An Efficient Quasi-Static Condensation-Based Framework for Seismic Analysis of Multi-Supported Secondary Structures

Multi-supported non-structural components (NSCs) are prone to seismic damage, yet their response prediction remains challenging when support motions are spatially incoherent. This study proposes an enhanced quasi-static condensation (EQSC) method for linear, lightweight, dynamically detuned multi-supported NSCs under the neglect of primary–secondary structure interaction (PSSI). The proposed method reconstructs the approximate coupled modes of the primary–secondary (P-S) system from the independently available modal properties of the primary and support-fixed secondary substructures, thereby avoiding both the global coupled eigenproblem and the cumbersome cross-correlation calculation required in classical multiple support excitation formulations. By introducing frequency shifting into the conventional static condensation framework and combining it with a truncated spectral decomposition, EQSC retains a quasi-static algebraic form while capturing the essential inertial effects. The seismic response is then evaluated directly through the standard complete quadratic combination (CQC) rule. Two case studies show close agreement with exact modal and time history references, while non-classical damping can still be treated conveniently within the present framework by assigning subsystem specific damping ratios to different modes during the CQC step.