Stability of elastic plane frames including soil-structure interaction

Abstract

In this paper the analysis of linear elastic plane frames interacting with an elastic Winkler foundation, consisting of rafts and piles, is studied with respect to the stability of the entire structure. The theory is based on small deformation beam theory with second order effects included. The differential equation describing the behavior of each element of the frame is solved exactly and, thus, no discretization errors occur. A new exact finite element is presented for a beam on elastic foundation according to second order theory. This new exact element gives a significant reduction in calculation effort compared to standard elements used in commercial computer codes. Stiff areas, hinges and rollers are defined by a general formulation of the coupled boundary value problem. The problem becomes non-linear in axial force parameters and is solved with a secant iteration procedure. Soil-structure interaction is idealized by using uncoupled load transfer functions in both lateral and axial directions, when perfectly elastic soil properties are assumed. In order to demonstrate the accuracy and the efficiency obtained when exact solutions are used a few numerical examples are included. Firstly, the exact solution to a compressed beam on Winkler foundation is given, and secondly, the elastic stability of one single pile is studied. Finally, the elastic stability of a multi-storey frame resting on a piled/raft foundation is studied with respect to the relative stiffness between the structure and the soil medium.