A Theory of Torsion Bending for Multicell Beams

Differential equations and boundary conditions, relating warping displacements and rotations to the applied torsional load, are developed for nonuniform beams with thin-walled multicell cross sections. The loading distribution and end conditions are arbitrary. A formula resembling the flexure formula is given for the normal stress in terms of a warping moment. The torsion-bending theory is of approximately the same accuracy as engineering bending theory and is exactly analogous to the case of bending with axial tension when shearing strains are taken into account.