The Critical Shear Crack Theory for punching design: from a mechanical model to closed-form design expressions

The Critical Shear Crack Theory (CSCT) is a consistent approach used for shear design of one- and two-way slabs failing in shear and punching shear respectively. The theory is based on a mechanical model allowing to determine the amount of shear force that can be carried by cracked concrete accounting for the opening and roughness of a critical shear crack leading to failure. The theory was first developed for punching design of slab-column connections without shear reinforcement. Its principles were later extended to other cases such as slabs with shear reinforcement, fibre-reinforced concrete or slabs strengthened with CFRP strips and one-way slabs without shear reinforcement. The generality, accuracy and ease-of-use of this theory led to its implementation into design codes (such as the fib Model Code 2010 or the Swiss Code for concrete structures). The design expressions of the CSCT consist of a failure criterion and a load-deformation relationship, whose intersection defines the load and the deformation capacity at punching failure. They are clear and physically understandable, and can be written in a compact manner to be used for design of new structures. With respect to the assessment of the maximum punching capacity, the conventional design expressions of the CSCT can also be used, although they required to be solved iteratively. In order to enhance the usability of the design equations of the CSCT, particularly for the punching assessment of existing structures, this paper presents closed-form design expressions developed within the frame of the CSCT. These expressions allow for direct design and assessment of the failure load. The closed-form expressions keep the generality and advantages of the CSCT approach, but they allow for a faster and more convenient use in practice. In this paper, the derivation of these expressions on the basis of the CSCT principles is presented as well as its benefits and comparison to experimental results and the original design formulation.