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U.S. Geological Survey Open-File Report 2010-1328

In Cooperation with the Pacific Earthquake Engineering Research Center, University of California, Berkeley

Documentation for Assessment of Modal Pushover-Based Scaling Procedure for Nonlinear Response History Analysis of “Ordinary Standard” Bridges

By Erol Kalkan and Neal S. Kwong


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The earthquake engineering profession is increasingly utilizing nonlinear response history analyses (RHA) to evaluate seismic performance of existing structures and proposed designs of new structures. One of the main ingredients of nonlinear RHA is a set of ground-motion records representing the expected hazard environment for the structure. When recorded motions do not exist (as is the case for the central United States), or when high-intensity records are needed (as is the case for San Francisco and Los Angeles), ground motions from other tectonically similar regions need to be selected and scaled. The modal-pushover-based scaling (MPS) procedure recently was developed to determine scale factors for a small number of records, such that the scaled records provide accurate and efficient estimates of “true” median structural responses. The adjective “accurate” refers to the discrepancy between the benchmark responses and those computed from the MPS procedure. The adjective “efficient” refers to the record-to-record variability of responses. Herein, the accuracy and efficiency of the MPS procedure are evaluated by applying it to four types of existing “ordinary standard” bridges typical of reinforced-concrete bridge construction in California. These bridges are the single-bent overpass, multi span bridge, curved-bridge, and skew-bridge. As compared to benchmark analyses of unscaled records using a larger catalog of ground motions, it is demonstrated that the MPS procedure provided an accurate estimate of the engineering demand parameters (EDPs) accompanied by significantly reduced record-to-record variability of the responses. Thus, the MPS procedure is a useful tool for scaling ground motions as input to nonlinear RHAs of “ordinary standard” bridges.

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Menlo Park, California 94025

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Suggested citation:

Kalkan, Erol, and Kwong, Neal S., 2011, Documentation for assessment of modal pushover-based scaling procedure for nonlinear response history analysis of "ordinary standard" bridges: U.S. Geological Survey Open-File Report 2010-1328, 58 p.




MPS Procedure for Bridges

Ground Motions Selected

Description of Bridges and Computer Models

First – “Mode” SDF-System Parameters

Evaluation of MPS Procedure



References Cited


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