Residual displacements for non-degrading bilinear oscillators under seismic actions

•A novel approach for estimating the residual displacements of SdoF models is provided.•The infuence of earthquake characteristics is investigated using synthetic accelerograms.•Residual displacement spectra are provided.•The propoded relationship can be used to estimate residual displacements.•A design procedure can be built upon the proposed method. This work aims to provide a relationship to assess the residual displacements for one-storey buildings standing in seismic-prone areas. The maximum residual displacement that a structure can possibly sustain is clearly identified by means of its structural characteristics alone. It is demonstrated that the upper bound is independent of the peak displacement. The proposed procedure can help in controlling the structural residual deformations, which is an issue that is gaining momentum into the seismic community: a large body of research has been dealing with post-seismic damage. However, no general rule or theoretical mechanic model with general validity are reported in the literature. The solely valuable approach, though widely accepted, for predicting seismic-induced residual displacements is a statistical one. In order to frame the given relationship into the established probabilistic framework, an extensive numerical campaign has been carried out by means of nonlinear time-history analyses. Artificial spectrum-compatible accelerograms are used as proxies to account for seismic events. As a final result, residual displacement response spectra are proposed.