Modeling of flexural behavior of RC beams strengthened with mechanically fastened FRP strips

An alternative to fiber reinforced polymer (FRP) materials adhesively bonded to the concrete substrate is the implementation of mechanically fastened FRP (MF-FRP) systems using steel anchors to secure the laminate to the substrate. The benefit of MF-FRP, compared to adhesive bonding for FRP flexural strengthening, is the speed of installation with unskilled labor, minimal or absent surface preparation under any meteorological condition and immediate use of the strengthened structures. Some of the potential shortcomings are: possible concrete damage during anchoring and limited opportunity of installation in the presence of congested internal reinforcement in the members to be strengthened. Laboratory testing and a number of field applications have shown the effectiveness of the MF-FRP method. In this paper, an analytical model is discussed for reinforced concrete (RC) members strengthened with MF-FRP strips. The model accounts for equilibrium, compatibility and constitutive relationships of the constituent materials; in particular, it accounts explicitly for the slip between the substrate surface and the FRP strip due to the behavior of the fasteners. The proposed flexural model, coupled with the computation algorithm, is able to predict the fundamentals of the behavior of RC flexural members strengthened with MF-FRP strips, in terms of both ultimate and serviceability limit states. Comparisons between the analytical predictions and the experimental results have been successfully performed.     

Deflection behaviour of FRP reinforced concrete beams and slabs: An experimental investigation

The flexural response of FRP RC elements is investigated through load–deflection tests on 24 RC beams and slabs with glass FRP (GFRP) and carbon FRP (CFRP) reinforcement covering a wide range of reinforcement ratios. Rebar and concrete strains around a crack inducer are used to establish moment–curvature relationships and evaluate the shear and flexural components of mid-span deflections. It is concluded that the contribution of shear and bond induced deformations can be of major significance in FRP RC elements having moderate to high reinforcement ratios. Existing equations to calculate short-term deflection of FRP RC elements are discussed and compared to experimental values.     

Ultimate strength prediction for RC beams externally strengthened by composite materials

A simple and efficient computational analysis to predict the nominal moment capacity of RC beams strengthened with external FRP laminates is presented. It considers the determination of the limits on the laminate thickness in order to assure tensile failure due to steel yielding and to avoid tensile failure due to FRP laminate rupture. The study presents the design of laminate thickness to attain a specified moment capacity in a given beam. Furthermore, the study affords the approach to determine the laminate thickness of any type of composite material available that is equivalent to FRP laminate required to achieve the desired moment capacity. This approach helps in studying comparative costs of rehabilitation using different FRP materials. The analytical and experimental results of series of beams strengthened with different number of layers of glass/epoxy or carbon/epoxy FRP laminates are presented. The results show that the design guidelines presented in this study performed well in prediction of experimental results.     

Analysis and design of RC structures strengthened with mechanically fastened FRP laminates: A review

The use of Mechanically Fastened Fiber Reinforced Polymer (MF-FRP) laminates is emerging as a viable alternative to adhesively bonded FRP laminates for the rehabilitation of reinforced concrete (RC) members such as beams and slabs. A recently published state-of-the-art review of the experimental research has demonstrated the viability and effectiveness of MF-FRP systems. This paper provides a state-of-the-art review of the analytical and numerical studies performed over the last decade with the aim of: (a) predicting the strength, the load-deformation response and the failure mode of rehabilitated RC members, and (b) accounting for the interfacial behavior between the concrete and the MF-FRP laminate. Ultimate strength models and constitutive models are critically reviewed based on their key assumptions and formulations and compares the analytical predictions with previously reported experimental results.     

