The seismic control effect of reinforced concrete structures with low energy dissipating capacity due to stiffness degradation is investigated through nonlinear time history analysis. The primary structure is idealized as a SDOF system of modified Takeda hysteresis rule and an elasto-perfectly-plastic nonlinear spring is added to represent a hysteretic damping device. Based on statistics of the numerical analysis, equivalent linearization techniques are evaluated, and empirical equations for response prediction are proposed. As a result, estimation of the ductility demand with proposed empirical equations is more desirable than the equivalent linearization techniques. The optimal yield strengths based on empirical equations are significantly different from the optimal yield strength of elasto-perfectly-plastic systems. Also, the results indicate that the reduction effect of the ductility demand is more remarkable for smaller natural periods.