When the response of a structure is influenced significantly by multiple vibration modes, the seismic demands determined by response history analyses with ground motions selected to match a single conditional mean spectrum (CMS) may be unconservative for several response quantities. An existing solution to this problem is to determine the demand as the maximum of mean demands from several CMSs. To reduce the computational effort while maintaining accuracy and precision, we introduce an alternative engineering solution that is based on a simplified version of the generalized CMS, where two specified conditioning spectral accelerations share a common hazard level. vector-valued disaggregation is developed herein to provide a single earthquake scenario for the target spectrum. The results from a realistic case study suggest that the proposed spectrum provides seismic demands that are as accurate and precise as those obtained from analyzing the structure with multiple CMSs while simultaneously reducing the computational effort by a factor of 2 or more.
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References
1.
AbrahamsonN. A., 1988.
Statistical properties of peak ground accelerations recorded by the SMART 1 array,
Bulletin of the Seismological Society of America78, ,
26–
41.
2.
Al AtikL., AbrahamsonN., 2010.
An improved method for nonstationary spectral matching,
Earthquake Spectra26, ,
601–
617.
3.
American Society of Civil Engineers, 2010.
Minimum Design Loads for Buildings and Other Structures ,
American Society of Civil Engineers: Structural Engineering Institute,
Reston, Va.
4.
AnchetaT. D., DarraghR. B., StewartJ. P., SeyhanE., SilvaW. J., ChiouB. S.-J., WooddellK. E., GravesR. W., KottkeA. R., BooreD. M., KishidaT. D., DonahueJ. L., 2014.
NGA-West2 database,
Earthquake Spectra30, ,
989–
1005.
BakerJ. W., 2011.
Conditional Mean Spectrum: Tool for ground-motion selection,
Journal of Structural Engineering-ASCE137, ,
322–
331.
7.
BakerJ. W., CornellC. A., 2005.
A vector-valued ground motion intensity measure consisting of spectral acceleration and epsilon,
Earthquake Engineering & Structural Dynamics34, ,
1193–
1217.
8.
BakerJ. W., CornellC. A., 2006.
Spectral shape, epsilon and record selection,
Earthquake Engineering & Structural Dynamics35, ,
1077–
1095.
9.
BakerJ. W., JayaramN., 2008.
Correlation of spectral acceleration values from NGA ground motion models,
Earthquake Spectra24, ,
299.
10.
BarbosaA. R., 2011.
Simplified Vector-Valued Probabilistic Seismic Hazard Analysis and Probabilistic Seismic Demand Analysis: Application to the 13-Story NEHRP Reinforced Concrete Frame-Wall Building Design Example.
Ph.D. Thesis, UC San Diego.
11.
BazzurroP., CornellC., 2002.
Vector-valued probabilistic seismic hazard analysis (VPSHA),
inProceedings of the 7th U.S. National Conference on Earthquake Engineering ,
Earthquake Engineering Research Institute, Oakland, CA,
pp.
21–
25.
BradleyB. A., 2010.
A generalized conditional intensity measure approach and holistic ground-motion selection,
Earthquake Engineering & Structural Dynamics39, ,
1321–
1342.
14.
BradleyB. A., 2012.
The seismic demand hazard and importance of the conditioning intensity measure,
Earthquake Engineering & Structural Dynamics41, ,
1417–
1437.
15.
BradleyB. A., 2013.
A comparison of intensity-based demand distributions and the seismic demand hazard for seismic performance assessment,
Earthquake Engineering & Structural Dynamics42, ,
2235–
2253.
16.
CampbellK. W., BozorgniaY., 2008.
NGA ground motion model for the geometric mean horizontal component of PGA, PGV, PGD and 5% damped linear elastic response spectra for periods ranging from 0.01 to 10 s,
Earthquake Spectra24, ,
139–
171.
17.
CarltonB., AbrahamsonN., 2014.
Issues and approaches for implementing conditional mean spectra in practice,
Bulletin of the Seismological Society of America104, ,
503–
512.
18.
FieldE. H., GuptaN., GuptaV., BlanpiedM., MaechlingP., JordanT. H., 2005.
Hazard calculations for the WGCEP-2002 earthquake forecast using OpenSHA and distributed object technologies,
Seismological Research Letters76, ,
161–
167.
19.
GouletC. A., HaseltonC. B., Mitrani-ReiserJ., BeckJ. L., DeierleinG. G., PorterK. A., StewartJ. P., 2007.
Evaluation of the seismic performance of a code-conforming reinforced-concrete frame buildingfrom seismic hazard to collapse safety and economic losses,
Earthquake Engineering & Structural Dynamics36, ,
1973–
1997.
