Calculation of the formation of normal cracks in a reinforced concrete element based on the deformation theory of plasticity of concrete by G.A. Geniev

Abstract

The authors present a refined method of determining the moment of cracking in reinforced concrete bar constructions using the diagram of deformation of concrete built on the basis of the deformation theory of plasticity by G.A. Geniev in which the stress and strain invariants of concrete are linked by nonlinear dependences. In the resulting defining equations, the hypothesis of flat sections, as well as the premise of reaching the limit values of concrete deformations on the stretched fibers of the cross-section are used. Stresses in concrete are determined through deformation values in accordance with the nonlinear deformation diagram of concrete. On the basis of the assumptions accepted, analytical dependences for determining the moment of cracking in the sections of bending elements with single and double reinforcement have been acquired. The formulas obtained were used in the analysis of various factors influence on crack resistance of bendable reinforced concrete elements. It was found out that the moment of crack formation practically does not change when percentage of reinforcement of longitudinal tensile or compressed reinforcement changes. The most effective method of crack resistance improvement is the increase of concrete strength. The proposed methodology is verified by comparison with experimental results on reinforced concrete prototypes. It is concluded that the use of the diagram of nonlinear deformation of concrete on the basis of the theory of plasticity by G.A. Geniev allows to estimate more strictly the crack resistance of reinforced concrete rod elements.