Experimental and analytical investigation of reinforced high strength concrete continuous beams strengthened with fiber reinforced polymer

Carbon and glass fiber reinforced polymer (CFRP and GFRP) are two materials suitable for strengthening the reinforced concrete (RC) beams. Although many in situ RC beams are of continuous constructions, there has been very limited research on the behavior of such beams with externally applied FRP laminate. In addition, most design guidelines were developed for simply supported beams with external FRP laminates. This paper presents an experimental program conducted to study the flexural behavior and redistribution in moment of reinforced high strength concrete (RHSC) continuous beams strengthened with CFRP and GFRP sheets. Test results showed that with increasing the number of CFRP sheet layers, the ultimate strength increases, while the ductility, moment redistribution, and ultimate strain of CFRP sheet decrease. Also, by using the GFRP sheet in strengthening the continuous beam reduced loss in ductility and moment redistribution but it did not significantly increase ultimate strength of beam. The moment enhancement ratio of the strengthened continuous beams was significantly higher than the ultimate load enhancement ratio in the same beam. An analytical model for moment–curvature and load capacity are developed and used for the tested continuous beams in current and other similar studies. The stress–strain curves of concrete, steel and FRP were considered as integrity model. Stress–strain model of concrete is extended from Oztekin et al.’s model by modifying the ultimate strain. Also, new parameters of equivalent stress block are obtained for flexural calculation of RHSC beams. Good agreement between experiment and prediction values is achieved.     

Structural behaviour of RC beams with external flexural and flexural–shear strengthening by FRP sheets

This paper presents experimental research on reinforced concrete (RC) beams with external flexural and flexural–shear strengthening by fibre reinforced polymer (FRP) sheets consisting of carbon FRP (CFRP) and glass FRP (GFRP). The work carried out has examined both the flexural and flexural–shear strengthening capacities of retrofitted RC beams and has indicated how different strengthening arrangements of CFRP and GFRP sheets affect behaviour of the RC beams strengthened. Research output shows that the flexural–shear strengthening arrangement is much more effective than the flexural one in enhancing the stiffness, the ultimate strength and hardening behaviour of the RC beam. In addition theoretical calculations are developed to estimate the bending and shear capacities of the beams tested, which are compared with the corresponding experimental results.     

Studies on ductility and evaluation of minimum flexural reinforcement in RC beams

Some experimental investigations on ductility and prediction of minimum flexural reinforcement in reinforced concrete (RC) beams are reported. The minimum flexural reinforcement was evaluated using optimum ductility in RC beams. Beams of size 100 mm, 200 mm and 400 mm were tested, which were designed with varying percentages of flexural reinforcement i.e. 0.15, 0.30, 0.60 and 1.0. The beams were tested under four-point loading to study the flexural behaviour under uniform bending moment. The experimentally obtained average compressive strength of concrete was 30 MPa. The influence of beam size (depth) on cracking and normalised ultimate flexural strength, ductility and overall average rotation has been studied. The cracking in RC beams is complex phenomenon in small size beams, while the cracking strength decreases as the depth increases beyond 200 mm. The flexural strength of RC beams, from the present study, appears to decrease as the depth increases. The ductility of RC beams increases as the percentage of flexural reinforcement increases. The ductility number has been derived from dimensional analysis using fracture mechanics principles. The ductility of RC beams decreases as the depth of beams increases. An optimum percentage of flexural reinforcement has been established using optimum ductility number, N_p, which is equal to 0.20. The minimum flexural reinforcement was found to decrease as the beam depth increases, and decreases as the yield strength of reinforcement increases.     

持续荷载作用下外贴FRP片材加固混凝土梁承载力影响因素分析

为探讨结构不卸载或部分卸载情况下外贴纤维片材加固时,结构初始状态对承载力设计计算的影响,根据极限状态和容许应力法分析了受弯构件加固后承载力计算公式,考查了初始弯矩对承载力的不同影响。在改变配筋率、截面尺寸、初始弯矩、加固量等参数情况下,讨论了不同初始弯矩对加固梁分别按容许应力法和按极限状态计算的承载力变化影响情况。分析显示,初始弯矩对承载力的影响均比较小;而对大尺寸的等效桥梁模型试验结果表明,初始弯矩大小对承载力计算影响最大为6.2%,为保证安全和简化计算,加固设计时可在未考虑初始弯矩情况下承载力设计值基础上考虑一定的折减系数(0.9)进行设计,且偏于安全。     

Performance of reinforced concrete beams strengthened by hybrid FRP laminates

In the last two decades, the use of advanced composite materials such as Fiber Reinforced Polymers (FRP) in strengthening reinforced concrete (RC) structural elements has been increasing. Research and design guidelines concluded that externally bonded FRP could increase the capacity of RC elements efficiently. However, the linear stress–strain characteristics of FRP up to failure and lack of yield plateau have a negative impact on the overall ductility of the strengthened RC elements. Use of hybrid FRP laminates, which consist of a combination of either carbon and glass fibers, or glass and aramid fibers, changes the behaviour of the material to a non-linear behaviour. This paper aims to study the performance of reinforced concrete beams strengthened by hybrid FRP laminates.

