Incorporating energy-dissipating fuses (EDFs) into structures can enhance their seismic performance. However, there is a lack of unified understanding regarding the general laws of the residual displacement response of such structural systems. Therefore, in this study, EDFs are incorporated into traditional single-degree-of-freedom (SDOF) systems (the primary structure, PS), and their mechanical relationship is controlled through two parameters: the initial stiffness ratio (/3) and the yield displacement ratio (alpha). Nonlinear dynamic time-history analyses are conducted using 242 ground motions under four site classes as input, and the resulting residual displacement ratio (Cr) spectra are generated through statistical analysis. The central tendency and dispersion of Cr spectra and the effect of design parameters on Cr spectra are analyzed. The results indicate that EDFs can effectively control the post-earthquake residual displacement of structures, with better control achieved at higher values of yield strength ratio (gamma) and postyield stiffness ratio (b). When gamma is fixed, a smaller value of alpha and a larger value of /3 lead to better control. Furthermore, both alpha and /3 have critical values, which are 0.8 and 1.6, respectively. Finally, a simplified equation for the Cr-R-alpha-/3-T relationship in SDOF systems with EDFs is established through nonlinear regression analysis to provide a basis for the damage prediction and seismic design of such structures, and the predictive accuracy of this equation is verified.
