5.1 Introduction

A beam-column is a kind of beam subjected to both lateral loads and axial compression simultaneously. Additional moments developed by an axial force can also be of importance. This effect of the axial force is referred to as the beam-column effect or P-delta effect (P-$\Delta$ effect). Secondary moments from the compressive axial load may have a deleterious effect on the strength and stability of a beam-column. Deflections, bending moments, and shear forces in a beam-column are not proportional to the applied loads. Thus the superposition of deflections cannot be applied. Equilibrium equations are based on the deformed geometry of the structure. An analysis of a beam-column is a nonlinear problem. In an analysis of frames, axial forces are generally not known at the outset. Accordingly, a set of axial forces of the members is determined as a linear structure. At the second iteration, the axial forces from the first iteration are used. If the results show that the axial forces obtained by the second iteration differ greatly from those of the first iteration, the calculated values will be used to find new values, and the analysis is repeated.