This paper presents an experimental program conducted to study the behaviour of RC beams strengthened with hybrid fiber reinforced polymer (HFRP) laminates. The program consists of a total of twelve T-beams with overall dimensions equal to 460 × 300 × 3250 mm. The beams were tested under cyclic loading up to failure to examine its flexural behaviour. Different reinforcement ratios, fiber directions, locations and combinations of carbon fiber reinforced polymer (CFRP) and glass fiber reinforced polymer (GFRP) laminates were attached to the beams to determine the best strengthening scheme. Different percentages of steel reinforcement were also used. An analytical model based on the stress–strain characteristics of concrete, steel and FRP was adopted. Recommendations and design guidelines of RC beams strengthened by FRP and HFRP laminates are introduced.     

Flexural response predictions of reinforced concrete beams strengthened with prestressed CFRP plates

Existing experimental studies showed that the reinforced concrete (RC) beams strengthened with prestressed carbon fiber-reinforced polymer (CFRP) plates had three possible flexural failure modes (including the compression failure, tension failure and debonding failure) according to the CFRP reinforcement ratio. Theoretical formulas based on the compatibility of strains and equilibrium of forces were presented to predict the nominal flexural strength of strengthened beams under the three failure modes, respectively, and a limitation on the tensile strain level developed in the prestressed CFRP plate was proposed as the debonding failure occurred. In addition, the calculation methods for cracking moment, crack width and deflection of strengthened beams were provided with taking into account the contribution of prestressed CFRP plates. Experimental studies on five RC beams strengthened with prestressed CFRP plates and a nonlinear finite element parametric analysis were carried out to verify the proposed theoretical formulas. The available test results conducted by other researchers were also compared with the predicted values.     

Shear capacity of reinforced concrete members strengthened in shear with FRP by using strut-and-tie models and genetic algorithms

Substantial research has been performed on the shear strengthening of reinforced concrete (RC) beams with externally bonded fibre reinforced polymers (FRP). However, referring to shear, many questions remain opened given the complexity of the failure mechanism of RC structures strengthened in shear with FRP. This paper is concerned with the development of a simple automatic procedure for predicting the shear capacity of RC beams shear strengthened with FRP. The proposed model is based on an extension of the strut-and-tie models used for the shear strength design of RC beams to the case of shear strengthened beams with FRP. By the formulation of an optimization problem solved by using genetic algorithms, the optimal configuration of the strut-and-tie mechanism of an FRP shear strengthened RC beam is determined. Furthermore, unlike the conventional truss approaches, in the optimal configuration, compressive struts are not enforced to be parallel, which represents more consistently the physical reality of the flow of forces. The proposed model is validated against experimental data collected from the existing literature and comparisons with predictions of some design proposals are also performed.     

Flexural behavior of reinforced concrete (RC) beams retrofitted with hybrid fiber reinforced polymers (FRPs) under sustaining loads

This paper reports experimental studies of reinforced concrete (RC) beams retrofitted with new hybrid fiber reinforced polymer (FRP) system consisting carbon FRP (CFRP) and glass FRP (GFRP). The objective of this study is to examine effect of hybrid FRPs on structural behavior of retrofitted RC beams and to investigate if different sequences of CFRP and GFRP sheets of the hybrid FRPs have influences on improvement of strengthening RC beams. Toward that goal, 14 RC beams are fabricated and retrofitted with hybrid FRPs having different combinations of CFRP and GFRP sheets. The beams are loaded with different magnitudes prior to retrofitting in order to investigate the effect of initial loading on the flexural behavior of the retrofitted beam. The main test variables are sequences of attaching hybrid FRP layers and magnitudes of preloads. Under loaded condition, beams are retrofitted with two or three layers of hybrid FRPs, then the load increases until the beams reach failure. Test results conclude that strengthening effects of hybrid FRPs on ductility and stiffness of RC beams depend on orders of FRP layers.     

