Size Effect In Shear Research Articles

Shear performance and size effect of CFRP strengthened RC beams

In this study, a 3D meso-scale numerical simulation method is established for analyzing the shear failure of carbon fiber reinforced polymer (CFRP) strengthened RC beams without stirrups. The inhomogeneity of concrete, the bond-slip relationship between steel bars and concrete, and the interaction between CFRP and concrete are considered. Based on this method, effects of shear-span ratio and CFRP fiber ratio on the shear performance and nominal shear strength size effect of CFRP strengthened RC beams are investigated. Results indicate that the size effect of CFRP strengthened RC beams is obvious, however, the shear-span ratio has little impact on the size effect of nominal shear strength of RC beams. The CFRP fiber ratio enhances the shear strength of RC beams on the one hand, while weakens the shear size effect of RC beams on the other hand. However, its influence on the shear performance of RC beams remains basically unchanged with varying shear-span ratios, indicating that there is no coupling effect between the shear-span ratio and CFRP fiber ratio. The shear-span ratio significantly influences both the shear bearing capacity of RC beams and the shear contribution of CFRP sheets, with the increase in the shear-span ratio, the shear bearing capacity of RC beams decreases to varying degrees, and the shear contribution of CFRP sheets increases initially and then decreases. Finally, the shear strength size effect law (SEL) of CFRP strengthened RC beams is proposed, which can quantitatively describe the effects of the shear-span ratio and the CFRP fiber ratio.

Evaluation of the shear size effect in glued laminated timber using a stochastic FE model calibrated on 17000 glue-line tests

Glue-line tests provide the shear resistance and failure mode of samples extracted from laminated timber products. Several papers questioned the practical use of such tests affirming the lack of correlation between the capacity of the beam and the outcomes of glue-line tests. However, no studies provide a probabilistic framework for interpreting glue-line tests. This paper presents and discusses the largest database of glue-line tests ever published, consisting of approximately 17000 tests on glued laminated timber (GLT) beams, carried out at the Treteknisk, the Norwegian Institute of Wood Technology (Norway). This database has been used to develop in Abaqus a stochastic FE model to predict the shear capacity of glued laminated timber beams (GLT) using advanced modelling concepts, including discrete cracking and plasticity. The authors examine the dependence of the shear capacity on the beam size to assess the shear size effect in GLT components. The methodology is based on Montecarlo simulations. The mechanical properties of the elementary volumes composing the beam are assigned using a random field model calibrated on the glue-line tests.

Detailed crack‐based assessment of a 4‐m deep beam test specimen

AbstractWhen shear cracking occurs in existing reinforced concrete deep members, engineers are faced with the challenge of determining the safety of the members. This paper presents a crack‐based assessment approach that utilizes the Two‐Parameter Kinematic Theory (2PKT) as a framework for the assessment of lightly reinforced concrete deep beams. The paper presents three assessment approaches with progressively increasing levels of approximation (LoAs). The first level of approximation (LoA I) involves using the 2PKT in a predictive manner for situations where the crack shapes are unknown, LoA II improves upon LoA I by incorporating more detailed modeling of the strain in the transverse reinforcement at the location of the critical cracks, and LoA III includes the details of LoA II but also uses the detailed crack geometry as an input in the assessment. Each of the LoAs is presented and compared with experimental data from a 4‐m deep beam test in the literature. The shear carrying mechanisms determined from the kinematic model are evaluated and compared across LoAs. Finally, the paper utilizes LoA III to study the size effect in shear for deep beams. The results quantify the influence of aggregate interlock on the size effect in shear critical deep beams.

