Cracking and crushing in reinforced and prestressed high performance concrete T-beams

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. Cracking and crushing instability phenomena occurring in RC and PC mechanical behaviour have been demonstrated to be governed by a couple of dimensionless parameters, such as the matrix brittleness number, s, and the reinforcement brittleness number, NP. These numbers are functions 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 behaviour of the concrete matrix. In this framework, 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 T-shaped cross-sections highlight the existence of a scale-dependent minimum reinforcement percentage that is able to guarantee a stable post-cracking behaviour and a scale-dependent maximum reinforcement percentage that is able to guarantee steel yielding prior to concrete crushing. These lower and upper bounds define the range in which reinforced and prestressed high-performance concrete beams can develop a safe ductile behaviour, allowing to formulate new standard requirements for an effective and rational structural design.