Chapter 1 - Structural Analysis—Stiffness Method

Abstract

This chapter introduces general plastic analysis methods, which take advantage of the availability of modern computational tools, such as linear elastic analysis programs and spreadsheet applications. The powerful number crunching capability of these tools enables plastic analysis and design to be performed for structures of virtually any size. The amount of computation required for structural analysis is largely dependent on the degree of statical indeterminacy of the structure. Structural analysis, whether linear or nonlinear, is mostly based on matrix formulations to handle the enormous amount of numerical data and computations. Matrix formulations are suitable for computer implementation and can be applied to two major methods of structural analysis: the flexibility (or force) method and the stiffness (or displacement) method. This chapter focuses on the stiffness method. Formulation of the matrix equations for the stiffness method is done routinely and the solution procedure is systematic. Therefore, the stiffness method is adopted in most structural analysis computer programs. This method is particularly useful for structures with a high degree of statical indeterminacy, although it can be used for both determinate and indeterminate structures. Furthermore, the stiffness method is used in the elastoplastic analysis described in this chapter. It concludes by stating that in structural analysis, the degree of statical indeterminacy is important, as its value may determine whether the structure is globally unstable or stable.