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.     

Model for Analysis of Short Columns of Concrete Confined by Fiber-Reinforced Polymer

This paper presents a numerical model for evaluating the behavior of axially loaded rectangular and cylindrical short columns of concrete confined by fiber-reinforced polymer (FRP) composites. The proposed formulation considers, for unconfined and confined compressed concrete, a uniaxial constitutive relation that utilizes the area strain as a parameter of measure of the material secant axial stiffness. For unconfined concrete, the model adopts an explicit relationship between axial strain and lateral strain, while for confined concrete, an implicit relation is considered. For this last case, the model employs a simple iterative-incremental approach that describes the entire stress-strain response of the columns. The behavior of the FRP is considered linear elastic until the rupture. To validate the model, a number of columns were analyzed and the numerical results were compared with experimental values published by other authors. This comparison between experimental and numerical results indicates that the model provides satisfactory predictions of the stress-strain response of the 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.     

Confinement Effectiveness in Rectangular Concrete Columns with Fiber Reinforced Polymer Wraps

An innovative mechanistic based method for passive confinement efficiency estimation is proposed based on the extension to rectangular sections of the pulley model previously proposed by the writers. A refined finite element model was developed using a nonlinear concrete constitutive law in order to analyze stresses in columns passively confined with fiber reinforced polymer wraps. Rectangular and square cross sections of variable corner radii were investigated with reference to a circular cross section. Results showed an increase in corner stresses with sharper corner radii, a localization of failure at the corners, and a decrease in confinement effectiveness with an increase in the rectangularity of the cross section or an increase in corner sharpness. A rigorous numerical method for calculating geometric confinement efficiency factors is proposed and typical factors are calculated and compared with the predictions of the simple pulley model showing good agreement.     

Concrete Contribution to the Shear Resistance of Fiber Reinforced Polymer Reinforced Concrete Members

Seven beams were tested in bending to determine the concrete contribution to their shear resistance. The beams had similar dimensions and concrete strength and were reinforced with carbon fiber reinforced polymer bars for flexure without transverse reinforcement. They were designed to fail in shear rather than flexure. The test variables were the shear span to depth ratio, varying from 1.82 to 4.5, and the flexural reinforcement ratio, varying from 1.1 to 3.88 times the balanced strain ratio. The test results are analyzed and compared with the corresponding predicted values using the American Concrete Institute, the Canadian Standard, and the Japan Society of Civil Engineers (JSCF) fiber reinforced polymer design recommendations. Based on these results and previous experimental data, it is shown that the ACI recommendations are extremely conservative whereas the Canadian and JSCE recommendations, albeit still conservative, are in closer agreement with the experimental data. Overall the Canadian Standard’s predictions are in better agreement with experimental data than the JSCE predictions.     

Behavior of Gravity Load-Designed Rectangular Concrete Columns Confined with Fiber Reinforced Polymer Sheets

This study concentrates on analytical evaluation of the effect of external confinement using fiber reinforced polymers (FRP) sheets on the response of concrete rectangular columns designed for gravity load only and having spliced longitudinal reinforcement at the column base. A general analytical scheme for evaluating the strength capacity and ductility of the columns under combined flexural–axial loads was developed. The analysis takes into account the bond strength degradation of the spliced reinforcement with increase in lateral load by incorporating a generalized bond stress–slip law, and considers the effect of FRP confinement on the stress–strain response of concrete material. Particular emphasis is placed in the analysis on the slip response of the spliced bars and the consequent fixed end rotation that develops at the column base. Results predicted by the analysis showed very good agreement with limited experimental data. A parametric evaluation was carried out to evaluate the effect of different design and strength parameters on the column response under lateral load. Without confinement, the columns suffered premature bond failure and, consequently, low flexural strength capacity. Confining the concrete in the columns end zone at the splice location with FRP sheets enhanced the bond strength capacity of the spliced reinforcement, increased the steel stress that can be mobilized before bond failure occurs, and consequently improved the flexural strength capacity and ductility of the columns. A general design equation, expressed as a function of the main parameters that influence the bond strength capacity between spliced steel bars and FRP confined concrete, is proposed to calculate the area of FRP sheets needed for strengthening of the subject columns.     

Response of Fiber Reinforced Polymer Confined Concrete Exposed to Freeze and Freeze-Thaw Regimes

Unidirectional carbon/vinylester composites and concrete cylinders wrapped with three layers of the same composite were exposed to ?18°C (0°F) conditions both with and without prior saturation by moisture and to freeze-thaw cycling after saturation. All specimens show degradation in strength, with the maximum degradation being due to the saturated freeze-thaw condition caused by cyclic effects of absorption, subsequent crack-opening and fiber-matrix debonding. Analytical predictions, based on approximation of hygrothermomechanical response models for composites combined with a simple confinement model, are shown to correlate well with experimental data for most of the exposure conditions.     

