Complex resistance of a compressed-bent rod taking into account elastic compliance of its support

Abstract

This work deals with the urgent problem in the mechanics of a deformable solid: studying factors of the stress-strain state of a single-span statically indeterminate beam with complex boundary conditions that is under conditions of complex resistance (axial compression with plane transverse bending). To solve the problem, both analytical methods (the method of forces in the form of “five” support moments, the method of initial parameters) and the numerical finite difference method with a “linear” grid with density n=8 were used. The necessary resolving equations and matrices are given to take into account changes in the rigidity parameter of the right hinged support and variations in concentrated and uniformly distributed loads, both along the axis of the beam and across it. In the final form, diagrams of deflections, bending moments and shear forces were constructed for specific values of bending rigidity and the degree of elastic compliance of the right hinge-yielding support. Reliability of the theoretical principles and applied results obtained by the authors is confirmed on the basis of the given alternative calculation methods.