Deflection behaviour of FRP reinforced concrete beams and slabs: An experimental investigation

The flexural response of FRP RC elements is investigated through load–deflection tests on 24 RC beams and slabs with glass FRP (GFRP) and carbon FRP (CFRP) reinforcement covering a wide range of reinforcement ratios. Rebar and concrete strains around a crack inducer are used to establish moment–curvature relationships and evaluate the shear and flexural components of mid-span deflections. It is concluded that the contribution of shear and bond induced deformations can be of major significance in FRP RC elements having moderate to high reinforcement ratios. Existing equations to calculate short-term deflection of FRP RC elements are discussed and compared to experimental values.     

Deflections of concrete beams reinforced with FRP bars

The aim of this study is to experimentally and theoretically investigate the flexural behavior of concrete beams reinforced with fiber reinforced polymer (FRP) bars. In this research, three types of experiments were made. First, the tensile properties of FRP and steel bars were tested, then the bond-slip behavior between bars and concrete was tested on standard specimens and, in the end, three series of concrete beams reinforced with GFRP, CFRP and steel bars were tested up to failure. The theoretical model for calculating deflections was developed, which included bond-slip behavior of FRP bars. The theoretical results were compared to the test results of beam deflections, as well to deflection results obtained by theoretical models developed by other authors.     

Flexural performance of FRP reinforced concrete beams

A numerical method for estimating the curvature, deflection and moment capacity of FRP reinforced concrete beams is developed. Force equilibrium and strain compatibility equations for a beam section divided into a number of segments are numerically solved due to the non-linear behaviour of concrete. The deflection is then obtained from the flexural rigidity at mid-span section using the deflection formula for various load cases. A proposed modification to the mid-span flexural rigidity is also introduced to account for the experimentally observed wide cracks over the intermediate support of continuous FRP reinforced concrete beams.     

Sensitivity analysis of reinforced concrete beams strengthened with FRP laminates

Numerical procedures are proposed to predict the failure of reinforced concrete (RC) beams strengthened in flexure with fiber-reinforced polymeric (FRP) laminates. The framework of damage mechanics was used during the modeling. Numerical results were validated against experimental data obtained from 19 beams strengthened with different types of FRP. These beams failed by concrete crushing, cover failure and plate debonding. The numerical models were capable of predicting the experimentally observed load–deflection, failure load and failure modes. The sensitivity of the numerical results was studied. In particular, the effect of the concrete constitutive behavior and different modeling considerations was evaluated. It was found that the fracture energy of the concrete–repair interface plays a central part in predicting plate-debonding failures.     

Viscoelastic analysis of FRP strengthened reinforced concrete beams

External bonding of FRP plates or sheets has become a popular method for strengthening reinforced concrete structures. Stresses along the FRP-concrete interface are critical to the effectiveness of this technique because high stress concentration along the FRP-concrete interface can lead to the FRP debonding from the concrete beam. Although the short-term stress distribution along the FRP-concrete interface has been studied extensively, very few studies have been conducted on the long-term stress distribution, which closely simulates the behavior of the structure during the service-life. In this study, we develop a viscoelastic solution for the long-term interface stress distribution in a FRP plate strengthened reinforced concrete beam. In this solution, the RC beam and the FRP plate are modeled as elastic materials; while the adhesive layer is modeled as a viscoelastic material using the Standard Linear Solid model. Closed-form expressions of the interface stresses and deflection of the beam are obtained using Laplace transform and calculated using the Zakian’s numerical method. The validation of this viscoelastic solution is verified by finite element analysis using a subroutine UMAT based on the Standard Linear Solid model.     

Shear design of reinforced concrete beams with FRP longitudinal and transverse reinforcement

The shear resisting mechanisms of reinforced concrete (RC) beams with longitudinal and transverse FRP reinforcement can be affected by the mechanical properties of the FRP rebars. This paper presents a mechanical model for the prediction of the shear strength of FRP RC beams that takes into account its particularities. The model assumes that the shear force is taken by the un-cracked concrete chord, by the residual tensile stresses along the crack length and by the FRP stirrups. Failure is considered to occur when the principal tensile stress at the concrete chord reaches the concrete tensile strength, assuming that the contribution of the FRP stirrups is limited by a possible brittle failure in the bent zone. The accuracy of the proposed method has been verified by comparing the model predictions with the results of 112 tests. The application of the model provides better statistical results (mean value V_test/V_pred equal to 1.08 and COV of 19.5%) than those obtained using the design equations of other current models or guidelines. Due to the simplicity, accuracy and mechanical derivation of the model it results suitable for design and verification in engineering practice.     

