Evaluation of Shear Design Equations of Concrete Beams with FRP Reinforcement

Several codes and design guidelines addressing fiber-reinforced polymer (FRP) bars as primary reinforcement for structural concrete have been recently published worldwide. This reflects the great progress in FRP research area that has been conducted by the research community over the past two decades. Most of these design provisions follow the traditional approach of Vc+Vs for shear design. Nevertheless, both equations of concrete contribution Vc and FRP stirrup contribution Vs to shear strength in these guidelines are different in the manner that they are calculated. In this paper, five methods for FRP shear design, currently used in design practice, were reviewed. These methods include the American Concrete Institute design guide, ACI 440.1R-06; the Canadian Standards Association, CAN/CSA-S806-02; the ISIS Canada design manual, ISIS-M03-07; the British Institution of Structural Engineers guidelines; and the design recommendations of the Japan Society of Civil Engineers. The five methods for shear design prescribed in these guidelines were compared with experimental database obtained from the literature. In addition, the modified compression field theory approach was reviewed and compared with the experimental database.     

Prestressed FRP Sheets for Poststrengthening Reinforced Concrete Beams

Four large-scale reinforced concrete beams were constructed and tested to investigate the effectiveness of external poststrengthening with prestressed fiber reinforced polymer (FRP) sheets. One of the beams served as a control specimen, another was strengthened with nonprestressed carbon FRP sheets, and the remaining two were strengthened with prestressed carbon FRP sheets. Presented is a method of prestressing multiple layers of the carbon fiber sheets during the application process and the experimental and analytical behavior of the beams under quasi-static loading. Comparisons are made between the control beam, the beam reinforced with nonprestressed carbon FRP sheets, and the beams strengthened with prestressed sheets. Serviceability and ultimate conditions are considered in the theoretical prediction of beam behavior, including the effects of multiple layer prestressing and external loading. The bonding of prestressed FRP sheets to the tensile face of concrete beams improved both the serviceability and the ultimate behavior of the reinforced concrete beams.     

Effect of Transverse Reinforcement on the Flexural Behavior of Continuous Concrete Beams Reinforced with FRP

Continuous concrete beams are structural elements commonly used in structures that might be exposed to extreme weather conditions and the application of deicing salts, such as bridge overpasses and parking garages. In such structures, reinforcing continuous concrete beams with the noncorrodible fiber-reinforced polymer (FRP) bars is beneficial to avoid steel corrosion. However, the linear-elastic behavior of FRP materials makes the ability of continuous beams to redistribute loads and moments questionable. A total of seven full-scale continuous concrete beams were tested to failure. Six beams were reinforced with glass fiber-reinforced polymer (GFRP) longitudinal bars, whereas one was reinforced with steel as control. The specimens have rectangular cross section of 200×300??mm and are continuous over two spans of 2,800?mm each. Both steel and GFRP stirrups were used as transverse reinforcement. The material, spacing, and amount of transverse reinforcement were the primary investigated parameters in this study. In addition, the experimental results were compared with the code equations to calculate the ultimate capacity. The experimental results showed that moment redistribution in FRP-reinforced continuous concrete beams is possible and is improved by increasing the amount of transverse reinforcement. Also, beams reinforced with GFRP stirrups illustrated similar performance compared with their steel-reinforced counterparts.     

Fracture Analysis of FRP Reinforced Concrete Beams

Carbon∕epoxy FRP (Fiber Reinforced Plastic) rebars were produced with the pultrusion technique. Concrete beams reinforced with these rebars were subjected to static and cyclic 3-point bending. Flexural cracking is arrested by an adequate bond between the FRP and the concrete because of the use of a carbon fiber overwrap on the otherwise smooth pultruded rods. In spite of the brittle nature of the FRP rods and the concrete, their combined behavior demonstrate ductility in excess of what is typically expected from reinforced concrete. An analytical evaluation of the fracture energy shows that such ductility is due to the large fraction of the total strain energy that is consumed in the formation of distributed cracking in concrete. Therefore, if an adequate bond can be provided, the strain-to-failure of the FRP determines the ductility and failure mode of FRP reinforced beams.     

Local Bond-Slip Relationship for FRP Reinforcement in Concrete

The objective of this paper is to define a rigorous numerical method to calibrate parameters of a given local bond-slip relationship using experimental results of pullout tests, taking into account the distribution of the slip and bond shear stress throughout the bar. The proposed method involves finding parameters of a given bond-slip relationship, such that results of pullout tests can be predicted in terms of applied pullout force and consequent slip at the loaded end and slip at the free end. The method is applied to some experimental data, and the results are discussed. For the application of the proposed method, two analytical expressions of the bond-slip relationship are selected, even though it could be applied to any analytical expression. An example of determination of anchorage length starting from the knowledge of the local bond-slip relationship is given.     

