Analysis of shear stresses in tapered beams under bending, shear and axial force

Abstract

This paper mainly studied the analytical fomula, basic properties and distribution regularities of the shear stresses in elastic tapered beams under a combined bending moment, shear force and axial force. First, an analytical expression for calculating shear stress in elastic tapered beams was derived based on the theory of elasticity. The additional shear stresses arising from the bending moment and axial force were involved due to the effect of the variable cross-section, which is quite different from the classical formula for prismatic beams. Additionally, it was mathematically proven that the additional shear stresses arising from the bending moment and axial force were self-balanced, which changed the distribution of shear stress but did not influence the shear stress resultant. The correctness of each sub item of the analytical formula and their distribution regularities were verified through comparisons between the theoretical results and numerical simulation through 12 purposely designed three-dimensional finite element models (FEMs) under three kind of loading conditions: pure bending, shearing-bending and compressing-bending. The correctness of the self-balanced properties of additional shear stresses arising from the bending moment and axial force were also verified using Free Body Cuts in ABAQUS program. These new findings are likely to promote the development and completion of non-prismatic beam theory.