Buckling of Inelastic I-Beams Under Moment Gradient

A model developed for the inelastic buckling of beams under uniform moment, which accounts for strain-hardening residual stresses and monosymmetry of the yielded cross section, is extended to the case of moment gradient by allowing for the effects of nonuniform yielding. A tangent modulus theory of buckling is used, and the governing differential equations are adopted from those which govern the elastic flexural-torsional buckling of tapered monosymmetric I-beams of constant depth. The critical central concentrated loads of simply supported I-beams are obtained by solving the governing differential equations numerically by using the method of finite integrals in an iterative process. The influence of the residual stresses, height of point of application of the load, and in-plane moment distribution on inelastic buckling are investigated, and the theoretical solutions are compared with design rules.