Nonlinear displacement ratio for seismic design of self-centering buckling-restrained braced steel frame considering trilinear hysteresis behavior

Self-centering buckling-restrained braced steel frames (SCBRBFs) have drawn increasing attention due to the resilience of this kind of structural system in post-earthquake repair. Constant-strength reduction factor (constant -R) inelastic displacement ratio (C-R) can be used for direct inelastic displacement evaluation or design of SCBRBFs. In previous studies, bilinear hysteresis assumption was generally adopted for the self-centering structures, although actual trilinear flag-shaped hysteresis was commonly observed for most of the previously proposed metallic energy-dissipation self-centering systems, such as SCBRBFs. In this study, trilinear hysteresis of the SCBRBF, presented as a combination of the bilinear elastoplastic restoring force of the energy dissipation (ED) system and the bilinear elastic restoring force of the self-centering (SC) system, is considered in the determination of the C-R ratio spectra of such system. Comparison between the bilinear SC systems and the trilinear SCBRBFs is discussed to highlight the effect of the trilinear hysteresis on the nonlinear displacement of SCBRBFs. Key parameters affecting the C-R ratio are determined, in which the initial stiffness ratio of the ED system to the SC system, alpha(c), is the additional parameter proposed to reflect the trilinear property of SCBRBF. Optimal ranges of these parameters and their effects on the C-R spectra are also discussed by nonlinear response history analysis. Nonlinear regression analysis is then performed to obtain the function of C-R with respect to the aforementioned parameters for quick and direct displacement evaluation. Nonlinear time history analysis (NTHA) demonstrates that the C-R ratios of SCBRBF, determined by the previously derived C-R functions from bilinear hysteresis, are often overestimated, while those predicted by the proposed C-R functions from trilinear hysteresis show better agreement with the numerical results in extremely-low and medium-to-long period region. Numerical nonlinear displacement ratios of a one-story six-bay and a six-story six-bay SCBRBFs are computed by NTHA to validate the effectiveness of the proposed C-R functions.