The normalized inelastic displacement spectra for seismic response estimation of a SDOF system with a generalized flag-shaped hysteretic model

Abstract In order to develop the inelastic displacement spectra suitable for self-centering structures with flag-shaped hysteretic behavior when subjected to near-fault pulse-like (NFPL) ground motions, the nonlinear time history analysis for a single degree of freedom (SDOF) system with a generalized flag-shaped (FS) hysteresis model is first realized by using Matlab software, a total of 85 NFPL records are selected as the seismic input, the variation ranges of all considered parameters, including the ductility, the vibration period, the energy dissipation coefficient and the post-yield stiffness ratio of the hysteresis model are specified, then the constant-ductility inelastic displacement spectra for different seismic records and different parameters are calculated and statistically processed. It is found the normalization of the natural period and the displacement by the pulse period, namely T / T p and x m / T p 2 , can significantly reduce the variation of displacement spectra. The influence of the post-yield stiffness ratio ranging from 0 to 0.20 on the normalized spectra is slight and can be neglected. Besides, as T / T p increases, the normalized displacement first increases and then slowly decreases, the normalized period corresponding to the peak displacement is approximately 1. When T / T p is about less than 0.7, the displacement spectra are positively correlated with the ductility, µ , followed by a negative correlation between them as T / T p grows larger. Moreover, increasing the energy dissipation coefficient will reduce the displacement response, but when the coefficient is greater than 1, its impact on the displacement is rather small. Finally, the equation of the normalized displacement spectra as a function of T / T p and µ is proposed, and an adjustment factor is added to account for the influence of the energy dissipation coefficient on the displacement spectra.