An analytical solution for the large deflection problem of Timoshenko beams under three-point bending

This article is conducted to analyze the large deflections of a straight prismatic shear-deformable beam resting on simple supports at both ends and subjected to a point load at its midspan. Taking into account the transverse shear deformation, based on the Timoshenko beam theory, the system of non-linear differential equations is derived. Exact solution of the boundary value problem is obtained for horizontal, vertical and angular displacements. The results are compared with available experimental data and those obtained for Euler–Bernoulli beam in the literature.