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 h 0.25 , 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.
In the present work, cohesive and overlapping crack models are integrated in a comprehensive numerical algorithm in order to investigate both tensile and compressive failures in plain or steel-bar reinforced concrete (RC) structural elements. These two fracture mechanics models offer a high capability in the investigation of non-linear phenomena occurring in the loading process of plain concrete or RC beams subjected to bending. Based on the crack-length control scheme, these non-linear models are able to describe snap-back and snap-through instabilities, crack formation/propagation, steel yielding/slippage, concrete crushing and scale effects on the structural brittleness. In the present work, some parametric studies are carried out on plain concrete or RC beams in order to highlight how the abovementioned structural phenomena, which are observed in engineering practice, can be effectively captured by means of a non-linear fracture mechanics approach. Moreover, dimensional analysis is adopted to confirm how the behaviour of lightly reinforced concrete beams can be effectively described by means of two non-dimensional brittleness numbers, leading to a scale effect on the minimum reinforcement percentage, ρmin, proportional to beam depth raised to −0.15.
Glass fiber‐reinforced polymer (GFRP)‐reinforced concrete (RC) can be defined as a cementitious material in which the reinforcing secondary phase consists in corrosion‐resistant GFRP rebars. For this next‐generation structural material, experimental flexural tests highlight how the postcracking response is strongly affected by the amount of GFRP area together with the structural size‐scale. In this work, the cohesive/overlapping crack model (COCM) is adopted to describe the transition between cracking and crushing failures occurring in GFRP‐RC beams by increasing the beam depth, the reinforcement percentage, and/or the concrete compression strength. Within this nonlinear fracture mechanics model, the tensile and compression 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 GFRP‐RC beams: tensile snap back and snap‐through, which are due to concrete cracking and reinforcement bridging action, and the compression snap‐back generated by the unstable growth of the crushing zone. In this context, the application of the COCM highlights that the ductility, which is represented by the plastic rotation capacity of the GFRP‐RC beam only when the reinforcement can slip, decreases as reinforcement percentage and/or beam depth increase. In this way, rational and quantitative definitions of hyperstrength and brittle compression crushing behaviors can be provided as a GFRP percentage depending on the beam depth.
Reinforced concrete (RC) and prestressed concrete (PC) structural elements need to be designed in order to guarantee large plastic deformations, avoiding any loss in their load bearing capacity. In this framework, the rotation capacity of RC and PC beams has been demonstrated to be a function of concrete mechanical properties, reinforcement characteristics, and of the structural size. On the other hand, Theory of Plasticity as well as the International Standards completely disregard size‐scale effects and ductile‐to‐brittle transitions, leading to an overlook of the strain‐softening behavior of the concrete matrix and of the rotation capacity of RC beams. On the other hand, the Cohesive/Overlapping Crack Model is able to evaluate concrete cracking in tension and concrete crushing in compression, as well as snap‐back and snap‐through unstable phenomena, steel yielding and/or slippage. This Nonlinear Fracture Mechanics model predicts a reduction in the moment versus rotation plastic plateau by increasing the beam depth and/or the reinforcement percentage. The numerical investigations carried out on reinforced and prestressed high‐performance concrete beams having rectangular or T‐shaped cross‐sections highlight the size‐scale effects on plastic rotation capacity that allow to formulate new scale‐dependent upper and lower limits of reinforcement percentage to guarantee a stable and ductile postpeak behavior of reinforced concrete structures.
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