Estimation of inelastic displacement ratio spectrum for existing RC structures via displacement response spectrum

In the present seismic design philosophy, the structures are designed to remain within the specified displacement limits for multiple earthquake hazard levels expected during their design life. Accordingly, the estimation of maximum inelastic displacement demand in a structure consistent with a given hazard level is of primary importance. Considering the complexity and inconvenience associated with the nonlinear response history analyses for a suite of hazard-consistent ground motions, it is preferred to estimate the maximum inelastic displacement demand by using the scaling models available for the inelastic displacement ratio $C$ in the single-degree-of-freedom (SDOF) structures. In this study, a new scaling model is developed for the inelastic displacement ratio $C_R\left(T\right)$ spectrum for a given response reduction factor R in the case of 5%-initial damping Bouc-Wen-Baber-Noori (BWBN) oscillators with stiffness and strength degradations and pinching. This model is based on the observed similarities between the $C_R\left(T\right)$ spectrum and the reciprocal of given displacement response SD($T$) spectrum in most cases, and thus, this indirectly accounts for the effects of seismological and site parameters. A new strong-motion duration definition is also proposed to identify shorter strong-motion segments of comparable relevance, and on using this definition, it is shown that the dependence of the mean $C_R\left(T\right)$ spectrum on strong-motion duration may be considered negligible. Accordingly, the regression parameters of the proposed scaling model for $C_R\left(T\right)$ spectrum are estimated as the exponential functions of only five governing BWBN parameters. The best-fit estimates of the regression coefficients of the resulting prediction equations are obtained for three values of R. The residual error spectra are also modeled to estimate the $C_R\left(T\right)$ spectrum for a given confidence level. The proposed scaling model can be applied to a wide range of existing reinforced concrete (RC) structures with 5% initial damping by using the input of the design displacement spectrum and BWBN parameters.