Theoretical and Computational Analysis of Circular Cantilever Tapered Beams

Abstract

Tapered beams are extensively used for structural applications due to their high stiffness-to-mass ratio. They provide many advantages over prismatic beams such as better shear carrying capacity, higher lateral stability, and weight savings. As it is known, axial stress σx=−My/t, from Navier’s flexure formula, may be used to estimate bending stresses in tapered beams to some extent, and this can be useful for primary design purposes. However, since the section modulus may vary along the axis of tapered beams, due to the additionally generated shear stress field, the maximum stress cannot necessarily occur at the cross section of the tapered beams where the largest bending moment is present. Nevertheless, classical beam theories do not predict the shear stress distributions in tapered beams if the taper angle is greater than 15°. This study aims at combining the advanced mechanics of a material approach with the theory of elasticity for three different loading conditions applied at the free end of the circular cantilever tapered beams. Derived equations provide the stress distribution across the circular cantilever tapered beams subjected to axial tensile stress, bending moment, and transverse shear force. In order to verify the analytical calculations, a FEM model is employed, and its results shows a reasonable agreement with the analytical results.