Search

In this paper, a numerical critical shear crack model, in which the shear‐flexural coupling effect is considered and the full process of stress and strain is captured, is proposed to evaluate the post‐peak behavior of reinforced concrete (RC) and steel fiber reinforced concrete (SFRC) beams. The shape of critical shear crack is identified by combining the modified compression field theory considering the bridge effect of steel fibers and the section analysis method. Based on the shape of critical shear crack, the shear capacity of beam members is provided by the shear tension zone and the shear compression zone. The shear capacity of the shear tension zone is calculated by the modified compression field theory and that of the shear compression zone is determined by multiaxial strength criterion of concrete. The vertical displacements caused by the flexure deformation and shear deformation are deduced by the moment area method and integration of shear strain. To verify the proposed numerical approach, a test database of 486 RC beams and 313 SFRC beams was established to predict the shear strength, and the force‐displacement relationships of twelve beam members are used to validate the feasibility for full process analysis. The stochastic analysis of beams with different failure modes is conducted via GF‐discrepancy‐based point selection method and probability density evolution method. The limitation between different failure modes is defined according to the degradation percent of shear capacity and it is taken as threshold value of failure domain, and the failure probability analysis indicates that the designed flexure beam member suffered severe degradation of shear capacity, resulting in a significant decline in safety probability. [ABSTRACT FROM AUTHOR]

In this study, concrete canvas (CC) layers were used as a novel method to strengthen reinforced concrete (RC) beams because of their flexibility, rapid installation, fast curing, and rapid strengthening. Due to the importance of the CC mechanical properties, various combinations of cement including ordinary (OPC) and High Alumina (HAC), as well as silica fume, were investigated to determine the optimal mixture for strengthening RC beams. The results indicate that substituting 75% of HAC with OPC significantly boosted flexural strength by 33%, and increased tensile strength in the warp and weft directions by 25% and 21%, respectively. The study examined six RC beam specimens in a four‐point flexural test, assessing their flexural properties, ductility, cracking behavior, and energy dissipation. The number of CC layers and the bonding method, which involved either the conventional externally bonded reinforcement (EBR) technique or the externally bonded reinforcement on grooves (EBROG) technique were studied. The experimental results revealed the superiority of the EBR method over the EBROG technique due to the uniform bond between CC and the concrete surface. Using the EBR technique, improvements of 35% and 51% were observed in the load‐carrying capacity of the beams strengthened with one and two CC layers, respectively. It is while for the beam with an improved loading capacity of 51%, the crack width decreased from 5.3 to 2.1 mm, and the energy dissipation increased by three times compared to the control specimen. Theoretical analysis also was performed to calculate the load‐carrying capacity of the RC beams strengthened with CC layers. [ABSTRACT FROM AUTHOR]

In this study, we designed six polypropylene fiber‐reinforced concrete (PP‐FRC) beams and three reinforced concrete (RC) beams for experimental studies. Then, we analyzed the effects of incorporating PP fibers on the cracking performance of PP‐FRC beams from the perspectives of load‐displacement response, crack distribution, crack depth, crack width, crack spacing, and deformation coordination. The research results showed that the cracking load and number of cracks were positively correlated with the volume ratio of PP fibers, while the maximum crack width, average crack spacing, and average crack depth were negatively correlated with the volume ratio of PP fibers. Due to the bridging effect of fibers, the PP‐FRC beam body and reinforcement could deform in a coordinated manner within a specific loading range after cracking, which increased the deformation coordination ability between the body and reinforcement. In this study, the cracking mechanism of PP‐FRC beams was investigated. Firstly, the formula for calculating the cracking moment of PP‐FRC beams was derived from the perspective of equivalent bending tensile strength. Then, based on the fiber bridging law and the bond strength between PP‐FRC and reinforcement, theoretical formulas were proposed to predict the average crack spacing and maximum crack width of PP‐FRC beams. Finally, through comparison, it was found that the proposed formulas could be used for characteristic crack prediction. [ABSTRACT FROM AUTHOR]

The study of damage processes in concrete and their effects on the residual properties represents a key point related to the service life of reinforced concrete (RC) structures. The use of steel fibers in RC beams mainly improves the cracking control and the shear bearing capacity. Considering the shear behavior, the presence of fibers not only leads to partial or total substitution of secondary reinforcement, but they can also result in a modification of the failure behavior from a shear failure (brittle) to a bending (ductile) one. The contribution of fibers on flexural and shear behavior of sound and damaged RC beams was investigated using alkali‐silica reaction as a damaging tool. First, the evolution of deformations and cracks were measured on creep tests of RC beams with and without fibers and reactive aggregates. Second, the flexural and shear behavior of damaged and undamaged beams incorporating steel fibers were compared. Results showed that alkali‐silica reaction damage can provoke a reduction of RC beam ductility, while the flexural strength is preserved. Regarding shear, it was observed that even in damaged concrete, fibers were able to control the crack propagation and increase the bearing capacity. [ABSTRACT FROM AUTHOR]

