Robust mechanical models for shear and punching strength of concrete slabs

The mechanical models in this paper are based on the nominal concrete tensile strength that is considered to be the average strength along a 150 mm long brittle failure crack. Fracture Mechanics principles are applied for addressing the size effect of brittle failures; increasing member size leads to decreasing failure stress. The shear force is assumed to be carried by the compression chord of the slab and by aggregate interlock along part of the initial shear crack. Shear failure occurs when the aggregate interlock reaches its failure force that is assumed to be constant for effective depths larger than 1.0 m. The slab outside the initial shear crack around the column in a flat slab is assumed to be suspended into the stable inverted pyramid above the column. Punching failure occurs when the suspension force fails. These failure modes are used for validation of the provisions for shear and punching in the new version of Eurocode 2 (EC2). It is found that EC2 still underestimates the size effect and the code also incorrectly claims that punching failure is related to shear failure. Corrections of these two cases are proposed in the paper. A formula for design of shear reinforcement for flat slabs is proposed where iteration is not required. The paradox that brittle punching failure can cooperate with flexible shear reinforcement is explained. An additional formula is derived that gives a flat slab such large ductility that brittle punching failure can be considered as eliminated.