Ultimate deformability of concrete in flexural over reinforced members

Abstract

The analysis of reinforced concrete members in section analysis relies on the application of deformation theory, which involves using the ultimate values of concrete compressive strains at the moment of failure. These strains can be determined by analysing the bearing capacity function at its highest point. Typically, this analysis assumes that the tensile reinforcement reaches its yield point and maintains a constant stress. However, in the case of overreinforced elements, the stresses in the reinforcement at the moment of failure do not reach the yield point and are not constant. Given that the failure of overreinforced members initiates from a compressed region, it is evident that the criterion for failure in such cases will be reaching the maximum strength of the compressed concrete area within the member. In such situations, an analytical criterion is proposed to determine the ultimate compressive strain of concrete in reinforced concrete members. This criterion, along with the commonly used criterion for extreme concrete strength in regular reinforced concrete members, forms the basis for calculating the strength of reinforced concrete structures. The ultimate compressive strains of concrete are determined by applying the derived criterion to a range of concrete classes, represented by a coefficient "k" ranging from 1 to 5. The resulting diagram can be used to standardize the ultimate values of concrete strains for different concrete classes. Additionally, the ultimate values of fiber strain can be utilized to determine the bearing capacity of members subjected to axial load and bending moment, where the tensile reinforcement operates within the elastic stage. Based on the deformation model, formulas for calculating the strength of flexural reinforced concrete members are derived using the calculated ultimate strains of concrete. These calculations are based on the equations of solid body mechanics and a complete stress-strain diagram of concrete and reinforcement. To facilitate practical calculations, a table of ultimate strains of concrete values and necessary coefficients for various concrete classes has been developed. The application of this method is illustrated through an example.