Abstract
The paper studies the stress-strain state of a rod with variable bending rigidity, compressed by an axial concentrated force in the presence of initial deflections along its axis. The initial differential equation of longitudinal bending is solved by the numerical finite difference method with the number of divisions along the axis equal to eight. Two problems are solved simultaneously: bending strength and stability under central compression. The calculated deflection diagrams are given depending on the change in the axial load value, taken as a fraction of the critical force, as well as depending on the conditions of fixing the ends of the rod. The results of the study are the formation of 7th order resolution matrices for the numerical calculation of longitudinal-transverse bending of the rod. Critical forces for various boundary conditions at the ends of the rod, and the values of the resulting deflections are determined.