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.

残余位移是结构非弹性的重要指标，可有效地用于结构地震后的地震评估中。对于多次地震下的结构进行地震评估，可以考虑该需求。这项研究引入了一种简单新颖的指标来预测主震破坏结构相对于后续余震的残余位移。拟议的指标定义为受损结构对余震的残余位移与完整结构在主震作用下的峰值非弹性位移之间的比率。在这项研究中，考虑到重要的结构特征和重要的地震参数的影响，开发了基于该指数的恒定强度谱。而且，考虑余震的正负极性影响，提出了解析方程来预测双线性单自由度（SDOF）系统的拟议指标。此外，提出了一个方程式来估计主震下完整系统的峰值非弹性位移，这是计算指标所必需的。