TABLE OF CONTENTS In the preceding chapter, the governing differential equations of a biaxially loaded beam-column have been solved approximately by the well-known numerical technique of finite difference method. Here, the actual beam-column is physically replaced by an assembly of finite segments. The elastic-plastic behavior of these segments throughout the entire range of loading up to ultimate load has been presented in Chap. 6. As a result, the beam-column problem can now be formulated and solved approximately in terms of the behavior of these segments without recourse to complex differential equations. In a sense, the finite segment approach may be considered as a physical interpretation of the finite difference method as applied numerically to solve differential equations. The systematic development and utilization of a more refined, discretized approximation of an actual beam-column known as the finite element method will be presented in the following chapter. The finite element method may be considered as a generalization of the finite segment method described herein.
The general analysis of a biaxially loaded beam-column by finite segment method is essentially the same as that of a space structure. In this method, the beam-column is assumed to consist of a number of segments and is treated as a space structure as shown in Fig. 11.1. Three dimensional displacements( u x, u y, u z), rotations ( ? x, ? y, ? z) and a warping ( w) are taken into account at each node cross section.
