Application of the principle of virtual work in the calculation of the displacements of structures

Abstract

Application of work and energy concepts and theorems in the study of equilibrium or movement conditions is an old idea, with considerable influence on the development of Mechanics and Structural Analysis. Principle of virtual work, formulated in terms of virtual forces or virtual displecements, represents an appropiate expression of equilibrium and compatibility requirements, foundation of Structural Analysis. This work, after reviewing the historic development and its capability to base main topics of Structural Analysis, deepen into its application to the evaluation of the deformation of structures. The combination of the principle of virtual work (unit load method) with appropiate numerical integration techniques, provides an extremely gewneral, efficient and powerful method to evaluate structures deformations. Actions if principle, this method allows to estimate accurately deflections of reinforced concrete beams, including the effects of non linear behaviour of concrete, variable reinforcement, cracking, tension stiffening, creep and shrinkage.