Real-valued modal response history analysis for asymmetric-plan buildings with nonlinear viscous dampers

Modal analysis, which is clear in concept and simple in computation, is widely applied to evaluate the seismic responses of elastic structures with proportional damping. Nevertheless, nonlinear viscous dampers commonly installed in real buildings result in non-proportionally damped structures, which impede the modal analysis in real number field for such structures. This study develops the approach of performing real-valued modal response history analysis for elastic two-way asymmetric-plan buildings with nonlinear viscous dampers. To this end, this study first constructs the nonlinear three-degree-of-freedom (3DOF) modal equations of motion for such structures. The nonlinear 3DOF modal equations of motion retain the non-proportional damping characteristics in the modal space. Hence, by solving the nonlinear 3DOF modal equations of motion, the total response history is effectively attained by arithmetically summing up the modal response histories. This study uses nine two-way asymmetric-plan buildings, each equipped with nonlinear viscous dampers subjected to three bi-directional ground motions to verify the proposed approach. The investigation results show that the proposed simplified analysis approach provides satisfactory estimation of the seismic responses of common asymmetric-plan buildings with nonlinear viscous dampers.