Statistics of SDF System Estimate of Roof Displacement for Pushover Analysis of Buildings



1 Introduction

It is now common in structural engineering practice to estimate seismic demands by the nonlinear static procedure (NSP) or pushover analysis detailed in FEMA-273 [1997] or ATC-40

guidelines [1996]. The seismic demands are computed by nonlinear static analysis of the structure subjected to monotonically increasing lateral forces with an invariant height-wise

distribution until a target value of roof displacement is reached. This roof displacement value is determined from the earthquake- induced deformation of an inelastic SDF system derived from the pushover curve.






Recently, much work has been done to develop and evaluate simplified methods for estimating the peak deformation of this inelastic SDF system, which has led to the capacity

spectrum method detailed in ATC-40 and FEMA-274 [1997] reports, and the “coefficient method” in the FEMA-273 guidelines. The ATC-40 version of the capacity spectrum method has been shown to be unreliable and inaccurate [Chopra and Goel, 2000]. The well-established

inelastic response (or design) spectrum [Veletsos and Newmark, 1960; Newmark and Hall, 1982] has been advocated as an alternative procedure [Bertero, 1995; Reinhorn, 1997; Fajfar, 1999]

and implemented graphically as a capacity-demand diagram method [Chopra and Goel, 1999]. This work investigates the basic premise that the roof displacement of a multistory

building can be determined from the deformation of an SDF system. For this purpose, the responses of both systems are determined rigorously by nonlinear response history analysis,

without introducing any of the approximations underlying the aforementioned simplified methods. The statistics of the SDF-system estimate of roof displacement are presented for a

variety of frame buildings and ground motion ensembles, and improved results are achieved by modal pushover analysis [Chopra and Goel, 2002].


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