The expanding and contracting hinge in a rapidly heated rigid-plastic beam

Abstract

In the simple rigid-plastic theory of the dynamic behaviour of isothermal beams, deformation usually takes place at discrete hinges, except in the early stages of certain types of blast loading. For a beam subjected to rapid thermal curvature, discrete hinges cannot provide an adequate mechanism of deformation, and they are replaced by expanding and contracting hinges occupying a finite length of the beam. The expanding and contracting phases of a hinge are governed by the same general equations, but their physical characteristics are quite different: in particular, the angular velocity is continuous along the beam during expansion but discontinuous during contraction. A general analysis is given for a beam free in space, and detailed results for a variation of thermal curvature such as would be found in a pulsed nuclear reactor experiment.