FE Modeling of FRP-Repaired Planar Concrete Elements Subjected to Monotonic and Cyclic Loading

In this paper, a nonlinear finite-element model is developed for the analysis of plane stress members, such as RC beams and walls, strengthened either unidirectionally or bidirectionally with fiber-reinforced polymer (FRP) composites and subjected to either monotonic or cyclic loading. The model takes into account the effects of the bonded interface between the FRP and concrete while allowing slippage in each direction. A two-dimensional membrane contact element is developed to model the effects of local bond-slip with debonding failure between the FRP and concrete capable of being captured. The model has been incorporated into a finite-element program for the analysis of RC members subject to plane stress with verification against test data of FRP-strengthened RC joints, beams, and walls. The numerical results show good agreement with the experimental data for both load-displacement responses and for the overall failure mechanisms.     

Intermediate Crack Debonding in FRP-Strengthened RC Beams: FE Analysis and Strength Model

Reinforced concrete (RC) beams strengthened in flexure with a bonded fiber-reinforced polymer (FRP) plate may fail by intermediate crack (IC) debonding, in which debonding initiates at a critical section in the high moment region and propagates to a plate end. This paper first presents a finite-element (FE) model based on the smeared crack approach for concrete for the numerical simulation of the IC debonding process. This finite-element model includes two novel features: (1) the interfacial behavior within the major flexural crack zone is differentiated from that outside this zone and (2) the effect of local slip concentrations near a flexural crack is captured using a dual local debonding criterion. The FE model is shown to be accurate through comparisons with the results of 42 beam tests. The paper also presents an accurate and simple strength model based on interfacial shear stress distributions from finite-element analyses. The new strength model is shown to be accurate through comparisons with the test results of 77 beams, including the 42 beams used in verifying the FE model, and is suitable for direct use in design.     

Size Effects for Reinforced Concrete Beams Strengthened in Shear with CFRP Strips

The principal motivation of this study is to obtain a clear understanding of size effects for fiber-reinforced polymer (FRP) shear-strengthened beams. The experimental program consists of seven beams of various sizes grouped in three test series. One beam of each series is used as a benchmark and its behavior is compared with a beam strengthened with a U-shaped carbon FRP (CFRP) jacket. The third test series includes an additional beam strengthened with completely wrapped external CFRP sheets. The experimental results show that the effective axial strains of the CFRP sheets are higher in the smaller specimens. Moreover, with a larger beam size, one can expect less strain in the FRPs. A nonlinear finite-element numerical analysis is developed to model the behavior of the CFRP shear-strengthened beams. The numerical model is able to simulate the characteristics of the shear-strengthened beams, including the interfacial behavior between the concrete and the CFRP sheets. Three prediction models available in current design guidelines for computing the CFRP effective strain and shear contribution to the shear capacity of the CFRP shear-strengthened beams are compared with the experimental results.     

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.     

Numerical Cracking and Debonding Analysis of RC Beams Reinforced with FRP Sheet

Bonding a fiber reinforced polymer (FRP) sheet to the tension-side surface of reinforced concrete (RC) structures is often performed to upgrade the flexural capacity and stiffness. Except for upper concrete crushing, FRP sheet reinforcing RC structure may fail in sheet rupture, sheet peeloff failure due to opening of a critical diagonal crack, or concrete cover delamination failure from the sheet end. Accompanying the occurrence of these failure modes, reinforcing effects of the FRP sheet will be lost and load-carrying capacity of the RC structures will be decreased suddenly. This study is devoted to developing a numerical analysis method by using a three-dimensional elasto-plastic finite element method to simulate the load-carrying capacity of RC beams failed in the FRP sheet peeloff mode. Here, the discrete crack approach was employed to consider geometrical discontinuities such as opening of cracks, slipping of rebar, and debonding of the FRP sheet. Comparisons between analytical and experimental results confirm that the proposed numerical analysis method is appropriate for estimating the load-carrying capacity and failure behavior of RC beams flexurally reinforced with a FRP sheet.     

