Distribution and Properties of Shear Stress in Elastic Beams with Variable Cross Section: Theoretical Analysis and Finite Element Modelling

It was found that additional shear stress arising from the bending moment should be involved in the formulation due to the effect of variable cross section, which is quite different from the conventional method of analysis for the prismatic members. This paper focuses on the analytical formulation, properties and distribution regularity of the shear stress for the elastic tapered beams with rectangular cross-section. Currently, an analytical expression for the shear stress in elastic tapered beams is derived theoretically based on the theory of elasticity. Most notably, it is strictly proved in mathematics that the additional shear stresses arising from bending moment are self-balanced which only change the distribution of shear stress in the section but will not affect the shear stress resultant. This new finding will be beneficial to promoting the development and consummation of non-prismatic beam theory. The correctness of the theoretical formula have been verified through comparisons with finite element (FE) results of two groups with a total of 12 three-dimensional FE models. The validity of self-balanced properties of additional shear stress in tapered beams under pure bending is additionally verified by using Free Body Cuts in ABAQUS program.