This paper aims to contribute to a more rational understanding of the shear strength behavior of steel fiber‐reinforced concrete beams without stirrups. For this purpose, an experimental program comprising eight slender beams varying the fiber content and type, tested in three‐point bending configuration with a complete monitoring of the displacement fields of the failure span, was carried out. A detailed analysis of the shape and kinematics of the critical crack, associated with the investigation of the shear transfer mechanisms during the test given by mechanical models available in the literature, was performed. The theoretical–experimental analyzes proved to be a promising approach for quantifying the contribution of each relevant parameter to the shear capacity, such as the fiber concrete residual tensile response. The study, therefore, presents a contribution toward a rational and comprehensive methodology for the shear design of concrete members. The influence of shape and kinematics of the critical crack on the shear response is also reported and a theoretical explanation is provided to justify the fact that beams with the same characteristics have different cracking patterns but similar shear strength. [ABSTRACT FROM AUTHOR]

This article presents an experimental study aimed to identify and quantify the cracking localization (CL) phenomenon in under‐reinforced R/SFRC beams. Results of current experiments together with those of previous tests published by the authors were used for quantification of the cracking localization level (CLL) considering the effect of fiber content, Vf, and of longitudinal reinforcement ratio, ρs, over a wide range of ρs and the effect of rebar yield and ultimate strengths. The experimental program consisted of four‐point bending tests of normal strength R/SFRC beam specimens with 400 and 500‐MPa steel and fiber volumetric contents Vf of 0.5 and 0.76%. A new definition is introduced for "significantly wide cracks" that yields a unique definition of the CLL when this phenomenon diminishes. Moreover, it is now proposed to change the definition of CLL. The study identified the existence of a transition point (TP), beyond which addition of fibers to the concrete mix do not affect CLL anymore. Observations from the experimental results prove the consistency of the newly proposed CLL definitions as well as the dependency of CL on both the amount and stress hardening of the tension steel. Their use enables a clear delineation of the CL phenomenon in R/SFRC beams. The importance of this finding refers to the reported decrease of flexural ductility in R/SFRC beams due to high CLL. Hence, the importance of the ability, achieved in the current findings, to quantify the conditions for TPs in various cases. [ABSTRACT FROM AUTHOR]

This paper describes an experimental program, which investigates the validity of using Expression 7.21 in Eurocode 2 for calculating shrinkage curvatures of loaded reinforced concrete beams cracked in flexure, this Expression having previously been validated for use with uncracked sections but not for cracked sections. The experimental method used a heating technique, which exploited the differing coefficients of expansion of limestone concrete and stainless steel reinforcement to impose simulated shrinkage strains on a range of rectangular beams of various sizes and reinforcement percentages. The results indicate that Expression 7.21 is valid for use with sections cracked in flexure but may overestimate curvatures by significant amounts. It is shown that improved estimates of curvature are given by using Expression 7.18 in conjunction with Expression 7.21 with the best results being obtained by setting β = 0.3 or by using an adjusted value for the cracking moment (Mcr), as detailed in the paper. [ABSTRACT FROM AUTHOR]

The bending performance of polypropylene fiber reinforced engineered cementitious composite (PP‐ECC) beams was studied. A total of five reinforced concrete (RC) beams were prepared and tested. The test variables include matrix type, longitudinal reinforcement diameter, and longitudinal reinforcement ratio. The study found that ECC is an ideal building material to improve the bending performance of RC beams. For the failure mode, even if the ultimate load is reached, no local cracks are observed in the ECC beam. On the contrary, due to the high ductility of the ECC material, multiple microcracks appear in the tension zone of the beam. From the perspective of bending performance, the use of ECC materials as the matrix of RC beams can not only increase the cracking load, yield load, and ultimate load of RC beams but also increase its ductility and energy absorption capacity. A method for predicting the flexural bearing capacity of ECC beams considering the effect of fiber tensile stress is proposed. The experimental data in this study are compared with the experimental data in the previous literature, and the prediction results of this model and other previous models are obtained. The average ratio of the predicted value of the flexural bearing capacity of the RC beam to the experimental value is 0.979, and the coefficient of variation is 0.016. [ABSTRACT FROM AUTHOR]