Cracking Characteristics of RC Beams Strengthened with FRP System

The cracking characteristics of fiber-reinforced polymer (FRP) strengthened reinforced concrete (RC) beams in both the short- and long-term is addressed in this paper. First, an empirical equation based on regression analysis of test results obtained from 36 beams was derived for the evaluation of crack widths in FRP-strengthened RC beams under short-term loading. The equation accounts for the effective concrete area in tension, steel stress, proximity of tensile longitudinal reinforcement, and primary crack height. Next, the long-term crack widths of glass FRP-strengthened RC beams under sustained loads were studied. Beams strengthened with glass FRP laminates showed improved cracking characteristics with smaller crack widths compared to conventional RC beams. Based on the investigation, two empirical equations are presented to compute the long-term crack widths in FRP-strengthened beams.     

Flexural and Interfacial Behavior of FRP-Strengthened Reinforced Concrete Beams

Although there is a large amount of experimental data available on the fiber-reinforced polymer (FRP) strengthening of concrete structures, a full understanding of the various debonding phenomena is somewhat lacking. As a contribution to fill this need, two-dimensional and three-dimensional (3D) nonlinear displacement-controlled finite-element (FE) models are developed to investigate the flexural and FRP/concrete interfacial responses of FRP-strengthened reinforced concrete beams. Interface elements are used to simulate the FRP/concrete interfacial behavior before and after cracking. The analysis is carried out using two different relations for the interface; namely, nonlinear and bilinear bond–slip laws. The results predicted using these two laws are compared to those based on the full-bond assumption. The FE models are capable of simulating the various failure modes, including debonding of the FRP, either at the plate end or at intermediate cracks. The 3D model is created to accommodate cases of FRP-strengthened reinforced concrete beams utilizing FRP anchorage systems. In addition, the models successfully represent the actual interfacial behavior at the vicinities of cracks including the stress/slip concentrations and fluctuations. Results are presented in terms of the ultimate load carrying capacities, failure modes and deformational characteristics. Special emphasis is placed on the FRP/concrete interfacial behavior and cracking of the concrete. The numerical results are compared to available experimental data for 25 specimens categorized in six series, and they show a very good agreement.     

Characterization of FRP Rods as Near-Surface Mounted Reinforcement

The use of near surface mounted (NSM) fiber-reinforced polymer (FRP) rods is a promising technology for increasing flexural and shear strength of deficient reinforced concrete (RC) members. As this technology emerges, the structural behavior of RC elements strengthened with NSM FRP rods needs to be fully characterized. Given the variability of material properties and groove geometry, this requires that the tensile properties of the FRP rod and the mechanics of load transfer between NSM FRP rods and concrete be investigated. Tensile and bond tests on commercially available carbon FRP deformed rods for application as NSM reinforcement were carried out using test methods that are expected to become standards in North America. Three full-size beams, one control beam and two beams strengthened in shear with NSM FRP rods, were tested. Test results are presented and compared with the predictions of a simple design approach, showing reasonable agreement.     

Strengthening RC Beams in Flexure Using New Hybrid FRP Sheet/Ductile Anchor System

This paper explores a new hybrid fiber-reinforced polymer (FRP) sheet/ductile anchor system for rehabilitation of reinforced concrete (RC) beams. The advantages of the proposed strengthening method is that it overcomes the problem of low ductility that is associated with brittle failure mode in conventional methods of strengthening beams using epoxy-bonded FRP sheets. The proposed system leads to a ductile failure mode by triggering yielding to occur in a steel anchor system (steel links) rather than by rupture or debonding of FRP sheets, which is sudden in nature. Four half-scale RC T-beams were tested under four-point bending. Three retrofitted beams were strengthened using one layer of carbon FRP sheet. The results of the two beams that were strengthened with the new hybrid FRP sheet/ductile anchor system were compared with the results from the beam strengthened with conventional FRP bonding method and the control beam. The results show the effectiveness of the proposed strengthening system in increasing flexural capacity and ductility of RC beams.     

