Analytical Model for Concrete Confined with Fiber Reinforced Polymer Composite

An analytical model to predict the behavior of concrete confined with fiber reinforced plastic (FRP) composites subjected to axial compressive loads was developed. First, a constitutive model for plain concrete was formulated from past experimental results obtained from triaxial compression tests of concrete, in which concrete specimens were maintained under constant confining stresses. This was an orthotropic constitutive model based on the concept of equivalent uniaxial strain. Subsequently, in the analytical model for FRP confined concrete, the proposed constitutive model for concrete materials was incorporated. The FRP was assumed to be a linear elastic material. Force equilibrium and strain compatibility between the concrete and the FRP as well were satisfied. When the proposed model was applied to FRP confined concrete, the model overestimated the axial stress. To rectify this, a subsequent maximum strength criterion was introduced to control the maximum strength in the postpeak region when confining stress was continuously increased. The proposed analytical model with the addition of the subsequent maximum strength criterion is in good agreement with the experimental results.     

Comparative Study of Models on Confinement of Concrete Cylinders with Fiber-Reinforced Polymer Composites

The use of fiber-reinforced polymer (FRP) composites for strengthening and/or rehabilitation of concrete structures is gaining increasing popularity in the civil engineering community. One of the most attractive applications of FRP materials is their use as confining devices for concrete columns, which may result in remarkable increases of strength and ductility as indicated by numerous published experimental results. Despite a large research effort, a proper analytical tool to predict the behavior of FRP-confined concrete has not yet been established. Most of the available models are empirical in nature and have been calibrated against their own sets of experimental data. On the other hand, the experimental results available in the literature encompass a wide range of values of the significant variables. The objective of this work is a systematic assessment of the performance of the existing models on confinement of concrete columns with FRP materials. The study is conducted in the following steps: the experimental data on confinement of concrete cylinders with FRP available in the technical literature are classified according to the values of the significant variables; the existing empirical and analytical models are reviewed, pointing out their distinct features; the whole set of available experimental results is compared with the whole set of analytical models; and strengths and weaknesses of the various models are analyzed. Finally, a new equation is proposed to evaluate the axial strain at peak stress of FRP-confined concrete cylinders.     

Long-Term Properties and Transfer Length of Fiber-Reinforced Polymers

This paper discusses the experimental results on properties and transfer length of the common types of fiber-reinforced polymer (FRP) tendons. Based on the experimental results, an equation is proposed for predicting the creep coefficient of aramid-based FRP (AFRP) tendons. The results show that the creep of carbon-based FRP (CFRP) is less than 0.2%. The test results show that the transfer length of CFRP is in the range of 300–800 mm and the concrete strength at transfer is one of the major factors affecting the transfer length of CFRP. A new factor accounting for the concrete strength is proposed for estimating the transfer length of CFRP tendons, and the verification is made for this equation. The transfer length was found to vary from 170 to 270 mm, which was 20–30 times the tendon diameter for these AFRP tendons. Despite the creep and shrinkage of concrete and the relaxation of the tendon itself, the range for transfer length did not vary with time.     

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.     

Analytical Model for Circular Normal- and High-Strength Concrete Columns Confined with FRP

This paper presents a new incremental stress-strain model for fiber-reinforced polymer (FRP)-confined concrete. The model, able to accommodate concrete with a wide range of strength (25–110 MPa), is based on material properties, force equilibrium, and strain compatibility, and uses newly developed models for constantly confined concrete. An expression is proposed to calculate a FRP jacket rupture strain in columns. Beyond the initiation of rupture, gradual failure of a FRP jacket is modeled to account for the size effect on the FRP-confined concrete columns. This proposed constitutive model is unique in that it accommodates a wide range of concrete strength and uses an analytical rupture strain of a FRP jacket to predict the complete stress-strain curve. Small and large specimens tested by the authors and other researchers are used to validate the proposed model. Very good to excellent agreements have been achieved between the analytical and experimental responses.     

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.     

