Stress–strain and deflection relationships of RC beam bonded with FRPs under sustained load

Fiber-reinforced polymer (FRP) systems that have a strong resistance against long-term deformation must provide improved serviceability to reinforced concrete (RC) members under sustained loads. Consequently, there is a need to develop a method for accurately predicting the time-dependent behavior of RC beams that are externally bonded with FRPs. However, there are very few previous studies that have been carried out or experimental results available, on the time-dependent behavior of RC beams externally bonded with FRP. In order to enable a reasonable prediction, correlations should first be clarified between the stress–strain relationship of the concrete, the reinforcement and the FRP that changes over time. By using these correlations, deflections under sustained loads should then be forecast. In this study, RC beams were fabricated for this purpose. Carbon reinforced polymer (CFRP) and glass reinforced polymer (GFRP) materials were bonded to the tension face of the two respective RC beams. The beams were then placed under sustained loads for 300 days. For the specimens that were externally bonded with FRPs and for the conventional specimen, the strain of the compression and tension reinforcement and the strain of FRP and deflection were measured respectively for comparison. In order to theoretically predict the time-dependent behavior of the RC Beam externally bonded with FRPs, creep coefficients for concrete and shrinkage strains were calculated by using the CEB-FIP and the ACI-209 Codes. For the method used to forecast the stress–strain relationships of the concrete, reinforcement and FRPs that change over time were theoretically clarified and were then compared with the experimental results. The deflection of the RC Beams externally bonded with FRP was predicted by using the ACI 318 Standard, EMM, AEMM, Branson’s method, and Mayer’s method. They were also compared to the experimental results. Subsequently, in the case of RC Beams externally bonded with FRPs under sustained loads, the proposed method proved that it is possible to accurately predict long-term deformations.     

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。     

Design equations for reinforced concrete members strengthened in shear with external FRP reinforcement formulated in an evolutionary multi-objective framework

Methods for predicting the shear capacity of FRP shear strengthened RC beams assume the traditional approach of superimposing the contribution of the FRP reinforcing to the contributions from the reinforcing steel and the concrete. These methods become the basis for most guides for the design of externally bonded FRP systems for strengthening concrete structures. The variations among them come from the way they account for the effect of basic shear design parameters on shear capacity. This paper presents a simple method for defining improved equations to calculate the shear capacity of reinforced concrete beams externally shear strengthened with FRP. For the first time, the equations are obtained in a multiobjective optimization framework solved by using genetic algorithms, resulting from considering simultaneously the experimental results of beams with and without FRP external reinforcement. The performance of the new proposed equations is compared to the predictions with some of the current shear design guidelines for strengthening concrete structures using FRPs. The proposed procedure is also reformulated as a constrained optimization problem to provide more conservative shear predictions.     

Improved model for plate-end shear of CFRP strengthened RC beams

In case of RC members strengthened by means of externally bonded reinforcement, a premature failure can be detected in addition to the conventional modes of failure observed in RC unstrengthened beams. The premature failure occurs mainly due to both shear and normal stresses induced in either the external reinforcement–concrete interface or at the level of steel reinforcement. This research is part of a complete programme aiming to set up design formulae to predict the strength of CFRP strengthened beams, particularly when premature failure through laminates-end shear or concrete cover delamination occurs. Series of RC beams were strengthened with carbon-fiber-reinforced plastic (CFRP) laminates and tested to estimate the extent of the applicability of the formulae proposed by the authors, as well as to study the influence of the layout of the external reinforcement in terms of unsheeted length (the distance between CFRP laminates-end and the nearer support) and cross-sectional area, on the behaviour of strengthened beams. The predictions using the proposed formulae are compared with the obtained experimental results, as well as with the calculated design limit states. The interfacial shear stress and the maximum deflection corresponding to the predicted values at maximum and service loads are also studied.     

Coupled flexural-shear design of R/C beams strengthened with FRP

The ultimate strength of reinforced concrete beams retrofitted in flexure and shear by means of externally bonded fiber reinforced polymers (FRP) has attracted the attention of many researchers due to the particularities highlighted by a wide set of experimental results. In fact, an increase of the external reinforcement area does not always lead to the expected increase of the beam load capacity, due to the interaction of flexural and shear behaviour within the discontinuity regions of the strengthened element. In this paper, the available experimental data are considered and, in the light of an equilibrated equivalent truss model, a theoretical explanation of the observed behaviour is presented. A new definition of the design strength of the externally bonded FRP reinforcement is proposed, for both flexural plates and shear ties, taking into account the ultimate anchorage force.In the first part of the paper, the model is presented and discussed; in the second part, the proposed model is validated by comparison with more than 100 experimental results. The application to the available experimental tests shows the robustness of the method, which appears to be fully eligible as a design practice procedure.     

