Unified Approach for Minimum Reinforcement of Concrete Beams

The structural behavior of lightly reinforced concrete (LRC) and fiber-reinforced concrete (FRC) beams in bending is similar and depends on the amount of reinforcing bars and fibers, respectively. For this reason, a unified approach is introduced herein for the evaluation of the minimum reinforcement. Such approach is based on the definition of the ductility index (DI), which is a function of the difference between the ultimate bending moment and the effective cracking moment. DI is higher than zero when LRC and FRC beams show a ductile response, whereas it is negative in the case of a brittle behavior. In accordance with several experimental data, the linear dependence of DI on the amount of reinforcement can be demonstrated. Thus, a new design-by-testing procedure can be established to determine the minimum reinforcement (that is, reinforcing bars or fibers) of a concrete beam, which corresponds to DI equal to zero.