Investigation of Bond in Concrete Structures Strengthened with Near Surface Mounted Carbon Fiber Reinforced Polymer Strips

Fiber reinforced polymer (FRP) materials are currently produced in different configurations and are widely used for the strengthening and retrofitting of concrete structures and bridges. Recently, considerable research has been directed to characterize the use of FRP bars and strips as near surface mounted reinforcement, primarily for strengthening applications. Nevertheless, in-depth understanding of the bond mechanism is still a challenging issue. This paper presents both experimental and analytical investigations undertaken to evaluate bond characteristics of near surface mounted carbon FRP (CFRP) strips. A total of nine concrete beams, strengthened with near surface mounted CFRP strips were constructed and tested under monotonic static loading. Different embedment lengths were used to evaluate the development length needed for effective use of near surface mounted CFRP strips. A closed-form analytical solution is proposed to predict the interfacial shear stresses. The model is validated by comparing the predicted values with test results as well as nonlinear finite element modeling. A quantitative criterion governing the debonding failure of near surface mounted CFRP strips is established. The influence of various parameters including internal steel reinforcement ratio, concrete compressive strength, and groove width is discussed.     

Rational Approach to Shear Design in Fiber-Reinforced Polymer-Prestressed Concrete Structures

The use of plasticity-based shear design methods for fiber-reinforced polymer (FRP) reinforced and prestressed concrete, as they are used at present, is inappropriate in the long term. In particular, the use of a plasticity-based truss model for shear behavior seems to be unsound, as reliance is placed on a predominantly elastic zone to redistribute stresses. A better approach to shear design would be to employ a model incorporating force equilibrium and compatibility of strains so that the elastic properties of the FRP could be included rationally. This would help to develop a real understanding and form a basis on which new guides and codes could be founded. In tandem with a more rational analytical approach, new configurations and types of FRP reinforcement need to be developed and researched so that these materials can be used more efficiently. An analytical approach to investigate the shear response of FRP-reinforced and -prestressed concrete has been developed, based on equilibrium and compatibility across a shear discontinuity. The analytical model presented here was developed in conjunction with an experimental program. Correlation between the analytical and experimental results is good and more accurate than the current guideline provisions for concrete beams containing FRP reinforcement.     

Analysis of the Flexural Behavior of Partially Bonded FRP Strengthened Concrete Beams

An investigation was conducted on the flexural behavior of partially bonded fiber-reinforced polymer (FRP) strengthened concrete beams focusing on the improvement of ductility. An analytical model was developed based on the curvature approach to predict the behavior of beams strengthened with partially bonded FRP systems. The result of the analysis showed that ductility of the partially bonded system was improved while sustaining high load carrying capacity in comparison to the fully bonded system. To verify the analytical model, an experimental program was carried out with reinforced concrete beams strengthened with the externally bonded FRP system. A comparison of the analytical prediction and experimental results showed good agreement.     

Effect of End Tapering on Crack-Induced FRP Debonding from the Concrete Substrate

The technique of bonding fiber-reinforced plastic (FRP) plates on the tensile side of concrete members has been proved to be an effective method for structural strengthening. For a RC beam strengthened with FRP plates, failure may occur by concrete cover separation near the plate end, or crack-induced debonding initiated by an opening crack away from the plate end. Experimental investigations have shown that tapering of the FRP plate at its ends is effective in reducing the stress concentrations and increasing the loading for plate end failure to occur. However, with reduced averaged thickness of the tapered plate, crack-induced debonding is also easier to occur. To optimize plate tapering in practical designs, an approach to analyze crack-induced debonding of tapered FRP plates is required. In the present investigation, FRP debonding is first studied with the finite-element method. In the analysis, a three-parameter model is employed for the shear slip relation between concrete and the FRP plate. Based on the findings from FEM analysis, simplifying assumptions are derived and an analytical model is developed for calculating the stresses in the FRP plate and along the concrete-to-FRP interface. The analytical stress distributions show good agreement with those from the FEM analysis. Using the analytical model, the effect of FRP tapering is quantitatively assessed. Also, the effects of various parameters on the ultimate failure load are simulated.     

