The constant damage inelastic displacement ratio for performance design of self-centering systems under far-field earthquake ground motions

In this research paper, the inelastic displacement ratio known as maximum nonlinear displacement to maximum elastic displacement is determined at different periods of vibration and constant damage indices based on the Park-Ang model for fully self-centering structures under 216 far-field earthquake ground motions. The effect of ground motion characteristics, including soil classification, magnitude, and source-to-site distance, are evaluated at different period ranges. Moreover, the influence of structural parameters is investigated, including the ultimate ductility of the structural system, the β factor related to the damage model, the stiffness-hardening ratio, and the dissipative-energy factor corresponding to the flag-shaped hysteresis behavior of the self-centering system. Then, a simple equation based on nonlinear regression analysis is proposed to estimate the constant damage inelastic displacement ratio. It is worth mentioning that the bias and standard deviation of the error in the suggested equation are presented for better understanding. Finally, the proposed equation is compared with the nonlinear responses obtained from the direct time history analysis in self-centering flag-shaped models under thirty earthquake records selected corresponding to desired seismic hazard level. The statistical analysis illustrates that the effect of ground motion characteristics on constant inelastic displacement ratio is not prominent, while the influence of some structural parameters like ultimate ductility and dissipative-energy factor is remarkable in higher damage levels. The verification analysis showed that the suggested equation could estimate the target displacement of the self-centering structural systems with a lower than 10% error.