Abstract
The authors analyze the theory used in many countries, containing two independent directions: 1) the theory of stability of rod systems, including flat frames; 2) the theory of calculation of structural elements from various materials. The main feature of these theories is the application of the principle of plastic fracture. The assumption about a plastic hinge, due to the inconsistency with the experimental data, is supplemented by the incorrect application of theories of infinite elastic deformations, as well as of infinite creep deformations, which are incompatible with this hinge. Using the rules of mathematics, the principles of mechanics and the results of reliable experiments, it has been revealed that the analyzed theory contains several theories for different applications that reject each other, including the erroneous ones.