RC beams shear-strengthened with FRP: Stress distributions in the FRP reinforcement

Reinforced concrete (RC) beams may be strengthened for shear with externally bonded fibre reinforced polymer (FRP) composites through complete wrapping, U-jacketing or bonding on their sides only. The two main shear failure modes of such strengthened beams are FRP rupture and debonding. In both modes of failure, the contribution of the bonded FRP reinforcement to the shear capacity of the beam depends strongly on the stress (or strain) distribution in the FRP at the ultimate limit state. This paper presents a numerical study of the FRP stress distribution at debonding failure in U-jacketed or side-bonded beams using a rigorous FRP-to-concrete bond–slip model and assuming several different crack width distributions. Numerical results indicate that Chen and Teng’s early simple assumption [Chen JF, Teng JG. Shear capacity of FRP-strengthened RC beams: FRP debonding. Constr Build Mater 2003;17:27–41] for the stress distribution in the FRP results in satisfactory predictions for the effective FRP stress in most cases for both U-jacketed and side-bonded beams. However, it may become unconservative for side-bonded beams that have only light flexural steel reinforcement.     

Evaluation of debonding failure of reinforced concrete girders strengthened in flexure with FRP laminates using finite element modeling

The use of Fiber-Reinforced Polymer (FRP) materials dates back to the early 1940s when they were used in aerospace and naval applications. During the 1970s and early 1980s, FRP started being used in civil engineering applications for new construction, but more importantly for repair and strengthening of existing structures. However, experimental research showed that the typical failure mode of reinforced concrete (RC) structures strengthened with FRP composite materials is due to the debonding that occurs at the interface between concrete and FRP. The bond between FRP and concrete is therefore the key factor controlling the behavior of these structures since it limits the full use of the FRP strength. The paper evaluates the effect of the debonding failure on the response of FRP-strengthened RC beams. A nonlinear RC beam element with bond-slip between the concrete and the FRP laminates is developed and used to analyze several test specimens and to investigate their corresponding failure mode. The model was also used to study the reduction factor of FRP tensile strength of simply supported strengthened RC girders due to debonding failure. This reduction factor proved to be affected by several parameters: (a) the bond strength between FRP and concrete interface; (b) the concrete strength; (c) the thickness of FRP; (d) the modulus of FRP; (e) the width of FRP laminate; and (f) the development length of the FRP sheet. A large number of beam specimens were analyzed in order to conduct a thorough evaluation of debonding failure of RC beams strengthened with FRP laminates. Based on these studies, new equations that account for the aforementioned parameters were proposed to address the reduction in FRP strength due to debonding failure.     

复材网格-UHTCC复合增强钢筋混凝土梁抗弯性能试验研究

文中进行7根复材（FRP）网格增强超高韧性纤维水泥基（UHTCC）复合加固钢筋混凝土梁的抗弯性能试验,将FRP网格类型、FRP网格增强率、FRP-UHTCC复合层黏结长度作为试验变量,分析各变量对FRP-UHTCC复合增强混凝土梁弯曲性能的影响。在试验研究的基础上,给出FRP-UHTCC复合增强混凝土梁的抗弯承载力计算方法。试验结果表明,FRP-UHTCC复合层与混凝土间没有发生相对滑移现象,可以有效抑制加固层端部剥离破坏,加固梁的破坏模式为FRP网格中纵向纤维筋被拉断破坏。BFRP格栅与UHTCC黏结基体没有发生脱黏现象,优于BFRP编织网与UHTCC的黏结效果。随着FRP网格增强率的增大,加固梁的抗弯承载力得到显著提高。与未加固的普通混凝土梁相比,加固梁的开裂、屈服和极限荷载最大提高幅度分别为97%、35%和33%。计算结果表明,预测值与试验值吻合较好,可以有效地预测FRP-UHTCC复合增强混凝土梁的抗弯承载力。     

