Critical Shear Crack Research Articles

Numerical investigation of the punching shear capacity of unbonded post‐tensioned concrete flat slabs

AbstractThis paper describes a numerical study of the punching shear resistance of unbonded post‐tensioned slabs without shear reinforcement. This research aimed to develop a methodology for modeling unbonded tendons and numerically evaluate the prestressing effects on the punching shear capacity. To validate the modeling approach, a series of well documented experimental tests were simulated using the finite element software DIANA. The nonlinear analyses were performed using three‐dimensional solid elements, incorporating the cracking behavior of concrete by the smeared crack approach. In addition, interface elements were included, providing bond‐slip properties to simulate the friction between tendons and concrete. A good agreement was found between the numerical results and experimental data. Load capacity, cracks patterns, and the prestressing effects were accurately simulated. After the validation, a parametric study was conducted to analyze the influence of distribution, force and profile of prestressing tendons. Finally, the numerical results were compared with current design code provisions and the approach provided by the Critical Shear Crack Theory.

Investigations on the influence of boundary and loading conditions on the shear resistance of FRP concrete beams without shear reinforcement

Although a large number of investigations on the shear behaviour of fibre-reinforced polymer (FRP) concrete members have been performed, most of the shear tests were conducted on simply supported beams that were subjected to one or two concentrated loads. It is, therefore, not possible to draw general conclusions from the results of such simple tests that can be applied to the shear design of structural members with different boundary and loading conditions. Inspired by recent investigations on the system effects in shear behaviour of reinforced concrete beams without shear reinforcement, a small experimental programme was performed that consisted of three FRP concrete beams without shear reinforcement and identical cross-sectional properties. The investigated parameters included system effects like the static system (i.e. simply supported and cantilever beams) and loading conditions (i.e. concentrated and uniformly distributed loads). The experimental results show remarkable differences with regard to the location of the critical shear crack and the shear resistance in the tested specimens. Based on this evidence and experimental observations from available shear tests of FRP concrete members collected from the literature, an extension of a shear model that was originally developed for steel reinforced concrete members was made. The proposed method can be effectively used to estimate the shear resistance of a large available test dataset and enables researchers to account for most cross-sectional parameters as well the influence of boundary and loading conditions.

Shear-Transfer Mechanisms and Strength Modeling of RC Continuous Deep Beams

Based on experimental results including the crack pattern and maximum applied strut stress, as well as on stress states obtained using a nonlinear finite-element analysis, it is identified that the typical critical shear crack of continuous deep beams is a web-shear crack, which has a large effect on shear-transfer mechanisms of deep beams. By theoretically considering the influence of the web-shear crack on the diagonal strut in a strut-and-tie model (STM) of continuous deep beams, a cracking strut-and-tie model (CSTM) has been developed. Shear-transfer mechanisms including aggregate interlock action, dowel action of longitudinal bars, and tension of web reinforcement are rationally considered. By comparing with a large database including 90 tests, the CSTM is verified to well predict the effect of main parameters including shear span-to-depth ratio, longitudinal reinforcement ratio, stirrup ratio, concrete compressive strength, and effective depth on the shear strength. Moreover, the proposed model is simplified to be used in the practical shear design, which shows a better prediction than the STM of a current standard.

Strength and ductility of lightweight reinforced concrete slabs under punching shear

Preventing a sudden punching failure and achieving an economic design, require reliable mechanical models that make physical sense. In addition, Lightweight (LW) concrete is gaining a lot of attention due to its economic advantage. Moreover, all design codes offer punching shear provisions for LW concrete as a viable alternative for the conventional Normal weight (NW) concrete. However, these punching shear provisions were developed for NW concrete slabs. The purpose of this study is to develop a mechanical model for the punching shear behavior of LW concrete slabs, that make physical sense. Inspired with the well-established critical shear crack theory, a punching shear mechanical model for LW concrete slabs was developed, validated, and proposed. In addition, using the proposed model, a parametric study was conducted in order to investigate the effect of concrete density, slab depth, flexure reinforcement ratio on the strength and ductility of LW concrete slabs under punching loads. The proposed model accounted for the effect of concrete type using both the aggregate size and the concrete density. Thus, resulted in a more consistent and more accurate strength and rotation predictions compared to existing models and design codes with respect to the experimental results of LW concrete slabs. The results of the parametric study showed that increasing the concrete density, decreasing the slab depth leads to an increase in the failure strength, the failure rotation, and the ductility. In addition, increasing the flexure reinforcement ratio increase the strength but decreases the failure rotation and ductility.