Concrete tensile stresses influence the cracking behaviour and the stiffness of reinforced concrete (RC) members. Most design codes account for this tension stiffening effect using an effective reinforcement ratio. Although this ratio has a significant influence on the design of RC structures, its quantification is controversial in many cases, and typically relies on empirical geometry‐based expressions. One main reason for this knowledge gap is that the area of concrete in tension can only be verified indirectly, for example, through crack widths and spacings and using a suitable mechanical model. This indirect validation is subject to considerable uncertainty as it depends on parameters that scatter (e.g., bond stresses and the concrete tensile strength), and further assumptions relating internal stresses to the applied loads are required. This article outlines how refined measurements of the reinforcing steel strains and the concrete deformations in the compression zone, combining distributed fibre optic sensing (DFOS) and digital image correlation (DIC), can be used in order to obtain a more reliable quantification of the parameters affecting tension stiffening and hence, the effective reinforcement ratio. Selected models are validated against experimental data of an RC beam tested under four‐point bending, underlining the potential of DFOS and DIC as valuable tools for a better understanding of RC structures and the enhancement of mechanical models. [ABSTRACT FROM AUTHOR]

The shear crack width, crack behavior, and crack development of 24 reinforced concrete beams have been experimentally investigated. All the beams reinforced with longitudinal reinforcement and hooked‐end steel fibers in place of transverse reinforcement. Hooked‐end steel fibers 35 and 60 mm long are used at volume fractions ranging from 0.75% to 1.5% in the first case, and from 0.5% to 1% in the latter case. For extending the scope of the investigation, two types of concrete matrices (normal‐strength of 25 MPa and medium‐strength of 45 MPa) have been investigated. A simple mechanics‐based mathematical model is developed by determining the strains in the transverse direction of shear cracks and the average horizontal spacing between the shear cracks. The accuracy of the model has been confirmed with the experimental results and conservative predictions have been observed with mean, SD, and coefficient of variation as 0.99, 0.19, and 18.96, respectively. Based on detailed mathematical and experimental investigation, the minimum approximately observed shear crack width has value of 0.4 mm for all SFRC beams therefore the allowable shear crack width of 0.4 mm, for steel fiber reinforced concrete has been recommended. [ABSTRACT FROM AUTHOR]

Modeling and assessing the load‐carrying capacity of reinforced concrete (RC) structures that are cracked is important because the condition of an RC structure changes due to natural aging and accumulated damage. The current approach to determining the residual capacity of a cracked RC structure is time‐consuming and error‐prone due to a limited capacity to obtain and process structural information. In this study, an automated approach was proposed to determining residual capacity by performing finite element (FE) analysis of an RC structure using point cloud three dimensional modeling. Two simply supported RC beams were subjected to bending tests to provide validation data. The initial activity was to extract dimensional data from laser‐scanned point cloud data of a beam. The information obtained was used to automatically generate nonlinear FE models of the beam that was used for nonlinear FE analyses in Abaqus. An initial crack was added to the beam to model a cracked beam in real conditions. Three different models were used to simulate initial cracks, a weakened element model, a cohesive zone model, and an extended FE model. The results indicate that the proposed method of automating the combination of point cloud data with nonlinear FE analysis provides a novel practical approach to modeling and assessing cracked RC beams. [ABSTRACT FROM AUTHOR]

The Cohesive/Overlapping Crack Model is able to describe the transition between cracking and crushing failures occurring in reinforced concrete beams by increasing beam depth and/or steel percentage. Within this Nonlinear Fracture Mechanics model, the tensile and compressive ultimate behaviors of the concrete matrix are modeled through two different process zones that advance independently one of another. Moreover, this model is able to investigate local mechanical instabilities occurring in the structural behavior of reinforced concrete structures: tensile snap‐back and snap‐through, which are due to concrete cracking or steel fracture, and the compressive snap‐back occurring at the end of the plastic plateau, which is generated by the unstable growth of the crushing zone. In this context, the application of the Cohesive/Overlapping Crack Model highlights that the ductility, which is represented by the plastic rotation capacity of a reinforced concrete element subjected to bending, decreases as reinforcement percentage and/or beam depth increase. Thus, a scale‐dependent maximum reinforcement percentage beyond which concrete crushing occurs prior to steel yielding is demonstrated to exist. In particular, the maximum steel percentage results to be inversely proportional to h0.25, h being the beam depth. In this way, a rational and quantitative definition of over‐reinforcement is provided as a steel percentage depending on the beam depth. [ABSTRACT FROM AUTHOR]

