Chapter 15 - Virtual Work and Energy Methods

Abstract

The majority of the structural problems we have encountered so far have involved structures in which the support reactions and the internal force systems are statically determinate. These include beams, trusses, cables and three-pinned arches and, in the case of beams, we have calculated displacements. Some statically indeterminate structures have also been investigated. These include the composite structural members in Section 7.10 and the circular section beams subjected to torsion and supported at each end in Section 11.1. These relatively simple problems were solved using a combination of statical equilibrium and compatibility of displacements. Further, in Section 13.6, a statically indeterminate propped cantilever was analysed using the principle of superposition (Section 3.7) while the support reactions for some cases of fixed beams were determined by combining the conditions of statical equilibrium with the moment-area method (Section 13.3). These methods are perfectly adequate for the comparatively simple problems to which they have been applied. However, other more powerful methods of analysis are required for more complex structures which may possess a high degree of statical indeterminacy. These methods will, in addition, be capable of providing rapid solutions for some statically determinate problems, particularly those involving the calculation of displacements.