Chapter 5 - Energy methods

Abstract

A powerful alternative but equally fundamental approach to structural analysis 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. Many structures that are statically indeterminate—they cannot be analyzed by the application of the equations of statical equilibrium alone—may be conveniently analyzed using an energy approach. Further, energy methods provide comparatively simple solutions for deflection problems not readily solved by more elementary means. Generally, modern analysis 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 are found using potential energy. This chapter is concerned with the solution of deflection problems and the analysis of statically indeterminate structures. It includes some methods restricted to the solution of linear systems, that is, the unit load method, the principle of superposition, and the reciprocal theorem.