During strong ground motions, members of reinforced concrete structures undergo cyclic deformations and experience permanent damage. Members may lose their initial stiffness as well as strength. Recently, Los Alamos National Laboratory has performed experiments on scale models of shear wall structures subjected to recorded earthquake signals. In general, the results indicated that the measured structural stiffness decreased with increased levels of excitation in the linear response region. Furthermore, a significant reduction in strength as well as in stiffness was also observed in the inelastic range. Since the in-structure floor response spectra, which are used to design and qualify safety equipment, have been based on calculated structural stiffness and frequencies, it is possible that certain safety equipment could experience greater seismic loads than specified for qualification due to stiffness reduction. In this research, a hysteresis model based on the concept of accumulated damage has been developed to account for this stiffness degradation both in the linear and inelastic ranges. Single and three degrees of freedom seismic Category I structures were analyzed and compared with equivalent linear stiffness degradation models in terms of maximum displacement responses, permanent displacement, and floor response spectra. The results indicate significant differences in responses between the hysteresis model and equivalent linear stiffness degradation models. The hysteresis model is recommended in the analysis of reinforced concrete shear-wall structures to obtain the in-structure floor response spectra for equipment qualification. Results of both cumulative and one shot tests are compared.