New Method for a Beam Resting on a Tensionless and Elastic-Plastic Foundation Subjected to Arbitrarily Complex Loads

Many soil-structure interaction problems can be idealized as foundation beam problems. In the present work, the tensionless contact problem of an Euler-Bernoulli beam of finite length resting on an elastic-plastic foundation and carrying arbitrarily complex static loads was investigated. Fourth-order difference equations dealing with the vertical displacement of a beam under three different soil support conditions were presented for each beam segment. On the basis of the continuity conditions at the junctions of two adjacent segments, the response of the whole beam was expressed through the response of the initial beam segment in a matrix form. A comparison with the results from the transfer displacement function method (TDFM) showed the expected complete agreement. A simple case was used to illustrate the influence of the foundation models (elastic model, tensionless-elastic model, and tensionless and elastic-plastic model), and the tensionless and nonlinear behavior of the soil on the beam responses. The lift-off length of the beam depends on both the load P and the property of the foundation model regardless of whether it is assumed to be tensionless. The maximum displacement of the beam and the maximum bending moment within the beam are influenced mainly by the acting load and the soil characteristics manifested by the coefficient of soil reaction and the yielding displacement.