Inelastic displacement demand for non‐degrading bilinear SDOF oscillators with self-centering viscous-hysteretic devices

The self-centering viscous-hysteretic device (SC-VHD) is an innovative self-centering system developed recently by the authors to improve structural seismic resilience. The goal of this research is to develop an inelastic displacement ratio Ci spectrum as well as inelastic displacement estimation methods for non‐degrading bilinear SDOF oscillators with SC-VHDs. Statistical analysis is conducted on non‐degrading bilinear SDOF oscillators with self-centering viscous-hysteretic devices (SC-VHDs) to investigate the effect of the design parameters of the bilinear oscillator and the SC-VHD on the constant-ductility inelastic displacement ratio Ci spectrum under the near-fault pulse-like earthquakes (NFPE) and the far-fault earthquakes (FFE). Results indicate that, except in very rare cases, the mean Ci spectrum under the NFPE is always larger than that under the FFE. Besides, the mean Ci spectrum has a significant and clear dependence on the ductility ratio, the ratio of preload to yield strength, the ratio of loading stiffness to elastic stiffness, the ratio of unloading stiffness to loading stiffness, and the viscous damping ratio. When estimating the Ci spectrum, both decreasing the ductility ratio and increasing the viscous damping ratio can cause a reduction in record-to-record variability. Based on the statistical data, a formula about ductility ratio and period considering the effect of the design parameters of the SC-VHD and earthquake motions is proposed and verified for the mean Ci spectrum. Then, a Ci spectrum method and an equivalent linearization method estimating the inelastic displacement demand of the bilinear oscillator with the SC-VHD are proposed, verified by comparing the estimation results and the statistical results, and evaluated through adopting an error measure. Finally, these two methods are adopted to estimate the maximum roof displacement of a two-story steel moment-resisting frame (MRF) with SC-VHDs, which demonstrates their application.