Stress-Strain Model for Fiber-Reinforced Polymer-Confined Concrete

The design of fiber-reinforced polymer (FRP)-confined concrete members requires accurate evaluation of the performance enhancement due to the confinement provided by FRP composite jackets. A strain ductility-based model is developed for predicting the compressive behavior of normal strength concrete confined with FRP composite jackets. The model is applicable to both bonded and nonbonded FRP-confined concrete and can be separated into two components: a strain-softening component, which accounts for unrestrained internal crack propagation in the concrete core, and a strain-hardening component, which accounts for strength increase due to confinement provided by the FRP composite jacket. A variable strain ductility ratio described in a companion paper is used to develop the proposed stress-strain model. Equilibrium and strain compatibility are used to obtain the ultimate compressive strength and strain of FRP-confined concrete as a function of the confining stiffness and ultimate strain of the FRP jacket.     

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.     

Theoretical Model for Fiber-Reinforced Polymer-Confined Concrete

Fiber-reinforced polymer (FRP) composites have found increasingly wide applications in civil engineering due to their high strength-to-weight ratio and high corrosion resistance. One important application of FRP composites is as a confining material for concrete, particularly in the strengthening or seismic retrofit of existing reinforced concrete columns by the provision of a FRP jacket. FRP confinement can enhance both the compressive strength and the ultimate strain of concrete significantly. This paper presents a new stress–strain model for FRP-confined concrete in which the responses of the concrete core and the FRP jacket as well as their interaction are explicitly considered. Such a model is often referred to as an analysis-oriented model. The key novel feature of the proposed analysis-oriented model, compared to existing models of the same kind, is a more accurate and more widely applicable lateral strain equation based on a careful interpretation of the lateral deformation characteristics of unconfined, actively confined, and FRP-confined concrete. Through comparisons with independent test data, the proposed model is shown to be accurate not only for FRP-confined concrete but also for concrete confined with a steel tube, demonstrating the wide applicability of the model to concrete confined with different confining materials. The accuracy of the proposed model is also shown to be superior to existing analysis-oriented stress-strain models through comparisons with test data.     

Refinement of a Design-Oriented Stress–Strain Model for FRP-Confined Concrete

This paper presents the results of a recent study conducted to refine the design-oriented stress–strain model originally proposed by Lam and Teng for fiber-reinforced polymer (FRP)-confined concrete under axial compression. More accurate expressions for the ultimate axial strain and the compressive strength are proposed for use in this model. These new expressions are based on results from recent tests conducted by the writers’ group under well-defined conditions and on results from a parametric study using an accurate analysis-oriented stress–strain model for FRP-confined concrete. They allow the effects of confinement stiffness and the jacket strain capacity to be separately reflected and accounts for the effect of confinement stiffness explicitly instead of having it reflected only through the confinement ratio. The new expressions can be easily incorporated into Lam and Teng’s model for more accurate predictions. Based on these new expressions, two modified versions of Lam and Teng’s model are presented. The first version involves only the updating of the ultimate axial strain and compressive strength equations. The second version caters to stress–strain curves with a descending branch, which is not covered by the original model.     

Posttensioned FRP Composite Shells for Concrete Confinement

Experiments have shown that externally bonded fiber-reinforced polymer (FRP) jackets for square and rectangular columns are not as effective as they are for circular columns. The results of experiments on shape-modified concrete columns using posttensioned FRP shells are presented. Posttensioning was achieved by radially straining the precured FRP shell outwards to a substantial strain level, using expansive cement concrete, over a period of 60?days. The prefabricated FRP shell was also used as a stay-in-place formwork. The effectiveness of shape modification using posttensioned FRP shells is compared to FRP-confined original square and rectangular columns, as well as shape-modified columns with nonshrink grout and externally bonded FRP jackets. It is shown that shape modification with posttensioning of FRP shells, using expansive cement concrete, can change the confinement from passive to active and improve significantly the axial strength and ultimate compressive axial strain capacity of square and rectangular columns.     

Masonry Confinement with Fiber-Reinforced Polymers

The application of fiber-reinforced polymer (FRP) as a means of increasing the axial capacity of masonry through confinement, a subject not addressed before, is investigated in this study. Four series of uniaxial compression tests, with a total of 42 specimens, were conducted on model masonry columns with these variables: number of layers, radius at the corners, cross-section aspect ratio, and type of fibers. It is concluded that, in general, FRP-confined masonry behaves very much like FRP-confined concrete. Confinement increases both the load-carrying capacity and the deformability of masonry almost linearly with the average confining stress. The uniaxial compression test results enabled the development of a simple confinement model for strength and ultimate strain of FRP-confined masonry. This model is consistent with the test results obtained here but should attract further experimental verification in the future to account for types of masonry materials other than those used in this study.     

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.     

