Seismic Analysis of Non Proportionally Damped Two-Way Asymmetric Elastic Buildings Under Bi-Directional Seismic Ground Motions

This study investigates the effectiveness of the modal analysis using three-degree-of freedom (3DOF) modal equations of motion to deal with the seismic analysis of two-way asymmetric elastic systems with supplemental damping. The 3DOF modal equations of motion possessing the non proportional damping property enable the two modal translations and one modal rotation to be non proportional in an elastic state. The simple approximation method is to use the single degree-of-freedom (SDOF) modal equations of motion, which are obtained by neglecting the off-diagonal elements of the transformed damping matrix. One, one-story and one, three-story non proportionally damped two-way asymmetric buildings under the excitation of bi-directional seismic ground motions are analyzed. The analytical results are obtained by using the proposed method, noted simple approximation method, and direct integration of the equation of motion. It is seen that the proposed method can significantly improve the accuracy of the analytical results compared with those obtained by using the simple approximation method. Moreover, the proposed method does not substantially increase the computational efforts.