The problem of determining the position of the dangerous section or the dangerous point at which the process of fracture or the development of plastic deformations in a beam is well studied and has been included in textbooks on the strength of materials. Experimental studies reveal processes that cannot be explained from the point of view of classical theory. For example, the position of the dangerous section in the middle of the beam in a state of the pure bending section, and not in all sections, as it should be according to the theory. Further development of the existing theory is required, which may help to explain the experimentally detected inconsistencies with the classical approach. The paper proposes a study based on the criterion of critical energy levels of a flat strip. The variational criterion of critical strain energy levels in combination with the rod approximation method makes it possible to find the weakest link in the rod model of the strip. Load-bearing capacity lost begins which the weak links removal started. To determine the extreme values of the forces in the rods, a mathematical model of the eigenvalue problem is used. The schemes of sequential failure of the elements of the rod model (progressive limit state) are presented. The variants of self-tension of the structure at particular stages of links elimination are given.