Analytical Solution of a Guided Simply Supported Beam under Three Point Bending
In the present paper, elastic field parameters of a guided simply supported beam under three point bending has been investigated by a new approach called displacement potential formulation. Guided beams involve mixed mode of boundary conditions which the classical beam theory cannot handle. In displacement potential formulation, all the elastic field parameters has been expressed in terms of a single function Ψ which gives rise to a fourth order partial differential equation. The solution of this equation has been determined by trial and error process satisfying all the boundary conditions. This solution is then inserted to reduce the partial differential equation into an ordinary one. The obtained analytical solution of the beam has been presented as graphs. The stress concentration occurs mainly at the point of application of the load and the support at two corners. The analytical solution has further been verified by finite element analysis.
