Multicomponent directional-cum-modal combination rule for seismic analysis of secondary systems

This study aims to improve the seismic analysis of secondary systems by introducing a novel approach based on the Multicomponent Directional-Cum-Modal Combination Rule. Secondary systems, also known as non-structural elements, are not part of the primary load-bearing structural system but are influenced by seismic excitation. These systems rely on their own structural characteristics to withstand these effects. Typically, secondary structures can be attached to the primary structure at multiple locations. However, this study focuses on single-support acceleration-sensitive secondary systems with a small mass ratio. The acceleration demand on a secondary system is typically expressed using the floor response spectrum (FRS). Under the assumption of a small mass ratio and/or significant separation between the natural frequencies of the non-structural element and those of the supporting structure, the dynamic interaction between the primary and secondary systems can be neglected. In such cases, the FRS can be constructed by considering the ground excitation in two forms: i) acceleration time series/ recorded ground motion; and ii) damped ground response spectra (GRS). This research focuses on the latter, also known as the spectrum-to-spectrum method. The primary system is considered a multiple degrees of freedom system (MDOF) subjected to six-component ground excitation. The work explores the extension of state-of-art ‘Multicomponent directional-cum-modal combination’ in the context of seismic analysis of single-support-secondary systems using FRS. A novel framework is proposed for developing FRS that considers both: i) correlation between the modal responses and ii) directional correlation. The multicomponent directional-cum-modal combination rule is extended by constructing the FRS using mean squared spectrum and single-period scaling. As an illustrative example, the seismic demand calculation is performed by constructing the floor response spectrum in all six directions using a series of single-degree-of-freedom oscillators mounted on top of a five-story structure. The FRS constructed using the proposed framework performs better than the ‘FRS-CQC’ combination rule and is in proximity with the benchmark FRS developed using the linear time history analysis. Overall, the proposed framework represents a significant advancement in seismic analysis of the secondary system.