Limit state of a bar structure under self-stress conditions

Introduction. The paper deals with the development of the theory of the limit state of structures. The method is proposed for determining the limit state of the structure, allowing to describe all possible formulations from a single position, based on a single mathematical model.

Materials and methods. The theory is based on several basic assumptions. The fields of external actions on the structure and the deformation field of the supporting system have different origins and laws of existence. The extreme values of the parameters of the deformable structure are limited by the limiting values of external influences. The extreme values of the deformation field parameters can be found from the eigenvalue problem for the stiffness or flexible matrices of the structure. The result of solving this problem coincides with the solution of the design optimization problem. Solving the eigenvalue problem makes it possible to find the global extremum and take into account solutions at the boundary of the feasible region. The formulation of the problem makes it possible to find the maximum and minimum possible values of the reactive response of the structure to external influences. These values form the domain of admissible values for the internal parameters of the supporting system. The difference between the limiting parameters and the work of external forces gives the value of the residual bearing capacity of the structure.

Results. The problem of calculating a two-bar system is considered. The results are given in the form of an ellipse of limit states, and the values of residual bearing capacity in displacements, forces and deformation energy.

Conclusions. The new formulation of limit states problems is proposed. The calculation method allows finding not only the maximum possible parameters of the structure, but also the residual bearing capacity of the structure in a deterministic form.

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