6 - Columns on elastic foundations

Abstract

Beams and columns supported elastically along their lengths are widely found in structural configurations. In some cases, the elastic support, called the elastic foundation, is provided by a medium that is the foundation supporting the beams or columns such as in railroad tracks, in underground piping for different uses, and in footings for large-scale structures. In other cases, the elastic support is provided by adjacent elastic structural elements such as in stiffened plate and shell configurations. Regardless of the particular application, the mathematical model consists of a column supported at its ends and with a continuous distribution of springs of stiffness, called the modulus of the foundation. The units of the modulus of the foundation are pounds per inch (force per length squared) and may be a constant or a function of position along the length of the column for linear spring behavior. In general, the spring behavior may be taken as nonlinear. This chapter presents the analysis of some simple models and provides insight into the behavior of such columns under destabilizing compressive loads. To derive the buckling equations for a column on an elastic foundation, the expression for the total potential is used to include the energy stored into the foundation.