Single-Parameter Methodology for the Prediction of the Stress-Strain Behavior of FRP-Confined RC Square Columns

The study presented in this paper proposes a new theoretical framework to interpret and capture the mechanics of the fiber-reinforced polymer (FRP) confinement of square reinforced concrete (RC) columns subjected to pure compressive loads. The geometrical and mechanical parameters governing the problem are analyzed and discussed. A single-parameter methodology for predicting the axial stress–axial strain curve for FRP-confined square RC columns is described. Fundamentals, basic assumptions, and limitations are discussed. A simple design example is also presented.     

Seismic Behavior of RC Columns with Bond-Critical Regions: Criteria for Bond Strengthening Using External FRP Jackets

In 2003, an experimental research program was initiated at the American University of Beirut with the objectives of (1) evaluating the effectiveness of external fiber-reinforced polymer (FRP) confinement in improving the bond strength of spliced reinforcement in reinforced-concrete (RC) columns and its implications on the lateral load capacity and ductility of the columns under seismic loading; and (2) establishing rational design criteria for bond strengthening of spliced reinforcement using external FRP jackets. This paper presents a discussion of recent experimental results dealing with rectangular columns and the results of a pilot study conducted on circular columns with particular emphasis on aspects related to the bond strength of the spliced column reinforcement. A nonlinear analysis model is developed for predicting the envelope load–drift response, taking into account the effect of FRP confinement on the stress–strain behavior of concrete in compression. Results predicted by the model showed excellent agreement with the test results. Design expressions of the bond strength of spliced bars in FRP-confined concrete were assessed against the current experimental data, and a criterion for seismic FRP strengthening of bond-critical regions in RC members is proposed.     

Ultimate Condition of Fiber Reinforced Polymer-Confined Concrete

One important application of fiber reinforced polymer (FRP) composites is as a confining material for concrete in the retrofit of existing concrete columns by the provision of FRP jackets. Such jackets are commonly formed in a wet layup process, with the fibers being only or predominantly in the hoop direction. It has been well established in recent studies that the rupture strains/strengths of FRP measured in tests on such FRP-confined concrete cylinders fall substantially below those from flat coupon tensile tests, but the causes are unclear. This paper presents the results of a study that is aimed at clarifying these causes. To this end, the paper reports and compares the ultimate tensile strains of two types of FRP (carbon FRP and glass FRP) obtained from three types of tests—flat coupon tensile tests, ring splitting tests, and FRP-confined concrete cylinder tests. Based on comparisons of these test results, it can be concluded that the FRP hoop rupture strains in FRP-confined concrete cylinders are reduced below the ultimate tensile strains from flat coupon tests by at least three factors—(1) the curvature of the FRP jacket; (2) the deformation localization of the cracked concrete; and (3) the existence of an overlapping zone. While the first factor that reduces the in situ strain capacity of FRP on confined concrete is material dependent, the last two factors that result in a nonuniform strain distribution in the jacket are independent of the FRP material properties. The third effect reduces the average hoop rupture but does not affect the distribution of the confining pressure, as the FRP jacket is thicker in the overlapping zone.     

Model of FRP-Confined Concrete Cylinders in Axial Compression

This paper introduces a dilatancy-based analytical model of the response of an axially loaded concrete cylinder, confined with a fiber-reinforced polymer (FRP) composite jacket. Model construction is based on the experimentally based observation that the relation between axial secant stiffness and the lateral (dilatancy) strain is effectively unique for cylinders with the same unconfined concrete strength, although the confinement levels may differ. Model development incorporates strength degradation of the concrete with dilatancy (lateral dilation); this feature allows one to demonstrate that the performance of FRP-confined concrete is consistent with the strength envelope obtained from triaxial tests. Model validation is accomplished by comparisons with existing test database and the new results on large-scale concrete cylinders. The results of the validation reveal good agreement with key response functions and parameters. The present study illustrates basic constitutive equations to model FRP-confined concrete in a more rational manner.     

Analytical Model for FRP-Confined Circular Reinforced Concrete Columns

One disadvantage of most available stress–strain models for concrete confined with fiber-reinforced polymer (FRP) composites is that they do not take into consideration the interaction between the internal lateral steel reinforcement and the external FRP sheets. According to most structural concrete design codes, concrete columns must contain minimum amounts of longitudinal and transverse reinforcement. Therefore, concrete columns that have to be retrofitted (and therefore confined) with FRP sheets usually contain lateral steel. Hence, the retrofitted concrete column is under two actions of confinement: the action due to the FRP and that due to the steel ties. This paper presents a new designed-oriented confinement model for the axial and lateral behavior of circular concrete columns confined with steel ties, FRP composites, and both steel ties and FRP composites. Comparison with experimental results of confined concrete stress–strain curves shows good agreement between the test and predicted results.     

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.     

