FRACTURE BASED NON LINEAR MODEL FOR REINFORCED CONCRETE BEAMS

An analytical model based on the fracture properties of concrete and the nonlinear hinge model is proposed in this paper for the flexural behavior modelling of simply supported reinforced concrete beams. The model supposes the development of a single crack in the midsection of the beam within a zone called the hinge. The cross section of the beam is divided into a finite number of layered strips of concrete and a reinforcement bar. Each strip has a single freedom degree which is the elongation. Stress-strain relationships proposed in Euro code 2 were adopted for concrete strips under uniaxial compression and steel under tension. For concrete strips in tension zone three cases were studied: without softening effect, linear strain-softening behavior, and power-law strain softening behavior. The proposed model gives the loaddeflection relationship, the development of the crack opening from cracking up to failure and the evolution of the crack height during loading. In order to validate the proposed model, the analytical results were compared with experimental ones of a set of beams selected from scientific references. Comparisons showed that the adequate prediction of flexural behavior requires the knowledge fracture properties with an adequate strain softening function beside basic mechanical properties of both concrete and steel. Moreover, the power law strain softening curve is the most suitable to model the experimental behavior of beams while linear softening function gives conservative results. The analytical results were supported by the results of 3D finite element analysis using ANSYS software.