Buckling of Lateral Restrained Thin-Walled Cantilevers of Open Cross Section

Herein is a method for determining the buckling load of lateral and torsional restrained thin walled cantilever of open cross section under uniform distributed axial load. It is assumed that the restraining medias are distributed along an axis parallel to the axis of the bar. It is supposed that the shear forces in the restraining medias are proportional to the derivatives of the respective displacement. This kind of restraints appears in the analysis of multistory structures in which the lateral and vertical loads are resisted by common action of shear walls and frames. The analytical model of such structures is a vertical cantilever with a thin walled open cross section representing the shear wall, lateral and torsional restraint. The restraining media idealizes the frames, which may be assumed to have the previously mentioned properties. The solution of the problem leads to a system of three third order homogenous differential equations with variable coefficients. The solution selected is in the form of an infinite power series.