Seismic response of multi-storey buildings including foundation interaction and P-Δ effects

This paper presents a method of seismic analysis of multi-storey buildings when both soil-structure interaction and P-Δ effects have been taken into account. The additional overturning moment at each storey due to P-Δ effects is replaced by two fictitious horizontal forces acting in opposite directions at the upper and lower ends of each storey. Then, the governing equation for each floor is developed in which these fictitious horizontal forces are incorporated along with seismic inertia forces. Considering the footing as a rigid disc resting on the surface of an elastic half-space, two equations expressing the equilibrium of the building as a whole in translation and rotation complete the set of equations in terms of floor displacements and two rigid body base displacements. Recognizing that the superstructure alone admits classical normal modes, floor governing equations are uncoupled and substituted into the remaining equations, which results in two coupled integro-differential equations in terms of two rigid body displacements. These two equations can be solved using numerical procedures. The method is applied to two unbraced steel buildings and numerical results are presented for different foundation soil conditions. The influence due to P-Δ effects and soil-structure interactions on the responses of these buildings is discussed.