BOOK_CONTENT
From Theory of Beam Columns: Space Behavior and Design, Volume 2

7.1 INTRODUCTION

In Chap. 3, the special case of flexural-torsional buckling strength of a plane beam-column subjected to loading in its plane is approached and solved from the standpoint of bifurcation. There, the out-of-plane deformations of a beam-column are assumed to remain zero until the critical loading condition is reached. Thus the in-plane behavior of the beam-column up to the critical load can be analyzed independently of the out-of-plane buckling behavior. The solutions from this in-plane analysis can then be substituted in the flexural-torsional equations which govern the out-of-plane buckling of the beam-column. However, this cannot be done for the more general loading case in which the beam-columns are subjected to biaxial bending moment as well as axial force.

In the particular case when the material remains in the elastic range, the three coupled differential equations of equilibrium for an elastic beam-column can be solved exactly or approximately by the use of formal mathematics. This has been presented in Chap. 4. In the plastic or non-linear range. however, these fourth-order coupled differential equations are intractable and recourse must be had to approximate methods or numerical methods to obtain solutions.

The numerical methods which have been used by various investigators include the numerical integration (Chap. 9). finite difference method (Chap. 10). and the finite element method (Chaps. 11 and 12). In this chapter. approximate deflection methods for obtaining the solutions of elastic-plastic beam-column problems are presented in which all the boundary conditions may not be satisfied. An improved and...

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