Dynamic shear failure and size effect in BFRP-reinforced concrete deep beam

The purpose of this study is to investigate the size effect on dynamic shear failure of deep concrete beams with Basalt Fiber Reinforced Polymer (BFRP) bars. In order to accurately simulate dynamic shear failure behavior of BFRP-reinforced concrete deep beams, a three-dimensional meso-scale numerical model was established, which considered the heterogeneity of concrete, the interaction between concrete and BFRP bars, and the strain rate effect of meso-components. Firstly, the measured data of the existing experiments were input into the numerical model to obtain ideal numerical calculation results, which proved the rationality and accuracy of the simulation method. Then, the shear failures of geometrical-similar BFRP-reinforced concrete deep beams with different sizes under different strain rates were studied. The influence of beam depth, stirrup ratio and strain rate on the shear failure of BFRP-reinforced concrete deep beams and the corresponding size effect law were investigated. The results indicate that: 1) The failure modes of beams under dynamic loading are different from those under static loading; 2) Both the strain rate and the stirrup rate can effectively improve the bearing capacity of the beam and weaken the shear size effect, but the effect of strain rate is significantly greater than that of stirrup rate. In addition, a size effect law which can quantitatively describe the effects of strain rate and stirrup ratio on BFRP-reinforced concrete deep beams was established. Finally, the size effect law was verified by the simulation results and the existing experimental results.

Size effect of square concrete-filled steel tubular columns subjected to lateral shear and axial compression: Modelling and formulation

Concrete-filled steel tubular (CFST) short columns under the action of wind and seismic load often endure high shearing force and show brittle shear failure, which may exhibit obvious size effect. In this study, a three-dimensional meso-scale simulation method that can consider both the concrete heterogeneity and the contact behavior between concrete core and steel tube was established to investigate the failure behavior and size effect of square CFST columns under combined lateral and axial loads. After verification of the meso-scale model, simulation tests were carried out to discuss the influence of shear-span ratio, axial compression ratio and steel ratio on the failure modes, the nominal shear strength, the ductility and the size effect of square CFST columns. Results indicate that, when the shear-span ratio increases from 1.0 to 3.0, the failure mode of CFST columns turns from brittle shear failure to ductile bending failure, the nominal shear strength decreases and ductility increases, and the size effect in shear would be weakened. The nominal shear strength increases and the column shows better ductility with the increasing axial compression ratio less than 0.4, while the nominal shear strength decreases and the columns present obvious brittleness with the increase of axial load larger than 0.4. Moreover, as steel ratio increases from 0.05 to 0.15, the nominal shear strength and ductility of CFST columns increase, and the size effect on nominal shear strength cannot be weakened. At last, a theoretical formula that can quantitatively show the influence of shear-span ratio on size effect in shear strength was proposed to predict the shear capacity of square CFST columns. The available test data and the simulation results illustrate the rationality and applicability of the theoretical formula.

On shear in members without stirrups and the application of energy‐based methods in light of 30 years of test observations

AbstractIn a recent paper in Structural Concrete, the authors Dönmez and Bažant explain that the theoretical background of the Model Code 2010 equations for one way and punching shear are not sufficiently grounded in theory and should instead use an energy‐based size effect law in their formulation to match behavior. To support this claim, finite element simulations were presented. In this paper the basic assumption that an energy‐based method must govern the shear failure of beams without stirrups is questioned. These questions are shown to be based on the hardening behavior of aggregate interlock tests and the inability for slip strains to localize during shear failure. In addition to these theoretical arguments finite element analyses were conducted with a constitutive model that is energy‐based but that also does an appropriate job at modeling aggregate interlock, an aspect that appears to be lacking in the analyses of Dönmez and Bažant. These new results are shown to better model the test results and confirm that aggregate interlock is important in explaining shear strength and therefore the size effect in shear for slender members. As such any concerns about the safety of the Model Code shear equations appear unwarranted.

Size effects in lattice-structured cellular materials: material distribution

This work presents a novel mechanism that causes stiffness size effects in periodic cellular materials in bending, but is absent in other boundary conditions. The work begins by demonstrating that in certain circumstances, a single set of micropolar elastic material properties can predict size effects accurately for either bending or shear but not both. This suggests that, for periodic cellular materials, size effects in shear and bending arise from different mechanisms. This work then presents a novel mechanism causing size effects in bending, called a material distribution effect. A sample with only a few unit cells can have its material concentrated close to the neutral axis, or far away, depending on topology and choice of unit cell. A sample with many cells must have its material spread more evenly. This can cause either a stiffening or softening size effect. This work derives formulas to predict the magnitude and direction of these size effects and shows that these formulas are able to predict size effects for a variety of different periodic cellular materials in different types of bending boundary conditions.