Punching of RC slabs without transverse reinforcement supported on elongated columns

The paper investigates the influence of support elongation on punching resistance at internal slab column connections without shear reinforcement. Nonlinear finite element analysis (NLFEA) with 3-D solid elements is used to study the influence of column elongation on stress and strain in the slab around the column. Punching failure is shown to be triggered by localised peaks in shear stress around the corners of the support. Significantly, one-way shear is shown to increase the shear resistance of slabs supported on columns with cross sectional dimensions greater than around six times the slab effective depth (d). The common laboratory practice of supporting slabs in punching tests on elongated plates rather than columns is investigated numerically and is found to be reasonable despite uplift occurring in the central region of elongated plates. NLFEA with solid elements gives useful insights into punching failure but nonlinear shell elements are better suited to the practical assessment of slabs in building structures. The disadvantage of conventional nonlinear shell elements is that shear failure can only be detected through post processing of results. To circumvent this, the authors have previously developed a novel modelling approach in which 3-D joint elements are used to connect shell elements located to either side of a punching control perimeter positioned at 0.5d from the column face. The joint shear resistance is calculated using the Critical Shear Crack Theory (CSCT) in which punching resistance is related to slab rotation. Based on insights gained using the solid element modelling, this paper extends the use of the joint model to the modelling of punching failure at elongated supports by including one-way joints to model linear shear.

Evaluation of design concepts for post-installed punching shear retrofitting

Punching shear is a brittle and sudden mode of failure observed in reinforced concrete slabs structures. This type of failure typically occurs around the slab-column connections, due to transverse forces being highly concentrated in these areas, thereby causing the column to punch through the slab. Several methods have been proposed for retrofitting and strengthening existing flat slabs against punching shear failure using different reinforcement-types. One of these methods relies on post-installed shear reinforcement for existing flat slab systems. The estimation of the punching shear resistance depends on several variables (geometry, mechanical, material properties, etc.) with some level of uncertainty. This study aims to assess the safety and economic performance of different methods for the design of post-installed reinforcement in an existing flat slab structure endangered by punching shear, using probabilistic analysis. The methods considered include the design procedure according to the American Concrete Institute (ACI) design code, the Canadian Standards Association (CSA) design code, the European Eurocode 2 (EC2) design code and analytical method based on the Critical Shear Crack Theory (CSCT). The probabilistic analysis was conducted based on the Monte Carlo simulation technique implemented using a MATLAB code developed in this study. The reliability index obtained for EC2 design procedure was found to be close to the EN 1990 target reliability level. CSCT and CSA, on the other hand, have a low-reliability index for most of the cases investigated.

Analysis of the crack development and shear transfer mechanisms of reinforced concrete beams with low amounts of shear reinforcement

Although a sufficient quantity of shear reinforcement can improve the shear resistance of reinforced concrete beams, the shear failure of beams with a low amount of shear reinforcement is normally characterized by the formation of a single shear crack. In this case, it is not possible to make the basic assumptions inherent in the parallel chord truss analysis or the compression-field approaches, namely, that distributed shears cracks form a pattern of quasi-parallel shear cracks. As an extension of an approach to describing the critical shear crack formation within the critical shear band, this paper presents an analysis of crack development and shear transfer mechanisms in beams with a low amount of shear reinforcement. The starting point for the analysis was the shear cracking state, which was described in the previous stage of the development for beams without shear reinforcement. The shear crack development and shear resisting mechanisms were analyzed using a group of appropriate equilibrium conditions, geometric conditions and constitutive relationships. The proposed method was validated by comparing the predicted shear resistance with the test results for rectangular, simply supported beams subjected to point loads included in the ACI-DAfStb databases. Furthermore, the validated analysis was used to investigate the relative contributions of different shear resisting mechanisms during the shear crack development. Through regression analyses of the concrete contribution and the ultimate crack length, a simplified model for the shear resistance of rectangular beams with a low mount of shear reinforcement was obtained. Predictions using both the analytical and simplified models are in good agreement with the test results, providing suitable tools for the transition from beams without reinforcement to those with high quantities of shear reinforcement.

Size Effect on Shear Strength of Reinforced Concrete: Is CSCT or MCFT a Viable Alternative to Energy-Based Design Code?

