Probabilistic Seismic Drift Demand on SMRF based on Extended Modal Analysis and Natural-Period-dependent Spectrum Intensity

Abstract

The objectives of this study is to develop a framework for estimating the exceedance probability (pex) of the maximum inter-story drift ratio (ISDR) at each story of an SMRF on the basis of previously proposed techniques for predicting the responses for a given ground motion, which comprises the use of the maximum displacement (dmax) of the inelastic oscillator equivalent to the first mode of the original frame and dmaxﾒs of the elastic oscillators equivalent to the higher modes, and takes into consideration a post-elastic first modal shape that would change as a function of dmax of the inelastic oscillator.

The authors have already developed a simple technique for dmax of the inelastic oscillators based on natural-period-dependent spectrum intensity SI?, defined as an integration of acceleration spectral response from elastic natural period to equivalent natural period of the oscillator. It was found that the relationship between dmax and SI? can be modeled using a simple linear function. Then dmax can be estimated as the intersection of the linear function and the integrated elastic response spectrum of a given ground motion. To estimate pex of dmax, it is proposed to use uniform hazard SI?; unlike spectral responses, correlation among SI?ﾒs with various integration rages are fairly high.

The post-elastic first modal shape changes complicated manner because of irregular formations of plastic hinges at the ends of members. To consider this problem, the authors have already proposed to approximate probability distribution of the inelastic first modal response of each story by shifted-lognormal distribution function. By using a three parameter distribution function, better approximation of pexcan be achieved than using a two parameter distribution function. The first modal responses of each story at three exceedance probabilities are estimated using the deflection shape of the frame corresponding to each of dmax as the modal shape.

This paper proposes a method to estimate pex of ISDR by composing dmax with higher modal responses considering probabilistic seismic hazard, which would be the last piece of this framework to be used in practice. The accuracy of the proposed method is investigated by comparing the pex estimated by the proposed method with the pex obtained via Monte Carlo simulations considering various seismic activities around a site and correlation among spectral accelerations.