Deflection Prediction of Steel and FRP-Reinforced Concrete-Filled FRP Tube Beams

This paper presents the results of experimental and theoretical investigations that study the flexural behavior of reinforced concrete-filled fiber-reinforced polymer (FRP) tubes (RCFFTs) beams. The experimental program consists of 10 circular beams [6 RCFFT and 4 control reinforced concrete (RC) beams] with a total length of 2,000?mm, tested under four-point bending load. The experimental results were used to review and verify the applicability of various North American code provisions and some available equations in the literature to predict deflection of RCFFT beams. The measured deflections and the experimental values of the effective moment of inertia were analyzed and compared with those predicted using available models. The results of the analysis indicated that the behavior of steel and FRP-RCFFT beams under the flexural load was significantly different than that of steel and FRP-RC members. This is attributed to the confining effect of the FRP tubes and their axial contribution. This confining behavior in turn enhanced the overall flexural behavior and improved the tension stiffening of RCFFT beams. For that, the predicted tension stiffening of steel and FRP-RCFFT beams using the conventional equations (steel or FRP-RC member) underestimates the flexural response; therefore, the predicted deflections are overestimated. Based on the analysis of the test results, the Branson’s equation for the effective moment of inertia of RC structures is modified, and new equations are developed to accurately predict the deflection of concrete-filled FRP tube (CFFT) beams reinforced with steel or FRP bars.     

Flexural Response of Concrete Beams Prestressed with AFRP Tendons: Numerical Investigation

This paper presents the flexure of concrete beams prestressed with aramid fiber-reinforced polymer (AFRP) tendons. Three-dimensional nonlinear finite-element analysis and iterative sectional analysis are conducted to predict the behavior of AFRP-prestressed members, including experimental validation. The beams are simply supported and monotonically loaded until failure occurs. The sectional properties of the beams include a reinforcement ratio of 0.15% to 0.36% and an Ig/Icr ratio of 25 to 77, where Ig and Icr are the gross and cracked moment of inertia, respectively. Various prestressing levels are applied to the beams to evaluate the load versus displacement response, variation of neutral axis depth, effective moment of inertia, and deformability of the beams. The applicability of code provisions and existing predictive equations are examined. The prestress level in the AFRP tendons significantly influences the flexural behavior of the beams, namely, cracking load, strain development of AFRP, and neutral axis depth. Sectional properties such as the Ig/Icr ratio are an important parameter that affects the deflection characteristics of AFRP-prestressed beams, including a deformability index. Recommendations to improve the current design provisions are addressed.     

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.     

FRP-Reinforced Concrete Beams: Unified Approach Based on IC Theory

In general, steel-reinforced concrete involves a ductile steel material and a very strong and ductile bond between the steel reinforcement and concrete, so that debonding rarely governs the design. In contrast, fiber-reinforced polymer (FRP) reinforcement is a brittle material with a weak and brittle bond, making debonding a major issue. Consequently, there has been an extensive amount of research on FRP debonding and in particular intermediate crack (IC) debonding. This paper shows that the very good research by the FRP research community on the mechanics of IC debonding can be applied to a wide range of apparently disparate reinforced concrete behaviors to produce a unified approach. Hence, a single mechanism, or unified approach, based on IC debonding is proposed in this paper for dealing with moment rotation, tension stiffening and deflections, member ductility and moment redistribution, shear capacity, confinement, and fiber concrete for FRP RC beams.     

Critical Review of Deflection Formulas for FRP-RC Members

The design of fiber-reinforced polymer reinforced concrete (FRP-RC) is typically governed by serviceability limit state requirements rather than ultimate limit state requirements as conventional reinforced concrete is. Thus, a method is needed that can predict the expected service load deflections of fiber-reinforced polymer (FRP) reinforced members with a reasonably high degree of accuracy. Nine methods of deflection calculation, including methods used in ACI 440.1R-03, and a proposed new formula in the next issue of this design guide, CSA S806-02 and ISIS M03-01, are compared to the experimental deflection of 197 beams and slabs tested by other investigators. These members are reinforced with aramid FRP, glass FRP, or carbon FRP bars, have different reinforcement ratios, geometric and material properties. All members were tested under monotonically applied load in four point bending configuration. The objective of the analysis in this paper is to determine a method of deflection calculation for FRP RC members, which is the most suitable for serviceability criteria. The analysis revealed that both the modulus of elasticity of FRP and the relative reinforcement ratio play an important role in the accuracy of the formulas.     

