The stability of the shape of an unattached elastic rod with stiff flanges on its ends

The stability of an unattached column consisting of an elastic rod with stiff flanges on its ends under longitudinal compression is investigated. The load under which the plane of the flange surface is tilted from the plane of the support surface is found. This tilting is accompanied by considerable rotation (reversing) of the flanges and corresponding bending of the rod axis. Abrupt replacement of the rectilinear or bent equilibrium shape by an equilibrium shape that is non-contiguous to it occurs. It is established that the columns behave differently when this a change in the equilibrium shape occurs, depending on the ratio of the length of the rod to the length of the flanges.