Limit states design theory based on critical energy levels criterion in force method form

Abstract

The article deals with the development of the theory of limit states of structures. There are various approaches to the formulation of limiting states of structures. They are related to issues of strength, structural stability (ULS) or safe operational requirements (SLS). All known theories are oriented to a certain hypothesis of the limiting state and exist separately from each other. Therefore, there is an opinion that there is no systematic view of the limit state theory. The article suggests a general approach to creating the theory of limit states based on the criterion of critical levels of internal energy proposed by one of the authors. The problem of determination of the structure limit state is formulated as finding critical energy levels by varying system stresses. The change of energy level is accompanied by removal of linkages in the structure. Self-stressing states of the system make it possible to find out the most loaded elements. Mathematical model of general approach is the eigenvalue problem. It is formulated in the force method form and the resolving equations are derived. The physical meaning of the obtained relations and the links between the variables are explained. The proposed technique allows making a forecast that shows the element and the load from which destruction of the system will begin and trace the progressive failure of structural elements. Depending on the hypothesis of the ultimate limit state of the structure or serviceability limit state, we can analyze the behavior of the structure under load and predict violation of the conditions LSD. The problem solving method of finding the limit states is shown in the example of the pin-jointed structure.