Seismic Response Spectra for Probabilistic Analysis of Nonlinear Systems

Abstract

In the conventional seismic analysis of a system, the input motion is defined either by a probabilistic response spectrum or by ground-motion histories whose spectra “match” the probabilistic response spectrum. In both cases, it is implicitly assumed that the spectral values at different periods on a probabilistic response spectrum are fully correlated with one another. A nonlinear system changes its “effective” period during seismic shaking; hence, its response depends on spectral values at many natural periods. The assumption of complete correlation between spectral values at different periods results in an overestimation of the response of a nonlinear system. For the case analyzed in this paper, the conventional use of a 500-year mean return period (MRP) response spectrum in nonlinear analysis produces responses that have 20–30% longer MRPs. Also, the larger-component response acceleration was 11% higher than the geometric-mean response acceleration, and the larger component response deformation was 33% higher than the geometric-mean response deformation. This paper presents a more accurate way of using the response spectrum in the probabilistic analysis of nonlinear systems.