Finite element simulation of debonding in FRP-to-concrete bonded joints

The behaviour of reinforced concrete (RC) structures strengthened with externally bonded fibre-reinforced polymer (FRP) reinforcement in the forms of thin plates or sheets is often dominated by debonding of the FRP reinforcement from concrete. As a result, a large number of studies have addressed debonding failures in FRP-strengthened RC structures, with many of them being focussed on understanding the behaviour of simple FRP-to-concrete bonded joints in which an FRP plate/sheet is bonded to a concrete prism and is subject to a tensile force. Despite the many existing studies, there are still substantial uncertainties and difficulties with the finite element modelling of debonding failures due to the complex behaviour of cracked concrete. This paper explores the use of different crack models in modelling and compares their predictions of the debonding behaviour of FRP-to-concrete bonded joints. The results presented in this study show that a non-coaxial rotating angle crack model (RACM) is required to accurately predict this debonding behaviour. Furthermore, the debonding mechanism is also examined using results obtained with a non-co-axial RACM.     

Shear capacity of FRP-strengthened RC beams: FRP debonding

Many studies have been undertaken on shear strengthening of reinforced concrete (RC) beams by externally bonding fibre-reinforced polymer (FRP) composites. These studies have established clearly that such strengthened beams fail in shear mainly in one of two modes: FRP rupture; and FRP debonding, and have led to preliminary design proposals. This paper is concerned with the development of a simple, accurate and rational design proposal for the shear capacity of FRP-strengthened beams which fail by FRP debonding. Existing strength proposals are reviewed and their deficiencies highlighted. A new strength model is then developed. The model is validated against experimental data collected from the existing literature. Finally, a new design proposal is presented.     

FRP片材增强钢筋混凝土梁刚度与变形计算

FRP（fiber reinforced polymer）片材增强钢筋混凝土梁纵筋屈服前刚度是其正常使用阶段的刚度,而纵筋屈服后刚度（又称二次刚度）则能够控制超载情况下梁的变形,因此,两个阶段的刚度都很重要。本文对FRP增强钢筋混凝土梁在受拉纵筋屈服前和屈服后两个阶段的刚度进行了理论分析,将纵筋屈服前后截面弯矩表达为受拉纵筋和FRP应变的函数,推导了增强材料应变不均匀系数的计算式,通过全过程分析得到了受压区混凝土边缘平均应变综合系数随截面弯矩的变化规律,发现屈服后阶段的变化规律明显不同于普通钢筋混凝土梁;通过对80根试验梁数据和40根模拟梁的全过程分析数据进行回归,得到了FRP增强钢筋混凝土梁的刚度和挠度计算式;将计算值与本文试验的实测值以及全过程分析结果进行对比,最后用文献中的试验数据进行了验证。结果表明,本文提出的刚度和挠度计算式具有较高的精度。     

混凝土梁外贴FRP抗剪加固承载力计算

剥离破坏是外贴FRP片材加固混凝土梁主要的破坏形式。回顾了对外贴FRP混凝土梁的试验研究、有限元分析和国内外现有的受剪剥离承载力计算公式。讨论了斜裂缝宽度分布规律,建立了FRP滑移分布模型,在此基础上分析了受剪剥离破坏时FRP的应力分布,讨论了FRP抗剪贡献与粘结长度、粘结方式等参数之间的关系。提出了受剪剥离承载力计算公式,与大量试验结果的对比表明,给出的设计建议公式与试验结果吻合良好,可供设计应用参考。     

TESTS ON STRUCTURALLY DEFICIENT RC SLABS STRENGTHENED WITH FIBRE REINFORCED POLYMER (FRP) COMPOSITES

This paper reports the results of a series of tests on fibre reinforced polymer (FRP) strengthened reinforced concrete (RC) slabs, which were recently undertaken at the University of Technology,Sydney. The slabs were reinforced with high-strength low-ductile steel reinforcement and strengthened with either carbon FRP (CFRP) or glass FRP (GFRP) composites. The unstrengthened control slabs failed by fracture of the steel tension reinforcement while the FRP strengthened slabs failed by debonding of the FRP followed by rupture of the tension steel. The FRP-strengthened slabs were stronger than their unstrengthened counterparts and displayed considerable ductility.     

