Symmetrically loaded beam on a two-parameter tensionless foundation

Abstract

Static response of an elastic beam on a two-parameter tensionless foundation is investigated by assuming that the beam is symmetrically subjected to a uniformly distributed load and concentrated edge loads. Governing equations of the problem are obtained and solved by pointing out that a concentrated edge foundation reaction in addition to a continuous foundation reaction along the beam axis in the case of complete contact and a discontinuity in the foundation reactions in the case of partial contact come into being as a direct result of the two-parameter foundation model. The numerical solution of the complete contact problem is straightforward. However, it is shown that the problem displays a highly non-linear character when the beam lifts off from the foundation. Numerical treatment of the governing equations is accomplished by adopting an iterative process to establish the contact length. Results are presented in figures to demonstrate the linear and non-linear behavior of the beam-foundation system for various values of the parameters of the problem comparatively.