Strength reduction factor for inelastic-displacement estimation and design of self-centering viscous-hysteretic systems

This study focuses on developing strength reduction factor Rμ 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 Rμ 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 Rμ 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 Rμ spectrum is primarily affected by the ductility ratio, period and viscous damping ratio, while the parameters of ring springs have little effect on it. Rμ spectrum under the NFPE is significantly lower than that under the FFE except for periods from 0.2 s to 0.6 s. The Rμ 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.