ABSTRACT
This chapter explores two principal energy methods and illustrates their use with a variety of examples. The first deals with the finite deformation experienced by load-carrying components. Second the variational methods based on a virtual variation in stress or displacement. Stresses and strains associated with both components of the strain energy are also very useful in describing the plastic deformation. Internal work stored in an elastic body is the internal energy of deformation or the elastic strain energy. Castigliano's theorems are in widespread use in the analysis of structural displacements and forces. They apply with ease to a variety of statically determinate as well as indeterminate problems. Compression members having low slenderness ratios show essentially no instability and are called short columns. Beams subjected simultaneously to axial compression and lateral loads are called beam–columns. Energy approaches often more conveniently yield solution than equilibrium techniques in the analysis of elastic stability and buckling.
