Normalized Residual Displacements for Bilinear and Pinching Oscillators

Abstract

A correct estimation of residual displacements due to an earthquake event is crucial in satisfying the limit state of repairability after the event and for assessing the safety of structures against future earthquake events. An attempt is made in this study to obtain the statistical estimates of constant-ductility residual displacement spectra, for bilinear and pinching oscillators with 5% initial damping, in terms of the 5%-damping elastic displacement spectrum. The normalized residual displacement spectra (at the mean level and 0.1- and 0.9-fractile levels) are described as three-coefficient and four-coefficient mathematical functions for pinching and bilinear models, respectively. The coefficients of these functions are proposed to be estimated through scaling equations in terms of three model parameters for a given set of the ductility ratio and hysteretic energy capacity coefficient in the case of a bilinear model and for a given set of the pinching parameters, ductility ratio, and hysteretic energy capacity coefficient in the case of a pinching model.