Gravity Effects on Earthquake Response of A Flexure Building: A Shear Building Comparison

An analytical building model including the nonlinear effects caused by gravity is presented in this paper. Governing equations are derived for both single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) models with large displacements taken into account, and solutions are obtained by direct integration and modal analysis. The response of typical structures subjected to harmonic ground excitation was expressed in exact and approximate forms, compared with the response of an equivalent shear building. Numerical examples show that while gravity generally decreases the natural frequency of elastic SDOF systems with small displacement approximations, actual natural frequency increases with ground motion. The difference in the natural frequency and response of MDOF systems to the equivalent shear building is not only due to gravity, but also caused by the geometry of the structure. Exact solution shows that the frequency varies with ground motion amplitude.