Prediction of Tensile Capacity of Bond Anchorages for FRP Tendons

Past test data show that the bond stress distribution of bond anchorages is nonuniform along the bonded length and that the point of the peak bond strength shifts from the entry of the tendon to an inside point of the anchorage as the applied load increases. Based on these results, this paper analyzes the working mechanism of bond anchorages for fiber-reinforced polymer (FRP) tendons and presents a conceptual model to calculate the bond stress at the tendon-grout interface and the tensile capacity of bond anchorages for FRP tendons. Experimental and analytical results show that the geometry of FRP tendon and steel sleeve and the mechanical properties of filling grout are the relevant parameters in the development of tendon-grout interface stresses. The characteristic bond strength depends mainly on the properties of the bonding agent-cement grout, the geometry and surface conditions of the tendon, and the radial stiffness of the confining medium. A comparison of the calculated and experimental results showed good agreement.     

Variable Strain Ductility Ratio for Fiber-Reinforced Polymer-Confined Concrete

The encasement of concrete in fiber-reinforced polymer (FRP) composite jackets can significantly increase the compressive strength and strain ductility of concrete columns and the structural system of which the columns are a part, be it a building or a bridge. Due to the approximate bilinear compressive behavior of FRP-confined concrete, analysis and design of FRP-confined concrete members requires an accurate estimate of the performance enhancement due to the confinement provided by FRP composite jackets. An analytical model is presented for predicting the bilinear compressive behavior of concrete confined with either bonded or nonbonded FRP composite jackets. This article describes the basis of the model, which is a variable plastic strain ductility ratio. The variable plastic strain ductility ratio defines the increase in plastic compressive strain relative to the increase in the plastic compressive strength of the FRP-confined concrete, which is a function of the hoop stiffness of the confining FRP composite jacket, the plastic dilation rate, and the type of bond between the FRP composite and concrete.     

Modeling Debonding Failure in FRP Flexurally Strengthened RC Members Using a Local Deformation Model

Reinforced concrete (RC) beams and slabs can be strengthened by bonding fiber-reinforced polymer (FRP) composites to their tension face. The performance of such flexurally strengthened members can be compromised by debonding of the FRP, with debonding initiating near an intermediate crack (IC) in the member away from the end of the FRP. Despite considerable research over the last decade, reliable IC debonding strength models still do not exist. The current paper attempts to correct this situation by presenting a local deformation model that can simulate IC debonding. The progressive formation of flexural cracks, and the associated crack spacings and crack widths are modelled from initial cracking to the onset of debonding. The bond characteristics between the longitudinal steel reinforcement and concrete, and the FRP and concrete, as well as the tension stiffening effect of the reinforcement and FRP to the concrete, are considered. The FRP-to-concrete bond-slip relation is used to determine the onset of debonding. The analytical predictions compare well with experimental results of FRP-strengthened RC cantilever slabs.     

Full Torsional Behavior of RC Beams Wrapped with FRP: Analytical Model

Torsion failure is an undesirable brittle form of failure. Although previous experimental studies have shown that using fiber-reinforced polymer (FRP) sheets for torsion strengthening of reinforced concrete (RC) beams is an effective solution in many situations, very few analytical models are available for predicting the section capacity. None of these models predicted the full behavior of RC beams wrapped with FRP, account for the fact that the FRP is not bonded to all beam faces, or predicted the ultimate FRP strain using equations developed based on testing FRP strengthened beams in torsion. In this paper, an analytical model was developed for the case of the RC beams strengthened in torsion. The model is based on the basics of the modified compression field theory, the hollow tube analogy, and the compatibility at the corner of the cross section. Several modifications were implemented to be able to take into account the effect of various parameters including various strengthening schemes where the FRP is not bonded to all beam faces, FRP contribution, and different failure modes. The model showed good agreement with the experimental results. The model predicted the strength more accurately than a previous model, which will be discussed later. The model predicted the FRP strain and the failure mode.     

