Based on the experimental data that include maximum shear crack width, residual shear crack width, angle of the main crack and shear drift ratio, a simplified equation are proposed to predict the shear deformation of the highstrength reinforced concrete hsrc beam member. Nucleation of a cleavage crack occurs when a critical value of effective shear stress is attained due to a critical grouping ideally a pileup of dislocations which can create a crack nucleus, i. Section of maximum shear since the shear, v, at any transverse section of the beam is the algebraic sum of the transverse forces to the left of the section, the shear, in. Applications of the critical shear crack theory to. The proposed approach is based on a physical model and overcomes most limitations of current codes of practice. The failure of a material is usually classified into brittle failure or ductile failure.
Critique of critical shear crack theory csct for model. Punching resistance of internal slabcolumn connections with. If an initial crack size is known, then a critical stress can be determined using the strain energy release rate criterion. With no shear reinforcement provided, the member failed immediately upon formation of the critical crack in the highshear region near the right support. Figure 32 position of critical shear crack developing through compression strut from engineerin 101 at abant izzet baysal university. Validation of the critical shear crack theory for punching of slabs. Critical shear stress article about critical shear stress. The aspects criticized have however been largely discussed in previous works of the csct, proving the validity of the theory.
Online learning aci university on applications of critical shear crack theory to punching of reinforced concrete slabs with transverse reinforcement. The theory is based on a mechanical model that allows the amount of shear force that can be carried by cracked concrete to be determined. In that document, donmez and bazant raise a number of criticism on the hypotheses critical shear crack theory csct. Shear crack in concrete beams structural engineering. Re shear cracks in pt members, a principal tensile shear crack would not extend to the tension face, as a flexure shear crack would. Applications of the critical shear crack theory to punching of rc. Critique of critical shear crack theory csct for b model code articles on shear strength and size e ect of rc beams abdullah d onmez1 and zden ek p. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the materials resistance to fracture. Shear reinforcement design requirements chapter 4b.
Free online education presentations on applications of critical shear crack theory to punching of reinforced concrete slabs with transverse reinforcement videos there are no web sessions on applications of critical shear crack theory to punching of reinforced concrete slabs with transverse reinforcement. Pdf some specific documents related to punching shear provisions in draft proposal of model code 2010 can be downloaded from the following links. Faculty of engineeringuniversity of sulaimani, kurdistan region of iraq accepted 19 oct 2014, available online 25 oct 2014, vol. Punching resistance of internal slabcolumn connections. The theoretical principles of the critical shear crack theory for. A critical section is one where a critical or maximum stress occurs. The shear failure process of rc members without shear reinforcement includes several interacting effects of material behavior. Experimental investigation of the shear behavior of a. However, artificial manmade cracks several orders of magnitude longer and wider than natural flaws have required a correction factor term y that can be up to about 3 times the recorded experimental value. The theory is based on a mechanical model that allows the amount of shear force that can be carried by cracked concrete to be determined, accounting for the opening and roughness of a critical shear crack leading to failure. Recent improvements of the critical shear crack theory for. In the critical shear crack theory csct 21 22 23 the shear stress transferred across the crack is an explicit function of the crack width in the critical shear region. Sometimes they do happen at other locations when stresses are reversed during dynamic loads. Figure 32 position of critical shear crack developing.
The shear performance of concrete beams is known to be an important mechanical feature. This theory was based on the hypothesis that the shear strength of concrete slabs without transverse reinforcement depends on the width and roughness of a crack that. Normally, the failure of the concrete specimen is mainly caused by the opening of the csc, but. The theory is developed with a clear link to experimental observations, explaining the observed phenomena and calculating their response. Effect 1 is the crack localization within the fracture process zone fpz. As previously shown,3,4,6 the width of the critical shear crack can be correlated to a physical parameter a reference. This theory, based on a mechanical model, is shown to provide a unified approach for one and twoway shear in slabs, leading to simple design expressions for estimating the strength and deformation capacity of such members. Principal tensile shear cracks happen in low flexural stress zones normally fully compressive near points of contraflexure or at free ends where there will not be a flexural crack at all. The critical shear crack theory csct was developed following a scientifically. Critique of critical shear crack theory for fib model code. Effect of point loads on reinforced concrete slabs without.