Numerical Modeling of FRP Shear-Strengthened Reinforced Concrete Beams

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

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.     

纵筋锈蚀无腹筋混凝土梁抗剪性能细观数值研究

以钢筋混凝土梁为研究对象,考虑钢筋非均匀锈蚀膨胀效应,建立三维钢筋混凝土梁剪切破坏分析的数值分析模型。通过多阶段分析方法(钢筋锈蚀阶段,构件性能退化阶段)探索锈蚀对结构力学行为的影响。钢筋的非均匀锈蚀膨胀以施加非均匀径向位移的方式模拟,获得保护层的破坏状态,并以此“最终状态”作为之后混凝土梁静载试验的“初始条件”输入,进而模拟构件的力学行为。在验证了多阶段数值模型合理性的基础上,分析了纵筋锈蚀、剪跨比对无腹筋混凝土梁抗剪性能的影响规律。结果表明,纵筋锈蚀使混凝土梁产生明显的纵向裂缝。纵筋锈蚀率增大,保护层开裂区域增加,梁的抗剪承载力下降严重。另外,剪跨比对梁的抗剪承载力产生影响,剪跨比对未锈蚀梁的影响明显大于对锈蚀梁的影响程度。最后,基于模拟结果对相关设计规范中的抗剪承载力计算公式进行了讨论,发展建立了考虑锈蚀影响的无腹筋混凝土梁抗剪承载力计算方法。      

New Approach for Modeling the Contribution of NSM FRP Strips for Shear Strengthening of RC Beams

This paper presents the main features of an analytical model recently developed to predict the near-surface mounted (NSM) fiber-reinforced polymer (FRP) strips shear strength contribution to a reinforced concrete (RC) beam throughout the beam’s loading process. It assumes that the possible failure modes that can affect the ultimate behavior of an NSM FRP strip comprise: loss of bond (debonding); concrete semiconical tensile fracture; mixed shallow-semicone-plus-debonding; and strip tensile fracture. That model was developed by fulfilling equilibrium, kinematic compatibility, and constitutive law of both the adhered materials and the bond between them. The debonding process of an NSM FRP strip to concrete was interpreted and closed-form equations were derived after proposing a new local bond stress-slip relationship. The model proposed also addressed complex phenomena such as the interaction between the force transferred to the surrounding concrete through bond stresses and concrete fracture as well as the interaction among adjacent strips. The main features of the proposed modeling strategy are shown along with the main underlying physical-mechanical concepts and assumptions. Using recent experimental data, the predictive performance of the model is assessed. The model is also applied to single out the influence of relevant parameters on the NSM technique effectiveness for the shear strengthening of RC beams.     

Prestressed FRP Sheets for Poststrengthening Reinforced Concrete Beams

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

Flexural Strengthening of RC Beams with Externally Bonded CFRP Systems: Test Results and 3D Nonlinear FE Analysis

This paper presents experimental results and a numerical analysis of the reinforced concrete (RC) beams strengthened in flexure with various externally bonded carbon fiber-reinforced polymer (CFRP) configurations. The aim of the experimental work was to investigate the parameters that may delay the intermediate crack debonding of the bottom CFRP laminate, and increase the load carrying capacity and CFRP strength utilization ratio. Ten rectangular RC specimens with a clear span of 4.2?m, categorized in two series, were tested to evaluate the effect of using the additional U-shaped CFRP systems on the intermediate crack debonding of the bottom laminate. Two different configurations of the additional systems were proposed, namely, continuous U-shaped wet layup sheets and spaced side-bonded CFRP L-shaped laminates. The fiber orientation effect of the side-bonded sheets was also investigated. A numerical analysis using an incremental nonlinear displacement-controlled 3D finite-element (FE) model was developed to investigate the flexural and CFRP/concrete interfacial responses of the tested beams. The finite-element model accounts for the orthotropic behavior of the CFRP laminates. An appropriate bond-slip model was adopted to characterize the behavior of the CFRP/concrete interface. Comparisons between the FE predictions and experimental results show very good agreement in terms of the load-deflection and load-strain relationships, ultimate capacities, and failure modes of the beams.     

