The torsional analysis of bars with hollow square cross-sections

Abstract

The torsional behavior of square, hollow tubing sections is an important design consideration in many mechanical systems. If such sections have thin walls, closed-form solutions for torsional stiffness and torsional shear stress can be found in various design handbooks. Thick wall sections, however, must be solved by a more complex method, typically a three-dimensional finite element analysis. An alternative torsional analysis of hollow square tubes with finite elements, using a two-dimensional thermal analogy, is presented in this paper. The dependence of torsional properties on wall thickness is investigated. These results are then used to generated closed-form algebraic expressions for torsional stiffness and maximum shear stress, which are valid for any wall thickness/width ratio from negligibly thin to solid. These closed-form equations provide an efficient, accurate and computationally simple alternative for determining the torsional properties of square, hollow sections. This work demonstrates how finite element analysis can be used to extract valuable design information for whole classes of problems, information which can be condensed into closed-form approximations suitable for inclusion in design handbooks.