Scale effects in prestressed concrete structures: Maximum reinforcement percentage to avoid brittle crushing

The structural behaviour of prestressed concrete beams is considerably affected by different nonlinear phenomena occurring in post-cracking and crushing regimes, such as snap-back or snap-through instabilities. Design procedures included in current technical Standards are not able to take into account the actual crushing regime, since the adopted constitutive laws overlook the strain-localization and softening behaviour of the concrete matrix. Moreover, design provisions are usually based on Plasticity Theory, leading to completely disregard size-scale effects and ductile-to-brittle transitions as functions of the beam depth. In the present paper, the above-mentioned shortcomings are overtaken by means of a Fracture Mechanics approach. The Cohesive/Overlapping Crack Model is able to simulate the strain-localization and softening regime of concrete both in tension and compression, predicting the nonlinear crushing behaviour of prestressed concrete beams. Then, a scale-dependent maximum reinforcement percentage formulation is provided in order to avoid concrete crushing failure. In this way, the field in which prestressed concrete structures can develop a safe ductile behavior can be defined, formulating new standard requirements for an effective structural design.