Subject of the paper is a simply supported thin-walled beam. The beam carries uniformly distributed transverse load, small axial force and two different moments located at its both ends. The elastic potential energy and the work of the loads for the beam are described. Basing on the minimum of the total potential energy the general algebraic equation of the critical state for the beam is obtained. The equation describes a convex hyper-surface. Particularly simply load cases are studied. Based on the general equation of the critical state numerical investigations are realized. The results are shown in figures.