After sketching the history of the size effect models for the shear strength of reinforced concrete (RC) in design codes, the energy-based size effect law (SEL), recently incorporated into the American Concrete Institute (ACI) design code articles for beam shear and slab punching, is briefly discussed. A general derivation of the SEL based only on the first principles involving energy conservation and dimensional analysis (or laws of similitude) is presented. Attention is then focused on recent articles that present a severe critique of the SEL and various arguments in support of the Muttoni et al.’s critical shear crack theory (CSCT)—an update of the Collins et al.’s modified compression field theory (MCFT)—that some researchers propose to be introduced into the fib Model Code and the Eurocode as an alternative to the SEL. In a point-by-point analysis, it is shown that this critique and these arguments are incorrect and baseless. It is hoped that the present clarification would lead to progress in design codes, enhancing the safety and efficiency of RC structures.

A mechanical model for the shear capacity of slender reinforced concrete members without shear reinforcement

A new approach to shear capacity of slender concrete beams without shear reinforcement based on principles of structural mechanics is presented. It is assumed that the shear capacity corresponds to a failure that takes place at the neutral axis when the principal tensile stress of concrete reaches the effective concrete tensile strength, resulting in a sudden crack connecting to the critical shear crack tip. Realistic values of material and structural properties such as concrete tensile strength, elastic modulus, fracture energy, crack width and crack spacing are analysed and directly taken into account in the new model. In contrast to many existing shear models, the size effect is considered naturally through the fracture energy of concrete together with the crack spacing. The accuracy of the proposed method has been verified by comparing model predictions with experimental results of different concrete members. The new shear model shows a consistent and higher accuracy of shear capacity prediction than most existing shear models including those in current codes. The validation results and other aspects of the shear model are discussed, leading to some conclusions on the new shear model and its applications.

Authors' closure on the discussion of the article: “From experimental evidence to mechanical modeling and design expressions: The Critical Shear Crack Theory for Shear Design” (discussion by Dönmez et al.)

<scp>Authors' closure on the discussion of the article</scp>: “From experimental evidence to mechanical modeling and design expressions: The Critical Shear Crack Theory for Shear Design” (discussion by Dönmez et al.)

New approach for shear design of reinforced concrete slabs under concentrated loads based on tests and statistical analysis

Despite the international research activity, the shear strength of reinforced concrete slabs without shear reinforcement is not yet satisfactorily resolved. In particular, deck slabs of existing bridges often show significant deficits in design shear capacity, although no damage has been reported so far. A test series of 14 large-scale cantilever slabs subjected to concentrated loads was conducted and analysed at the Hamburg University of Technology. Varying the distance between the concentrated load and the support in a previously unexamined wide range led to new considerations regarding the shear capacity in RC slabs.The ultimate and residual loads of the test specimens, as in many other studies on this topic, clearly exceeded the values for vehicle load assumptions in the current standards. In contrast to previous studies, a large shear slenderness in the load arrangement could be realized in the tests. This was the basic requirement for one of the key findings: The critical shear crack occurs locally in the area of load application and not at the support. Thus, shifting the design section for shear close to the concentrated load is reasonable, while in many approaches a critical section close to the support is chosen. Furthermore, the often-used effective width beff, which depends on the distance of single loads to the support, does not seem justified. The shear forces should be determined by finite element analysis, a common method in practice, which can consider the spatial load transfer and the stiffness of the support in a realistic manner.The new design method presented here is therefore not primarily concerned with the shear resistance, as other investigations are, but first on the side of determining the relevant internal shear forces, which are initially higher in the design section proposed here. Only in a second step is a preliminary factor C*Rd,c for the calculated resistance determined by means of a well-founded statistical evaluation. For this purpose, a database with 45 tests on RC slabs has been established. The new design approach provides significant greater shear capacities than the current regulations.

