The variational criterion of critical strain energy levels used by the authors determines changes in a state of self-stress of the structure due to the shutdown of internal links in it. The technique of progressive limit state, based on this criterion, provides an opportunity to trace the process of disabling links within the structure, until the load-bearing capacity is completely exhausted, when the system becomes unstable. In addition to this, the use of the rod approximation method allows to represent a structure of almost any shape as a system of rod elements. In this case, the technique of progressive limit state becomes more visual. The paper investigates a structure in the form of a portal frame. To determine the extreme self-stress forces in the rod structure, a mathematical model of the problem in the form of an eigenvalue problem is used. The schemes of sequential disconnection of the links, which were obtained during the analysis of self-stresses in the structure, are presented. The diagrams of unstable structures that appear when their bearing capacity is exhausted are also given.