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.     

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.     

Design Approach for Calculating Deflection of FRP-Reinforced Concrete

Deflection of reinforced concrete is typically computed with an effective moment of inertia Ie that accounts for nonlinear behavior after the concrete cracks. Existing expressions for Ie tend to overpredict the member stiffness of concrete reinforced with fiber-reinforced polymer (FRP) bars, and an alternative expression is used as the basis for developing a practical design approach to compute deflection. The proposed expression has a rational basis that incorporates basic concepts of tension stiffening to provide a reasonable estimate of deflection for both steel and FRP-reinforced concrete without the need for empirically derived correction factors. Calculation of deflection with the proposed expression for Ie is recommended using the code value for the elastic modulus Ec of concrete because computed values of deflection are relatively insensitive to variations in Ec, and shrinkage restraint is taken into account by using a reduced cracking moment less than the code-based value of the cracking moment Mcr. Ie is conservatively based on the moment at the critical section (where the member stiffness is lowest), unless more accuracy is required with an integration-based expression that gives an equivalent moment of inertia Ie′ to account for the variation in stiffness along the member length. Recommendations are validated by comparison with a database of deflection test results for FRP-reinforced concrete.     

Flexural Behavior and Deformability of Fiber Reinforced Polymer Prestressed Concrete Beams

After a brief review of the ductility and deformability indices currently used in the design of concrete beams reinforced or prestressed with steel or fiber reinforced polymer (FRP) tendons, a new definition of a deformability index (factor) for prestressed concrete beams is proposed. The new factor is defined in terms of both a deflection factor and a strength factor. The deflection factor is the ratio of the deflection at failure to the deflection at first cracking, while the strength factor is the ratio of the ultimate moment (or load) to the cracking moment (or load). The proposed deformability factor is verified not only by test results obtained by the writer, but also by other test results available in the literature and it appears to be a suitable measurement of the deformability of concrete beams prestressed with either FRP tendons or steel tendons.     

Maximum Shear Strength of RC Beams Retrofitted in Shear with FRP Composites

In reinforced concrete (RC) beams strengthened in shear with fiber-reinforced polymer (FRP), crushing of the web can be a potential mode of failure. The guidelines provided by codes and standards for the design of structures strengthened with externally bonded FRP recommend limiting the maximum shear strength to avoid such an undesirable failure scenario. However, these limitation provisions are not based on specific research studies performed on beams strengthened in shear with FRP. Rather, they simply duplicate provisions used in conventional concrete codes and standards. The main objective of this research study is to assess the suitability of the limits specified by the guidelines, and propose, if necessary, an alternative equation as an upper limit for shear strength against web crushing failure in such structures. To this end, an analytical approach was developed based on the static theorem of the theory of plasticity. The predictions of the equations resulting from this approach were compared with those obtained from tests reported in the literature and with those predicted by ACI Committee 440-02, Canadian Standard S6-06, and the European recommendations fib TG 9.3. The study shows that the current ACI Committee 440-02 and Canadian Standards provisions are overly conservative and therefore need to be reviewed.     

Verifications of Design Equations of Beams Externally Strengthened with FRP Composites

Based on the test information available in the literature since 1990, a comprehensive database is assembled for an extensive survey of existing studies on the flexural behavior of reinforced concrete beams externally strengthened with fiber-reinforced polymer (FRP) composites. Beam dimensions, material properties (concrete, steel reinforcement, FRP composites, etc.), and corresponding flexural responses such as failure modes, moment capacities, and so on, are collected in this database. The purpose of this database is to verify the design formulas presented in ACI 440.2R-02, Guide for the Design and Construction of Externally Bonded FRP Systems for Strengthening Concrete Structures. The performance of some other simple strength design models is investigated based on the same database and compared with that of the ACI model, which is found to have the least scattered prediction compared to others. Finally, a modified maximum strain FRP equation is recommended.     