Shear size effect in simply supported RC deep beams

The shear size effect refers to the phenomenon that the shear strength of reinforced concrete (RC) beams decreases as the beam depth increases. The shear strength of RC deep beams is sensitive to boundary conditions (in this case, load- and support-bearing plate (or column) sizes), which in turn affect the shear size effect of deep beams. In this study, to separate and identify the influences of the bearing plate size on the shear size effect, existing deep beam tests on shear size effect are classified. It is verified that the shear size effect of deep beams with a fixed bearing plate size is stronger compared to deep beams with proportionally varied plate sizes. By using a non-linear analysis software ATENA based on concrete fracture and plasticity theory and a mechanical model called cracking strut-and-tie model (CSTM), the shear size effects of the classified test groups are accurately predicted, and the maximum height of each beam group is extrapolated to 4 m. Through in-depth analysis of the finite element model and CSTM results, it is inferred that the possible reasons that lead to the shear size effect of RC deep beams are: (1) bearing plate size effect, that is the reduced relative strut width caused by the disproportionately varied bearing plate size with the beam height; and (2) beam depth effect, which refers to the deterioration of the shear transfer strength by aggregate interlock of the critical shear crack due to the increase of the beam depth. In addition, based on the prediction results for the 4 m high beams and the existing test results, the STM in the ACI 318-14 is evaluated. The results show that the ACI STM can not inherently consider the beam depth effect, resulting in the safety of large-size deep beams designed according to the ACI STM is lower than that of small-size deep beams. For this reason, proposals for considering the beam depth effect in STM design are put forward.

Size effect in shear and punching shear failures of concrete members without transverse reinforcement: Differences between statically determinate members and redundant structures

Large efforts have been devoted in the past to understanding size effect in shear failures of members without transverse reinforcement. Experimental works have demonstrated that increasing the size reduces the nominal shear strength provided that the failure mode is brittle. For large specimen sizes where a linear behavior can be assumed between the opening of the shear cracks and the acting shear force, the size effect agrees with linear‐elastic fracture mechanics (LEFM). In this case, the reduction of nominal shear strength is characterized with respect to the specimen size by an asymptotic slope (in double‐log scale) of −1/2. However, such a linear relationship between crack widths and applied shear force is not present in most reinforced concrete structures, where the response is characterized by a nonlinear behavior at a cracked stage. In these cases, the influence of size effect shall be milder, and the slope (in double‐log scale) characterizing it shall be lower than −1/2. In this paper, the influence of size effect on structures characterized by internal redundancy (continuous one‐way members and slabs in case of punching shear with a nonlinear response) is investigated in the frame of the critical shear crack theory. The theory predicts the same influence as LEFM with respect to size effect when a linear behavior can be assumed, but it yields consistently milder influence of size effect for structurally redundant elements with a nonlinear response.

Predicting the behaviour of storage cells in early Condeep structures

RASP, also now called VecTor6, is a nonlinear finite element program for the analysis of reinforced concrete structures that uses 3-dimensional stress–strain relation of cracked concrete based on the modified compression field theory. RASP was used to predict the behavior of a 3-dimensional 1:13 scale model of a typical upper dome-cell wall junction of a storage cell in an early Condeep structure. It predicted a flexure-shear failure at the top of the cell wall when it was subjected to a pressure differential equivalent to 129–134 m head of water. Yet, there was deviation between the theoretical and the observed response of the model since the analysis ignored the detrimental effect of water pressure in the cracks. Before applying the results of the pressure test on the scale model to the prototype structure the size effect in shear was examined. It was concluded that because the failure was triggered by flexural yielding the size effect in shear was not significant for this case.

