Load Bearing Capacity Calculation of the System “Reinforced Concrete Beam – Deformable Base” under Torsion with Bending

¹ South-West State University, 50 let Oktyabrya street, 94, Kursk, 305040, Russia
² National Aviation University, Kosmonavta Komarova av., 1, Kiev, 03580, Ukraine
³ V.I. Vernadsky Crimean Federal University, Vernadskogo av., 4, Simferopol, 295007, Crimea

^* Corresponding author: i2103@ukr.net

Abstract

It is presented the formulation and solution of the load bearing capacity of statically indeterminable systems “reinforced concrete beam – deformable base” by spatial cross-sections under force and deformation effects. The solution of problem is currently practically absent in general form. It has been established the relationship between stresses and strains of compressed concrete and tensile reinforcement in the form of diagrams. The properties of the base model connections are described based on a variable rigidity coefficient. It is constructed a system of n equations in the form of the initial parameters method with using the modules of the force (strain) action vector. The equations of state are the dependences that establish the relationship between displacements which are acting on the beam with load. Constants of integration are determined by recurrent formulas. It makes possible to obtain the method of initial parameters in the expanded form and, consequently, the method of displacements for calculating statically indefinable systems. The values of the effort obtained could be used to determine the curvature and rigidity of the sections in this way. It is necessary not to set the vector modulus P, the deformation is set in any section (the module is considered as an unknown) during the problem is solving. This allows us to obtain an unambiguous solution even in the case when the dependence M–χ has a downward section, i.e one value of moment can correspond to two values of curvature.