Method for Calculating Assembly Stresses in Frame Structures Strengthened in Deformed State

The methodology and results of calculating the stress-strain state of metal frame structures when they are strengthened by attaching additional elements to the original ones. With such strengthening, additional assembly stresses emerge in the structure. This paper presents a mathematical model and a variational method for determining assembly displacements and stresses, where the equations for displacement of the system due to unit concentrated forces are not used in solving the problem. The proposed mathematical model and method can be used with equal success for solving linear and nonlinear problems. The mathematical model and the calculation method for analyzing the stress-strain state of a frame structure strengthened during operation allow to successively determine displacements and stresses in the structure from the effects of initial, assembly and additional operational loads. The basic hypotheses of the bar theory, taking shearing into account, and the Lagrange variational principle are applied. A distinguished feature of the calculation method is that in the process of solving the problem, constraints are imposed on the displacements of the original and strengthening structural elements and, taking into account these constraints, the assembly displacements and stresses due to the initial loads are calculated. This feature significantly simplifies the solution of the problem and allows to expand the range of questions under study, since it removes the limitations associated with the determination of assembly forces. The test problems have been solved. Comparison of the values of assembly displacements and stresses obtained in the test problems and determined by other methods demonstrate reliability and high accuracy of the calculations.