Slip effects in reinforced concrete beams with mechanically fastened FRP strip

This investigation concerns the flexural behavior of reinforced concrete (RC) beams strengthened with a mechanically fastened pultruded FRP strip (MF-FRP beams). Twelve small size MF-FRP beams and two control RC beams were tested under flexural loading. The main failure mode observed in this experimental program was nail rotation and bearing damage under increasing flexural load, which resulted in FRP slip with respect to the soffit of the RC-beam and loss of stress transfer. Strain gage data and visual observations obtained during the experiments provided useful insight for developing a new procedure for estimating the nominal moment capacity of the MF-FRP beams. The proposed method is guided by experimental evidence pointing to the significance of nail rotation associated with flexural cracking in RC beams. The developed procedure, based on a “strain reduction factor” of 24%, is able to estimate the nominal moment capacity of the MF-FRP beams with good accuracy.     

Shear enhancement of reinforced concrete beams strengthened with FRP composite laminates

This paper presents the results of an experimental investigation on shear strength enhancement of reinforced concrete beams externally reinforced with fiber-reinforced polymer (FRP) composites. A total of nine full-scale beam specimens of three different classes, as-built (unstrengthened), repaired and retrofitted were tested in the experimental evaluation program. Three composite systems namely carbon/epoxy wet layup, E-glass/epoxy wet layup and carbon/epoxy precured strips were used for retrofit and repair evaluation. Experimental results indicated that the composite systems provided substantial increase in ultimate strength of repaired and strengthened beams as compared to the pre-cracked and as-built beam specimens. A comparative study of the experimental results with published analytical models, including the ACI 440 model, was also conducted in order to evaluate the different analytical models and identify the influencing factors on the shear behavior of FRP strengthened reinforced concrete beams. Comparison indicated that the shear span-to-depth ratio (a/d) is an important factor that actively controls the shear failure mode of beam and consequently influences on the shear strength enhancement.     

Comparison between FRP and steel plating of reinforced concrete beams

Very advanced design rules have already been developed for adhesive bonding steel plates to reinforced concrete beams in order to prevent premature debonding by either shear peeling or flexural peeling. The aim of this study is to determine experimentally whether these design rules that were developed for steel plated beams and slabs, can be applied to fiber reinforced plastic (FRP) plated beams. This paper compares, with the help of test results, the shear and flexural debonding mechanisms of steel and FRP plated beams.     

Flexural analysis and design of reinforced concrete beams with externally bonded FRP reinforcement

This work addresses the flexural analysis of reinforced concrete beams with externally bonded FRP (Fibre Reinforced Polymer) reinforcement. A numerical method has been developed for the computation of the bending moment capacity of FRP-plated reinforced concrete beams and prediction of the flexural failure modes. The expressions for the upper and lower values of the characteristic plate reinforcement ratios are derived for rectangular and T-sections using the Eurocode 2 model for concrete. A flow-chart of the numerical procedure, suitable for computer implementation, is included and its accuracy is validated with available experimental results. Some of the novel features of the numerical analysis are demonstrated through a brief investigation of the effects of loads acting at the stage of strengthening on the ultimate flexural capacity and deformation behaviour of FRP-plated R.C. beams.

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Résumé Ce travail analyse le comportement en flexion de poutres en béton armé avec renforcement extérieur par PRF (polymères renforcés de fibres). Une méthode numérique a été développée pour le calcul de la capacité du moment de flexion de poutres en béton renforcé de plaques en PRF, et pour la prévision des modes de défaillance en flexion. Des expressions pour les valeurs supérieures et inférieures des rapports caractéristiques de ce renforcement ont été dérivées pour une section rectangulaire et des sections en T en utilisant le modèle d'Eurocode 2 pour le béton. Un organigramme du procédé numérique, approprié à l'exécution numérique, est inclus et son exactitude est validée par les résultats expérimentaux disponibles. Certaines des caractéristiques originales de l'analyse numérique ont été démontrées par la brève recherche sur les effets du chargement précédemment appliqué sur la capacité en flexion finale et les déformations des poutres en béton armé renforcés de plaques en PRF.

