Scale-dependent maximum reinforcement percentage in reinforced concrete beams

The Cohesive/Overlapping Crack Model is able to describe the transition between cracking and crushing failures occurring in reinforced concrete beams by increasing beam depth and/or steel percentage. Within this Nonlinear Fracture Mechanics model, the tensile and compressive ultimate behaviors of the concrete matrix are modeled through two different process zones that advance independently one of another. Moreover, this model is able to investigate local mechanical instabilities occurring in the structural behavior of reinforced concrete structures: tensile snap-back and snap-through, which are due to concrete cracking or steel fracture, and the compressive snap-back occurring at the end of the plastic plateau, which is generated by the unstable growth of the crushing zone. In this context, the application of the Cohesive/Overlapping Crack Model highlights that the ductility, which is represented by the plastic rotation capacity of a reinforced concrete element subjected to bending, decreases as reinforcement percentage and/or beam depth increase. Thus, a scale-dependent maximum reinforcement percentage beyond which concrete crushing occurs prior to steel yielding is demonstrated to exist. In particular, the maximum steel percentage results to be inversely proportional to h0.25, h being the beam depth. In this way, a rational and quantitative definition of over-reinforcement is provided as a steel percentage depending on the beam depth.