Lateral Buckling of I Beams Beyond the Limit of Proportionality

摘要

The study is concerned with the problem of lateral buckling of I beams when the stresses exceed the limit of proportionality. It is assumed that the cross section is bi-symmetrical and that the stress-strain law is the same in tension and in compression. If these assumptions are not made, the problem will become more involved, but it can be treated by analogy. The Shanley principle is accepted. The effective modulus of elasticity is consequently the tangent modulus, and the effective modulus of rigidity is determined by application of the total theory of plasticity. The governing differential equation of lateral buckling is derived by means of the energy principle of stability. An explanation is given for the use of a direct method (Ritz method) for determination of the critical load. Two numerical examples are presented: (1) a concentrated force applied at the middle of a simply supported beam, and (2) a uniformly-loaded, simply supported beam. A graphical presentation is provided of the relationships found between the critical load and the slenderness ratio of the beam. (Author)