Structural Stability Theory and Practice

4Beam columns

4.1 Introduction

In the previous chapters we studied the axial loading on columns and its effect on the stability of columns. The presence of bending moment either due to small accidental eccentricities or imperfections was studied. In these cases, the predominant effect was the axial load that was accompanied by small bending effects. In this chapter we study the effect of combined axial load and bending moment on the bending and buckling of a member. Members are supposed to carry simultaneously significant values of both moments and axial loads. Members that are subjected to axial loads and bending moments simultaneously are called beam columns. In this chapter, beam columns containing different supports and loadings will be analyzed for buckling. In the case of beams subjected to lateral loads and moments, it is assumed for small deflection analysis that the deformed shape of the beam does not significantly affect the analysis. Thus, it is possible to make calculations for shear forces, bending moments, stresses, and deformations on the basis of the initial shape of the member. However, the transverse forces and moments cause bending moments and lateral deflections in beam columns that are called primary effects. Furthermore, the axial force acts along with this lateral deflection causing additional lateral deflections and moments in the member that are called secondary effects. Therefore, the problem becomes nonlinear and the principle of superposition cannot ...