Inelastic seismic spectra including a damage criterion: A stochastic approach

•Describe earthquakes as non-stationary stochastic process.•Obtaining seismic spectra of sdof system modeled by non-linear BW model.•Response evaluation in terms of displacement/acceleration/energies is evaluated for different scenario.•Use a damage-based seismic spectra using the Park–Ang damage model.

In this paper, a stochastic approach for obtaining damage-based inelastic seismic spectra is proposed. The Park and Ang damage model, which includes displacement ductility and hysteretic energy, is adopted to take into account the cumulative damage phenomenon in structural systems under strong ground motions. Differently from previous studies in this field, damage-based seismic spectra are obtained by means of peak theory of stochastic processes. The following stochastic inelastic seismic spectra are constructed and then analyzed: damage-based displacement and acceleration inelastic spectra, damage-based response modification factor spectra, damage-based yield strength demand spectra and damage-based inelastic displacement ratio spectra.