Chapter 10 - Shear of Beams

Abstract

This chapter examines the physical relationship between bending and shear. Shear stress distributions in beam cross sections depend upon the geometry of the beam section. Generally in civil engineering one is not concerned with shear stresses in unsymmetrical sections except where they are of the thin-walled type. “Thick” beam sections usually possess at least one axis of symmetry and are subjected to shear loads in that direction. In thin-walled I-sections the horizontal shear stress can produce shear distortions of sufficient magnitude to redistribute the direct stresses due to bending, thereby seriously affecting the accuracy of the basic bending theory. This phenomenon is known as shear lag. The shear flow and shear stress distributions in a closed section, thin-walled beam are determined in a manner similar to that of an open section beam but with two important differences. First, the shear loads may be applied at points in the cross section other than the shear center so that shear and torsion occur simultaneously. Second, it is not generally possible to choose an origin for s that coincides with a known value of shear flow.