U形CFRP条带混锚加固混凝土梁抗剪试验

为解决纯粘贴U形纤维增强聚合物基复合材料（FRP）加固钢筋混凝土梁中FRP端部容易发生剥离破坏等问题,自主研发了对纤维布条带端部进行自锁锚固的方法和锚板,提出了端锚与粘贴并用的混锚U形条带抗剪加固方法。通过2根未加固梁、1根纯粘贴和2根混锚U形碳纤维增强聚合物基复合材料（CFRP）带抗剪加固梁的对比试验,证实了混锚抗剪加固的有效性：混锚能够对纤维带端部进行可靠锚固,阻止端部剥离破坏的发生,实现纤维拉断破坏,大幅度提高材料强度利用率。混锚加固在抑制混凝土梁斜裂缝开展、延缓箍筋屈服、提高箍筋和CFRP的极限应变以及提高抗剪承载力等多个方面的表现均明显优于纯粘贴加固。     

环境温差下FRP-混凝土界面粘结行为分析

为明确环境温差对纤维增强聚合物(FRP)加固混凝土构件的界面粘结性能的影响,基于粘结界面的双参数内聚力指数模型,建立了FRP-混凝土粘结结点在温差作用下的界面微分平衡方程,采用边界条件叠加的方法,解析推导了界面相对滑移、界面剪应力和FRP应力-应变分布计算公式。基于解析理论模型,提出了FRP-混凝土界面最大承载温差的计算方法,分析了粘结长度、温差变化和粘结层数对界面粘结性能的影响。结果表明:该文推导出的理论公式计算结果与界面试验结果吻合良好,建立的解析理论模型能够较好地预测温差作用下FRP-混凝土界面粘结行为;界面最大承载温差随粘结长度的增加存在上限值,且由于界面粘结性能的退化,FRP温度应力的最大值出现在达到界面最大承载温差之前;界面剪应力集中在粘结端部区域,受温差变化和FRP粘结层数影响较大,且当环境温差进入胶黏剂玻璃化转变区域后影响最为明显。该结论可用于强日照和高温车间等大温差环境下桥梁和建筑加固构件的温度应力分析和界面承载力评估。     

Prediction of the ultimate strength of reinforced concrete beams FRP-strengthened in shear using neural networks

In the last years, a great number of experimental tests have been performed to determine the ultimate strength of reinforced concrete beams retrofitted in shear by means of externally bonded fibre-reinforced polymers (FRP). Most of design proposals for shear strengthening are based on a regression analysis from experimental data corresponding to specific configurations which makes very difficult to capture the real interrelation among the involved parameters. To avoid this, an artificial neural network has been developed to predict the shear strength of concrete beams reinforced with this method from previous tests. Furthermore, a parametric study has been carried out to determine the influence of some beam and external reinforcement parameters on the shear strength with the purpose of reaching more reliable designs. Finally, some modifications of the design expressions are proposed and checked with experimental results.     

Strengthening RC beams with composite fiber cement plate reinforced by prestressed FRP rods: Experimental and numerical analysis

This paper deals with the development of a new strengthening system for reinforced concrete beams with externally-bonded plate made of composite fiber cement reinforced by rebars made of fiber-reinforced plastic (FRP) [1]. The proposed strengthening material involves the preloading of FRP rod before mortar casting. The paper presents experimental and numerical analysis carried out on many large-scale beams strengthened by well-known reinforcement techniques, such as externally bonded Carbon Fiber-Reinforced Plastic (CFRP) plate and the Near Surface Mounted (NSM) technique, which are compared to the proposed new strengthening material through four-point bending tests. Results are analyzed with regard to the load-displacement curve, bending stiffness, cracking load, yield strength and failure load. The developed numerical model is in agreement with the experimental results. It clearly shows the effects of prestressed FRP rod on cracking mechanisms and internal strength distribution in the analyzed beams.     