Interaction between Steel Stirrups and Shear-Strengthening FRP Strips in RC Beams

RC beams shear strengthened with either fiber-reinforced polymer (FRP) U-jackets/U-strips or side strips commonly fail due to debonding of the bonded FRP shear reinforcement. As such debonding occurs in a brittle manner at relatively small shear crack widths, some of the internal steel stirrups may not have reached yielding. Consequently, the yield strength of internal steel stirrups in such a strengthened RC beam cannot be fully used. In this paper, a computational model for shear interaction between FRP strips and steel stirrups is first presented, in which a general parabolic crack shape function is employed to represent the widening process of a single major shear crack in an RC beam. In addition, appropriate bond-slip relationships are adopted to accurately depict the bond behavior of FRP strips and steel stirrups. Numerical results obtained using this computational model show that a substantial adverse effect of shear interaction generally exists between steel stirrups and FRP strips for RC beams shear strengthened with FRP side strips. For RC beams shear strengthened with FRP U-strips, shear interaction can still have a significant adverse effect when FRP strips with a high axial stiffness are used. Therefore, for accurate evaluation of the shear resistance of RC beams shear strengthened with FRP strips, this adverse effect of shear interaction should be properly considered in design.     

Numerical Model for Tracing the Response of FRP-Strengthened RC Beams Exposed to Fire

This paper presents the development of a numerical model for evaluating the performance of fiber-reinforced polymer (FRP)-strengthened RC beams under fire conditions. The model is based on a macroscopic finite-element approach and utilizes moment-curvature relationships to trace the response of insulated FRP-strengthened RC beams from linear elastic stage to collapse under any given fire exposure and loading scenarios. In the analysis, high temperature properties of constitutive materials, load and restraint conditions, material and geometric nonlinearity are accounted for, and a realistic failure criterion is applied to evaluate the failure of the beams. The model is validated against fire test data on FRP-strengthened RC beams and is applied to study the effect of FRP-strengthening, insulation scheme, and failure criterion on the fire response of FRP-strengthened RC beams. Results from the analysis indicate that FRP-strengthened RC beams should be protected with supplemental fire insulation to satisfy fire resistance requirements. A case study is presented to illustrate the application of the model for optimizing the fire insulation scheme to achieve required fire resistance in FRP-strengthened concrete beams.     

Debonding in RC Beams Shear Strengthened with Complete FRP Wraps

Substantial research has been conducted on the shear strengthening of reinforced concrete (RC) beams with bonded fiber reinforced polymer (FRP) strips. The beams may be strengthened in various ways: complete FRP wraps covering the whole cross section (i.e., complete wrapping), FRP U jackets covering the two sides and the tension face (i.e., U jacketing), and FRP strips bonded to the sides only (i.e., side bonding). Shear failure of such strengthened beams is generally in one of two modes: FRP rupture and debonding. The former mode governs in almost all beams with complete FRP wraps and some beams with U jackets, while the latter mode governs in all beams with side strips and U jackets. In RC beams strengthened with complete wraps, referred to as FRP wrapped beams, the shear failure process usually starts with the debonding of FRP from the sides of the beam near the critical shear crack, but ultimate failure is by rupture of the FRP. Most previous research has been concerned with the ultimate failure of FRP wrapped beams when FRP ruptures. However, debonding of FRP from the sides is at least a serviceability limit state and may also be taken as the ultimate limit state. This paper presents an experimental study on this debonding failure state in which a total of 18 beams were tested. The paper focuses on the distribution of strains in the FRP strips intersected by the critical shear crack, and the shear capacity at debonding. A simple model is proposed to predict the contribution of FRP to the shear capacity of the beam at the complete debonding of the critical FRP strip.     

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.     

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.