Ductility index for deflection hardening of FRC beams in bending

A new method for the evaluation of the minimum reinforcement of fiber-reinforced concrete (FRC) beams is presented in the paper. The aim is to identify the volume of fibers necessary to produce a hardening behavior in the post-cracking regime of concrete under bending actions. Similarly to lightly reinforced concrete (RC) beams, this condition can be achieved when the ductility index is higher than, or equal to, zero. To validate this approach, both theoretical model and experimental analyses have been undertaken. As a result, the introduction of the ductility index also reveals the equivalence between the minimum reinforcement area and the minimum fiber volume fraction of RC and FRC beams, respectivel