Fatigue strengthening of damaged metallic beams using prestressed unbonded and bonded CFRP plates

Bonded fiber reinforced polymers (FRPs) reinforcement systems have traditionally been found to be an efficient method for improving the lifespan of fatigued metallic structures and have attracted much research attention. Nevertheless, the performance of a bonded FRP reinforcement system under fatigue loading is basically dependent on the FRP-to-metal bond behavior. In this paper, a prestressed unbonded reinforcement (PUR) system was developed. The proposed PUR system can be used as an alternative to bonded FRP reinforcement, particularly when there is concern about the effects of high ambient temperatures, moisture, water and fatigue loading on the FRP-to-metal bond behavior. The performance of cracked beams strengthened by the PUR system was compared with that of cracked beams strengthened by the prestressed bonded reinforcement (PBR) system. A theoretical method was developed to estimate the level of prestressing sufficient to arrest fatigue crack growth (FCG). Furthermore, the method was used to examine different passive, semi-active and active crack modes with a loaded, strengthened beam. The mechanism by which a prestressed FRP plate forms a compressive stress field at the vicinity of the crack tip was also examined. Finite element (FE) modeling was conducted and the results were compared with experimental results.     

Influence of the properties of externally bonded CFRP on the shear behavior of concrete/composite adhesive joints

This paper concerns the strengthening of concrete structures with externally bonded composite reinforcement, and focuses mainly on the influence of the FRP characteristics on the mechanical behavior of the composite to concrete interface. An experimental investigation was conducted, based on the characterization of such bonded assemblies and using a double lap joint shear test. Twelve different series of specimens were studied in order to evaluate the influence of various parameters related to the FRP material (i.e. the use of carbon or aramid and of fiber reinforced systems, the type of manufacturing process, the values of the Young modulus, the thickness of the FRP and the bonded length) as well as several parameters related to the adhesive joint (i.e. the lap joint thickness, the curing conditions and the elastic modulus of the epoxy adhesive). Analyses of the strain and shear stress distributions along the lap joints emphasized significant effects of the FRP properties and epoxy curing conditions on the interfacial strength. In addition, a bond strength model is proposed in the last part of the study.     

有粘结和无粘结相结合的预应力FRP筋混凝土梁抗弯承载力研究

纤维增强塑料筋(简称FRP 筋)是一种高强线弹性材料,非常适合用做侵蚀环境下的预应力筋,采用有粘结和无粘结相结合是提高预应力FRP 筋混凝土梁延性的一种新方法。对有粘结和无粘结相结合的预应力FRP 筋混凝土梁的抗弯承载力进行了理论分析和试验研究,基于平衡配筋率定义了有粘结和无粘结相结合的预应力FRP筋混凝土梁的破坏形态,推导了平衡配筋率和相应抗弯承载力的计算公式。为了验证公式的正确性,进行了9 根预应力FRP 筋混凝土梁的试验研究,计算结果与试验结果吻合良好。研究结果表明,在相同配筋的条件下,体内有粘结预应力FRP 筋混凝土梁的承载力最高,体内无粘结预应力FRP 筋混凝土梁的承载力其次,而无转向块的体外无粘结预应力FRP 筋混凝土梁的承载力最低。采用体内有粘结和无粘结预应力相结合,可以改善预应力FRP筋混凝土梁的延性。     

Interfacial shear stress in FRP-plated RC beams under symmetric loads

A recently popular method for retrofitting reinforced concrete (RC) beams is to bond fibre-reinforced polymer (FRP) plates to their soffits. An important failure mode of such plated beams is debonding of the FRP plates from the concrete due to high level interfacial stresses near the plate ends. A closed-form rigorous solution for the interfacial stresses in simply supported beams bonded with thin plates and subjected to arbitrary loads has been found, in which a non-uniform stress distribution in the adhesive layer was taken into account. This paper uses the rigorous solution to investigate the impact of symmetric loading configurations on the interfacial shear stress distributions, and concludes that the bending moments on the cross sections at the plate ends play a significant role in terms of stress concentration, while the shear forces on the same cross-section contribute little to the concentration. On the basis of this observation, this paper proposes a simplified approximate solution to the shear stress along the interface between concrete and adhesive layer. Compared with the rigorous and other approximate solutions, the simplified solution exhibits sufficient accuracy in terms of stress distribution and stress concentration localized near the plate ends. Due to its compact feature, the simplified solution is more suitable for engineering applications using a portable calculator and to be adopted in the codes of practices.     

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.     

