A peculiar value of M to Mcr ratio: reconsidering assumptions of curvature analysis of reinforced concrete beams

Abstract The paper critically evaluates design code techniques (ACI 318-14, ACI 318-19, and Eurocode 2) for the instantaneous curvature analysis of reinforced concrete (RC) beams. The study examines the soundness of the assumption that a fully cracked section represents the lower bound of the effective moment of inertia (or bending stiffness) used along with the hypothesis of plane sections. Experimental RC beams were investigated to find a load corresponding to the stiffness of a fully cracked section. The load was identified as a condition when the resultant tension stiffening force, inversely calculated from the test moment-curvature response, equals zero. The conducted analysis showed that for the majority of the experimental beams, the stiffness of a fully cracked section was reached at a bending moment of 3Mcr (with Mcr defined by ACI 318), irrespective of the geometrical and material characteristics of the beams. As these results conflict with the abovementioned hypothesis regarding the lower bound of bending stiffness, the hypothesis was reformulated accordingly, and a new curvature model was proposed. A comparison of the predicted and experimental curvatures of 69 RC beams reported in the literature demonstrates the superiority of the proposed model over the design code techniques.