Stability

Abstract

The phenomenon that we meet in the Stability of the elastic equilibrium is so diffused and dangerous that we have to talk about it, even though briefly. We consider the problem of Fig. 6.1.1. It evidently reenters within the theory of the deflected beams, whose one-dimensional mathematical model admits one and only one solution. Nevertheless this doesn’t happen anymore if the cross section of the beam has moments of inertia, with respect to the principal axes of its inertia centroidal ellipse, very different among them (Fig. 6.1.2). In such case in fact it is intuitive and experimentally verified that the cantilever of Fig. 6.1.1 admits, for some values of F, other deformed configurations (Fig. 6.1.3) over the one furnished by the one-dimensional mathematical model. This phenomenon, that we call buckling by torsion and bending, happens even if the intensity of the load is such that in the solution furnished by the one-dimensional mathematical model the deformations are small.