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

• The large deflection of shear-deformable beams under three-point bending is analyzed for the first time.
• A first-time analytical solution is present for the boundary value problem of large deflections of beams.
• Lower values for maximum deflection and slope are obtained, in comparison with the Euler–Bernoulli model.

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.