Shear repair of RC beams using epoxy injection and hybrid external FRP

This experimental study aims at investigating the behavior of reinforced concrete (RC) beams strengthened by unidirectional and hybrid bidirectional fiber-reinforced polymer (FRP) sheets and subjected to cyclic loading. RC beams tested under cycled loading were subsequently repaired using both epoxy injection and external FRP sheets, and then re-tested under monotonic loading. Six RC beam specimens, two of which were control specimens and four were shear deficient, were upgraded with side-bonded FRP sheets in the first phase of the experimental program. In the second phase, three of the damaged beams were repaired using epoxy injection and unidirectional carbon fiber polymer (CFRP) sheets. The repairing method, FRP type, and FRP wrapping scheme were the test variables investigated. Test results show that the repair schemes imparted significant mechanical improvements in terms of ultimate shear capacity and ductility. The simultaneous application of epoxy injection and externally bonded FRP sheets was found to be a highly effective repair technique.     

Analytical approach for the flexural analysis of RC beams strengthened with prestressed CFRP

The objective of this paper is to propose a simplified analytical approach to predict the flexural behavior of simply supported reinforced-concrete (RC) beams flexurally strengthened with prestressed carbon fiber reinforced polymer (CFRP) reinforcements using either externally bonded reinforcing (EBR) or near surface mounted (NSM) techniques. This design methodology also considers the ultimate flexural capacity of NSM CFRP strengthened beams when concrete cover delamination is the governing failure mode. A moment–curvature (M–χ) relationship formed by three linear branches corresponding to the precracking, postcracking, and postyielding stages is established by considering the four critical M–χ points that characterize the flexural behavior of CFRP strengthened beams. Two additional M–χ points, namely, concrete decompression and steel decompression, are also defined to assess the initial effects of the prestress force applied by the FRP reinforcement. The mid-span deflection of the beams is predicted based on the curvature approach, assuming a linear curvature variation between the critical points along the beam length. The good predictive performance of the analytical model is appraised by simulating the force–deflection response registered in experimental programs composed of RC beams strengthened with prestressed NSM CFRP reinforcements.     

FRP约束RC矩形空心截面桥墩分析模型及试验验证

针对纤维复合材料(FiberReinforcedPolymer,FRP)约束钢筋混凝土(RC)矩形空心截面墩的抗震性能分析问题,该文提出了一种考虑有效强度系数和面积配箍率的FRP有效侧向约束力的简化计算方法。并通过与试验体桥墩的墩顶水平位移-承载力、墩底截面转动变形-弯矩曲线的对比分析,验证了该文提出简化计算模型的正确性。最后,基于该文提出的简化计算方法,对不同种类FRP约束RC矩形空心截面墩截面的抗弯承载力、曲率、塑性转动能力等抗震性能参数进行了研究,结果表明环包FRP布对空心墩的延性贡献较大,对提高其承载力影响较小。     

Experimental investigations and verification of debonding strain of RHSC continuous beams strengthened in flexure with externally bonded FRPs

Although many in-situ RC beams are of continuous constructions, there has been very little research on the behavior of such beams with external reinforcement. This article presents an experimental program conducted to study the flexural behavior and redistribution of moment of reinforced high strength concrete (RHSC) continuous beams strengthened with carbon and glass-fiber-reinforced polymer (CFRP and GFRP) sheets. The program consists of six RHSC continuous (two-span) beams with overall dimensions equal to 250 × 150 × 6000 mm. One beam was not strengthened and was tested as a control beam. Five beams were strengthened with CFRP and GFRP in flexure along their sagging and hogging regions. The main parameters including type of FRP (GFRP or CFRP), the different ratios of CFRP sheet and effectiveness of end anchorage. The test results showed that the use of GFRP sheet in strengthening of continuous beam reduced loss in ductility and moment redistribution but it did not significantly increase the ultimate strength of them. The use of end anchorage in strengthened continuous beams increased the ultimate strength and moment redistribution. The moment enhancement ratio of the strengthened continuous beams was significantly higher than the ultimate load enhancement ratio in the same beam. Also existing international codes and model such as ACI, fib, JSCE, Teng and Toutanji for prediction of IC debonding strain or stress of strengthened continuous beams are verified. Verifications were carried out based on the test results in this research and the published literature on RC continuous beams strengthened with FRP.     

