Minimum reinforcement and crack width of reinforced concrete beams

According to building codes, the minimum reinforcement must prevent both the growth of wide cracks in service, and the brittle failure of concrete beams in bending. Concerning the ultimate conditions, a ductility index, lower than zero in under-reinforced beams, has been introduced for calculating the minimum amount of steel rebar. The results of a general model and of several tests reported in the literature reveal the existence of a linear relationship between this ductility index and the amount of reinforcement. Moreover, a further linear relationship between a normalized service crack width and the amount of reinforcement can be obtained. The above relationships are generally valid, regardless of geometry and mechanical properties. If few tests are combined with these linear relationships, a new design-by-testing procedure can be used to calculate the minimum reinforcement which satisfy both the ultimate and the serviceability limit states