     

Modelling of mixed mode debonding in externally FRP reinforced beams

In this paper a refined model able to analyze edge debonding problems in beams strengthened with externally bonded composite laminated plates, is presented. The structural system is viewed as composed by three physical different components: the base beam (made of steel or concrete), the adhesive layer and the bonded plate. Each component may be comprised by one or several mathematical layers which adopts the first-order shear deformation laminate theory. Bonding and continuity conditions between different layers are simulated by using the interface modelling technique. Strong and collapsed interface models are introduced in order to capture stress singularities and to reduce the complexity of the analysis, respectively. Governing equations for displacement fields complemented with boundary and continuity conditions, are obtained by a variational approach. According to a fracture mechanics approach, the analysis is carried out by evaluating the total and individual mode components of energy release rate (ERR).Applications for typical strengthened systems, carried out by numerical integration procedures, are proposed in which the energy release rates are evaluated by means of interface displacement jumps, leading to a very efficient numerical procedure. The approximations introduced in the model with respect to the adopted number of mathematical layers are analyzed and comparisons with existent models are given. For the simpler two-layer model of the structure, comparisons are given with the closed-form solutions obtained in [Greco F, Nevone Blasi P, Lonetti P. An analytical investigation of debonding problems in beams strengthened using composite plates. Eng Fract Mech 2006, in press]. The convergence to the results from continuum analysis is investigated when a refined assembly of layers is adopted, by means of comparisons with predictions from very careful FE solutions. Finally, the effect of different debonding modes on the overall behaviour of the structural system is analyzed. These results show the capability and the accuracy of the proposed approach to predict debonding failure behaviour in both steel and concrete strengthened beams. As a matter of fact, the proposed approach involves reduced computational cost with respect to FE solutions based on 2D continuum elements and the use of a multi-layer structural model leads to avoid some complexities related to the classical elasticity theory for bimaterial interface cracks.     

FRP增强重组竹梁受弯性能数值模拟

通过有限元软件ABAQUS对纤维增强聚合物基复合材料（FRP）增强重组竹梁受弯性能进行了分析,有限元模拟结果与试验结果相一致,两者荷载-位移曲线相吻合,跨中截面应变发展过程基本一致,70 kN荷载时,截面应变误差在13.96%内,承载力预测具有很好的精度,预测最大误差为9.04%,FRP的增强使竹梁截面的应力重新分布,受压区竹材得到更加充分的利用;进一步参数化分析了截面宽高比、FRP层数、FRP种类对FRP增强重组竹梁受弯性能的影响。发现:FRP层数的增加对重组竹梁极限承载力和截面刚度提升作用显著;相同层数、相同种类FRP增强重组竹梁时,截面高度减小,极限承载力和截面刚度提高幅度增加;相同截面宽高比和FRP层数时,碳纤维增强聚合物基复合材料（CFRP）增强效果优于玄武岩纤维增强聚合物基复合材料（BFRP）增强效果。      

Performance of reinforced concrete beams strengthened by hybrid FRP laminates

In the last two decades, the use of advanced composite materials such as Fiber Reinforced Polymers (FRP) in strengthening reinforced concrete (RC) structural elements has been increasing. Research and design guidelines concluded that externally bonded FRP could increase the capacity of RC elements efficiently. However, the linear stress–strain characteristics of FRP up to failure and lack of yield plateau have a negative impact on the overall ductility of the strengthened RC elements. Use of hybrid FRP laminates, which consist of a combination of either carbon and glass fibers, or glass and aramid fibers, changes the behaviour of the material to a non-linear behaviour. This paper aims to study the performance of reinforced concrete beams strengthened by hybrid FRP laminates.

This paper presents an experimental program conducted to study the behaviour of RC beams strengthened with hybrid fiber reinforced polymer (HFRP) laminates. The program consists of a total of twelve T-beams with overall dimensions equal to 460 × 300 × 3250 mm. The beams were tested under cyclic loading up to failure to examine its flexural behaviour. Different reinforcement ratios, fiber directions, locations and combinations of carbon fiber reinforced polymer (CFRP) and glass fiber reinforced polymer (GFRP) laminates were attached to the beams to determine the best strengthening scheme. Different percentages of steel reinforcement were also used. An analytical model based on the stress–strain characteristics of concrete, steel and FRP was adopted. Recommendations and design guidelines of RC beams strengthened by FRP and HFRP laminates are introduced.     