Analytical Models for Concrete Confined with FRP Tubes

Concrete columns encased in fiber-reinforced polymer (FRP) tubes offer an attractive solution to enhance behavior of concrete in terms of strength as well as ductility. Analytical models for development of stress-strain curves for concrete confined with FRP are proposed in this paper. The predicted stress-strain curves for confined concrete using the proposed models are compared with those of tests for concrete specimens confined with FRP. It is demonstrated that the proposed models predict the stress-strain behavior of confined concrete very well. Based on the confidence gained in the proposed models, the effects of using different fibers, the presence of voids, and the number of layers are established.     

Simple Carbon-Fiber-Reinforced-Plastic-Confined Concrete Model for Moment-Curvature Analysis

This paper presents a simple model to calculate concrete properties for reinforced concrete members that are confined by carbon-fiber-reinforced plastic (CFRP) sheets. The model simplifies and incorporates formulas from some of the existing models. Results are examined for typical circular and square columns with a range of cross-section dimensions and axial loads. Results demonstrate that the proposed simple model is quite sufficient in calculating moment-curvature relationships of CFRP-confined members.     

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.     

Global Constitutive Model for Reinforced Concrete Plates

A new constitutive model for reinforced concrete plates using global variables is discussed in this work. It includes the modeling of concrete cracking (through damage) and the plastic yielding of steel. The yield surface, derived from limit analysis, generalizes the Johansen’s criterion by taking into account both membrane and bending behaviors in reinforced concrete plates. Compared to three-dimensional models, this stress resultant model gives reliable results and can be applied to the study of large shell structures.     

Role of Fiber Reinforced Plastic Sheets in Shear Response of Reinforced Concrete Beams: Experimental and Analytical Results

The paper is principally aimed at analyzing the role of externally applied fiber reinforced plastic (FRP) sheets in the shear ultimate behavior of reinforced concrete elements. A theoretical model for predicting the shear resisting contribution of FRP sheets is illustrated. The proposal is based on a complete equilibrium/compatibility approach for reinforced concrete beams failing in shear and considers the possible interactions between the composite contribution and the resisting mechanisms of an ordinary reinforced concrete beam. The proposal is discussed and tested by means of an experimental investigation carried out on beams reinforced by glass FRP composite sheets with a shear span to depth ratio equal to 3. Further comparisons are then performed that consider the predictions of other existing approaches reported in the literature.     

Dynamic Behavior of Reinforced Concrete Beams Strengthened with Composite Materials

The dynamic behavior of reinforced concrete (RC) beams strengthened with externally bonded composite materials is analytically investigated. The analytical model is based on dynamic equilibrium, compatibility of deformations between the structural components (RC beam, adhesive, composite material) and the concept of the high order approach. The equations of motion along with the boundary and continuity conditions are derived using Hamilton’s variational principle and the kinematic relations of small deformations. The mathematical formulation also includes the constitutive laws that are based on beam and lamination theories, and the two-dimensional elasticity representation of the adhesive layer including the closed form solution of its stress and displacement fields. The Newmark time integration method, which is directly applied to the resulting set of coupled partial differential equations, is adopted. This procedure yields a set of ordinary differential equations, which are analytically or numerically solved in every time step. The response of a strengthened beam to different dynamic loads that include impulse load, harmonic load, and seismic base excitation is numerically investigated. The numerical study highlights some of the phenomena associated with the dynamic response and explores the capabilities of the proposed model. The paper closes with a summary and conclusions.     

Ductile Design of Reinforced Concrete Beams Retrofitted with Fiber Reinforced Polymer Plates

For reinforced concrete beams retrofitted with fiber-reinforced polymer (FRP) plates, an analytical method is derived for determining the allowable plate area to achieve a targeted value of ductility. Nonlinear models for concrete and reinforcement are applied, and the effects of concrete confinement and spalling and of FRP plate rupture are considered. The derivation of equilibrium and compatibility equations for a rectangular cross section is presented, and the solution to the nonlinear equation for determining the allowable plate area is demonstrated with examples. Analytical results are compared with numerical and experimental data reported in the literature. Subsequently a simplified version of the method is derived, based on regression analysis, to relate the curvature ductility to the FRP plate ratio. It is noted that additional conditions need to be checked to ensure ductile performance, such as local failure of the concrete layer between tension reinforcement and FRP plate or debonding of the plate itself.     

