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.     

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.     

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.     

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.     

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.     

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.     

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).

     

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.     

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.     

Neutral axis depth and moment redistribution in FRP and steel reinforced concrete continuous beams

The neutral axis depth is considered the best parameter for quantifying the moment redistribution in continuous concrete beams, as exemplified in various design codes worldwide. It is therefore important to well understand the variation of neutral axis depth against moment redistribution. This paper describes a theoretical investigation into the neutral axis depth and moment redistribution in concrete beams reinforced with fibre reinforced polymer (FRP) and steel bars. A finite element model has been developed. The model predictions are in favourable agreement with experimental results. Three types of reinforcement are considered, namely, glass fibre, carbon fibre and steel. Various levels of reinforcement ratio are used for a parametric evaluation. The results indicate that FRP reinforced concrete continuous beams exhibit significantly different response characteristics regarding the moment redistribution and variation of neutral axis depth from those of steel reinforced ones. In addition, it is found that the code recommendations are generally unsafe for calculating the permissible moment redistribution in FRP reinforced concrete beams, but the neglect of redistribution in such beams may be overconservative.     

Effect of steel and synthetic fibers on flexural behavior of high-strength concrete beams reinforced with FRP bars

Six high-strength concrete beam specimens reinforced with fiber-reinforced polymer (FRP) bars were constructed and tested. Three of the beams were reinforced with carbon FRP (CFRP) bars and the other three beams were reinforced with glass FRP (GFRP) bars as flexural reinforcements. Steel fibers and polyolefin synthetic fibers were used as reinforcing discrete fibers. An investigation was performed on the influence of the addition of fibers on load-carrying capacity, cracking response, and ductility. In addition, the test results were compared with the predictions for the ultimate flexural moment. The addition of fibers increased the first-cracking load, ultimate flexural strength, and ductility, and also mitigated the large crack width of the FRP bar-reinforced concrete beams.     

Experimental investigation into flexural retrofitting of reinforced concrete bridge beams using FRP composites

End cover separation and shear crack debond are the two most critical debonding modes in beams retrofitted with fibre reinforced polymer composites due the brittle nature of the failures. However, these failures are still not fully understood. A testing program including 18 rectangular reinforced concrete beams is carried out to investigate the failure mechanisms and the influence of several parameters on these debond modes. Testing shows that end cover separation starts from FRP ends and fails in the form of shear failure at steel reinforcement level at the root of the concrete teeth between shear cracks. Shear crack debond failure is due to the opening of one of those inclined cracks. Several debond prediction models are then verified with the experiment proving to work relatively well.     

Comparison of numerical behaviors of FRP reinforced concrete beams using three smeared crack models

The numerical behaviors of fiber reinforced polymer (FRP) bar reinforced concrete beams using three non-linear finite element models are compared with the recorded data. First approach is based on strain decomposition into elastic and crack strain and is capable of simulating multiple non-orthogonal cracks. The remaining two approaches are based on the total strain crack model and include a rotating crack model (RCM) and an orthogonal fixed crack model (FCM). The analysis is carried out with the help of 2D-isoparametric plane-stress elements. Compression softening and tension stiffening effects of cracked concrete are considered. Tension reinforcement consists of either steel or FRP bars. The accuracy of the models has been discussed with reference to the authors?? tests as well as various studies reported in the literature. Both RCM and orthogonal FCM models showed good agreement with the recorded data which was also found consistent with every type of FRP bar.     

Analysis of plates reinforced with beams

 In this paper a solution to the problem of plates reinforced with beams is presented. The adopted model takes into account the resulting inplane forces and deformations of the plate as well as the axial forces and deformations of the beam, due to combined response of the system. The analysis consists in isolating the beams from the plate by sections parallel to the lower outer surface of the plate. The forces at the interface, which produce lateral deflection and inplane deformation to the plate and lateral deflection and axial deformation to the beam, are established using continuity conditions at the interface. The solution of the arising plate and beam problems which are nonlinearly coupled, is achieved using the analog equation method (AEM). The adopted model describes better the actual response of the plate–beams system and permits the evaluation of the shear forces at the interface, the knowledge of which is very important in the design of composite or prefabricated ribbed plates. The resulting deflections are considerably smaller than those obtained by other models. Received 21 April 1999     

A theoretical study on shear strengthening of reinforced concrete beams using composite plates

The present paper deals with shear strengthening of reinforced concrete beams by means of thin fiber-reinforced composite plates. First, the theoretical model is presented. It is then applied to the shear strengthening of a T-beam. This beam is also used to investigate the effects of some design parameters on the ultimate shear strength.     

Shakedown with softening in reinforced concrete beams

Critical softening parameters for first-formed highes at any location in a two-span beam are derived, and the relationship between positive load increments and softening parameter less than critical for midspan or interior support highes are also determined. The effect of non-critical softening on the well known static collapse and shakedown loads for an elastic-plastic beam is found. It is shown that the combined effect of softening and residual moments (such as caused by differential settlements) on the static collapse and shakedown loads may be dramatic.