Analytical estimation of fundamental periods of coupled systems

This study provides an in-depth analytical investigation to accurately estimate the seismic responses of coupled systems while considering primary–secondary system interactions (PSSIs). A practical modal analysis-based approach was proposed to estimate the fundamental period of multi degrees-of-freedom (MDOF) steel moment-resisting frame structures. A follow-up numerical investigation was performed to successfully verify the results obtained from the proposed relationship. Subsequently, the effects of the secondary system multiplicity, number of frame storeys, mass ratio, and distribution of secondary systems along the frame height were assessed on the fundamental period of the coupled system. Based on the results, the seismic response of the short-period coupled systems was improved by increasing the period of the overall system under the effect of the secondary structure period. The findings of this study confirm that the presence of multiple secondary structures significantly influences the fundamental period of a coupled system when PSSI effects are considered. In contrast to current design code recommendations, it was found that the total mass of the secondary structures cannot be ignored in calculations owing to the multiplicity of secondary systems.