Abstract
The purpose of this work is to numerically implement the determination of residual deflections of reinforced concrete elements based on a nonlinear deformation model. To solve the equations in a physically nonlinear formulation, the iteration method is used in combination with Microsoft Excel and VBA. Most of the existing engineering methods for the verification calculation and reinforcement of bent elements are based on approaches based on the determination of integral stiffness characteristics of the section by simplified methods. This problem acquires new relevance when using the current norms, when it is necessary to take into account the features of nonlinear deformation of materials, loading mode, and the background of the structure. The article considers the application of a nonlinear deformation model in the calculation of residual deflections. To solve this problem, the bent element is divided into separate sections, on each of which stiffness is calculated based on a nonlinear deformation model. When solving systems of equilibrium equations of a nonlinear deformation model, the iteration method is used. In areas with cracks, the stresses in the reinforcement are adjusted by a coefficient that takes into account the unevenness of their distribution in the section with the crack and between them. After determining the stiffness coefficients in each section, the displacement is determined by integrating the values in the sections of unit moments and the calculated curvature by the numerical method of trapezoids. A load-deflection graph is constructed and approximated by a square polynomial with the derivation of an analytical dependence to determine the residual deflections as well as the stress-strain state of the bent elements as a whole. The analysis and comparison of the results with the normative methodology is given. Numerical example of calculation of good convergence with the normative methodology
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