Review article

A fast inverse numerical-analytical method is used for the development of practical recommendations for the stability calculation of steel elements of operating structures with spatial axis curvature and local damage. Geometrical nonlinearity in the form of bending and bending-torsion displacements of element sections affecting the forces is determined by the results of the analytical solution of the corresponding deformation problems, in which the physical nonlinearity and local damage are taken into account by the corresponding equivalent loading of an elastic defect-free element with fictitious forces. The problem is solved by increments of the given i-х deformed states in the most loaded defective section with parameter _{max, i}_{max, i} E / R_y, by which the actual force and the mentioned fictitious forces are determined using the algorithm “section”. Then, the end eccentricities of the acting force are established by an inverse analytical solution.By keeping the end eccentricities constant as they grow ε _{max, i} 0 8 , _{max, i} 4 , the maximum values ϕ_{e x i ,}and ϕ_{y c i ,}corresponding to the stability loss coefficients for bending ϕ_ex and bending-torsion ϕ_yc forms are set.