Analytical Model for Fictitious Crack Propagation in Reinforced Concrete Beams without Debonding

The non-linear fracture mechanical problem of combined crack growth and reinforcement action is modelled by adopting a simplified fictitious crack model for concrete and a linear elastic-plastic action for the reinforcement. The softening relation of the concrete is assumed to be linear, however, the crack growth is further simplified by introducing a continuous layer of springs at the midsection mainly representing a simplified material response around the fracture zone. In the reinforcement the strain condition is assumed to be equal to the strain condition in the concrete. the important question of de-bonding between the reinforcement and the concrete is therefore not considered. The model gives closed form solutions for the whole load displacement curve. Further, the model can describe important effects qualitatively correct. For instance the change of behaviour from brittle to ductile when the reinforcement area is increased and from ductile to brittle when the size scale is increased. Experiments are performed with two types of reinforcement, notched and un-notched reinforcements. Comparisons between the model and the experiments show that the assumption of a linear softening relation is not adequate and that the de-bonding problem should be taken into account.