Constant-ductility inelastic displacement ratio (Cμ) spectra can be utilized for the estimation of peak inelastic structural displacements in the seismic design procedure. Currently, suitable analytical estimates of Cμ are lacking for base-isolated buildings with inelastic behavior of superstructures in a beyond design basis earthquake. This paper attempts to fill this research gap and hence conducts parametric studies on the Cμ spectra of base-isolated inelastic superstructures with lead-rubber bearings (LRBs). For that purpose, the inelastic model and equations of motion, boundary conditions of the analytical formulation of Cμ, and controlling parameters for the two-degree-of-freedom (2DF) superstructure-isolator system with LRBs are presented first. Subsequently, by analyzing the parameterized 2DF systems using an ensemble of strong earthquake records representative of a site with stiff soil conditions, the influence of controlling parameters, namely, displacement ductility ratios, superstructure periods, post-yielding stiffness ratios of superstructures, mass ratios, isolation periods and normalized isolator strength, on the mean and dispersion of Cμ are discussed, and the boundary conditions of Cμ are validated based on the calculated data. Comparisons of how the controlling parameters influence the Cμ and earlier investigated CR (i.e. constant-strength inelastic displacement ratio) spectra are also presented. Lastly, a predicting equation with reasonable accuracy is proposed for the mean Cμ using the nonlinear multivariable regression analysis method. The outcome of this study allows the application of displacement-based design via inelastic displacement ratio for new base-isolated structures under beyond design basis earthquakes.
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