NONLINEAR CALCULATION OF A REINFORCED CONCRETE BEAM ON AN ELASTIC BASE USING THE “STIFFNESS–CURVATURE” RELATIONSHIP

A reinforced concrete beam on an arbitrary elastic base under the action of an external load is considered. Its movements and the distribution of internal forces in its sections are determined. The calculation is performed by the variation-difference method using finite differences of increased accuracy. Initially, the beam is divided into identical rectangular sections and a stiffness matrix is constructed for the elastic base as the inverse of the malleability matrix. The functional of the total potential energy is compiled as the sum of the energy of the bending of the beam, the deformation of the elastic base and the work of the external load in the form of a quadratic function of the displacements of the centers of the sections on the beam. By differentiating the latter for each displacement, a system of linear algebraic equations is formed, the solution of which is the displacement of the centers of the sections on the beam. An iterative algorithm is organized, where at each iteration, according to the “stiffness-curvature” relation ship, the bending stiffness on each section of the beam is specified. Examples of calculation of rectangular cross-section beams on an elastic layer and a Winkler base are given.