Mathematical and finite element investigation on time period of coupled steel frames subjected to earthquake excitations

Current design codes of practice ignore the effect of interaction between primary and secondary systems when addressing the seismic response of coupled structures. The present investigation offers a robust mathematical representation of such interaction through a closed-form calculation of time periods in coupled primary-secondary systems. On this wise, an analytic framework was established to determine the fundamental period of a threedimensional (3D) steel moment-resisting frame structures. The successful verification of the analytic formulation followed using a finite element (FE) modeling approach. Subsequently, a parametric study was carried out to address the effect of number and location of secondary systems, as well as number of frame stories, on the overall seismic response of the coupled system. The mass of secondary system was considered less than 20% of that of the primary system. Based on the FE modeling results, the most significant effect of secondary system on the response of coupled system relates to time period, which should be taken into account in current design procedures. Despite the very low mass of secondary system, time period of the coupled frame changed significantly, when the secondary system was added to primary structure. This causes the amplification of lateral drifts and deformations, leading to structural and non-structural damage, and potential failure. On the contrary, the fundamental period of short-rise frames increased with increasing secondary-to-coupled-system mass ratio. Based on this finding, it is viable to increase the time period of short-rise structures under the effect of secondary system period, and thus improve their seismic performance.