STATIC CALCULATION OF A REGULAR SYSTEM OF REINFORCED CONCRETE BEAMS AND SLABS ON AN ELASTIC BASE TAKING INTO ACCOUNT THE PHYSICAL NONLINEARITY OF THE STRUCTURAL MATERIAL

Abstract

An infinite regular system of reinforced concrete beams and slabs on an elastic base is considered. As an elastic base, a single-layer isotropic artificial base is accepted – as an elastic layer, limited in thickness and rigidly connected to a non-deformable base.

The elastic base is replaced by a computational domain, which is approximated by a symmetric volumetric center grid with constant steps in the XYZ axes, consisting of volumetric cubic cells. When solving the problem in displacements, the deformation energy is calculated for each cell of the computational domain, after which it is integrated over the entire volume of the elastic base. For rigid bases (such as reinforced concrete), the thickness of the elastic layer does not affect the stress-strain state (VAT) of an infinite regular system of reinforced concrete beams or slabs, which was shown earlier in the author's works and confirms the hypotheses of rigid bases.

Static nonlinear calculation of an infinite regular system of beams and plates on an elastic base on a spatial load is performed by an iterative algorithm of the variation-difference method (VRM), which is a numerically analytical method for calculating building structures. This method is characterized by the replacement of differential equations by finite-difference approximations using the finite difference method. It is also worth noting that the VRM is close to the real operating conditions of the foundation – foundation system.

An iterative algorithm is organized in which, at each iteration, the bending stiffness on each section of a reinforced concrete beam or slab is specified according to the "stiffness – curvature" relationship. The algorithm of the given solution is numerically implemented using the MATHEMATICA computer algebra software package.