As pointed out in Section 1.4, instead of the equilibrium methods, displacements and forces can be ascertained through the use of energy methods. The latter are based on the concept of strain energy, which is of fundamental importance in analysis and design. Application of energy techniques is effective in cases involving members of variable cross sections and problems dealing with elastic stability, trusses, and frames. In particular, strain energy approaches can greatly ease the chore of obtaining the displacement of members under combined loading.

In this chapter, we explore two principal energy methods and illustrate their use with a variety of examples. The first deals with the finite deformation experienced by loadcarrying components (Sections 5.2 through 5.7). The second, the variational methods, based on a virtual variation in stress or displacement, is discussed in the remaining sections. Literature related to the energy approaches is extensive [1-19].