Interfacial shear stress concentration in FRP-strengthened beams

This paper reports the results of an experimental programme designed to study the interfacial shear stress concentration at the plate curtailment of reinforced concrete (RC) beams strengthened in flexure with externally bonded carbon fibre-reinforced polymer (CFRP). Specifically, the study looks at the relationship between the CFRP plate thickness and the interfacial shear stress concentration at the plate curtailment, the failure modes of the CFRP-strengthened beams as well as the efficiency of the CFRP external reinforcing system. Comparing the experimental results with existing models' predictions is another objective of this study. The experimental programme included five RC beams 115 mm×150 mm in cross-section and 1500 mm in length. Four of the RC beams were reinforced externally with CFRP plates of different thicknesses. Tests in this study showed that the thickness of CFRP plate affects not only the load-carrying and deflection capacities of the strengthened beam, but also the shear stress concentration at the CFRP/concrete interface and the beam failure mode.     

FRP strengthening of steel and steel-concrete composite structures: an analytical approach

A recent technique for strengthening steel and steel-concrete composite structures by the use of externally bonded Fiber Reinforced Polymer (FRP) sheets, to increase the flexural capacity of the structural element, is described. Several researches developed FRP strengthening of reinforced concrete and masonry structures, but few experimental studies about steel and steel-concrete composite elements are available. Some examples of guidelines for the design and construction of externally bonded FRP systems for strengthening existing metal structures are available, but the method used to predict the flexural behaviour of FRP strengthened elements is usually based on the hypothesis of elastic behaviour of materials and FRP laminate is mainly considered only under the tensile flange. In this paper, an analytical procedure to predict the flexural behaviour of FRP strengthened steel and steel-concrete composite elements, based on cross-sectional behaviour and taking into account the non-linear behaviour of the materials with any configuration of FRP reinforcement, is given. Analytical predictions are compared with some experimental results available in the literature on the flexural behaviour of FRP strengthened steel and steel-concrete composite elements, showing good agreement of the results, even in the non-linear phase, until failure.     

Shear strengthening of RC deep beams using externally bonded FRP systems

According to the available methods of analysis and design for reinforced concrete deep beams, addition of web reinforcement beyond the minimum amount provides only a marginal strength gain, if it does at all. This casts serious doubts on the feasibility and extent of strengthening by placing external reinforcement in the web, whenever such a need arises. This study therefore explores the prospect of strengthening structurally deficient deep beams by using an externally bonded fibre reinforced polymer (FRP) system. Six identical beams were fabricated and tested to failure for this purpose. One of these beams was tested in its virgin condition to serve as reference, while the remaining five beams were tested after being strengthened using carbon fibre wrap, strip or grids. The results of these tests are presented and discussed in this paper. Test results have shown that the use of a bonded FRP system leads to a much slower growth of the critical diagonal cracks and enhances the load-carrying capacity of the beam to a level quite sufficient to meet most of the practical upgrading requirements.     

Strengthening of RC beams with epoxy-bonded fibre-composite materials

Strengthening of concrete beams with externally bonded fibre-reinforced plastic (FRP) materials appears to be a feasible way of increasing the load-carrying capacity and stiffness characteristics of existing structures. FRP-strengthened concrete beams can fail in several ways when loaded in bending. The following collapse mechanisms are identified and analysed in this study: steel yield-FRP rupture, steel yield-concrete crushing, compressive failure, and debonding. Here we obtain equations describing each failure mechanism using the strain compatibility method, concepts of fracture mechanics and a simple model for the FRP peeling-off debonding mechanism due to the development of shear cracks. We then produce diagrams showing the beam designs for which each failure mechanism is dominant, examine the effect of FRP sheets on the ductility and stiffness of strengthened components, and give results of four-point bending tests confirming our analysis. The analytical results obtained can be used in establishing an FRP selection procedure for external strengthening of reinforced concrete members with lightweight and durable materials.     

Effective strain of RC beams strengthened in shear with FRP

The failure modes of Reinforced Concrete (RC) beams strengthened in shear with Fiber Reinforced Polymer (FRP) sheets or strips are not well understood as much as those of RC beams reinforced with steel stirrups. When the beams are strengthened in shear with FRP composites, beams may fail due to crushing of the concrete before the FRP reaches its rupture strain. Therefore, the effective strain of the FRP plays an important role in predicting the shear strength of such beams. This paper presents the results of an analytical and experimental study on the performance of reinforced concrete beams strengthened in shear with FRP composites and internally reinforced with conventional steel stirrups. Ten RC beams strengthened with varying FRP reinforcement ratio, the type of fiber material (carbon or glass) and configuration (continuous sheets or strips) were tested. Comparisons between the observed and calculated effective strains of the FRP in the tested beams failing in shear showed reasonable agreement.     

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.