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.     

Evaluation of ductility requirements in current design guidelines for FRP strengthening

Advanced composites are widely used for the strengthening of existing concrete structures. Current design guidelines give basic requirements on how to model the enhancement of structural performance of concrete members using surface bonded FRP (fibre reinforced polymer) reinforcement. With respect to this, it is of interest to evaluate the ductility requirements which are explicitly or implicitly imposed by design guides. Based on an evaluation of four major design guidelines in Europe, Japan and North-America, and a small parametric study, the ductility aspect of the design of FRP strengthened concrete members is verified. It appears that the ductility of flexural members strengthened with FRP should be considered with care, as reduced deformability is obtained at ultimate, though generally a minimum deformability is implicitly obtained in a proper design. At the other hand, ductility enhancement by means of FRP confinement is explicitly considered in the design guidelines.     

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.     

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。     

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.     

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.     

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.     

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.     

Design provisions for crack spacing and width in RC elements externally bonded with FRP

Verification of serviceability is a key issue in reinforced concrete (RC) elements; for RC elements externally bonded with fibre reinforced plastic (FRP) laminates and sheets cracking phenomena are usually verified by adopting the same approach used for steel RC elements. The available code provisions for crack width and spacing in steel RC elements are reviewed in this paper in order to ascertain the reliability of their application to RC elements strengthened with FRP sheets. Experimental results belonging to test programmes performed by the authors and other researchers on RC elements externally bonded with FRP were compared with existing code provisions in terms of crack width and spacing.A new formula for crack spacing, calibrated on the experimental results, is proposed for use in the expression given by the published version of EC2 for calculating crack width in RC elements externally bonded with FRP.     

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.     

Efficacy of CFRP-based techniques for the flexural and shear strengthening of concrete beams

Near surface mounted (NSM) and externally bonded reinforcement (EBR) strengthening techniques are based on the use of carbon fiber reinforced polymer (CFRP) materials and have been used for the structural rehabilitation of concrete structures. In the present work, the efficacies of the NSM and EBR techniques for the flexural and shear strengthening of reinforced concrete beams are compared carrying out two experimental groups of tests. For the flexural strengthening, the efficacy of applying CFRP laminates according to NSM is compared to those resulting from applying CFRP laminates and wet lay-up CFRP sheets according to EBR technique. The influences of the equivalent reinforcement ratio (steel and laminates) and spacing of the laminates on the efficiency of the NSM technique for the flexural strengthening is also investigated. A numerical strategy is implemented to analyze the applicability of the FRP effective strain concept, proposed by ACI and fib in the design of FRP systems for the flexural strengthening. To assess the efficacy of the NSM technique for the shear strengthening of concrete beams, four beam series of distinct depth and longitudinal tensile steel reinforcement ratio are tested. Each series is composed of one beam without any shear reinforcement and one beam using the following shear reinforcing systems: conventional steel stirrups; strips of wet lay-up CFRP sheet of U configuration applied according to EBR technique; and laminates of CFRP embedded into vertical or inclined (45°) pre-cut slits on the concrete cover of the beam lateral faces, according to the NSM technique. Using the obtained experimental results, the performance of the analytical formulations proposed by ACI, fib and Italian guidelines is appraised.     

Design limits for RC slabs strengthened with hybrid FRP–HPC retrofit system

A polymeric hybrid composite system made of high-performance concrete (HPC) and an innovative carbon/epoxy reinforced polymer (CFRP) unidirectional laminates was proposed as a retrofit system to enhance flexural strength and ductility of reinforced concrete (RC) slabs. The effectiveness of the proposed system was confirmed through experimental evaluation of three full-scale one-way slabs having two continuous spans. In this study, the results of the loading tests for the hybrid high-performance retrofit system are presented and discussed. Design limits to derive a flexural failure of a continuous RC slab strengthened with the hybrid retrofit system are extracted. Using the proposed design limits, the procedure of a flexural failure design for a continuous RC slab strengthened with the hybrid retrofit system is demonstrated with numerical examples for two types of the retrofit systems with respect to overlay strength. The flexural failure design limits can be extended for flexural and shear strengthening design with externally bonded FRP to ensure flexure failure for a continuous flexural members.     

