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A self-centering viscous-hysteretic device (SC-VHD), composed of a viscous damper and ring springs in parallel, which combines velocity-proportional viscous energy dissipation and displacement-proportional hysteretic energy dissipation is studied. To evaluate the seismic behavior of structures with self-centering viscous-hysteretic devices and obtain appropriate parametric combinations between the main structure and the added self-centering viscous-hysteretic devices, a parametric study was conducted on SDOF elastoplastic structures with SC-VHDs. The results show that the SC-VHD can reduce about 30–50% of peak displacement and more than 80% of residual deformation, whilst a small increase in peak acceleration was observed. The reduction of the residual deformation is mainly influenced by the ring springs damping ratio and the ratio of preload to structural yielding strength, while the reduction of the peak displacement is significantly influenced by the viscous damping ratio and the ratio of loading stiffness to structural elastic stiffness. When the SC-VHD was designed with a viscous damping ratio of no less than 5%, a ring springs damping ratio of 15% at most, a ratio of preload to yielding strength of no less than 0.1 and a ratio of loading stiffness to elastic stiffness of no less than 0.1, the 2% peak drift and 0.2% residual drift criteria can be satisfied. Based on the parametric analysis results and an improved equivalent damping model parallel to ASCE 7, a displacement-based design method of SDOF elastoplastic structure was then proposed and evaluated by comparison with nonlinear time-history history analysis results. [ABSTRACT FROM AUTHOR]