Free–Free Beam Resting on Tensionless Elastic Foundation Subjected to Patch Load

Despite the popularity of a completely free beam resting on tensionless foundation in construction industry, existing bending analysis solutions are limited to certain types loads (mostly point and uniformly distributed loads); these also quite complex for practicing engineers handle. To overcome associated complexity, simple iterative procedure is developed this study, which uses Ritz method free–free subjected patched load. The formulation first presented with polynomials being used approximate deflection unknown constants be determined through minimization potential energy. account action, subgrade reaction set zero when negative. non-zero zone defined by αlL/2<x<αrL/2 where coefficients αl αr iteratively. A numerical example illustrate applicability proposed symmetrical asymmetrical problems. obtained results show high negative deflection, proves occurrence separation between supporting foundation. This location called lifted zone, while that separates positive lift-off point. parametric study then performed effect amount load, stiffness beam, length zone. indicate same modulus ratio (EI/k), remains beams lower stiffnesses or higher deflect more.