Chapter 5 - Torsion in Structures

Abstract

This chapter analyzes the geometry, stress function, and properties of torsional movements. Torsion develops in structures along with bending from unintended eccentricities of transverse loading due to the limitation of workmanship or from unavoidable eccentricities as can be found in spandrel beams. Purely torsional loading rarely occurs in structures except in the power-transmitting shafts of automobiles or generators. Generally, thin-walled sections do not behave according to the law of the plane sections employed by Euler-Bernoulli-Navier. A thin-walled section is referred to as a rolled shape in which the thickness of an element is less than one-tenth of the width. A thin-walled section becomes “warped” when it is subjected to end couples (torsional moment). Hence, the cross section does not remain plane after deformation. Another distinct feature of the response of structural members to torsion is that the externally applied twisting moment is resisted internally by some combination of uniform torsion and nonuniform torsion depending on the boundary conditions, that is, whether a member is free to warp or whether warping is restrained. The analysis of uniform torsion is greatly simplified by the fortuitous fact that certain relationships exist between the torsion problem and the deformations of a soap film stretched across an opening equal in size and shape to the cross section for which torsional behavior is sought. An approximate analysis of nonuniform torsion of a member with a general thin-walled open cross section may be developed within the confinement of assumptions employed.