Stability of Elasto-Plastic Wide-Flange Columns

In the past (1963), it has not been possible to obtain analytic solutions of the differential equations of bending of elasto-plastic compression members composed of the common structural sections. In part, this difficulty was due to the inability to express curvature explicitly in terms of moment and thrust. Appropriate functions can be derived by assuming that the flange elements of wide-flange and box sections are thin. With the aid of the latter, the differential equations are solved in two steps of integration, which is made possible by the introduction of appropriate variables of integration. Use of a suitable buckling criterion and a simple graphical or numerical procedure makes it possible to obtain interaction curves for structural members loaded in compression and bending. Thus, the necessary number of numerical or graphical steps is reduced considerably, and no simplified assumption as to the defleeted shape of a column need be made. The solution includes the previously treated column of solid rectangular cross section as a special case. An approximate, semiempirical equation, based on the derived curves, is suggested.