Analytical determination of critical forces during buckling of systems consisting of two pinned connected rods

Columns and rod systems are quite common in engineering practice. For the correct design of such structures, it is necessary to have analytical expressions for critical forces for all possible load cases. The article is devoted to a theoretical study on determining critical forces in compressed-bent rod systems in the elastic stage and checking the numerical calculation methods of such rods using the displacement method. The study examines the issues of stability of rod systems, studies the effect of the rods’ own weight, final values of possible displacements of system nodes, and the direction of distributed load on the values of compressive critical forces. A differential equation for the bending of a rod is obtained taking into account the eccentricity of the application of the axial force. As a result of theoretical studies, analytical expressions were obtained for calculating the critical axial compressive force acting on a vertical rod system. The article derives and presents analytical dependencies that determine the critical forces for a rod system resting on hinged-fixed and elastically compliant supports in a transverse direction only and without semi-rigid connections in the rotational direction. The correctness of the obtained expressions is verified based on a comparison with the results of the static method for determining the critical load. The obtained expressions for determining critical forces can be used by designers when assessing the buckling resistance of rod systems.