Discussion of the article “From experimental evidence to mechanical modeling and design expressions: The critical shear crack theory for shear design”

Discussion of the article “From experimental evidence to mechanical modeling and design expressions: The critical shear crack theory for shear design”

One‐way shear strength of wide reinforced concrete members without stirrups

AbstractThe calibration of most analytical models that assess the shear strength of wide reinforced concrete members without shear reinforcement is based on simply supported beam tests, which may not be representative of slabs and wide members failing in shear. This paper addresses the knowledge on the shear strength of wide members, identification of their most important parameters, and an evaluation of the accuracy and precision of the main models presented in codes of practice and literature. A database of 170 shear tests was built on wide members loaded over the entire width, with the ratio width to effective depth b/d &gt; 1. This database includes members under concentrated loads (CLs) and distributed loads (DLs) in the span direction. A parameter analysis revealed such shear strength is mostly influenced by the shear slenderness and size effect rather than by the ratio b/d. Furthermore, the results show a clear decrease in the shear strength of continuous members under DLs to higher shear slenderness, similar to the behavior of members under CLs. This trend was well observed with the proposed model of shear slenderness, which assumes that continuous members with higher bending moment in the span than over the inner support behave closer to simply supported members. A comparison of the shear capacities predicted by the physical‐mechanical and semiempirical approaches showed the higher accuracy and precision of models based on the critical shear crack theory and critical shear displacement theory, regardless of the ratio b/d. Therefore, the same models derived based on beam tests are valid for wide members. Apart from that, the analyses of nonslender members with some strain‐based models combined with reducing factors of the acting shear load provide accurate results of shear strength for members without stirrups.

Punching shear design of RC flat slabs supported on wall corners

AbstractReinforced concrete buildings are typically braced with shear walls positioned around lift shafts and stairs. Vertical transfer of load from slab to walls leads to a concentration of shear stress in the slab at wall ends and corners, which needs to be considered in punching shear design. This issue is not addressed in EN 1992 (2004) and only partially addressed in fib Model Code 2010 leaving engineers to resort to their own judgment. Consequently, consideration of punching shear at wall corners can be overlooked entirely or not properly addressed through lack of knowledge. The paper addresses this issue by proposing a method for calculating the design shear stress at wall corners for use in conjunction with the Critical Shear Crack Theory. The method is initially validated against test results for slabs supported on elongated columns as well as numerical simulations. Subsequently, the method is extended to the punching design of a slab supported by a wall corner. The proposed analysis of the slab‐wall corner junction is validated against the predictions of nonlinear finite element analysis (NLFEA) employing 3‐D solid elements as well as the joint‐shell punching model (JSPM) previously developed by the authors.

Influence of Longitudinal Reinforcement Ratio on Shear Strength of RC Slender Beam Under Different Loading Rates

. A primary current focus in concrete shear design is how to ensure the shear resistance of the concrete structures to withstand the possible adverse creep effects during the service life. All shear-carrying actions are supposed to depreciate due to the enhanced critical shear cracks under sustained loads. However, only a few studies that evaluated the performance of concrete structures failing in shear due to long-term loading. As the longitudinal tensile reinforcement strain influences the shear strength of RC beam, the shear resistance of the beam under sustained load may also be affected by the amount of longitudinal reinforcement. The present study aims at investigating the influence of flexural reinforcement ratio on the shear creep failures of reinforced concrete (RC) beams without stirrups by non-linear finite element analysis. In this study, the numerical model of RC beams with reinforcement ratios varying from 0.4% to 3.2% was evaluated under different loading rates. A loading rate of 1000 and 10000 times slower than the static loading rate were adopted to reveal the creep effects of RC beams.

Mechanical model for the shear strength of steel fiber reinforced concrete (SFRC) beams without stirrups

Numerous studies have shown that adding steel fibers to the concrete mixture improves both the shear strength and ductility of reinforced concrete beams. Most current shear design formulations for steel fiber reinforced concrete beams are empirically based and their predictions provide acceptable results when compared with tests results, but only in limited ranges of the parameters involved. On the other hand, many shear theoretical models suggested in the literature are derived by extending previous formulations for conventional reinforced concrete beams, just introducing the stresses transferred across the critical shear crack. Since the effects of steel fibers on the others shear resisting mechanisms are not accounted for, “adjusting” empirical factors must be used to fit the experimental results. There is, therefore, the need for developing mechanical models capable to rationally account for the effects of steel fibers on the global shear strength and on each shear resisting mechanisms. In this paper, the previously derived and validated Multi Action Shear Model for RC elements is extended to steel fiber reinforced concrete beams without stirrups. The effects of steel fibers on each resisting mechanism have been identified and incorporated in the formulation of each shear component and in the Multi-Action Shear Model equilibrium equations. The residual tensile stresses of fibrous concrete, obtained through a simple formulation, has been used to: capture the enhancement of the compression chord contribution; the shear transferred by bridging effect of the fibres along the critical shear crack and by dowel action. The proposed model is shown to properly estimate the shear resistance of a large set of available test data, being able to account for most influencing parameters, like fibers types and amounts, concrete strength, longitudinal reinforcement ratios and beam geometry.

