Stability of the Hinge Formed in an Ideal Rigid-Plastic Beam

Abstract

The hinge formed at yield in an ideal rigid-plastic beam is considered plastically stable if the moment of resistance increases after a small deformation, and unstable if the moment decreases. An initially curved beam of strain-hardening material and rectangular section is considered, and the change in moment of resistance due to a small change in curvature calculated. It is shown that, for a material which does not strain harden, the yield hinge is unstable if the initial curvature and the change in curvature are of the same sign. However, the initial rate of change of moment of resistance is small. The change of yield moment of a straight beam is initially zero. The minimum initial hardening rate required for stability of a curved beam is calculated.