The analysis of reinforced concrete slabs strengthened by composite fabrics by the finite element method

The finite element method of calculation of reinforced concrete slabs strengthened with composite fabrics based on carbon fibers, implemented in the PRINS program, is considered. The method is designed for analyzing the stress-strain state of reinforced concrete structures when cracks in concrete and plastic deformations in the reinforcement arise. The calculation is carried out in increments, and at each stage of loading a variable stiffness matrix is used. Its constant part represents the stiffness matrix at the beginning of the loading stage, and the variable one is calculated taking into account the stress-strain state at the end of the current iteration. The variable part of the stiffness matrix, multiplied by the displacement vector found at the previous iteration, is transferred to the right side of the equation system and is considered to be an additional load. When cracks occur or when plastic strains appear, the stresses are corrected in accordance with the specified deformation diagrams. Therefore, at the end of the loading step the equilibrium conditions are checked. If necessary, the external and internal forces are balanced. When considering plastic deformations in concrete and reinforcement, the theory of plastic flow and the Huber - Mises yield criterion, modified taking into account the experimental studies of Kupfer et al., are used. An example of the reinforced concrete slab analysis with different variants of strengthening by composite and without strengthening is given. The results of the calculation are analyzed. The possibility of studying the stress-strain state throughout the entire path of loading of reinforced concrete slabs up to destruction is shown.