Calculation of Continuous Flanged Beams for Overall Stability

In the regulatory documents regulating the design of beam structures, insufficient attention is paid to checking the overall stability of thin-walled beams. Recommendations for testing the stability of single pin-ended beams and rigidly sealed cantilevers are given. There are no recommendations for calculating the stability of continuous multi-span beams. Insufficient attention to the general stability of thin-walled beams can be explained by the fact that the load on the beam structures is transmitted, as a rule, through other beams, decking, etc., that is, additional connections are imposed on the beam, preventing the rotation and lateral displacement of the loaded sections, which positively affects its stability. The specifics of the working conditions of crane beams, namely, the lack of additional connections and the level of load application, negatively affect their stability. The lack of recommendations for checking the overall stability of continuous crane beams leads to an unjustified assignment of geometric cross-section parameters during design, and, as a result, to serious accidents. In this paper, the solution of the equations of stability of a flat bending shape is given by the finite difference method. The derivatives of the deflection and the angle of torsion of the beam are replaced by the central finite differences of the second order. The boundary conditions are written for the extreme and intermediate supports. The use of the finite difference method in solving the stability equations allows obtaining a result for continuous multi-span crane beams, taking into account the level of load application and the influence of neighboring spans on the stability of the most loaded span.