Multi-scale tension stiffening approach for the minimum reinforcement of hybrid concrete beams

To reinforce cementitious matrix, a combination of steel rebar and fibers can be used in massive concrete members, e.g., tunnel linings. Due to their large cross-sections, and to the moderate state of stress, these Hybrid Reinforced Concrete (HRC) elements typically contain the minimum reinforcement to prevent the brittle failure. Thus, a model capable to predict the flexural behavior of such HRC members is of practical interest. The multi-scale approach proposed herein is based on the flexural response of both Lightly Reinforced Concrete (LRC) and Fiber-Reinforced Concrete (FRC) beams, containing only rebar and fibers, respectively. As for LRC and FRC elements, the model provides the so-called Ductility Index (DI), used to define the minimum reinforcement of HRC beams. According to the results of several tests, the transition be-tween the brittle (DI<0) and ductile (DI>0) response indicates the optimal value of the hybrid reinforcement.