Analyzing the Deformation Behavior of a Beam Using the Elastic Foundation Method Taking into Account the Gap in the Tensile Stress Zone

Abstract

A finite element differential method was proposed in this paper to analyze the deformation behavior of a beam with variable cross-sectional dimensions, taking into account the gap in the tensile stress zone. In the analysis, the deformation of the beam and settlement of the subsoil were defined separately so as to have different functions with or without positive stresses in the tensile zone. Then, by introducing the Winkler and the elastic semi-infinite space models, a basic reaction equation was established that was subsequently solved using the Lemke algorithm. Lastly, two practical examples were analyzed and the results indicated better accuracy when the gap in the tensile stress zone was taken into account.