Improving shear capacity of existing RC T-section beams using CFRP composites

This paper presents the shear performance of reinforced concrete (RC) beams with T-section. Different configurations of externally bonded carbon fiber-reinforced polymer (CFRP) sheets were used to strengthen the specimens in shear. The experimental program consisted of six full-scale, simply supported beams. One beam was used as a bench mark and five beams were strengthened using different configurations of CFRP. The parameters investigated in this study included wrapping schemes, CFRP amount, 90°/0° ply combination, and CFRP end anchorage. The experimental results show that externally bonded CFRP can increase the shear capacity of the beam significantly. In addition, the results indicated that the most effective configuration was the U-wrap with end anchorage. Design algorithms in ACI code format as well as Eurocode format are proposed to predict the capacity of referred members. Results showed that the proposed design approach is conservative and acceptable.     

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.     

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.     

基于集成学习的FRP加固混凝土梁抗弯承载力预测研究

为解决当前纤维增强复合材料(FRP)加固钢筋混凝土梁抗弯承载力预测中模型不统一、计算繁琐、精度有限等问题,建立了统一化的抗弯承载力预测模型。根据既有文献收集外贴式、端锚式和嵌入式3种FRP典型加固方式加固钢筋混凝土梁试验数据,确定影响加固梁承载力的关键因素,通过XGBoost(极限梯度提升树)算法训练回归各影响因素与加固后梁抗弯承载力间的非线性映射关系,得到统一化的FRP加固钢筋混凝土梁抗弯承载力预测模型。随后在测试样本集上对该模型的预测精度进行了验证,与基于支持向量回归(SVR)和人工神经网络(ANN)两种代表性机器学习算法得到的预测模型进行了横向对比,并分析了不同加固方式下的预测精度。研究结果表明：该文得到的基于XGBoost的抗弯承载力预测模型拟合优度R²=0.9417,可见整体精度较高,有良好的性能;相比基于传统机器学习算法SVR和ANN建立的预测模型,基于集成学习算法XGBoost的拟合优度分别提升了8.00%及6.70%,均方根误差减少了33.94%和30.72%,平均绝对误差减少了32.38%和30.51%,表明基于XGBoost的模型精度更高,远优...     

Behavior of RC T-section beams strengthened with CFRP strips,subjected to cyclic load

This paper presents results of an experimental investigation on T-section reinforced concrete (RC) beams strengthened with externally bonded carbon fiber-reinforced polymer (CFRP) strips. Specimens, one of which was the control specimen and the remaining six were the shear deficient test specimens, were tested under cyclic load to investigate the effect of CFRP strips on behavior and strength. Five shear deficient specimens were strengthened with side bonded and U-jacketed CFRP strips, and remaining one tested with its virgin condition without strengthening. The type and arrangement of CFRP strips and the anchorage used to fasten the strips to the concrete are the variables of this experimental work. The main objective was to analyze the behavior and failure modes of T-section RC beams strengthened in shear with externally bonded CFRP strips. According to test results premature debonding was the dominant failure mode of externally strengthened RC beams so the effect of anchorage usage on behavior and strength was also investigated. To verify the reliability of shear design equations and guidelines, experimental results were compared with all common guidelines and published design equations. This comparison and validation of guidelines is one of the main objectives of this work. The test results confirmed that all CFRP arrangements differ from CFRP strip width and arrangement, improved the strength and behavior of the specimens in different level significantly.     