Size Effect in Shear for Steel Fiber Reinforced Concrete Members without Stirrups

Size Effect in Shear for Steel Fiber Reinforced Concrete Members without Stirrups

Shear response of lightweight steel fiber reinforced concrete members without stirrups

Available studies on the shear strength of lightweight steel fiber reinforced concrete (SFRC) members without stirrups are scarce. Meanwhile, the overall depth of reported specimens in these prior studies did not exceed h = 300 mm, preventing verification of a so-called size effect in shear for lightweight SFRC. In this paper, the laboratory results of six large-scale lightweight SFRC specimens without stirrups having overall heights from 308 to 1,000 mm and shear span to effective depth ratios of 3.0 are reported. The specimens contained 1 % volume-fraction of hooked-end steel fibers and different longitudinal reinforcement ratios. It was observed that the normalized shear stress at failure decreases with an increase in the member depth. This indicates that a size effect in shear is present for lightweight SFRC members without stirrups. Nevertheless, for all specimens, the observed shear capacities were higher than the shear strengths predicted by the ACI 318-11 and CSA A23.3-04 standards for geometrically similar reinforced lightweight plain concrete members. The fib MC2010 models for lightweight SFRC gave more accurate predictions of strength compared to the ACI 318-11 and CSA A23.3-04 models for lightweight RC members without steel fibers.

Shear strength of full-scale steel fibre-reinforced concrete beams without stirrups

Although shear reinforcement in beams typically consists of steel bars bent in the form of stirrups or hoops, the addition of deformed steel fibres to the concrete has been shown to enhance shear resistance and ductility in reinforced concrete beams. This paper presents a model that can be used to predict the shear strength of fibrous concrete rectangular members without stirrups. The model is an extension of the plasticity-based crack sliding model originally developed for plain concrete beams. The crack sliding model has been improved in order to take into account several aspects: the arch effect for deep beams, the post-cracking tensile strength of steel fibre reinforced concrete and its ability to control sliding along shear cracks, and the mitigation of the shear size effect due to presence of fibres. The results obtained by the model have been validated by a large set of experimental tests taken from literature, compared with several models proposed in literature, and numerical analyses are carried out showing the influence of fibres on the beam failure mode.

Are steel fibres able to mitigate or eliminate size effect in shear?

This paper reports some recent results of an experimental campaign on fibre reinforced concrete (FRC) beams under shear loading tested at the University of Brescia: nine full scale beams, having a height varying from 500 to 1,500 mm, were tested for investigating the effect of steel fibres on key-parameters influencing the shear response of concrete members, with special emphasis on size effect. All tested members contained no conventional shear reinforcement and different amounts of steel fibres: 0, 0.64 or 1 % by volume. Results show that a relatively low volume fraction of fibres can significantly increase bearing capacity and ductility. The latter determines visible deflection and prior warning of impending collapse, which is not possible in plain concrete beams (without transverse reinforcement). The size effect issue is substantially limited. Results were compared against the shear formulation incorporated in the final draft of fib Model Code, which can be considered a valuable analytical model for FRC beams under shear loading, even in the case of the three deepest elements herein tested.

Shear Size Effect Analysis of Reinforced Concrete Column Based on Truss-Arch Model

With the development of modern constructional technique, more attention on the size effect is paid by academics and engineers. Shear failure mechanism of reinforced concrete column is analyzed firstly, and then the advances on the size effect of reinforced concrete column is introduced. the effects of sectional size on the shear behaviors of reinforced concrete column is studied by theoretical analysis and experimental summary, and the formula of the size effect of shear resistance of reinforced concrete column is proposed.

