The estimation of residual displacements in a structure due to an anticipated earthquake event has increasingly become an important component of performance-based earthquake engineering because controlling these displacements plays an important role in ensuring cost-feasible or cost-effective repairs in a damaged structure after the event. An attempt is made in this study to obtain statistical estimates of constant-ductility residual displacement spectra for bilinear and pinching oscillators with 5% initial damping, directly in terms of easily available seismological, site, and model parameters. None of the available models for the bilinear and pinching oscillators are useful when design spectra for a seismic hazard at a site are not available. The statistical estimates of a residual displacement spectrum are proposed in terms of earthquake magnitude, epicentral distance, site geology parameter, and three model parameters for a given set of ductility demand and a hysteretic energy capacity coefficient in the case of bilinear and pinching models, as well as for a given set of pinching parameters for displacement and strength at the breakpoint in the case of pinching model alone. The proposed scaling model is applicable to horizontal ground motions in the western U.S. for earthquake magnitudes less than 7 or epicentral distances greater than 20 km.

由于预期地震事件导致的结构残余位移的估计已日益成为基于性能的地震工程的重要组成部分，因为控制这些位移对于确保在地震发生后对受损结构进行成本可行或经济高效的修复起着重要作用。事件。本研究试图直接根据容易获得的地震学、场地和模型参数，获得具有 5% 初始阻尼的双线性和箍缩振子的恒定延性残余位移谱的统计估计。当某个地点的地震危险的设计谱不可用时，双线性和箍缩振荡器的可用模型都无用。残余位移谱的统计估计是根据地震震级、震中距、场地地质参数和给定一组延性需求的三个模型参数以及双线性和尖缩模型情况下的滞后能量容量系数提出的，如下所示以及在单独夹紧模型的情况下，对于给定的一组给定的夹紧参数，断点处的位移和强度。所提出的比例模型适用于美国西部地震震级小于 7 或震中距离大于 20 公里的水平地面运动。