Range of applicability of real mode superposition approximation method for seismic response calculation of non-classically damped industrial buildings

An industrial building is a non-classically damped system due to the different damping properties of the primary structure and equipment. The objective of this paper is to quantify the range of applicability of the real model superposition approximation method to the seismic response calculation of industrial buildings. The analysis using lumped mass-and-shear spring models indicates that for the equipment-to-structure frequency ratios γf > 1.1 or γf < 0.9, the non-classical damping effect is limited, and the real mode superposition approximation method provides accurate estimates. For 0.9 < γf < 1.1, the system may have a pair of closely spaced frequency modes, and the non-zero off-diagonal damping terms have a non-negligible effect on the damping ratios and mode shape vectors of these modes. For 0.9 < γf < 1.1 and the equipment-to-structure mass ratios γm < 0.07, the real mode superposition approximation method results in large errors, while the approximation method can provide an accurate estimation for 0.9 < γf <1.1 and γm > 0.07. Furthermore, extensive parametric analyses are conducted, where both steel structures and reinforced concrete structures with equipment with various damping ratios are considered. Finally, the finite element analysis of a five-story industrial building is adopted to validate the proposed range of applicability.