Chapter 18 - Torsion of beams

Abstract

The theory for the torsion of solid sections was developed using both the Prandtl stress function approach and the St. Venant warping function solution. From that point, via the membrane analogy, the torsion of a narrow rectangular strip was looked at. The results of this analysis are used to investigate the torsion of thin-walled open section beams. This chapter examines the torsion of thin-walled closed section beams because the theory for this relies on the general stress, strain, and displacement relationships. The chapter starts with the discussion of torsion of closed section beams. The theory of the torsion of closed section beams is known as the Bredt–Batho theory and the equation for it provided in the chapter is often referred to as the Bredt–Batho formula. The chapter includes the discussion on displacement associated with the Bredt–Batho shear flow and the condition for zero warping at a section. The chapter ends with a discussion of torsion of open section beams, including warping of the cross-section.