Analytical Solution for Fracture Analysis of CFRP Sheet–Strengthened Cracked Concrete Beams

Fiber-reinforced polymer (FRP) composite materials have been widely used in the field of retrofitting. Theoretical analysis of FRP plate- or sheet-strengthened cracked concrete beams is necessary for estimating service reliability of the structural members. In previous studies, the effect of a perfectly bonded FRP plate or sheet was equivalent to a cohesive force acting at the bottom of crack to delay the crack propagation in concrete and reduce the crack width. However, delamination between FRP and cracked beam is inevitable due to interfacial shear stress concentration at the bottom of crack. The intention of this paper is to present an analytical solution for fracture analysis of carbon FRP (CFRP) sheet–strengthened cracked concrete beams by considering both vertical crack propagation in concrete and interfacial debonding at CFRP-concrete interface. The interfacial debonding is modeled as the interfacial shear crack propagation in this paper. Four different stages are discussed after initial cracking state of the concrete. At the first stage, only fictitious crack propagation occurs in the concrete. At the second stage, macrocrack propagates in the concrete without interfacial debonding. At the third stage, both vertical macrocrack propagation in the concrete and horizontal shear crack propagation at the CFRP-concrete interface occur in the strengthened beam. The tensile stress in the CFRP sheet and interfacial shear stress along the span are formulated based on the deformation compatibility condition at the CFRP-concrete interface at this stage. Finally, macroshear crack propagates at the interface until the CFRP sheet is completely peeled out from the beam, and then the member is fractured. The applied load is determined as a function of the referred two crack lengths at different stages. At the beginning, the applied load increases to one peak value with the full propagation of fictitious crack at the first stage. At the third stage, the applied load is improved to another peak value due to the relatively high cohesive effect of the CFRP sheet. Then the two peak values are determined by the Lagrange multiplier method. The validity of the proposed analytical solution is verified with the experimental results and numerical simulations. It can be concluded that the proposed analytical solution can predict the load-bearing capacity of CFRP sheet-strengthened cracked concrete beams with reasonable accuracy.     

CFRP Tendons for the Repair of Posttensioned, Unbonded Concrete Buildings

The deterioration attributable to corrosion of concrete structures reinforced with unbonded, posttensioned tendons is a costly problem. Recent research has shown composite materials such as fiber-reinforced polymers (FRP) to be suitable alternatives to steel because they provide similar strength without susceptibility to electrochemical corrosion. Carbon-FRP (CFRP) in particular has great promise for prestressed applications because it shows resistance to corrosion in environments that might be encountered in concrete and experiences less relaxation than steel. This paper outlines the testing and implementation of a posttensioned system that uses CFRP tendons to replace corroded, unbonded posttensioned steel tendons. This system was then implemented in a parking garage in downtown Toronto. To the writers’ knowledge, this is the first example of an unbonded, posttensioned tendon replacement using FRP tendons. The system used split-wedge anchors designed specifically for CFRP tendons. The dead end was anchored by directly bonding the tendon to the concrete slab. The CFRP tendon was successfully inserted in the opening created by the removal of the corroded tendon and stressed. Although the system was shown to be feasible, the current anchorage configuration results in load losses of up to 60% during the transfer. Changing the orientation of the anchor was found to reduce the load loss to an acceptable range of 1–9%.     

