Closed-form solution for the cross-section warping in short beams under three-point bending

The transverse shear behavior of composite beams can be critical and therefore must be properly represented by the various models of structures usually employed either to predict their behavior or to identify experimentally their properties. In this work, a simple analytical approach based on higher-order theories is proposed that accounts for the cross-section warping in beams. Then the solution of a beam under three-point bending is solved and the accuracy of both displacement and strain distribution predictions is shown through comparisons with the FE analysis results. In this formulation, the cross-section locking at mid-span is ensured owing to the dependence of the transverse shear strain upon the position along the beam axis. Eventually, comparisons with experimental measurements demonstrate the ability of these simple analytical solutions to grasp the main phenomena which control the response of composite beams under three-point bending loading, i.e. the arising of transverse shear.