Approximate Analytical Solution for a Simply Supported Beam on Tensionless Winkler Foundation Under Multiple Concentrated Loads

Abstract

This work presents an approximate analytical solution for simply supported beams resting on a tensionless Winkler foundation and subjected to multiple point loads. The foundation is modeled as a series of discrete linear independent springs and gaps may exist between the beam and the springs. The two-stage technique approximates the response of the tensionless foundation: in the first stage, the technique identifies the contact and noncontact regions based on an iterative procedure, while in the second stage, the technique redistributes the springs in the contact region only. Results are validated and compared with a benchmark solution. The numerical examples confirm the efficiency and accuracy of the proposed method.