Development of FRP Reinforcement Guidelines for Prestressed Concrete Structures

Several national programs define the testing protocols and design guidelines for fiber reinforced polymer (FRP) reinforcement in concrete structures. This paper offers a review of these documents, comparing the materials testing and design philosophies for FRP reinforcement of different working groups. The work references Canadian, European, and Japanese efforts to codify these materials and assess the relative merits of each approach. The emphasis is on prestressing applications since the demands for sustained load capacity and full bond are more severe than for reinforced concrete.     

Numerical Modeling of FRP Shear-Strengthened Reinforced Concrete Beams

An attractive technique for the shear strengthening of reinforced concrete beams is to provide additional web reinforcement in the form of externally bonded fiber-reinforced polymer (FRP) sheets. So far, theoretical studies concerning the FRP shear strengthening of reinforced concrete members have been rather limited. Moreover, the numerical analyses presented to date have not effectively simulated the interfacial behavior between the bonded FRP and concrete. The analysis presented here aims to capture the three-dimensional and nonlinear behavior of the concrete, as well as accurately model the bond–slip interfacial behavior. The finite-element model is applied to various strengthening strategies; namely, beams with vertical and inclined side-bonded FRP sheets, U-wrap FRP strengthening configurations, as well as anchored FRP sheets. The proposed numerical analysis is validated against published experimental results. Comparisons between the numerical predictions and test results show excellent agreement. The finite-element model is also shown to be a valuable tool for gaining insight into phenomena (e.g., slip profiles, debonding trends, strain distributions) that are difficult to investigate in laboratory tests.     

New Approach for Estimating the Deflection of Beams Reinforced with FRP Reinforcement

Due to concerns with corrosion, the use of fiber-reinforced polymer (FRP) as a replacement to conventional steel reinforcement has greatly increased over the last decade. Researchers have identified the distinctive mechanical and bond properties of FRP reinforcement that prevent the use of existing relationships to establish serviceability of concrete structures reinforced with such products. Although studies have modified these empirical relationships to describe the behavior of structures reinforced with FRP reinforcement, this paper will provide a new approach to estimate deflection of concrete beams by considering material properties of the reinforcement and incorporating the effects of tension stiffening. Accuracy and precision of the approach was established by performing a statistical analysis on a database containing 171 FRP-reinforced concrete beams. Results were compared to those from existing proposed relationships and indicate the potential of the method to estimate deflection at various service conditions.     

Moment Redistribution in FRP and Steel-Plated Reinforced Concrete Beams

Research on retrofitting reinforced concrete (RC) beams and slabs using externally bonded (EB) fiber reinforced polymer (FRP) or steel plates has reached the stage where the flexural strength can be determined with confidence. Research has also shown that EB plated structures tend to debond at relatively low strains and to such an extent that guidelines often preclude moment redistribution which can severely restrict the use of plating. However, recent research on retrofitting using FRP and steel near surface mounted plates (NSM) has shown that NSM plates tend to debond at high strains which can allow substantial amounts of moment redistribution. A moment redistribution approach has been developed for both NSM and EB plated beams that allows for the wide range of debonding strains that can occur. This allows RC beams to be retrofitted for both strength and ductility which should help expand the use of this convenient and inexpensive form of retrofitting.     

Concrete Beams Strengthened with Externally Bonded FRP Plates

The structural behavior of reinforced concrete beams strengthened with adhesively bonded fiber-reinforced plastics (FRP) is presented. The experimental work included flexural testing of 2.3-m-long concrete beams with bonded external reinforcements. The test variables included the amount of conventional (internal) reinforcement and also the type and amount of external reinforcement. For comparison, some of the beams were strengthened with bonded steel plates. Theoretical analyses included 2D nonlinear finite-element modeling incorporating a “damage” material model for concrete. In general there were reasonably good correlations between the experimental results and nonlinear finite-element models. It is suggested that the detachment of bonded external plates from the concrete, at ultimate loads, is governed by a limiting principal stress value at the concrete∕external plate interface.     