钢筋混凝土T梁HB-FRP抗剪加固试验和数值模拟

基于室内模型试验,开展了混合黏结纤维增强复合材料(HB-FRP)抗剪加固钢筋混凝土T梁的受力性能研究.对未加固、外贴纤维增强复合材料(EB-FRP)加固及HB-FRP加固T梁进行了破坏性对比试验,并采用Abaqus软件建立了精细化有限元模型,对比分析了试验和数值计算结果,验证了有限元模型的准确性;在此基础上进行参数分析,研究了混凝土强度、箍筋间距、FRP条带数量及FRP厚度对加固梁抗剪承载能力的影响.结果 显示:HB-FRP抗剪加固梁的剪切裂缝间距要小于EB-FRP加固梁的裂缝间距;EB-FRP加固梁发生黏贴区域大面积剥离,而HB-FRP加固梁仅在相邻钢扣件间有裂缝的区域出现了剥离,钢扣件有效抑制了裂缝剥离扩展;HB-FRP抗剪加固梁的FRP应变水平为EB-FRP抗剪加固梁的2倍,表现出了较好的延性.综合考虑未加固梁、EB-FRP加固梁及HB-FRP加固梁的参数分析结果,对钢筋混凝土T梁抗剪承载能力的影响因素按照重要性降序为:混凝土强度、箍筋间距、FRP间距、FRP厚度.     

Behavior and capacity of RC beams strengthened in shear with NSM FRP reinforcement

A recent and promising method for shear strengthening of reinforced concrete (RC) members is the use of near-surface mounted (NSM) fiber-reinforced polymer (FRP) reinforcement. In the NSM method, the reinforcement is embedded in grooves cut onto the surface of the member to be strengthened and filled with an appropriate binding agent such as epoxy paste or cement grout. Only a few studies have been conducted to date on the use of NSM FRP reinforcement for shear strengthening of RC beams. These studies identified some critical failure modes related to debonding between the NSM reinforcement and the concrete substrate. However, more tests need to be conducted to identify all possible failure modes of strengthened beams. Moreover, virtually no test results are available on the behavior of shear-strengthened beams containing steel shear reinforcement, and on the effect of variables such as the type of epoxy used as groove filler. This paper illustrates a research program on shear strengthening of RC beams with NSM reinforcement, aimed at gaining more test results to fill the gaps in knowledge mentioned above. A number of beams were tested to analyze the influence on the structural behavior and failure mode of selected test parameters, i.e. type of NSM reinforcement (round bars and strips), spacing and inclination of the NSM reinforcement, and mechanical properties of the groove-filling epoxy. One beam strengthened in shear with externally bonded FRP laminates was also tested for comparison purposes. All beams had a limited amount of internal steel shear reinforcement to simulate a real strengthening situation. Test results are presented and discussed in the paper.     

钢-连续纤维复合筋嵌入式加固RC梁承载力分析

新型钢-连续纤维复合筋（SFCB）是一种以普通钢筋为内芯,外包纵向连续纤维的新型筋材。SFCB由于良好的力学性能、高耐久性和高性价比而在嵌入式加固中具有独特的优势。对SFCB嵌入式加固RC梁的承载力分析方法进行介绍,首先根据平截面假定及力的平衡,提出了SFCB嵌入式加固钢筋混凝土梁非粘结破坏时的受弯承载力计算方法;然后对嵌入式加固RC梁始于加载点附近开始的剥离破坏现象进行了理论分析,并给出了是否会发生粘结剥离破坏的判别方法和极限承载力的计算方法;最后,将计算结果与嵌入式加固RC梁试验结果进行了比较,认为该方法对破坏模式和极限承载力的预测均具有较好的精度。     

