TABLE OF CONTENTS Many structural problems are statically determinate, i.e., 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. The second, based on strain energy, can provide approximate solutions of complex problems for which exact solutions do not exist and is discussed in Chapter 5. In some cases the two methods are equivalent since, although the governing equations differ, the equations themselves are identical.
In modern structural analysis, computer-based techniques are widely used; these include the flexibility and stiffness methods (see Chapter 6). However, the formulation of, say, stiffness matrices for the elements of a complex structure is based on one of the above approaches so that a knowledge and understanding of their application is advantageous.
Before we consider the principle of virtual work in detail, it is important to clarify exactly what is meant by work. The basic definition...