20.
JayaramN., BakerJ. W., 2008.
Statistical tests of the joint distribution of spectral acceleration values,
Bulletin of the Seismological Society of America98, ,
2231–
2243.
21.
JayaramN., LinT., BakerJ. W., 2011.
A computationally efficient ground-motion selection algorithm for matching a target response spectrum mean and variance,
Earthquake Spectra27, ,
797–
815.
22.
KwongN. S., ChopraA. K., 2015a.
Evaluation of the exact conditional spectrum and generalized conditional intensity measure methods for ground motion selection,
Earthquake Engineering & Structural Dynamics45, ,
757–
777.
23.
KwongN. S., ChopraA. K., 2015b.
Selection and Scaling of Ground Motions for Nonlinear Response History Analysis of Buildings in Performance-Based Earthquake Engineering, PEER Report 11 ,
PEER Center,
Berkeley, CA.
24.
LinT., HarmsenS. C., BakerJ. W., LucoN., 2013a.
Conditional spectrum computation incorporating multiple causal earthquakes and ground-motion prediction models,
Bulletin of the Seismological Society of America103, ,
1103–
1116.
25.
LinT., HaseltonC. B., BakerJ. W., 2013b.
Conditional spectrum-based ground motion selection. Part I: Hazard consistency for risk-based assessments,
Earthquake Engineering & Structural Dynamics42, ,
1847–
1865.
26.
LinT., HaseltonC. B., BakerJ. W., 2013c.
Conditional spectrum-based ground motion selection. Part II: Intensity-based assessments and evaluation of alternative target spectra,
Earthquake Engineering & Structural Dynamics42, ,
1867–
1884.
27.
LothC., 2014.
Multivariate Ground Motion Intensity Measure Models, and Implications for Structural Reliability Assessment,
Ph.D. Thesis, Stanford University, Stanford, CA.
28.
LothC., BakerJ. W., 2015.
Rational design spectra for structural reliability assessment using the response spectrum method,
Earthquake Spectra31, ,
2007–
2026.
29.
McGuireR. K., 2004.
Seismic Hazard and Risk Analysis ,
Earthquake Engineering Research Institute,
Oakland, CA.
30.
McKennaF., ScottM. H., FenvesG. L., 2009.
Nonlinear finite-element analysis software architecture using object composition,
Journal of Computing in Civil Engineering24, ,
95–
107.
31.
NEHRP Consultants Joint Venture, 2011.
Selecting and Scaling Earthquake Ground Motions for Performing Response-History Analyses, NIST GCR 11-917-15. Tech. Rep. ,
National Institute of Standards and Technology,
Washington, D.C.
PEER GMSM Working Group, 2009.
Evaluation of Ground Motion Selection and Modification Methods: Predicting Median Interstory Drift Response of Buildings, PEER Report 01 ,
PEER Center,
Berkeley, CA.
34.
PowerM., ChiouB., AbrahamsonN., BozorgniaY., ShantzT., RobleeC., 2008.
An overview of the NGA project,
Earthquake Spectra24, ,
3–
21.
35.
ReiterL., 1991.
Earthquake Hazard Analysis: Issues and Insights ,
Columbia University Press,
New York City, NY.
36.
ShomeN., CornellC. A., BazzurroP., CarballoJ. E., 1998.
Earthquakes, records, and nonlinear responses,
Earthquake Spectra14, ,
469–
500.
37.
SomervilleP., ThioH., et al.,
2011.
Development of ground motion time histories for seismic design,
inProceedings of the Ninth Pacific Conference on Earthquake Engineering: Building an Earthquake-Resilient Society ,
pp.
14–
16.
38.
WassermanL., 2004.
All of Statistics: A Concise Course in Statistical Inference ,
Springer,
NY.
39.
YamamotoY., 2011.
Stochastic Model for Earthquake Ground Motion Using Wavelet Packets.
Ph.D. Thesis, Department of Civil and Environmental Engineering, Stanford University, Stanford, CA.
40.
ZhangD.-Y., XieW.-C., PandeyM. D., 2012.
Synthesis of spatially correlated ground motions at varying sites based on Vector-valued Seismic Hazard Deaggregation,
Soil Dynamics and Earthquake Engineering41, ,
1–
13.
41.
ZimmermanR. B., BakerJ. W., HooperJ. D., BonoS., HaseltonC. B., EngelA., HamburgerR. O., CelikbasA., JalalianA., 2015.
Response history analysis for the design of new buildings in the NEHRP provisions and ASCE/SEI 7 standard: Part III-Example applications illustrating the recommended methodology,
Earthquake Spectra ,
in press.
