From experimental evidence to mechanical modeling and design expressions: The Critical Shear Crack Theory for shear design

Many research efforts have so far been devoted to the topic of shear design of members without transverse reinforcement since the first development in structural concrete. This has allowed a number of significant advances in the understanding of the phenomenon, which is currently acknowledged to depend upon a number of shear-transfer actions in cracked concrete such as aggregate interlocking related to crack opening and sliding, the residual tensile strength of concrete after cracking, dowelling of the reinforcement and the inclination of the compression chord. In the last years, independent teams of researchers have confirmed this by means of detailed measurements on tests performed with Digital Image Correlation and by integrating constitutive laws governing the transfer of shear. In agreement to the observed physical reality, clear and scientifically based theories have been developed allowing researchers to reproduce the shear response in a realistic manner and to perform more accurate predictions on the strength of members. One of these theories, grounded on experimental facts and supported by mechanical modeling, is the Critical Shear Crack Theory (CSCT). In this paper, the fundamentals of the theory are reviewed, linking them to the experimental response of beams in shear. Based upon these fundamentals, a general physical-mechanical model is presented to implement the CSCT basic ideas. On the basis of these results, the aptness of defining a criterion to assess failures in shear is justified, which can be formulated in a simplified manner and is suitable for design. The aim of this criterion is to lead to consistent design expressions, sufficiently simple to be used in practice. It is particularly interesting that the mechanical basis of the model allows natural reproduction of physical phenomena, such as size and reinforcement strain effects, that can be assessed in an accurate manner considering the nonlinear response of a potentially cracked reinforced concrete member. This approach is consistent with the underlying physics and is significantly more general than approaches followed in the past, where empirical formulas were corrected with a size effect term to account for this phenomenon (imposing an effect on a formula which is not necessarily consistent or valid outside its ranges of calibration). Based on the evidence reviewed, this article replies in a scientific, detailed, and transparent manner to a number of criticisms by A. A. Donmez and Z. P. Baant on the assumptions of the CSCT