Crack spacing has been identified as an important parameter in predicting the crack widths in reinforced concrete (RC) structures. An experimental program has been conducted to investigate the crack spacings when reinforced concrete beams are subjected to both axial tension and flexure. The stochastic nature of cracking behavior makes the experimental program complicated. A large sample size of the crack spacing data was recorded, in order to give a statistical overview. Recent studies in the literature were used to verify the experimental results. The existing crack spacing prediction models have been developed based on different theoretical approaches, namely bond‐slip, no‐slip, and combined approaches. In this study, Eurocode 2, Model Code 2010, Japanese Code, Eurocode 2 with German Annex and Beeby's crack spacing models were selected, as they represent each theoretical approach. Experimental results of this study and from selected literature were compared with the aforementioned prediction models. Japanese Code gave better predictions for axial tensile tests. For the four‐point bending test, all the calculation models gave good agreement with the results, except for Eurocode 2 with German Annex. [ABSTRACT FROM AUTHOR]

The use of fibers in reinforced concrete (RC) beams mainly improves both the bearing capacity and the cracking control. In this way, positive effects on the service life of RC structures can be expected. In this paper, the fiber influence on the flexural behavior of RC beams with different longitudinal reinforcement ratios (0.5% ≤ ρs ≤ 1.2%) is analyzed by testing small‐scale RC beams. Concretes incorporating 0, 25 and 50 kg/m3 of steel, 6 and 12 kg/m3 of glass macrofibers, and 5 and 10 kg/m3 of polymer macrofibers were studied. Crack and deflection control, as well as bearing capacity and crack localization were evaluated for a broad range of fiber‐reinforced concrete (FRC) toughness. It is verified that fibers, in the longitudinal reinforcement ratio considered, improve the bending behavior at serviceability limit state (SLS) and ultimate limit state (ULS) of RC beams, without limiting the structure ductility. It was also confirmed the philosophy of the fib Model Code 2010, such that FRC can be considered as a composite material where performance parameters govern its mechanical behavior. Finally, the several data available allowed to deeply analyze fib Model Code 2010 formulations (mean crack spacing and flexural bearing capacity) and to propose modifications where needed. [ABSTRACT FROM AUTHOR]

For this purpose, a database of experimental crack widths for load-induced flexural cracking was compiled from reputable sources to obtain the measured maximum crack widths, I w i SB exp sb . Design crack width predictions were obtained for each of the three crack models as a best estimate of the predicted maximum crack widths, using the geometric and material properties from the experimental data. The predicted maximum crack width corresponds to a 5% probability of exceedance[3] by design code formulations, which may not probabilistically match the measured maximum crack width, thus contributing to model uncertainty. [Extracted from the article]

The size effect of Muttoni et al.'s critical shear crack theory (CSCT) is shown to be quite close (with differences up to 15%) and asymptotically identical to the energetic size effect law (SEL), which has been extensively verified experimentally and theoretically (and is adopted for the 2019 ACI Code, Standard 318, for both beam shear and punching). However, the CSCT derivation and calculation procedure obfuscates the mechanics of failure. It is shown to rest on six scientifically untenable hypotheses, which would have to be taught to students as an article of faith. They make CSCT untrustworthy outside the testing range; ditto for beams with T, I and box cross section, or for continuous beams. The present conclusions are supported by experimentally calibrated finite element simulations of crack path and width, of stress distributions and localizations during failure, and of strain energy release. The simulations also show the CSCT to be incompatible with the "strut‐and‐tie" model, which is (for 2019 ACI Code) modernized to include the size effect in the compression strut. Finally, further deficiencies are pointed out for the Modified Compression Field Theory (MCFT), currently embedded in the Model Code. [ABSTRACT FROM AUTHOR]

The dual potential capacity model (DPCM) was proposed in this study to evaluate the shear strengths of short and deep reinforced concrete (RC) members with the shear span‐to‐depth ratios less than 2.5. In the proposed model, the nonlinear flexural analysis considering the bond mechanism between steel reinforcements and surrounding concrete was conducted to estimate the local stress increase in the steel reinforcements between flexural cracks, and the shear demand force of the cracked tension zone in an RC section can also be determined on this basis. The crack concentration factor was introduced to consider the size effect in estimation of the potential shear capacity corresponding to the shear demand force to be resisted by the cracked tension zone. For the compression zone, different plasticity models were adopted depending on the shear span‐to‐depth ratio to estimate the potential shear capacity of the intact compression zone. For the verification of the proposed model, a total of 466 test results of RC short and deep beams with various shear span‐to‐depth ratios less than 2.5 were collected from existing literature, and accuracy of the proposed model was verified in detail by comparing the shear strengths of the RC short and deep test specimens estimated from the proposed DPCM with those of the test results. [ABSTRACT FROM AUTHOR]