Tests on the Ductility of Reinforced Concrete Beams Retrofitted with FRP and Steel Near-Surface Mounted Plates

Reinforced concrete beams are now commonly retrofitted using externally bonded (EB) fiber reinforced polymer (FRP) plates as the technique is both inexpensive and unobtrusive. However, tests have shown that EB carbon FRP plates tend to debond at low strains, which can severely limit the ductility or moment redistribution to such an extent that guidelines often preclude moment redistribution. This paper reports the moment redistribution achieved in tests on nine near full-scale two-span continuous reinforced concrete beams that were retrofitted with near-surface mounted (NSM) plates. The plates were either carbon FRP or high yield steel strips which were adhesively bonded within saw grooves cut into the concrete cover on the tension face or sides of the beam. It was found that the debonding strains of these NSM plates were considerably larger than those associated with EB plates and that substantial amounts of moment redistribution occurred. These tests suggest that NSM plates can be used to increase the strength of reinforced concrete structures with little, if any, loss of ductility.     

Computer-Based Mathematical Model for Performance Prediction of Corroded Beams Repaired with Fiber Reinforced Polymers

A new mathematical model for predicting the inelastic flexural response of corroded reinforced concrete (RC) beams repaired with fiber reinforced polymer (FRP) laminates is presented. The model accounts for the effect of the change in the bond strength at the steel-to-concrete interface due to corrosion and/or FRP wrapping on the beam load–deflection response. The effects of FRP strengthening and the reduction in the steel reinforcement area due to corrosion on the beam strength are predicted by the model. A computer program was coded to carry out the modeling procedure and the model’s predictions were compared with the results of an experimental study undertaken to investigate the model’s reliability. A comparison of the predicted and the experimental results showed that the model accurately predicted the load–deflection relationships for corroded RC beams repaired with FRP laminates.     

Flexural Behavior of Continuous GFRP Reinforced Concrete Beams

The results of testing two simply and three continuously supported concrete beams reinforced with glass fiber-reinforced polymer (GFRP) bars are presented. The amount of GFRP reinforcement was the main parameter investigated. Over and under GFRP reinforcements were applied for the simply supported concrete beams. Three different GFRP reinforcement combinations of over and under reinforcement ratios were used for the top and bottom layers of the continuous concrete beams tested. A concrete continuous beam reinforced with steel bars was also tested for comparison purposes. The experimental results revealed that over-reinforcing the bottom layer of either the simply or continuously supported GFRP beams is a key factor in controlling the width and propagation of cracks, enhancing the load capacity, and reducing the deflection of such beams. Comparisons between experimental results and those obtained from simplified methods proposed by the ACI 440 Committee show that ACI 440.1R-06 equations can reasonably predict the load capacity and deflection of the simply and continuously supported GFRP reinforced concrete beams tested.     

Bond Performance of GFRP Bars in Tension: Experimental Evaluation and Assessment of ACI 440 Guidelines

The development/splice strength and the pullout local bond stress-slip response of glass fiber-reinforced polymer (GFRP) bars in tension were experimentally investigated using beam specimens and pullout specimens, respectively. Two types of 12-mm (0.47-in.)-diameter GFRP bars were evaluated, namely, thread wrapped and ribbed. The test parameters included the concrete cover, the splice length, and the area of steel confinement for the beam specimens, and the concrete compressive strength for the pullout specimens. Companion steel reinforced beams were also tested for comparison. All beam specimens reinforced with thread-wrapped GFRP bars experienced pullout mode of bond failure, while all specimens reinforced with ribbed GFRP bars or steel bars experienced splitting mode of bond failure. It was found that the bond strength of FRP bars is largely dependent on the surface conditions of the bars. The pullout local bond stress-slip response of ribbed GFRP bars is intrinsically similar to that of steel bars reported in the literature. The bond strength of both types of GFRP bars investigated was about two to three times lower than that of steel bars. Predictions of the development/splice strength of GFRP bars in accordance with the ACI Committee 440 guidelines were unconservative in comparison with the test data. Also, in contradiction with the current ACI 440 report, the use of transverse confining reinforcement increased the bond strength by a sizable 15–30%.     

