Simplified method of calculating a beam on a two-parameter elastic foundation

Abstract

When calculating beams lying on a solid elastic foundation, the simplest foundation model proposed by Winkler-Zimmerman is often used. This hypothesis has been repeatedly subjected to well-founded criticism, because the deformation of the base occurs only in the area of the load applied to it. In order to clarify the Winkler-Zimmerman hypothesis, many authors have proposed other models that allow mitigating the disadvantage of this model to varying degrees. The paper deals with the method of obtaining an analytical solution to the problem of beam bending on a two-parameter elastic foundation. A new version of the elastic foundation model is proposed. The account of the elastic foundation is produced by means of parameter of the flexural rigidity. The resolving differential equation of bending of beams resting on a two-parameter elastic foundation is obtained. An analytical solution for this equation is derived, and solutions for various boundary conditions of beams resting on a two-parameter elastic foundation are discussed. The accuracy of the proposed method is verified through examples, and they showed an excellent agreement with the Winkler and Vlasov models.