Overview

In Chapter 2 we have seen that the elasticity method of structural analysis embodies the determination of stresses and/or displacements by employing equations of equilibrium and compatibility in conjunction with the relevant force-displacement or stress-strain relationships. In addition, in Chapter 4, we investigated the use of virtual work in calculating forces, reactions and displacements in structural systems. A powerful alternative but equally fundamental approach is the use of energy methods. These, while providing exact solutions for many structural problems, find their greatest use in the rapid approximate solution of problems for which exact solutions do not exist. Also, many structures which are statically indeterminate, i.e. they cannot be analysed by the application of the equations of statical equilibrium alone, may be conveniently analysed using an energy approach. Further, energy methods provide comparatively simple solutions for deflection problems which are not readily solved by more elementary means.

Generally, as we shall see, modern analysis1 uses the methods of total complementary energy and total potential energy. Either method may be employed to solve a particular problem, although as a general rule deflections are more easily found using complementary energy, and forces by potential energy.

Although energy methods are applicable to a wide range of structural problems and may even be used as indirect methods of forming equations of equilibrium or compatibility,1,2 we shall be concerned in this chapter with the solution of deflection problems and the analysis of statically indeterminate structures. We shall also include some methods restricted to...