Inelastic displacement ratios of fully self-centering controlled rocking systems subjected to near-source pulse-like ground motions

• CR spectra of SC-CR systems strongly depends on modeling and ground motion parameters.
• New formulas are proposed for estimating inelastic displacement ratios of SC-CR systems subjected to far-field and near-field pulse-like ground motions.
• Effects of source-to-site distance, earthquake magnitude, and site classes on CR spectra of SC-CR system are not as much important of effects of pulse period and predominant period of ground motion.

Modern self-centering controlled rocking (SC-CR) systems are capable of reducing residual drift after severe earthquakes by swaying on their bases and concentrating damage in energy dissipation devices. The present research determines constant-strength (CR) spectra for SC-CR systems subjected to far-field and near-field pulse-like (NF-pulse) ground motions. SC-CR systems are simulated as single degree of freedom models with a flag shape behavior. Nonlinear time-history analyses are conducted using 91 NF-pulse and 44 far-field records to derive the CR spectra. Each point of CR spectrum of a SC-CR system is the ratio of maximum inelastic to maximum elastic displacement. An extensive statistical study is carried out to examine the effects of ground motion and modeling parameters on the CR spectra. It is found that the influences of pulse period, predominant period of ground motion, and modeling parameters on inelastic displacement ratios (CR ratios) of SC-CR are significant, while other effects such as the source-to-site distance, earthquake magnitude, and site classes are not as much important. Finally, using two-stage regression analyses, formulas are developed for determining un-normalized (code-compliant) and normalized CR spectra of SC-CR systems subjected to far-field and NF-pulse ground motions.