Effects of Loading Rate and Duration on Axial Behavior of Concrete Confined by Fiber-Reinforced Polymer Sheets

In this study, 18 concrete cylinder specimens were tested either under uniaxial compression at different loading rates or exposed to sustained axial stresses after being jacketed externally with carbon-fiber-reinforced polymer (CFRP) sheets. The specimens were cast using medium strength concrete. All the specimens had identical dimensions and level of confinement. Loading rate and applied sustained stress level were the main test parameters. Applied loading rate varied between 0.0002 and 0.04 strain/min. Four stress levels between 0.52 and 0.85fcc′ (0.90 and 1.46fco′) were used in short-term creep tests. Test results showed that the stress-strain behavior of CFRP confined concrete was influenced by the change in loading rate, and CFRP confinement provided considerable increase in the creep performance of concrete. The strength enhancement was more pronounced for specimens loaded at higher strain rates, while specimens loaded at slower strain rates exhibited better deformability. Results obtained from short-term monotonic loading tests were also compared with the results of two analytical approaches originally developed for plain concrete. None of the specimens failed during the short-term creep tests. However, the lifetime of the specimen, which was subjected to 0.85fcc′ (1.46fco′) sustained axial stress, was predicted as 20 days. Results of residual strength tests showed that specimens did not have any strength loss due to sustained loading.     

Strength-Fatigue Behavior of Fiber Reinforced Polymer Strengthened Prestressed Concrete T-Beams

Strengthening concrete girders with fiber-reinforced polymers (FRP) is becoming an increasingly common practice as more research investigations are favorably qualifying the technique. However, important behavioral aspects, such as fatigue in prestressed concrete beams, are yet to be adequately evaluated. An experimental program was conducted to test five pretensioned, prestressed concrete T beams designed for specific prestressing strand stress ranges under live-load conditions. The experimental testing consisted of precracking the beams, strengthening them with carbon FRP, and mechanically loading them to study the effect of increasing the live load on strand fatigue. The beams were either loaded monotonically to ultimate capacity or cyclically fatigued and then loaded monotonically to failure. All the beams were monotonically loaded past their cracking moment at midspan prior to strengthening, to simulate girders in the field. Beam 1 was tested as a control specimen under static loading up to failure. Beams 2 and 3 were strengthened with carbon FRP to have a design stress range of 124 MPa (18 ksi) under service load condition. Beams 4 and 5 were strengthened to have a higher stress range of 248 MPa (36 ksi). For all the strengthened beams, the failure mode observed was FRP rupture. The results favorably qualify the application of FRP strengthening to increase the live load of concrete beams prestressed with straight strands.     

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.     

Development of the Nonlinear Bond Stress–Slip Model of Fiber Reinforced Plastics Sheet–Concrete Interfaces with a Simple Method

A new analytical method for defining the nonlinear bond stress–slip models of fiber reinforced plastics (FRP) sheet–concrete interfaces through pullout bond test is proposed. With this method, it is not necessary to attach many strain gauges on the FRP sheets for obtaining the strain distributions in FRP as well as the local bond stresses and slips. Instead, the local interfacial bond stress-slip models can be simply derived from the relationships between the pullout forces and loaded end slips. Based on a series of pullout tests, the bond stress–slip models of FRP sheet–concrete interfaces, in which different FRP stiffness, FRP materials (carbon FRP, aramid FRP, and glass FRP), and adhesives are used, have been derived. Only two parameters, the interfacial fracture energy and interfacial ductility index, which can take into account the effects of all interfacial components, are necessary in these models. Comparisons between analytical results and experimental ones show good accordance, indicating the reliability of the proposed method and the proposed bond stress–slip models.     

Fiber Reinforced Polymer Shear Strengthening of Reinforced Concrete Beams with Transverse Steel Reinforcement

The paper aims to contribute to a better understanding and modeling of the shear behavior of reinforced-concrete (RC) beams strengthened with carbon fiber reinforced polymer (FRP) sheets. The study is based on an experimental program carried out on 11 beams with and without transverse steel reinforcement, and with different amounts of FRP shear strengthening. The test results provide some new insights into the complex failure mechanisms that characterize the ultimate shear capacity of RC members with transverse steel reinforcement and FRP sheets. After the discussion of the above topics, a new upper bound of the shear strength is introduced. It should be capable of taking into account how the cracking pattern in the web failing under shear is modified by the presence of FRP sheets, and how such a modified cracking pattern actually modifies the anchorage conditions of the sheets and their effective contribution to the ultimate shear strength of the beams.     

Reinforced Concrete T-Beams Strengthened in Shear with Fiber Reinforced Polymer Sheets

This research studies the interaction of concrete, steel stirrups, and external fiber reinforced polymer (FRP) sheets in carrying shear loads in reinforced concrete beams. A total of eight tests were conducted on four laboratory-controlled concrete T-beams. The beams were subjected to a four-point loading. Each end of each beam was tested separately. Three types of FRP, uniaxial glass fiber, uniaxial carbon fiber, and triaxial glass fiber, were applied externally to strengthen the web of the T-beams, while some ends were left without FRP. The test results show that FRP reinforcement increases the maximum shear strengths between 15.4 and 42.2% over beams with no FRP. The magnitude of the increased shear capacity is dependent not only on the type of FRP but also on the amount of internal shear reinforcement. The triaxial glass fiber reinforced beam exhibited more ductile failure than the other FRP reinforced beams. This paper also presents a test model that is based on a rational mechanism and can predict the experimental results with excellent accuracy.