Simple Interaction Equations for Beam-Columns

Computations to obtain the ultimate strength of an inelastic beam-column are fairly involved and, at present, only numerical methods are available to get the best possible solutions in most cases. This paper presents simple approximate forms of solutions by assuming an idealized relationship among moment, curvature and thrust in the ultimate state. The ultimate strengths of beam-columns are obtained in simple closed forms. Although they are approximate solutions and their validity has been shown only by comparison with exact solutions for strong axis bending of a side-flange section in symmetrically loaded cases, the method developed can be applied to other shapes of section with only a slight modification. This validity is considered to be true in unsymmetric cases also as long as the unsymmetricity is not very large. The formulas for the ultimate strength of beam-columns may be considered as suitable bases for a method of design for symmetrically as well as unsymmetrically loaded compression members.