Parametric Study of Beams on Elastic Foundations

Abstract

Even though the two‐parameter model developed by Vlasov for beams on elastic foundations represents the interaction between the beams and the foundation better than the Winkler model, it requires an estimation of a third parameter, γ, which represents the distribution of the displacements within the foundation. Using variational calculus, the value of γ is shown to be a function of some nondimensional parameters of the beam, the foundation, and the mode of loading. By using an iterative procedure, a consistent value of γ is calculated. An example of a beam carrying a uniformly distributed load is solved and the results are compared with a more rigorous finite element solution.