Review article

To develop practical recommendations for calculating the stability of rod elements of steel structures with an asymmetric cross-section, which is formed as a result of uneven corrosion damage, strengthening or reduction of the cross-section, there is proposed a numerical and analytical solution of the deformation problem, taking into account physical and geometric (according to the spatially deformed scheme) nonlinearities. It allows reducing the calculation time by several orders of magnitude as compared to the existing numerical solutions. The analytical solution of the deformation problem of elastic rods compressed-bent in two planes is based on the qualitative proximity of bending forms of deformation under central compression, namely, sinusoids with corresponding forms obtained by non-deformational calculation, on a square parabola. The latter was replaced by a sinusoid, which allowed obtaining a general solution. The manifestations of physical nonlinearity are compensated by additional loading of the elastic rod with a fictitious force with biaxial eccentricities, which is assessed using the «section» algorithm in the most loaded section, taking into account its spatial displacements. As a result, there was obtained a system of numerical-analytical equilibrium equations in dimensionless parameters, the solutions of which, as the load increases, allow assessing the coefficient of loss of spatial stability.