Analytical solution of beams on elastic foundation

Abstract

The paper deals with a new manner of obtaining an analytical solution of the problem of bending of a beam on an elastic foundation. In the design of such structures, to describe the foundation response to applied loads, the mechanical model of Winkler is often used, for almost one and a half century. However, it has some shortcomings, mainly because it assumes no interaction between the adjacent springs and thus neglects the vertical shearing stress that occurs within subgrade materials. In this paper proposes a felicitous approach for solving the equilibrium equation and applying the boundary conditions, used to static analysis of beams resting on elastic foundations, is presented as an alternative to the classical Winkler and Vlasov models. The resolving equation of bending of a beam on an elastic foundation is obtained. The account of the elastic foundation is produced by means of parameter of flexural stiffness. This idealization provides much more information on the stress and deformation within soil mass compared to the well-known Winkler model, and it has the important advantage of eliminating the necessity of arbitrarily determining the values of the foundation parameters. The solutions of sample problems, obtained by using the new analytical model, are compared with results obtained by the Winkler and Vlasov models