Behavior of full-scale reinforced concrete beams retrofitted for shear and flexural with FRP laminates

Four full-scale reinforced concrete beams were replicated from an existing bridge. The original beams were substantially deficient in shear strength, particularly for projected increase of traffic loads. Of the four replicate beams, one served as a control and the remaining three were implemented with varying configurations of carbon fiber reinforced polymers (CFRP) and glass FRP (GFRP) composites to simulate the retrofit of the existing structure. CFRP unidirectional sheets were placed to increase flexural capacity and GFRP unidirectional sheets were utilized to mitigate shear failure. Four-point bending tests were conducted. Load, deflection and strain data were collected. Fiber optic gauges were utilized in high flexural and shear regions and conventional resistive gauges were placed in eighteen locations to provide behavioral understanding of the composite material strengthening. Fiber optic readings were compared to conventional gauges.Results from this study show that the use of fiber reinforced polymers (FRP) composites for structural strengthening provides significant static capacity increases approximately 150% when compared to unstrengthened sections. Load at first crack and post cracking stiffness of all beams was increased primarily due to flexural CFRP. Test results suggest that beams retrofit with both the designed GFRP and CFRP should well exceed the static demand of 658 kN m sustaining up to 868 kN m applied moment. The addition of GFRP alone for shear was sufficient to offset the lack of steel stirrups and allow conventional RC beam failure by yielding of the tension steel. This allowed ultimate deflections to be 200% higher than the pre-existing shear deficient beam. If bridge beams were retrofit with only the designed CFRP failure would still result from diagonal tension cracks, albeit at a 31% greater load. Beams retrofit with only the designed shear GFRP would fail in flexure at the mid-span at an equivalent 31% gain over the control specimen, failing mechanism in this case being yielding of the tension steel. Successful monitoring of strain using fiber optics was achieved. However, careful planning tempered by engineering judgement is necessary as the location and gauge length of the fiber optic gauge will determine the usefulness of the collected data.     

Revisiting the shear design equations for concrete beams reinforced with FRP rebar and stirrup

Current design guidelines and codes use modified shear equations for calculating the shear strength contribution of fiber reinforced polymer (FRP) transverse reinforcement (stirrup) in concrete beams reinforced with longitudinal steel or FRP rebar. These equations, originally developed for steel as longitudinal and transverse reinforcement, are semi-empirical in nature and were developed with a core analytical equation where the coefficients were determined from regression analysis. Here, a comparative study among various code equations was conducted to predict the shear strength of FRP reinforced concrete beams. To facilitate this comparison a database was established from the published literature, which was composed of slender concrete beams (shear span to depth ratio, a/d >2.5) with FRP longitudinal and transverse reinforcement. The database contained 114 beams without transverse reinforcement and 46 beams with transverse reinforcement. The guidelines, codes and models that were implemented and compared in this study consisted of ACI 440.1R-06, JSCE 1997, CNR-DT 203, CSA S806-02, CSA S6-06, unpublished CSA S6-06 Addendum, ISIS-M03-01, simplified Modified Compression Field Theory, cracked section analysis model and modified Zsutty equations. It was observed from the statistical analysis that the CSA S806-02 produced greater coefficients of variation than the CSA S6-09. The ACI 440.1R-06 and JSCE 1997 produced more conservative results in calculating the transverse shear strength. The CSA S6-09 Addendum exhibited the best all-around performance in predicting the shear contribution of FRP reinforced beams compared to that of other design codes and guidelines.     

A design model for fibre reinforced concrete beams pre-stressed with steel and FRP bars

This paper presents a design oriented model to determine the moment–curvature relationship of elements of rectangular cross section failing in bending, made by strain softening or strain hardening fibre reinforced concrete (FRC) and reinforced with perfectly bonded pre-stressed steel and fibre reinforced polymeric (FRP) bars. Since FRP bars are not affected by corrosion, they have the minimum FRC cover thickness that guaranty proper bond conditions, while steel bars are positioned with a thicker FRC cover to increase their protection against corrosion. Using the moment–curvature relationship predicted by the model in an algorithm based on the virtual work method, a numerical strategy is adopted to evaluate the load–deflection response of statically determinate beams. The predictive performance of the proposed formulation is assessed by simulating the response of available experimental results. By using this model, a parametric study is carried out in order to evaluate the influence of the main parameters that characterize the post cracking behaviour of FRC, and the pre-stress level applied to FRP and steel bars, on the moment–curvature and load–deflection responses of this type of structural elements. Finally the shear resistance of this structural system is predicted.     

