Chapter 4 - Virtual work and energy methods

Abstract

Many structural problems are statically determinate, that is, the support reactions and internal force systems may be found using simple statics, where the number of unknowns is equal to the number of equations of equilibrium available. In cases where the number of unknowns exceeds the possible number of equations of equilibrium, for example, a propped cantilever beam, other methods of analysis are required. The methods fall into two categories and are based on two important concepts; the first, which is presented in this chapter, is the principle of virtual work. This is the most fundamental and powerful tool available for the analysis of statically indeterminate structures and has the advantage of being able to deal with conditions other than those in the elastic range. Before considering the principle of virtual work in detail, the chapter clarifies what exactly is meant by work and describes the principle of virtual work. The establishment of the principle is carried out in stages. First, a particle is considered, then a rigid body, and finally a deformable body, which is the practical application required when analyzing structures. This is followed by the calculation of work done by internal force systems and virtual work due to external force systems. the chapter ends with a discussion of applications of the principle of virtual work.