Influence of the plastic hinge rotations on shear strength in continuous reinforced concrete beams with shear reinforcement

Continuous reinforced concrete (RC) beams may develop significant plastic rotations to enable the redistribution of bending moments. These rotations occur at plastic hinges, which are subject to high shear forces. The influence of rotations on the shear strength for statically determined beams without shear reinforcement failing in shear after yielding of the flexural reinforcement has already been experimentally verified. However, this influence has not been studied in continuous members with shear reinforcement. An innovative tests system has been specially designed to develop shear failures before and after yielding of the flexural reinforcement in both statically determinate and indeterminate structures.Nine beams (9000 mm long, 250 mm wide, 450 mm high) with a shear reinforcement of ϕ8/30 (ρw = 0.13%) and different longitudinal reinforcement ratios were tested under different load and support conditions.The shear strength provided by shear reinforcement and that provided by the other mechanisms of resistance (shear strength provided by concrete) for each specimen were calculated based on the critical shear crack width measurements performed by Digital Image Correlation (DIC). Bending rotation and crack rotation along the development length of the critical shear crack were also obtained by DIC.Based on the test results, the shear strength provided by concrete was studied in relation to the bending rotation and the average crack width in reinforced concrete beams with shear reinforcement. It was confirmed that the shear strength provided by concrete decreased with increasing both bending rotations and crack widths. The shear strength values predicted by different design codes (ACI 318-19, Eurocode 2 and Model Code 2010) were compared with the test results, and showed that these formulations did not properly capture the loss of shear strength caused by bending rotation.

Crack-Based Shear Strength Assessment of Reinforced Concrete Members Using a Fixed-Crack Continuum Modeling Approach

With the inventory of aging and deteriorating concrete infrastructure continuing to grow throughout much of North America and other regions of the world, there is a need for cost-effective tools that can provide meaningful assessments regarding structural damage. This paper presents a crack-based analysis procedure that can be used to estimate the residual shear strength of cracked reinforced concrete beam-type elements, based on a member-idealized, fixed-crack-continuum analysis procedure. Easy-to-obtain concrete crack measurements, which serve as input, are used in combination with basic material mechanical properties, member geometry and detailing, and cracked concrete dedicated behavioral modeling to provide estimates of the residual/remaining member shear capacity and to forecast critical shear crack widths to be referenced in future inspection and monitoring efforts. The fixed-crack continuum modeling approach is presented in a manner that can accommodate transverse confining stresses stemming from disturbed regions and relevant to the analysis of reinforced concrete beams. Two different procedure solution methods were investigated: one employing an assumption regarding the longitudinal stress acting on the idealized element and one using an estimate of average longitudinal strain based on known loading proportions. Data pertaining to 48 different beam specimens, comprising five different experimental programs documented in the literature, were employed for validation. The results presented in this paper demonstrate that even with the use of easy-to-obtain crack data and simple cracked-concrete modeling techniques, crack-based assessment procedures can be used to provide meaningful structural performance assessment data for existing concrete infrastructure.

Design considerations on the influence of slab continuity on punching resistance of flat slabs

abstract: This paper assesses the influence of slab continuity on the punching resistance of a realistically proportioned flat slab floor plate without shear reinforcement. The edge column punching resistance of a symmetric flat slab extending bays in each direction was assessed by means of NLFEA with TNO DIANA, MC2010 levels II, III, IV, Eurocode 2 and NBR 6118. Both Eurocode 2 and NBR 6118 are seen to give similar predictions for punching resistance, while MC2010, which is based on the Critical Shear Crack Theory and depends on how rotations are calculated and FE modelling assumptions, varies significantly with its levels of approximation with Level IV agreeing reasonably well with predictions from NLFEA. Direction for the critical rotations is shown to vary and can also be influenced by the reinforcement over the span. For EC2, NBR 6118 and MC2010 LoA II and III punching shear design are independent of span, unlike the results obtained with MC2010 LoA IV.

Shear Strength of Members without Transverse Reinforcement Based on Development of Critical Shear Crack

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