Holistic design of RC beams and slabs strengthened with externally bonded FRP laminates

Structural strengthening with externally bonded reinforcement is now recognized as a cost-effective, structurally sound and practically efficient method for rehabilitating deteriorated and damaged reinforced concrete structures. Although a variety of worldwide on-site applications using composite materials have been realized for the rehabilitation and reinforcement of structural elements, the technology is now at a stage where its future development and competitiveness with conventional methods will depend on the definition of valid design guidelines based on sound engineering principles rather than on the availability of new materials or production processes.The main objective of this paper is to present a general design philosophy for externally plated reinforced concrete beams and slabs, based on a holistic approach, in which appropriate strategies for achieving durable and safe strengthened structures are described.Essential to the design for safety, durability and ductility is the availability of structural models which are: (i) based on sound engineering principles; (ii) capable of reflecting the physical behaviour of strengthened members; (iii) of general applicability, irrespective of the type of external reinforcement material (steel or fiber-reinforced polymer), and the reinforcement configuration (web or tension plate); (iv) capable of describing all possible failure modes, in order to predict the weakest link chain of resistance of a structural member.It will be shown, with a series of numerical/experimental comparisons, that such requirements can be conveniently obtained with a unified approach in which materials and structures, calculation and experimental verification, modelling and analysis are integrated.     

A new ductility model of reinforced concrete beams strengthened using Fiber Reinforced Polymer reinforcement

Despite the superior performance of Fiber Reinforced Polymer (FRP) as compared with conventional steel bars in terms of high strength-to-weight ratio, corrosion resistance, and high fatigue performance, FRP strengthened beams exhibit lower ductility due to the linear elastic response of the FRP reinforcement. Several ductility and deformability models were developed in order to account for the elastic behavior, i.e. high elastic energy, of FRP when used for strengthening existing steel reinforced concrete or for new construction. In this paper, a new ductility expression that relates the deformability of a reinforced concrete (RC) structure strengthened using FRP to the energy dissipated, was developed. The developed expression also considers the type of loading, static or fatigue. The new expression was validated against experimental test results of RC beams strengthened using prestressed Near Surface Mounted (NSM) carbon FRP un-fatigued and fatigued beams. Furthermore, the ductility index at which the deformability of the structure equals the ratio of total energy dissipated to elastic energy, defined as the optimum ductility index, was investigated for both the un-fatigued and fatigued beams. The prestress strain corresponding to the optimum ductility index was found to be 2830 με (the strain value can be determined using an accepted arbitrary test such as monotonic test) while no optimum ductility was achieved for the case of the un-fatigued beams. It is noteworthy that the optimum ductility index is subject to the variability of design, beam geometry, and prestressing level. Therefore, the ductility evaluation of the NSM CFRP strengthened beams was meant to give only an insight into the problem and not to propose certain limits.     

A new ductility model of reinforced concrete beams strengthened using Fiber Reinforced Polymer reinforcement

Despite the superior performance of Fiber Reinforced Polymer (FRP) as compared with conventional steel bars in terms of high strength-to-weight ratio, corrosion resistance, and high fatigue performance, FRP strengthened beams exhibit lower ductility due to the linear elastic response of the FRP reinforcement. Several ductility and deformability models were developed in order to account for the elastic behavior, i.e. high elastic energy, of FRP when used for strengthening existing steel reinforced concrete or for new construction. In this paper, a new ductility expression that relates the deformability of a reinforced concrete (RC) structure strengthened using FRP to the energy dissipated, was developed. The developed expression also considers the type of loading, static or fatigue. The new expression was validated against experimental test results of RC beams strengthened using prestressed Near Surface Mounted (NSM) carbon FRP un-fatigued and fatigued beams. Furthermore, the ductility index at which the deformability of the structure equals the ratio of total energy dissipated to elastic energy, defined as the optimum ductility index, was investigated for both the un-fatigued and fatigued beams. The prestress strain corresponding to the optimum ductility index was found to be 2830 με (the strain value can be determined using an accepted arbitrary test such as monotonic test) while no optimum ductility was achieved for the case of the un-fatigued beams. It is noteworthy that the optimum ductility index is subject to the variability of design, beam geometry, and prestressing level. Therefore, the ductility evaluation of the NSM CFRP strengthened beams was meant to give only an insight into the problem and not to propose certain limits.