Chapter 17 - Shear of beams

Abstract

This chapter establishes the equations of equilibrium and expressions for strain necessary for the analysis of open section beams supporting shear loads and closed section beams carrying shear and torsional loads. It discusses the general stress, strain, and displacement relationships for open and single-cell closed section thin-walled beams. The chapter defines the position of the shear center as the point in the cross-section through which shear loads produce no twisting. It may be shown by use of the reciprocal theorem that this point is also the center of twist of the sections subjected to torsion. There are, however, some important exceptions to this general rule. Clearly, in the majority of practical cases, it is impossible to guarantee that a shear load will act through the shear center of a section. Equally apparent is the fact that any shear load may be represented by the combination of the shear load applied through the shear center and a torque. The stresses produced by the separate actions of torsion and shear then may be added by superposition. It is, therefore, necessary to know the location of the shear center in all types of section or to calculate its position. The chapter describes that the solution for a shear loaded closed section beam follows a similar pattern to that described for an open section beam but with two important differences. First, the shear loads may be applied through points in the cross-section other than the shear center, so that torsional effects, as well as shear effects, are included.