The mechanical model of the critical shear crack theory csct has been used in the past to investigate a number of shear. Shear cracks are diagonal and flexural cracks are vertical. Fatigue crack initiation normally occurs due to repeated plasticity on shear planes in individual grains. A comparison between the treatments of punching by ec2. Shear strength of members without transverse reinforcement as. Complex nature of diagonal tension accompanied by the formation of new cracks as well as closing and propagating preexisting cracks has deterred researchers to achieve an analytical and mathematical procedure for accurate predicting shear behavior of reinforced concrete, and there is the lack of a unique theory accepted universally. Comprehensive design example for prestressed concrete psc. Punching shear strength of reinforced concrete slabs. The critical shear crack theory for punching design researchgate. Critical stress intensity factor bulk material values mpam 12 3. For stirrup design, the section located a distance d from the face of the support is called the critical. Application of critical shear crack theory to punching of reinforced concrete slabs with transverse reinforcement.
The critical shear crack theory for punching design american. The method is based on an estimate of the crack width in the shear critical region and provides a rational basis for the evaluation of the shear and punching shear strength of members without stirrups. Evaluation of shear strength of concrete flat plates. The shear stress needed to cause slip in a given direction along a given crystallographic plane of a single crystal explanation of critical shear stress. Results of the refined calculation of the failure criterion of critical shear crack theory csct. Despite the intensive efforts dedicated in the last decades to better understanding punching shear failures, there is still no consensus on the. The main variable considered in the study is the shearspan to depth ratio. Critique of critical shear crack theory for fib model code articles on. Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. The theory is based on a mechanical model that allows the amount of shear force that can be carried by cracked concrete to be determined, accounting for the opening and roughness of a.
By integration of the stresses at the critical shear crack, 86 the contribution of each shear transfer action is determined as well as its governing parameters. Criteria for formation of diagonal cracks in concrete beams v ave v bd can be regarded as rough measure of stress distribution of v is not known exactly, as reinforced concrete is nonhomogeneous. Request pdf on apr 1, 2017, aurelio muttoni and others published the critical shear crack theory for punching design. This has been explained by muttoni and schwartz12 as follows. Material failure theory is the science of predicting the conditions under which solid materials fail under the action of external loads. Accurate critical stress intensity factor griffith crack. Types of cracks in concrete beams cracks in beams due to increased shear stress. This paper outlines the theoretical background of the punching shear provisions implemented in the fib model code 2010 and presents a practical example of its applica tion. Re shear cracks in pt members, a principal tensile shear crack would not extend to the tension face, as a flexureshear crack would. Validation of the critical shear crack theory for punching of. Critical stress intensity factor k ic has been an approximation for fracture toughness using only loadcell measurements. Applications of critical shear crack theory to punching of reinforced concrete slabs with transverse reinforcement. The theory was first developed for punching design of slabcolumn connections without shear reinforcement.
The method is based on an estimate of the crack width in the shear critical region and provides a rational basis for the evaluation of the shear and punching shear strength of. Critical shear stress article about critical shear. The theoretical principles of the critical shear crack theory for punching shear failures and derivation of consistent closed. Critical plane approach an overview sciencedirect topics. Background to fib model code 2010 shear provisions part. The theoretical principles of the critical shear crack. Relative shear stress is defined as the ratio of the force of friction acting on the substrate shear stress to the frictional force required to set a given size of particles in motion critical shear stress. Critique of critical shear crack theory csct for fib.
In this paper, the fundamentals of the critical shear cracktheory csct are introduced. How to distinguish between a shear force crack and a bending. The limitations of such an approach are discussed in this paper and a new theoretical model, based on the critical shear crack theory, is presented to investigate the strength and ductility of shearreinforced slabs. Applications of critical shear crack theory to punching of. These elementary effects are exemplarily sketched in fig. How to distinguish between a shear force crack and a. This document compiles such previous knowledge as a reply to the authors of the report. Pdf application of critical shear crack theory to punching of. This theory, based on a mechanical model, is shown to provide a unified approach for one and twoway shear in slabs, leading to simple design expressions for estimating the. There are no online learning courses on applications of critical shear crack theory to punching of reinforced concrete slabs with transverse reinforcement. Cracks in concrete beams due to increase in shear stress appears near the support such as wall or column. Pdf application of critical shear crack theory to punching. Mar 09, 2017 shear cracks usually happen near the supports.
