Initial Buckling of Channels in Compression

An exact analysis of the behavior of thin rectangular plates subjected to uniform shear and widthwise direct stresses, and a longitudinal compressive stress which is constant in the longitudinal direction, and small edge forces applied to the longitudinal edges which vary sinusoidally with the longitudinal coordinate, is outlined. Hence, the initial buckling stree (or frequency of vibration) and mode of any structure consisting of a series of such plates connected along their longitudinal edges can be found (e.g., open sections, polygonal tubes, various types of stiffened plates and corrugated core sandwich panels). Uniformly compressed symmetrical channels are specifically considered in this paper. The modes are shown to be either symmetrical or antisymmetrical, but interaction between local and overall deformation, of either the Euler or flexural-torsional type, is automatically included and is always present to a greater or lesser extent. Numerical results for the buckling stresses and modes of a family of channels are obtained and compared with recently published approximate results. Appreciable discrepancies are found.