CFRP加固混凝土梁各受力阶段的剥离机理

粘贴碳纤维片加固混凝土梁的试验数据和破坏模式表明,在锚固措施可靠的情况下,界面粘贴失效或基面混凝土剥离是加固混凝土梁的主要早期破坏形态。为研究混凝土梁不同受力阶段对界面粘结失效或混凝土剥离的影响程度,针对实际加固工程中常见的混凝土梁损伤状况并结合室内试验结果,分别研究了粘贴碳纤维片加固完整梁及不同开裂程度梁在不同受力阶段中的界面应力分布与剥离机理,指出了加固梁的开裂或裂缝扩展是导致界面或粘贴基面混凝土剥离的主要原因。最后,结合实际混凝土梁的损伤特点,提出了加固设计施工过程中的注意事项及应采取的技术措施。     

碳纤维布加固复合受力钢筋混凝土箱梁抗扭性能的非线性有限元分析

采用有限元方法对碳纤维布加固钢筋混凝土构件进行非线性分析,是对有限的试验研究的有效补充和进一步深入探讨。根据4根碳纤维布加固钢筋混凝土箱梁的试验研究结果,建立了合理的三维有限元模型,对碳纤维布加固钢筋混凝土箱梁在弯剪扭复合受力下的抗扭性能进行了非线性有限元分析。计算得到的扭矩-扭转角关系曲线、钢筋和碳纤维布的应变曲线以及界面粘接单元的恢复力曲线等与试验结果吻合较好,可以较好地模拟碳纤维布加固箱梁的受扭性能。进一步通过对7根数值梁的计算结果分析,提出碳纤维布加固钢筋混凝土箱梁在复合受力下的剪扭相关性符合直线方程。     

Effect of steel and synthetic fibers on flexural behavior of high-strength concrete beams reinforced with FRP bars

Six high-strength concrete beam specimens reinforced with fiber-reinforced polymer (FRP) bars were constructed and tested. Three of the beams were reinforced with carbon FRP (CFRP) bars and the other three beams were reinforced with glass FRP (GFRP) bars as flexural reinforcements. Steel fibers and polyolefin synthetic fibers were used as reinforcing discrete fibers. An investigation was performed on the influence of the addition of fibers on load-carrying capacity, cracking response, and ductility. In addition, the test results were compared with the predictions for the ultimate flexural moment. The addition of fibers increased the first-cracking load, ultimate flexural strength, and ductility, and also mitigated the large crack width of the FRP bar-reinforced concrete beams.     

高强钢绞线网--聚合物砂浆加固混凝土及预应力混凝土梁的抗弯性能试验研究

该文侧重研究了采用高强钢绞线网--聚合物砂浆加固技术三面加固普通钢筋混凝土(RC)梁和预应力混凝土(PRC)梁的抗弯性能.进行了6 片RC 梁及5 片PRC 梁的抗弯静载试验,探讨了不同初始损伤程度、有效预应力大小和加载方式等对高强钢绞线网--渗透性聚合物砂浆加固梁的抗弯性能影响.结果表明：采用高强钢绞线网--聚合物砂浆加固技术加固RC/PRC梁能够有效抑制裂缝的开展,能有效地提高RC/PRC 加固梁的抗弯承载能力和抗弯刚度;重复加载会导致加固梁刚度一定程度的退化,初始损伤程度大小不会显著改变加固后RC/PRC梁的抗弯承载力;该文研究对于大量既有RC/PRC梁的抗弯加固具有一定的参考价值.