHS
›Pass all checks for each CMS
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7. Assessment approach
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Ground motion
target & selection
(three alternatives)
Response history
analysis
•42-story RC core wall
•Nonlinear OpenSees
model
•MCE (2,475-year) ground
motion
Compare resulting
building demands
•Max story drift
•Base shear
•Roof acceleration
Bassman, Zhong, and Baker (2022). “Evaluation of conditional mean spectra
code criteria for ground motion selection.” ASCE Journal of Structural
Engineering.

8. CMS-based ground motion selection methods
CMS
ASCE: Compliant with ASCE 7
•Two target spectra
•Envelope of targets > 75% of UHS
(within prescribed range)
CMS
theor: theoretical approach
•Many target spectra
Demand = max of the mean demands
from the spectra
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9. Can code-based CMS produce acceptable building
demands?
T* chosen based on the building’s modal
properties
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Mode
Period
(s)
1 4.2
2 1.0
3 0.5
T*=1s
T*=5s

10. Can code-based CMS produce acceptable building
demands?
T* chosen based on the building’s modal
properties
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Mode
Period
(s)
1 4.2
2 1.0
3 0.5
Demand
Type
UHS
% of UHS Results
CMS
theorCMS
ASCE
Story Drift2.6% 74% 74%
Base
Shear
0.21W 86% 86%
Roof
Accel
1.3g 91% 83%
T*=1s
T*=5s

11. How does the choice of conditioning period (T*)
impact building demands?
Three choices of T*
T* = {1s, 5s} (good)
T* = {3s, 8s} (not very good)
T* = {0.15, 9s} (really bad)
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Mode
Period
(s)
1 4.2
2 1.0
3 0.5
Deman
d Type
UHS
% of UHS Results
CMS
theorCMS
ASC
E
CMS
ASC
E
CMS
ASC
E
Story
Drift
2.6%74% 74% 71% 84%
Base
Shear
0.21W86% 86% 79% 76%
Roof
Accel
1.3g91% 83% 81% 81%

12. Conclusions
The Conditional Mean Spectrum (CMS) has gained popularity over the past 15
years as a tool to develop realistic ground motions and avoid the conservatism of
the UHS
The CMS is now adopted in U.S. Building Codes, with some simplified rules to
ensure robustness
Those rules were initially judgment-based, but we have developed a testing
procedure and found (for a representative case study) that the rules produce
accurate demand estimates
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www.jackwbaker.com
Baker (2011). "Conditional Mean Spectrum: Tool for ground motion
selection," ASCE Journal of Structural Engineering.
Bassman, Zhong, and Baker (2022). “Evaluation of conditional mean spectra
code criteria for ground motion selection.” ASCE Journal of Structural
Engineering.