Critical shear crack theory csct was first developed for punching failures of slabcolumn connections without shear reinforcement muttoni. Critique of critical shear crack theory csct for fib model code articles on shear strength and size effect of rc beams. An important feature of this theory is the critical shear crack csc, which is suitably defined as follows. The traditional approach of codes of practice for estimating the punching strength of shearreinforced flat slabs is based on the assumption that. A comparison between the treatments of punching by ec2 and. Critique of critical shear crack theory csct for fib model. This paper discusses the limitations of the traditional approach for estimating the punching strength of shearreinforced flat slabs and proposes a new theoretical model, based on the critical shear crack theory, to investigate the strength and ductility of shearreinforced slabs.
Punching strength of reinforced concrete flat slabs without. Nonlinear finite element modeling of shearcritical. The critical shear crack theory csct is a consistent approach used for shear design of one and twoway slabs failing in shear and punching shear respectively. The limitations of such an approach are discussed in this paper and a new theoretical model, based on the critical shear crack theory, is presented to investigate the strength and ductility of shear reinforced slabs. 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. Critique of critical shear crack theory csct for fib model code.
Applications of the critical shear crack theory to punching. Principal tensile shear cracks happen in low flexural stress zones normally fully compressive near points of contraflexure or at free ends where there will. Faculty of engineeringuniversity of sulaimani, kurdistan region of iraq accepted 19 oct 2014, available online 25. Punching strength is a critical point in the design of flat slabs and due to the lack of a theoretical method capable of explaining this phenomenon, empirical formulations presented by codes of practice are still the most used method to check the bearing capacity of slabcolumn connections. Critical shear crack theory 7 aureliomuttoni,originally developed the critical shear crack theory in 1985, at the technical university of zurich. A comparison between the treatments of punching by ec2 and the critical shear crack theory csct slabs without shear reinforcement rizgar amin agha. Nucleation of a cleavage crack occurs when a critical value of effective shear stress is attained due to a critical grouping ideally a pileup of dislocations which can create a cracknucleus, i. This paper presents a study on the shear behavior of concrete beams without web reinforcement strengthened by external vertical prestressing rebars evprs. It is the aim to explain the mechanical model that forms the basis of the punching design equations, to justify the relevance of the provisions and to show their suitability for the design and assessment of structures. Today, it is the critical stress intensity factor k ic, found in the plane strain condition, which is accepted as the defining property in linear elastic fracture mechanics. Comprehensive design example for prestressed concrete psc girder superstructure bridge design step 5 design of superstructure design step 5. Shear failures in reinforced concrete members without transverse reinforcement. Aug 23, 2016 the main variable considered in the study is the shear span to depth ratio.
In theory the stress at the crack tip where the radius is nearly zero, would tend to infinity. The critical shear crack theory for punching design. This paper discusses the limitations of the traditional approach for estimating the punching strength of shear reinforced flat slabs and proposes a new theoretical model, based on the critical shear crack theory, to investigate the strength and ductility of shear reinforced slabs. Failure criterion based on critical shear crack theory critical shear crack theory as shown in fig. The most important factor as to whether a crack will propagate past the first grain and go on to cause fatigue failure is the microscopic shear stress in critical grains. Punching strength of reinforced concrete flat slabs.
These cracks are also called as shear crack and are inclined at 45 degrees with the horizontal. Shear crack propagation theory scpt the mechanical. The theoretical principles of the critical shear crack theory. Thus shear wave splitting opens a window into the analysis of small variations of the rock mass that probably no other geophysical measurement can match, and is the underlying reason why shear wave splitting is the key to monitoring the crackcritical crust discussed in, below. First of all, the scpt is used to analyze the critical shear crack of sc70, which is located at a distance of about 2700 mm from the support the method of section 4. The mechanical model of the critical shear crack theory csct has been used in the past to investigate a number of shearrelated problems, such as punching. An analysis of the critical shear crack development on the basis of test results f cavagnis, mf ruiz, a muttoni engineering structures 103, 157173, 2015. Shear strength of concrete members without transverse.
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