Seismic analysis of asymmetric building-foundation systems

A method of analysis for the earthquake response of three-dimensional multi-storey asymmetric buildings founded on a flexible foundation is presented. The building-foundation system considered in this study is a linear N-storey asymmetric building on a rigid footing resting on the surface of a linear elastic half-space. The whole system has 3N + 5 displacement degrees of freedom. The governing equations are developed considering the motions of each floor and the motions of the whole system. The governing equations of the floors are first uncoupled in terms of footing displacements using the mode superposition method. Substitution of structural deformations, in combination with the dynamic soil-structure interaction force-displacement relationships proposed by Veletsos and Verbic [ASCE J. Engng Mech. Div. 100, 189–201 (1974)]and Veletsos and Nair [ASCE J. Geotechn. Engng Div. 100, 225–246 (1974)]into the governing equations of the whole system results in five integro-differential equations for footing displacements, which are then solved by numerical step-by-step time-history analysis. A 10-storey asymmetric building on soft soil was subjected to an artificially generated earthquake excitation in order to obtain the soil-structure interaction and eccentricity effects. The results show that soft soil conditions increase the lateral deflections, but reduce the twists, storey shears, and torques. Increasing eccentricity increases the twists and torques, but does not modify the lateral deflections at the centre of mass, and the total storey shears.