Effective area in restrained reinforced concrete: Finite Element Analysis in relation to models presented in Eurocode 2

Abstract

Cracking of concrete is a well-known phenomenon in most concrete structures, due to the low tensile strength of the material. In a reinforced concrete element, cracking initiates a redistribution of stresses from the concrete to the reinforcement. Depending on the thickness of the element, redistribution of stresses in the surroundings of a crack may create an area of concentrated stresses, an effective area, where the next crack will be created. Cracking, though, does not imply failure, as well-designed elements allow for redistribution. Eurocode is a commonly used framework that is used as a basis for structural design, and therefore the presented models must be accurate and applicable to all elements, striving for well-designed and material-efficient structures. In the second generation of Eurocode, more specifically, SS-EN 1992-1-1, a model for the effective area in concrete structures is provided. The way of modelling this slightly changed between the old version from 2005 and the newer one published in 2023. Further on, the definition of the effective area in Eurocode is not primarily derived being applicable to restrained elements. This thesis investigates whether these models apply to restrained elements. Theory related to cracking in restrained reinforced concrete was investigated. The models provided in the two versions were studied and compared. Evaluation of the effective area was done by non-linear Finite Element Modelling in the software DIANA, using a linear concrete material and a non-linear bond-slip interface between concrete and reinforcement. The stress distribution for a restrained reinforced concrete element with varying geometry was used for the evaluation of the effective area. Analytical calculations based on the models in the second generation of Eurocode were also performed, and the results were compared with the numerical results. The final results obtained from Finite Element Analysis did not correlate with the models for effective area. However, the concept of effective areas, i.e stress concentrations in the concrete adjacent to reinforcement, was clearly observed, and a maximum tensile stress section was obtained, in line with the theory. The overall conclusion is that the existing models do not apply to restrained elements and that an improved model is required. Due to a lack of correlation in results, further investigation of the subject is needed.