Fiber volume fraction and ductility index of concrete beams

The mechanical response of fiber-reinforced concrete (FRC) beams depends on the amount of fibers, and the transition from brittle to ductile behavior in bending is related to a critical value of fiber volume fraction. Such quantity, which is mechanically equivalent to the minimum amount of steel rebars in reinforced concrete beams, can be defined according to the new approach proposed herein. It derives from the application of a general model and from the introduction of the so-called ductility index (DI). When FRC beams show a ductile behavior DI is positive, whereas DI is negative in the case of brittle response. Both the theoretical and experimental results prove the existence of a general linear relationship between DI and the fiber volume fraction. Accordingly, a new design-by-testing procedure can be used to determine the critical value of fiber volume fraction, which corresponds to a ductility index equal to zero