Closed-Form High-Order Analysis of RC Beams Strengthened with FRP Strips

A closed-form high-order analytical solution for the analysis of concrete beams strengthened with externally bonded fiber-reinforced plastic (FRP) strips is presented. The model is based on equilibrium and deformations compatibility requirements in and between all parts of the strengthened beam, i.e., the concrete beam, the FRP strip, and the adhesive layer. The governing equations representing the behavior of the strengthened beam, along with the appropriate boundary and the continuity conditions, are derived and solved with closed-form analytical solutions. Comparison of the closed-form high-order model with other simplified approaches, based on one- and two-parameter elastic foundation concepts, is included. It is shown that the current high-order model can be reduced, by omitting the appropriate terms, to the simplified theories. A numerical example of a typical RC beam strengthened with an externally bonded FRP strip is discussed with emphasis on the shear and peeling stress distributions at the edge of the FRP strip. Stress analysis results concerning the edge stresses determined by the high-order model are compared with those determined by the elastic foundation models and finite elements. Finally, a parametric study that characterizes the main parameters governing the magnitude and intensity of the edge stresses is performed. The paper is concluded with a summary and recommendations for the design of the strengthened beam.     

Prediction of Interfacial Bond Failure of FRP–Concrete Surface

The use of fiber-reinforced polymer (FRP) for strengthening concrete structures has grown remarkably during the past few years. In spite of exhibiting superior properties, the safety of usage is questionable as FRP undergoes brittle debonding failure. The aim of this study is to review and compare the existing research on bond failure between FRP and concrete substrates. Among the different failure modes, there has been little research in terms of intermediate crack-induced interfacial debonding and fewer strength models are developed for predicting such failures. Conducting a simple shear test on the FRP bonded to a concrete substrate can simulate this type of failure mode. Twelve specimens were tested to study the influence of concrete strength and the amount of FRP on the ultimate load capacity of a FRP–concrete bond under direct shear. Existing experimental work was collected from the literature and consists of an extensive database of 351 concrete prisms bonded to FRP and tested in direct shear tests. The analytical models from various sources are applied to this database and the results are presented.     

Design and Fabrication of FRP Grids for Aerospace and Civil Engineering Applications

This paper presents the results of experimental and analytical studies of the performance of composite grids as well as fiber-reinforced polymer (FRP) grid reinforced concrete columns. FRP grids and FRP grid confined concrete cylinders were instrumented and tested under uniaxial compressive loading. Test variables included types of composite materials and the spacing of composite circular ribs. It is shown that the proposed FRP grids can be constructed by filament winding, the process can be automated, and the manufacturing cost can be reduced. Results show that the proposed FRP grids have substantial ultimate load that make them attractive for use in aerospace applications, and that confinement of concrete by FRP grids can significantly enhance the strength, ductility, and energy absorption capacity of concrete as compared to steel confined concrete. Equations to predict the compressive strength and failure strain were developed. Comparisons between the experimental and analytical results indicate that the proposed models provide satisfactory predictions of ultimate compressive strength and failure strain.     

Transverse Thermal Expansion of FRP Bars Embedded in Concrete

Fiber reinforced polymers (FRPs) have a thermal expansion in the transverse direction much higher than in the longitudinal direction and also higher than the thermal expansion of hardened concrete. The difference between the transverse coefficient of thermal expansion of FRP bars and concrete may cause splitting cracks within the concrete under temperature increase and, ultimately, failure of the concrete cover if the confining action of concrete is insufficient. This paper presents the results of an experimental investigation to analyze the effect of the ratio of concrete cover thickness to FRP bar diameter (c/db) on the strain distributions in concrete and FRP bars, using concrete cylindrical specimens reinforced with a glass FRP bar and subjected to thermal loading from ?30?to?+80°C. The experimental results show that the transverse coefficient of thermal expansion of the glass FRP bars tested in this study is found to be equal to 33 (×10?6?mm/mm/°C), on average and the ratio between the transverse and longitudinal coefficients of thermal expansion of these FRP bars is equal to 4. Also, the cracks induced by high temperature start to develop on the surface of concrete cylinders at a temperature varying between +50 and +60°C for specimens having a ratio of concrete cover thickness to bar diameter c/db less than or equal to 1.5. A ratio of concrete cover thickness to glass fiber reinforced polymers (GFRP) bar diameter c/db greater than or equal to 2.0 is sufficient to avoid cracking of concrete under high temperature up to +80°C. The analytical model, presented in this paper, is in good agreement with the experimental results, particularly for negative temperature variations.