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

Résumé

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.

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Since the first applications of structural concrete, the shear behaviour of one-way slabs without transverse reinforcement has been largely investigated. Nevertheless, currently in the scientific community there is no general agreement on the mechanisms of shear failure, on the parameters governing the shear strength and on the predominant shear-transfer actions. Hence, several mechanical models, based on very different hypotheses, and empirical formulations, calibrated on the available experimental results, have been proposed in the last decades. In addition, these experimental results have been traditionally obtained from tests on simply supported beams subjected to point load, whereas in most one-way slabs without transverse reinforcement in practice (foundations, retaining walls, slabs of cut-and-cover tunnels, silos) the boundary and loading conditions are typically different. This thesis has therefore the objective to provide new experimental data on reinforced concrete members without transverse reinforcement tested with different loading and boundary conditions, to increase the understanding on the mechanisms of shear failure and to develop a mechanical model based on the new experimental evidence. In the first part of the thesis, the experimental results of 23 tests on 20 beams without transverse reinforcement subjected to different loading (concentrated or distributed) and boundary conditions (cantilevers, simply supported or continuous beams) are presented. Refined measurement techniques allowed detailed tracking of the development of the crack pattern up to failure. The results show that the location, inclination and kinematics of the critical shear crack play a major role on the shear strength. Moreover, the amount of shear transferred by the various potential shear-transfer actions has been estimated on the basis of the experimental measurements and by using suitable mechanical models for each shear-transfer action. The analyses show that, for slender members, the shear-transfer actions contributing to the shear capacity are the inclination of the compression chord, the residual tensile strength of concrete, the dowelling action and the aggregate interlock, and the latter is the predominant one. For squat members or members in which the critical shear crack develops below the theoretical compression strut, differently, the arching action is predominant. In the second part of the thesis, a mechanical model, consistent with the main ideas of the critical shear crack theory, is presented. The shear force that is transferred through the critical shear crack by the various shear-transfer actions is calculated by integration of simple constitutive laws and a failure criterion is obtained by summing the different contributions. The shear and deformation capacity can thus be calculated by intersection of the failure criterion with a load-deformation relationship. It is shown that the failure criteria obtained by integration of stresses at the crack surface can be approximated by power-law equations. Combining the power-law failure criteria with the load deformation relationship, a closed-form equation has been obtained. The closed-form equation provides almost identical results to the mechanical model and allows for direct design and assessment of existing structures. The accuracy of the mechanical model and the closed-form equation has been checked against a large database, showing a good agreement to the experimental results.

Miguel Fernández Ruiz, Aurelio Muttoni

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.

2016Miguel Fernández Ruiz, Aurelio Muttoni

Currently, there is no generally-accepted theory giving a physical explanation of the shear strength in one- and two-way slabs. Furthermore, for members without transverse reinforcement, shear strength is estimated in most codes of practice following empirical or semi-empirical approaches. In this paper, the fundamentals of the Critical Shear Crack Theory (CSCT) are introduced. This theory, based on a mechanical model, is shown to provide a unified approach for one- and two-way shear in slabs, leading to simple design expressions for estimating the strength and deformation capacity of such members. The paper also details a code-like formulation based on this theory and developed for the Swiss code for structural concrete. Comparisons of the theory to a wide range of test data are finally presented.