Behavior of FRP Strengthened Reinforced Concrete Beams under Torsion

The use of fiber reinforced plastics (FRPs) for flexural and shear strengthening of reinforced concrete beams has been scrutinized to a considerable depth by researchers worldwide. The area of torsional strengthening however has not been as popular. This paper presents the results of an experimental investigation together with a numerical study on reinforced concrete beams subjected to torsion that are strengthened with FRP wraps in a variety of configurations. In the experimental study, the increase in the ultimate torque for different strengthening configurations, failure mechanisms, crack patterns, and ductility levels are monitored and presented. Experimental results show that FRP wraps can increase the ultimate torque of fully wrapped beams considerably in addition to enhancing the ductility. The experimental results upgrade the weak archival data on torsional strengthening by application of FRP. The numerical section reports on analyses performed by the ANSYS finite element program. Predictions are compared with experimental findings and are in reasonable agreement.     

Flexural Performance of Concrete Beams Reinforced with FRP Grids

This paper evaluates the flexural performance of simply supported concrete beams subjected to four-point monotonic loading and reinforced with a 2D fiber-reinforced plastic (FRP) grid. The main parameter of the study is the amount of longitudinal FRP reinforcement. With respect to a balanced strain condition, three underreinforced and two overreinforced FRP designs were tested with three identical beams per design. Laboratory recorded load-deflection, failure mode, cracking behavior, and reinforcement strain data are compared with theoretical predictions calculated according to traditional steel-reinforced concrete procedures. The study concludes that, with respect to ACI 318-95, flexural capacity is accurately predicted, but shear strength is not. Deflection compatibility between test results and ACI predictions employing the Branson effective moment of inertia was dependent on the percentage of longitudinal reinforcement. In general, observed flexural stiffness was less than that predicted by Branson's equation. A moment-curvature deflection procedure employing a bilinear concrete model compared very well with measured deflections. Finally, the grid configuration provides an effective force transfer mechanism. Cracking occurred at transverse bar locations only, and FRP tensile rupture was achieved with no observed deterioration in force transfer mechanics.     

Empirical Approach for Determining Ultimate FRP Strain in FRP-Strengthened Concrete Beams

The flexural capacity of concrete beams can be efficiently and effectively improved through bonding fiber-reinforced plastic (FRP) plates to the tensile side. Failure of the strengthened member often occurs through debonding of the FRP from the concrete substrate. If the ultimate FRP strain at debonding failure is known, the moment capacity of the member can be obtained through a simple section analysis. In the American Concrete Institute (ACI) Design Guideline, simple empirical equations are proposed to find the ultimate FRP strain in terms of the FRP stiffness alone. However, when the proposed equations are compared to experimental data, a very large scatter is observed, indicating that the effect of other parameters cannot be neglected. In the present investigation, a new empirical approach to obtain the FRP debonding strain is developed. With a comprehensive experimental database of 143 tests, a neural network relating the ultimate FRP strain to various geometric and material parameters is trained and validated. Using the validated network, an empirical design curve and several correction equations are generated to provide a simple means to find the debonding strain in practical design. Through use of the chart and equations, the calculated ultimate failure moments for the 143 tests in our database are found to be in good agreement with experimental results. The applicability of the new empirical approach to the failure prediction of strengthened members is thus demonstrated.     

Analytical Method for Evaluating Ultimate Torque of FRP Strengthened Reinforced Concrete Beams

The behavior of fiber reinforced polymer (FRP) strengthened reinforced concrete beams subjected to torsional loads has not been well understood compared to other loads. Interaction of different components of concrete, steel, and FRP in addition to the complex compatibility issues associated with torsional deformations have made it difficult to provide an accurate analytical solution. In this paper an analytical method is introduced for evaluation of the torsional capacity of FRP strengthened RC beams. In this method, the interaction of different components is allowed by fulfilling equilibrium and compatibility conditions throughout the loading regime while the ultimate torque of the beam is calculated similarly to the well-known compression field theory. It is shown that the method is capable of predicting the ultimate torque of FRP-strengthened RC beams reasonably accurately.     

Quasi-Balanced Failure Approach for Evaluating Moment Capacity of FRP Underreinforced Concrete Beams

Failure of concrete beam sections underreinforced with fiber-reinforced polymer (FRP) is initiated by FRP rupture before concrete crushing. In such a case, the typical rectangular stress block based on the balanced failure mechanism may not apply. In the present study, rigorous sectional analyses are performed implementing existing concrete stress-strain models for a wide range of values of design parameters. Based on the results of the numerical analyses, the variation of parameters of equivalent stress block of concrete was investigated, and an alternative, yet simple, design method for evaluating moment-carrying capacity of FRP underreinforced concrete beam using quasi-balanced failure approach was developed. The proposed design method was verified by comparing the predicted moment-carrying capacity with existing test results.     