Performance Enhancement of Steel Columns Using Concrete-Filled Composite Jackets

This paper studies the cross-sectional behavior of steel columns strengthened with fiber-reinforced polymers (FRPs). The composite column is constructed by wrapping the steel I-section column with epoxy-saturated glass- and carbon-FRPs (GFRP and CFRP) sheets in the transverse direction and subsequently filling the voids between the FRP and the steel with concrete. Experimental tests were performed on stub columns under axial compression including one to three CFRP wraps. A corner treatment technique, to avoid stress concentration at the corners and to improve confinement efficiency, was also investigated. A simplified analytical model was developed to predict the axial behavior of the composite columns. Experimental results showed significant enhancement in the behavior of the composite columns primarily attributable to the confinement mechanism imposed by the FRP jacket and concrete. Increasing the corner radius resulted in higher compressive strength of the confined concrete and ultimate axial strain of the composite columns. Good agreement between the analytically developed axial load-displacement relationships and the test data indicates that the model can closely simulate the cross-sectional behavior of the composite columns.     

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.     

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.     

Shape Effect on the Performance of Carbon Fiber Reinforced Polymer Wraps

At present, fiber reinforced polymer (FRP) composite materials are extensively used to strengthen concrete structures and a main application is wrapping compression members such as building and bridge columns for improved strength and ductility. In this case, FRP laminates are intended to provide confinement to the concrete and the cross section shape plays an important role on the effectiveness of the method. The primary purpose of this paper is to introduce a test device and a test method designed to determine the effect of corner radius on the strength of the FRP laminate and on the distribution of the resulting radial stress on the substrate material. Various curvatures were investigated. In the proposed device, they can be realized by using interchangeable inserts. Strain distribution around the corner, failure load, and failure mode of the FRP laminate were monitored and analyzed. The stress concentration in the laminate is studied numerically using the finite element method and compared with experimental results. The relationship between radial stress distribution and corner radius is determined to provide guidance in practical cases.     

Experimental Study of Normal- and High-Strength Concrete Confined with Fiber-Reinforced Polymers

The experimental program reported here was conducted to gain insight into the behavior of concrete confined with fiber-reinforced polymers (FRPs). A total of 112 cylindrical concrete specimens, each 150 mm in diameter, 300 mm in height, and concrete strength up to 112 MPa, were tested under monotonic uniaxial compression. Test variables included amount of FRP, strength and stiffness of FRP, concrete strength, and the health of concrete at the time of strengthening. Results showed that, with an increase of the unconfined concrete strength, the strength enhancement, energy absorption capacity, ductility factor, and work (energy) index at rupture of FRP jackets all decreased remarkably. A positive correlation was found between concrete ductility and FRP rupture strain. A gradual post-peak failure of the specimens, observed previously from FRP-confined concrete columns tested at the University of Toronto, was also observed in some of the current tests. This ductile failure, attributed to the gradual unzipping failure of FRP jacket, is related to specimen size and is explained in terms of various confinement parameters.     

Long-Term Durability of State Street Bridge on Interstate 80

Destructive and nondestructive techniques were employed to evaluate the long-term durability of the carbon fiber reinforced polymer (CFRP) composite and externally CFRP-reinforced concrete of the State Street Bridge. Nondestructive evaluation was conducted through strain gauges, tiltmeters, thermocouples, and humidity sensors installed on the bridge bents for real-time health monitoring. Destructive tests were performed to determine the ultimate tensile strength, hoop strength, concrete confinement enhancement, and bond-to-concrete capacity of the CFRP composite for 3 years of exposure. Thermographic imaging was used for detection of voids between CFRP composite and concrete. Although environmental conditions were found to have an effect on the durability of the CFRP composite and CFRP-reinforced concrete substrate, no evidence of steel reinforcement corrosion was observed, and the CFRP composite retrofit is still effective after 3 years.     

3D Finite-Element Analysis of Substandard RC Columns Strengthened by Fiber-Reinforced Polymer Sheets

Numerical analyses are performed to predict the stress–strain behavior of square reinforced concrete columns strengthened by fiber-reinforced polymer (FRP) sheet confinement. The research focuses on the contribution of FRP sheets to the prevention of elastic buckling of longitudinal steel bars under compression, in cases of inadequate stirrup spacing. A new Drucker–Prager-type plasticity model is proposed for confined concrete and is used in constructed finite-element model. Suitable plasticity and elasticity models are used for steel reinforcing bars and fiber-reinforced polymers correspondingly. The finite-element analyses results are compared against published experimental results of columns subjected to axial compression, to validate the proposed finite-element model. Stress concentrations in concrete core and on FRP jacket are investigated considering circular or square sectioned, plain or reinforced concrete columns. Geometry of the section as well as the presence of steel bars and stirrups affect remarkably the variation and magnitude of stress on FRP as percentage of its tensile strength.