Advanced Mechanics of Materials and Applied Elasticity, Fifth Edition

Chapter 9. Beams on Elastic Foundations

9.1 Introduction

In the problems involving beams previously considered, support was provided at a number of discrete locations, and the beam was usually assumed to suffer no deflection at these points of support. We now explore the case of a prismatic beam supported continuously along its length by a foundation, itself assumed to experience elastic deformation. We shall take the reaction forces of the elastic foundation to be linearly proportional to the beam deflection at any point. This simple analytical model of a continuous elastic foundation is often referred to as the Winkler model.

The foregoing assumption not only leads to equations amenable to solution but also represents an idealization closely ...