Genetic algorithm model for shear capacity of RC beams reinforced with externally bonded FRP

A variety of on-site construction applications using FRP materials have been realized worldwide. However, this technology is currently at a stage where its future widespread implementation and competitiveness will depend on the development of reliable design guidelines based on sound engineering principles. This paper presents simple, yet improved, equations to calculate the shear capacity of FRP bonded-reinforced concrete beams based on the genetic algorithms (GAs) approach applied to 212 experimental data points available in the open literature. The performance of the proposed equations was compared to that of commonly used shear design methods, namely the ACI 440, Eurocode (EC2), the Matthys Model, Colotti model and the ISIS Canada guidelines. Results demonstrate that the proposed equations better agree with the available experimental data than the existing models investigated. Moreover, a sensitivity analysis was carried out to investigate the effect of the shear span-to-depth ratio on the shear capacity contributed by concrete, the ultimate effective strain in FRP sheets, and the ultimate effective stress in transverse rebars. Results indicate that the shear span-to-depth ratio has a significant effect on the shear behaviour of FRP bonded-reinforced concrete beams.     

Crack width evaluation in FRP reinforced concrete members

This study proposes a model for calculating the average width of cracks in reinforced concrete (RC) elements using non metallic reinforcement bars (FRP). This model has already been applied to the case of steel reinforcing bars successfully. It considers the influence of the percentage of reinforcement and the concrete strength. It emphasizes how the mechanical features of FRP (fiber reinforced polymer) bars, and particularly their modulus of elasticity, can affect the crack width. The model is validated with experimental results available in the literature. An example of its application for the calculation of the crack width is shown.

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Résumé  Cet article présente l'application d'un modèle de prévision de l'amplitude des fissures en présence d'armatures non métalliques et de classes de résistance du béton allant de 30 à 80 MPa. L'analyse théorique est utilisée pour interpréter les résultats d'essais expérimentaux sur des traverses en béton armé contenant des polymères renforcés de fibres (FRP) soumises à des forces de traction. Le but de cette recherche était d'étudier et de prévoir la largeur des fissures, en utilisant comme paramètres de base la contrainte dans l'acier et la distance moyenne entre les fissures. La recherche décrit aussi l'amplitude des fissures, pour la même traverse, en présence d'armatures en acier et en polymères renforcés de fibres (FRP).

     

Strengthening RC beams with composite fiber cement plate reinforced by prestressed FRP rods: Experimental and numerical analysis

This paper deals with the development of a new strengthening system for reinforced concrete beams with externally-bonded plate made of composite fiber cement reinforced by rebars made of fiber-reinforced plastic (FRP) [1]. The proposed strengthening material involves the preloading of FRP rod before mortar casting. The paper presents experimental and numerical analysis carried out on many large-scale beams strengthened by well-known reinforcement techniques, such as externally bonded Carbon Fiber-Reinforced Plastic (CFRP) plate and the Near Surface Mounted (NSM) technique, which are compared to the proposed new strengthening material through four-point bending tests. Results are analyzed with regard to the load-displacement curve, bending stiffness, cracking load, yield strength and failure load. The developed numerical model is in agreement with the experimental results. It clearly shows the effects of prestressed FRP rod on cracking mechanisms and internal strength distribution in the analyzed beams.     

Guidelines for flexural resistance of FRP reinforced concrete slabs and beams in fire

Several building codes are currently available for the design of concrete structures reinforced with fiber-reinforced polymer (FRP) bars. Nevertheless, there is little information provided about structural behavior in case of fire and no reliable design methods are available for FRP reinforced concrete (RC) members in fire. The goal of this paper is to provide guidelines for the calculation of the resistant bending moment of FRP-RC members exposed to fire in compliance with the provisions of Eurocodes, based on studies recently carried out by the authors. The paper provides a conceptual approach to fire safety checks for bending moment resistance of FRP-RC members. With reference to thermo-mechanical analysis, a simplified design method (for both thermal and mechanical analyses) for sagging bending moment resistance of FRP-RC slabs in fire situations is finally suggested.