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This study focuses on developing strength reduction factor R μ spectrum, a maximum inelastic displacement (MID) estimation method and a displacement-based design method for single-degree-of-freedom (SDOF) bilinear structures with self-centering viscous-hysteretic devices (SC-VHDs). The effects of design parameters on R μ spectrum are statistically investigated under near-fault pulse-like ground motions (NFPG) and far-field ground motions (FFG), and its prediction formula is fitted according to the statistical data. Following proposed R μ spectrum, a MID estimation method and a performance-based design method are proposed, respectively. Next, three SC-VHD frames are designed step-by-step to verify the proposed design method, and then their MIDs are calculated step-by-step to validate the MID estimation method. Finally, a risk assessment is conducted on a SC-VHD frame and a conventional frame to compare their collapse performance and the performance exceeding 0.2% residual drift in the probability framework. The results indicate that R μ spectrum is primarily affected by the ductility ratio, period and viscous damping ratio, while the parameters of ring springs have little effect on it. R μ spectrum under the NFPE is significantly lower than that under the FFE except for periods from 0.2 s to 0.6 s. The R μ spectrum formula and the MID estimation method both have errors that are typically less than 10%. The designed SC-VHD frame can achieve the target performance, and its probability of collapse and exceeding 0.2% residual drift in a period of 50-year is significantly smaller than that of the conventional frame. • Strength reduction factor spectrum is developed for self-centering viscous-hysteretic systems. • A maximum inelastic displacement estimation method is proposed. • A displacement-based design method is proposed. [ABSTRACT FROM AUTHOR]

This study evaluates the seismic performance of the steel frame with self-centering viscous-hysteretic devices (SC-VHD frame) and investigates the effect of design parameters of the SC-VHD, preload, loading stiffness, unloading stiffness and viscous damping ratio, on seismic performance through conducting nonlinear static pushover analysis, fragility analysis and risk assessment on 4-, 8-, and 12- story SC-VHD frames with different design parameters. Results indicate that the maximum normalized base shear and the ultimate roof drift ratios of the SC-VHD frames increase by more than 13.3% and 42.9%, respectively, compared with the conventional frames. The SC-VHD frames have acceptable low probabilities of collapse and probabilities exceeding considered residual drift under the maximum considered earthquake (MCE) and during a 50-year period. Accordingly, the most sensitive parameter regarding the probabilities of collapse is loading stiffness, followed sequentially by unloading stiffness, viscous damping ratio and preload. While for the probability exceeding considered residual drift under the MCE, the parameters of ring springs, preload, loading stiffness and unloading stiffness, have a significant effect on the 4- and 8-story SC-VHD frames, and the viscous damping ratio of the viscous damper has the most significant effect on the 12-story SC-VHD frame. For the probability exceeding considered residual drift during a 50-year period, the most sensitive parameter is the viscous damping ratio. [Display omitted] • Ductility capacity and seismic load-carrying capacity of SC-VHD frames are investigated. • Accuracy and efficiency of different fragility analysis methods are compared. • Collapse risk of SC-VHD frames is assessed. • Risk exceeding considered residual drift of SC-VHD frames is assessed. [ABSTRACT FROM AUTHOR]