A reliable estimation of maximum displacement demands of seismically isolated inelastic superstructures is crucial for assessment of base-isolated buildings under beyond-design earthquakes. Constant-strength inelastic displacement ratio, CR, spectra, as applied in the performance-based seismic assessment procedure, can be used to estimate the inelastic displacement demands of structures. Currently, a suitable analytical expression of CR is lacking for base-isolated structures considering the influencing parameters comprehensively. This paper seeks to fill this gap. The constant-strength spectra are computed from nonlinear dynamic analyses of simplified two-degree-of-freedom models considering the inelastic behavior of the superstructure and isolator system, using a set of earthquake ground motions recorded on stiff soil sites. The effects of strength reduction factor of superstructure, superstructure elastic period, secondary stiffness ratio of superstructure, mass ratio, isolation period, normalized strength of isolation system and superstructure viscous damping on the mean and dispersion of CR are investigated. In particular, the effects of variations in earthquake intensity and isolator strength on CR are taken into account by the normalized strength of isolation system. Besides, limiting values of CR as the superstructure elastic period tends to zero or infinity are discussed and verified using the statistical values of CR. Finally, based on the trends of CR with respect to the design parameters of the superstructure and isolation system, and the boundary conditions to the CR formula, an analytical estimating equation with reasonable accuracy is developed to approximate the mean constant-strength inelastic displacement ratios during seismic assessment of base-isolated building structures built on stiff soil sites.
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