Despite the various studies carried out to evaluate the effects of seismic sequences on structures, the matter of the time gap required to be considered between the mainshock and its corresponding aftershocks in dynamic analyses has never been focused on directly. This subtle but in the meantime effective subject, influences on the amount of accumulated damage caused by earthquake sequences. In the present study, 244 near fault ground motion components from 122 earthquakes were applied to a wide variety of single degree of freedom systems having vibrating period of 0.05 to 7 seconds with linear and nonlinear behavior. Furthermore, 2 planar steel moment-resisting frames, having 3 and 12 stories, were subjected to a set of 30 ground motion components. The purpose of this investigation was to estimate the required time for the structures to cease the free vibration at the end of the mainshock. The main purpose is to generate an estimation that is function of structural system's parameters and the strong motion duration. Excellent correlations were obtained between the rest time and the following parameters: the combination of natural period of single degree of freedom systems, as well as the strong motion duration of earthquake sequences. In consequence, a formula is proposed which estimates the required optimized rest-time of a structure based on natural vibration period, as well as the duration of strong motion. Additionally, results obtained from the dynamic analysis of the steel frames validate the rest-time values achieved from the proposed formula.