Shear Strength of Large Concrete Members with FRP Reinforcement

Increasing interest in the use of fiber-reinforced polymer (FRP) reinforcement for reinforced concrete structures has made it clear that insufficient information about the shear performance of such members is currently available to practicing engineers. This paper summarizes the results of 11 large shear tests of reinforced concrete beams with glass FRP (GFRP) longitudinal reinforcement and with or without GFRP stirrups. Test variables were the member depth, the member flexural reinforcement ratio, and the amount of shear reinforcement provided. Results showed that the equations of the Canadian CSA shear provisions provide conservative estimates of the shear strength of FRP-reinforced members. Recommendations are given along with a worked example on how to apply these provisions including to members with FRP stirrups. It was found that members with multiple layers of longitudinal bars appear to perform better than those with a single layer of longitudinal reinforcing bars. Overall, it was concluded that the fundamental shear behavior of FRP-reinforced beams is similar to that of steel-reinforced beams despite the brittle nature of the reinforcement.     

Performance of Mechanically Fastened FRP Strengthened Concrete Beams in Flexure

The use of adhesively bonded fiber-reinforced polymer (FRP) materials has become widely accepted for use in flexural strengthening applications; however, the method of attachment presents drawbacks in application. These include extensive time and labor investments, as well as a tendency of the system to fail in a brittle manner. This paper presents a study of a series of reinforced concrete beams each strengthened in flexure with an FRP strip attached with large diameter concrete screws. The concrete screws were arranged in a variety of patterns. The effect of fastener number and spacing, as well as the effect of fastener pattern on the behavior of the beam, was investigated through the use of two groups of specimens. The beams in each group were tested to failure to verify the behavior of the strengthening system. Measured behavior was then used to determine an analytical approach for prediction of load response behavior of mechanically fastened systems. It was found that the strengthening method investigated improved the flexural capacity of the specimens 12 to 39% with little or no loss in ductility.     

Experimental Study on Bond Behavior between Concrete and FRP Reinforcement

Bonding between fiber-reinforced polymer (FRP) sheets and concrete supports is essential in shear and flexural applications for transfer of stress between concrete structure and reinforcement. This paper aims at better understanding FRP–concrete bond behavior and at assessing some of the common formulations for effective bond length and bond–slip models (τ-s) by means of an extensive experimental program on 39 concrete specimens strengthened with various types and amounts of FRP strips and covering a wide range of FRP axial rigidities, subjected to both double-shear and bending tests. Effective bond length, maximum bond/shear stress, slip when bond stress peaks, and slip when bond stress falls to zero, were all experimentally measured. The influence of FRP stiffness on effective bond length and bond–slip behavior was observed. New expressions for (1) effective bond length; (2) maximum shear/bond stress; (3) slip at peak value of bond stress; and (4) slip at ultimate, taking into account the influence of FRP stiffness, are proposed.     

Analytical Model for FRP Confinement of Concrete Columns with and without Internal Steel Reinforcement

The paper aims to contribute to a better understanding of the behavior of reinforced concrete columns confined with fiber-reinforced polymer (FRP) sheets. In particular, some new insights on interaction mechanisms between internal steel reinforcement and external FRP strengthening and their influence on efficiency of FRP confinement technique are given. In this context a procedure to generate the complete stress-strain response including new analytical proposals for (1) effective confinement pressure at failure; (2) peak stress; (3) ultimate stress; (4) ultimate axial strain; and (5) axial strain corresponding to peak stress for FRP confined elements with circular and rectangular cross sections, with and without internal steel reinforcement, is presented. Interaction mechanisms between internal steel reinforcement and external FRP strengthening, shown by some experimental results obtained at the University of Padova with accurate measurements, are taken into account in the analytical model. Four experimental databases regarding FRP confined concrete columns, with circular and rectangular cross section with and without steel reinforcement, are gathered for the assessment of some of the confinement models shown in literature and the new proposed model. The proposed model shows a good performance and analytical stress-strain curves approximate some available test results quite well.     

Long-Term Deflections of Reinforced Concrete Beams Externally Bonded with FRP System

External bonding of fiber-reinforced polymer (FRP) composite laminates to the tension soffit of reinforced concrete beams has become a popular method for flexural strengthening. However, the long-term performance of FRP-bonded beams under service loads is still a concern. This study was therefore aimed at investigating, both analytically and experimentally, the long-term deflection characteristics of FRP-bonded beams under sustained loads. Nine reinforced concrete beams, six of which were externally bonded with glass FRP composite laminates, were subjected to sustained loads for 2 years. The test parameters were the FRP ratio and sustained load level. The long-term deflections of the beams were reduced 23 and 33% with a FRP ratio of 0.64 and 1.92%, respectively. The total beam deflections were accurately predicted by the adjusted effective modulus method, and overestimated by about 20% by the effective modulus method.