Brittle/ductile assessment of Hybrid Reinforced Concrete beams containing steel rebar and fibers

Many structures, such as precast and cast-in-situ tunnel linings, are nowadays realized with Hybrid Reinforced Concrete (HRC), where a combination of continuous steel rebar and discrete fibers is used to reinforce the cementitious matrix. Hence, the definition of a minimum amount of hybrid reinforcement (i.e., rebar and fibers), which prevents the brittle failure, is of practical interest. For predicting the brittle/ductile response of HRC beams in bending, a theoretical model is introduced and presented in this paper. It is based on the flexural response of both Lightly Reinforced Concrete (LRC) and Fiber-Reinforced Concrete (FRC) beams, separately analyzed. The numerical results of the model, and some experimental data as well, show that the minimum reinforcement of HRC beams can be determined with a new design procedure. It requires the definition of the ductility index (DI), which is proportional to the difference between ultimate and effective cracking load. As DI linearly increases with the amount of rebar and fibers, the minimum reinforcement in HRC members can be found when DI is equal to zero. In addition, the minimum hybrid reinforcement can be defined with a suitable linear combination of the minimum area of rebar and the minimum fiber volume fraction, related to LRC and FRC beams, respectively