Predicting the Residual Flexural Strength of Concrete Reinforced with Hooked-End Steel Fibers: New Empirical Equations

To characterize the tensile behavior of Steel Fiber Reinforced Concrete (SFRC), international codes generally adopt performance-based approaches that require to perform either indirect or direct tensile tests on concrete samples. The fib Model Code 2010 recommends to assess the tensile performance of SFRC by a Three Point Bending test on a notched beam able to provide a series of residual strengths corresponding to different crack mouth openings detected at midspan. Therefore, when designing SFRC structures, the tensile properties considered in the safety verifications must be checked by laboratory tests involving a suitable number of beam samples. On the contrary, especially in case of preliminary structure sizing, designers need simple tools for estimating the potential tensile performance of concrete by starting from its basic properties. The present paper proposes two equations for predicting the residual strengths f_R1 and f_R3 included in most of the equations reported by the fib Model Code 2010 for safety verification of SFRC members. The concrete compressive strength, the fiber aspect ratio and volume fraction are the only three parameters included in the formulations. The assessment of the model effectiveness has been based on a statistical analysis including the adoption of a modified Demerit Point classification method. The good predicted performance of the proposed equations has been also proved by comparison with other similar models reported by literature.