A design approach based on the simplified modified compression field theory, but with the advantage of not requiring an iterative procedure, is proposed for evaluating the shear capacity of beams without including shear reinforcement. This model is capable of simulating beams flexurally reinforced with steel and fiber reinforced polymer (FRP) systems. To appraise the predictive performance of the proposed model, a database (DB) composed of 215 reinforced concrete beams without shear reinforcement is set. By applying the model to this DB, an average value for Vexp./Vana. of 1.05 with a COV of 24% is obtained, where Vexp. and Vana. are the shear capacity registered experimentally and obtained with the model, respectively. By applying the approach proposed by ACI Building Code to the DB, average and COV values of 0.91 and 42% are determined, revealing the higher predictive performance of the proposed model. This was even higher in the beams flexurally reinforced with FRP systems, since the proposed model conducted to average and the COV values of 1.0 and 22%, while 0.76 and 32% were obtained with the ACI approach. When proposed model was applied to the beams tested in the experimental program carried out, an average and COV values of 1.02 and 5.23% were determined. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the shear failure mechanisms in beams exclusively reinforced with longitudinal glass fiber reinforced polymer bars and to propose a design‐based approach to predict the shear capacity of this type of beams. An experimental program composed of seven T cross section shaped concrete beams was executed to analyze the influence of the flexural reinforcement configuration on the shear capacity and deformability of the beams. Three values of the flexural reinforcement ratio ( ρl), 1%, 1.4%, and 1.80% were adopted. Digital image correlation technique was used to better capture and analyze the cracking process up to the formation of the shear failure crack. Test results indicated that the shear capacity was not dependent of ρl up to a limit of around 1.4%, but a tendency of the shear capacity to increase with ρl was registered above this limit due to a more pronounced favorable contribution of aggregate interlock and dowel effect. [ABSTRACT FROM AUTHOR]

The development of a nonlinear numerical computational model for the detailed description of destructive tests generally requires a multiple‐stage, strategic model updating procedure. In this contribution, a model updating procedure is applied to the simulation of prestressed reinforced concrete (RC) beams. The combined ultimate shear and flexure capacity of the beams is affected by many complex phenomena, such as the multi‐axial state of stress, the anisotropy induced by diagonal concrete cracking, the interaction between concrete and reinforcement (bond), and the brittleness of the failure mode. In this research, a series of material, small‐scale component fracture tests were carried out by two collaborating laboratories. These tests provided advanced statistical identification of the fracture‐mechanical parameters of the optimized concrete mixtures for the prestressed laboratory‐tested beams mentioned above (with a span of 5.00 m) and associated field‐tested, long‐span concrete TT roof elements (with a span of 30.00 m). Ten scaled laboratory‐tested beams with heights of 0.30, 0.45, and 0.60 m were used in a procedure for the comprehensive updating of the nonlinear numerical model with respect to shear resistance performance. The objectives of this research are, in addition to the analysis, the effective development of an updating process for nonlinear numerical modeling which is based on the information from different monitoring systems. Hence, this contribution focuses on the presentation of a comprehensive updating procedure for the shear capacity of nonlinear numerical models of prestressed beam elements using information about fracture‐mechanical material parameters gained from (a) different monitoring systems and (b) code‐based methods. [ABSTRACT FROM AUTHOR]

Authors' closure on the discussion of the article: "Assessing the influence of fibers on the flexural behavior of reinforced concrete beams with different longitudinal reinforcement ratios" (discussion by Marki'c et al.) The authors would like to thank the discussers for their interest and for opening a discussion on the ductility of RC elements with fibers, which is a very important topic. This possible negative influence is related to both longitudinal reinforcement (type and ratio) and the weighted ratio between the post-cracking performances of fiber reinforced concrete (FRC) and reinforcement strength properties. [Extracted from the article]

This article describes an experimental programme aimed at studying the effect of cover, ratio between diameter and effective reinforcement ratio (ϕ/ρs, ef) and the influence of stirrup spacing on the cracking behaviour of reinforced concrete elements. The experimental programme was conceived in order to contribute to the debate - fuelled by the publication in recent years of Eurocode 2 EN1992-1-1 and the revision of the Model Code under way when the tests were carried out (and now published as a finalized document) - regarding the influence of these parameters on cracking. Important theoretical aspects are discussed, including where the crack width is estimated by current code formulations and what relevance this may have on the correlation between crack opening and durability of RC structures, especially with regard to structures with large covers. The effect of stirrup spacing, a variable absent from current codes, is also discussed. [ABSTRACT FROM AUTHOR]