Shear strength prediction for reinforced concrete beams without stirrups

Traditionally, shear design of concrete beams without stirrups has relied on empirical equations derived from laboratory experiment data. However, such methods lack a sound theoretical basis for shear failure of reinforced concrete (RC) structures due to the complexity of the failure mechanism. In the 1980s, a relatively rational model based on the modified compression field theory (MCFT) was developed at the University of Toronto and subsequently accepted worldwide; it forms the basis of shear provisions in Canadian standards and American specifications for the design of concrete structures. This paper describes further research based on the MCFT. An expression for the average shear stress across a crack was derived and a simplified equation of shear strength considering the size effect in shear was developed. The obtained equations were verified with extensive sets of experimental data from different sources (598 beams in total). It was found that the variation coefficients of the ratio of shear strength calculated using the derived average shear stress across a crack based on the MCFT and the simplified expressions to the test data was small; the mean was about 0·8. It is thus considered that the simplified expressions are suitable for shear analysis and design of RC beams without stirrups.

Experimental Investigation on Size Effect in Shear of High-Strength Concrete Beams

In this paper, an experimental program on the size effect in high-strength reinforced concrete beams is described. A total of 18 deep and slender specimens with effective depth d ranging from 200 to 700 mm and shear span a ranging from 400 to 2450 mm were tested to failure under two-point symmetric top loading. Test variables were shear span to effective depth ratio a/d, web reinforcement percentage and the effective depth d. The compressive cylinder strengths f1 c of the beams vary from 75 to 104 MPa. The beams had the main steel ratio of 3.98 percent. Test results reveal that the ultimate shear stress is size dependent. Besides the shear span to effective depth ratio a/d, the effective depth d also has a significant influence on the failure mode and the ultimate shear stress; larger deep beams are more brittle in comparison with smaller ones. The 18 test results are then compared with predictions from the current ACI Code, Zsutty’s equation, Bazant’s method, and Strutand- Tie model. Comparison study shows that while the safety of the ACI Code and Zsutty’s equation reduces for larger concrete beams, Bazant’s equation predicts well the trend on the influence of effective depth d in highstrength concrete beams. The Strut-and-Tie model can predict the trend on the influence of effective depth in high-strength concrete deep beams, but overestimates the shear capacities of the beams.

Does Strength Test Satisfying Code Requirement for Nominal Strength Justify Ignoring Size Effect in Shear?

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Effect of Aggregate Size on Beam-Shear Strength of Thick Slabs

This study investigates the safety and accuracy of the American Concrete Institute shear design method when applied to thick slabs by focusing on the size effect in shear and the role played by the maximum coarse aggregate size in transferring shear stress across cracks. An experimental program was conducted in which 10 large-scale and 10 geometrically-similar, small-scale, shear-critical reinforced concrete slab-strip specimens were loaded to failure. It was found that the major mechanism of shear transfer in these element types is aggregate interlock, and that the maximum aggregate size plays an important role in beam-shear capacity of reinforced concrete members. The abilities of the ACI design method and a simplified design method based on the modified compression field theory (MCFT) to predict the failure loads are compared. Findings indicate that the ACI design method is unconservative when applied to thick slabs or large wide beams constructed without stirrups, but the simplified MCFT design method is both safe and accurate. The simplified method also can accurately predict the effects of decreasing the maximum aggregate size on the beam-shear behavior of lightly reinforced concrete members.

Repeating a Classic Set of Experiments on Size Effect in Shear of Members without Stirrups

The shear tests performed by Bazant and Kazemi in 1991 have been cited as strong evidence that the theory of fracture mechanics applies to the shear strength of beams without stirrups. It has also been noted in the past, however, that these results are not totally consistent with other size effect experimental series. This paper provides a detailed summary of duplicate experiments carried out to determine if the original 1991 results were reproducible. It was found that the repeat experiments were 31 to 70% stronger than the original results. All experimental results were stronger than the predictions of the ACI and CSA codes. Cracks patterns were observed to scale with the beam size. A comparison of historical data indicated that the higher strengths were likely not a result of random variation, but due to a systematic effect in the original testing, making them inconsistent with other tests. Potential reasons for the differences from the 1991 results are presented and discussed.