Seismic analysis of asymmetric multistorey buildings including foundation interaction and P-Δ effects

This paper presents a method of seismic analysis of three-dimensional asymmetric multistorey buildings founded on flexible foundations. The building-foundation system considered in this study is a linear elastic N-storey asymmetric building with a rigid footing resting on the surface of a linear elastic soil half-space. The method of analysis also includes the P-Δ effects, in which the additional overturning moment and torsional moment at each storey due to P-Δ effects have been replaced by fictitious lateral forces and torques. The whole system has 3N + 5 displacement degrees-of-freedom. The necessary governing equations have been developed considering the three motions of each floor and the five motions of the whole building. Recognizing that the superstructure alone admits classical normal modes, 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 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. The floor displacement responses, storey shears, storey torque, etc., are obtained by back substitution of footing accelerations into the relevant governing equations. As a demonstration of the method of analysis and in order to obtain the soil-structure interaction effects, P-Δ effects, and the eccentricity effects, a 10-storey asymmetric building on soft soil was subjected to El Centro 1940 earthquake excitations. The results show that the soft soil conditions increase the lateral deflections, but reduce the twists, storey shears and torques. Increasing eccentricity increases the floor twists and storey torques, however, it does not modify the lateral deflections at the centre of mass, and the total storey shears. The significance of P-Δ effects along with soil-structure interactions on the response of this building has also been discussed.