Residual displacement,as a significant measure of structural inelasticity,is effectively used in post-earthquake seismic assessment of structures.This demand can be considered for seismic evaluation of structures under multiple earthquakes.This study introduces a simple and novel index to predict the residual displacement of mainshock-damaged structures against subsequent aftershock.The proposed index is defined as a ratio between residual displacement of damaged structures against aftershock and peak inelastic displacement of intact structures under mainshock.In this study,constant-strength spectra based on the index are developed considering the effects of important structural characteristics and also significant seismic parameters.Moreover,analytical equations are presented to predict the proposed index for bi-linear single-degree-of-freedom (SDOF) systems considering both the effects of positive and negative polarities of aftershock.Furthermore,an equation is suggested to estimate the peak inelastic displacement of intact systems under mainshock,which is required to compute the index.