Flexural behavior and minimum reinforcement condition in hybrid-reinforced concrete beams

Hybrid reinforced concrete (HRC) can be defined as a cementitious material in which the reinforcing secondary phase consists of a combination of continuous steel rebars and of short discontinuous fibers, randomly distributed within the concrete matrix. For these structural elements, experimental flexural tests highlight how the postcracking response of the composite is strongly affected by the amount of steel bars together with reinforcing fibers. In the present work, it is shown that the action of these two contributions can be clearly interpreted in the framework of Fracture Mechanics through the Updated Bridged Crack Model (UBCM). The model assumes nonlinear constitutive laws to describe the toughening action of the reinforcing secondary phases, which are related to the yielding of steel rebars and to the pull-out of the short fibers. Under these assumptions, different postcracking regimes depending on three scale-dependent dimensionless numbers can be predicted: the bar-reinforcement brittleness number, NP, which is directly related to the steel bar area percentage, ρ; the fiber-reinforcement brittleness number, NP,f, which is directly related to the fiber volume fraction, Vf; and the pull-out brittleness number, Nw, which depends on the critical embedment length of the fiber-reinforcement, wc. The couples of critical values of the two reinforcement brittleness numbers define the minimum reinforcement conditions of the HRC structural element—that is, the combination of ρmin and Vf,min required to guarantee a stable post-cracking response—including its scale dependence. A parametrical analysis is presented together with the modeling of an experimental campaign reported in the literature in order to assess the effectiveness of the UBCM.