A new shear formula for tapered beamlike solids undergoing large displacements

In many engineering applications it is often necessary to determine the flow of shear stresses in the cross-sections of beamlike bodies. Taking a cue from Jourawski’s well-known formula, several scholars have proposed expressions for evaluating the shear stresses in non-prismatic linear elastic beams, where longitudinal variations in the size and shape of the cross-sections produces complex stress felds. In the present paper, a new shear formula, derived using a mechanical model developed in a previous work, is presented for tapered beams subject to even large displacements and small strains. Numerical examples and comparisons with results obtained using other formulas in the literature and non-linear 3D-FEM simulations show how the new formula constitutes an important generalization of the previous ones and is able to provide particularly accurate results.