Equivalent Moment of Inertia Based on Integration of Curvature

This paper evaluates the benefits of computing deflection with an equivalent moment of inertia based on integration of curvature to account for changes in member stiffness along the span. Results are evaluated for steel and fiber-reinforced polymer reinforced (FRP-reinforced) concrete flexural members with different loading arrangements and support conditions. Closed-form solutions of integrated expressions for deflection are expressed in terms of an equivalent moment of inertia Ie′ and compared to deflection computed with an effective moment of inertia Ie based on the stiffness at the critical section. Results from this comparison are validated with measured deflections from an experimental database for FRP-reinforced concrete. Current code-related approaches are also compared to the experimental database. It is shown herein that the use of an integration-based expression for the moment of inertia can lead to improved prediction of deflection, though the use of an effective moment of inertia based on member stiffness at the critical section gives a reasonably conservative estimate of deflection in many cases. The benefits of taking account of changes in stiffness along the member span are more evident when low reinforcing ratios are used in combination with FRP reinforcement, and use of the integration-based expression Ie′ may be warranted when deflection control is critical in such cases.     

Deflection Prediction for FRP-Strengthened Concrete Beams

Due to increasing popularity of using fiber-reinforced polymer (FRP) for external strengthening of concrete structures, an urgent demand for understanding the structural behavior of FRP-strengthened structures has been emerging. Unlike conventional reinforced concrete (RC) structures, FRP-strengthened members can exhibit additional flexural capacity in the postyielding stage. This makes RC models for predicting deflection inapplicable in case of FRP-strengthened structures. Therefore, some models have been explicitly developed for evaluating deflection of the strengthened structures. However, most existing models are empirically based, verified with limited experimental results, and require in some cases sophisticated calculation procedures. Accordingly, there is still a demand for a rational and more convenient model for predicting deflection of FRP-strengthened beams. In the current paper, Bischoff’s model, originally proposed for RC and FRP reinforced structures, was extended. Consequently, the developed model is applicable to FRP-strengthened concrete beams besides its validity to both RC and FRP reinforced beams. Validation of the model with some available test data confirmed its accuracy.     

Theoretical Study on Short-Term and Long-Term Deflections of Fiber Reinforced Polymer Prestressed Concrete Beams

This paper presents the methods for predicting the short-term and time-dependent deflections of fully or partially prestressed concrete beams with fiber reinforced polymer (FRP) tendons under sustained bending moment and axial force. The age-adjusted effective modulus method is used to model the creep behavior in the concrete and the relaxation in the FRP prestressing tendons. A tension-stiffening model is proposed to evaluate the stiffness of the section after cracking. The analytical values are compared to the test results and it is found that the analytical values are in good agreement with the experimental results.     

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.     

Flexural Behavior of Continuous FRP-Reinforced Concrete Beams

Continuous concrete beams are commonly used elements in structures such as parking garages and overpasses, which might be exposed to extreme weather conditions and the application of deicing salts. The use of the fiber-reinforced polymers (FRP) bars having no expansive corrosion product in these types of structures has become a viable alternative to steel bars to overcome the steel-corrosion problems. However, the ability of FRP materials to redistribute loads and moments in continuous beams is questionable due to the linear-elastic behavior of such materials up to failure. This paper presents the experimental results of four reinforced concrete beams with rectangular cross section of 200×300?mm continuous over two spans of 2,800 mm each. The material and the amount of longitudinal reinforcement were the main investigated parameters in this study. Two beams were reinforced with glass FRP (GFRP) bars in to different configurations while one beam was reinforced with carbon FRP bars. A steel-reinforced continuous concrete beam was also tested to compare the results. The experimental results showed that moment redistribution in FRP-reinforced continuous concrete beams is possible if the reinforcement configuration is chosen properly. Increasing the GFRP reinforcement at the midspan section compared to middle support section had positive effects on reducing midspan deflections and improving load capacity. The test results were compared to the available design models and FRP codes. It was concluded that the Canadian Standards Association Code (CSA/S806-02) could reasonably predict the failure load of the tested beams; however, it fails to predict the failure location.