Flexure and Torsion of Beams

Abstract

Beam bending theory is often used in the somewhat more general context in which the bending moment varies along the beam. In that case it follows from the equilibrium conditions discussed in Chapter 3 that shear forces will occur, and these shear forces in turn introduce shear stresses. The shear force is the total effect of the corresponding shear stresses over the cross-section, and thus the shear stress distribution determines the line of action of the shear force. The theory of nonhomogeneous bending – or flexure – of a beam thereby corresponds to a particular location of the transverse force with respect to the beam cross-section. If the load is offset from this line, it also produces a torsion moment, and the beam sections will rotate in twist. Modern structures often make use of beams with non-symmetric cross-sections, and it is important to identify possible contributions from a transverse load to torsion of the beam. The present chapter deals with the properties of flexure and torsion of beams and the proper separation of the two problems. A key point is the location of the so-called shear center – the point of action of the shear forces associated with beam flexure. The determination of the distribution of shear stresses in flexure and torsion is discussed in some detail for thin-walled cross-sections.