FRP-strengthened RC slabs anchored with FRP anchors

An abundance of tests over the last two decades has shown the bending capacity of flexural members such as reinforced concrete (RC) beams and slabs to be enhanced by the bonding of fibre-reinforced polymer (FRP) composites to their tension face. The propensity of the FRP to debond, however, limits its effectiveness. Different types of anchorages have therefore been investigated in order to delay or even prevent debonding. The so-called FRP anchor, which is made from rolled fibre sheets or bundles of lose fibres, is particularly suitable for anchoring FRP composites to a variety of structural element shapes. Studies that assess the effectiveness of FRP anchors in anchoring FRP strengthening in flexural members is, however, limited. This paper in turn reports a series of tests on one-way spanning simply supported RC slabs which have been strengthened in flexure with tension face bonded FRP composites and anchored with different arrangements of FRP anchors. The load-deflection responses of all slab tests are plotted, in addition to selected strain results. The behaviours of the specimens including the failure modes are also discussed. The greatest enhancement in load and deflection experienced by the six slabs strengthened with FRP plates and anchored with FRP anchors was 30% and 110%, respectively, over the unanchored FRP-strengthened control slab. The paper also discusses the strategic placement of FRP anchors for optimal strength and deflection enhancement in FRP-strengthened RC slabs.     

Application of improved hybrid bonded FRP technique to FRP debonding prevention

External bonding of fiber reinforced polymer (FRP) is one of the most efficient techniques for retrofitting and strengthening concrete structures. However, the bond interface is the weakest link in such retrofitted or strengthened concrete members, resulting in premature FRP debonding. Therefore, a newly improved hybrid bonded FRP (IHB-FRP) technique is developed in this paper for strengthening concrete members. Unlike the conventional mechanical fastening method, the mechanical fasteners in the technique do not penetrate the FRP strips and the capping plates serve to apply vertical pressure to the FRP strips. An experimental study on the flexural strength of IHB-FRP technique strengthened beams is conducted. It is found that all the beams strengthened with the IHB-FRP technique fail due to tensile rupture of FRP strips even for seven plies of FRP strips. Based on the experimental results, the effects of the steel reinforcement ratio, the number of FRP plies, and the fastener spacing on the ultimate load are evaluated. Finally, a simplified method is proposed for estimating the ultimate bending moment of the IHB-FRP strengthened beam. The validity of the method is verified with the experimental results.     

Strengthening of RC beams in shear using GFRP inclined strips – An experimental study

Though there have been a number of studies on shear strengthening of RC beams using externally bonded fiber reinforced polymer sheets, the behaviour of FRP strengthened beams in shear is not fully understood. This is partly due to various reinforcement configurations of sheets that can be used for shear strengthening and partly due to different failure modes a strengthened beam undergoes at ultimate state. Furthermore, the experimental data bank for shear strengthening of concrete beams using FRP remains relatively sparse due to which the design algorithms for computing the shear contribution of FRP are not yet clear. The objective of this study is to clarify the role of glass fiber reinforced polymer inclined strips epoxy bonded to the beam web for shear strengthening of reinforced concrete beams. Included in the study are effectiveness in terms of width and spacing of inclined GFRP strips, spacing of internal steel stirrups, and longitudinal steel rebar section on shear capacity of the RC beam. The study also aims to understand the shear contribution of concrete, shear strength due to steel bars and steel stirrups and the additional shear capacity due to glass fiber reinforced polymer strips in a RC beam. And also to study the failure modes, shear strengthening effect on ultimate force and load deflection behaviour of RC beams bonded externally with GFRP inclined strips on the shear region of the beam.     

A simple and rational beam segment model for analyzing intermediate crack-induced debonding in FRP-strengthened beams

Intermediate crack (IC) induced debonding failure of fibre reinforced polymer (FRP) plate strengthened reinforced concrete (RC) beams is one of the common debonding modes, in which debonding initiates at a major flexural crack and then propagates toward a plate end. Finite element (FE) method has been used to analyze the IC debonding failure and a whole strengthened beam has been taken as a mechanical model in existed researches. In view of that it is difficult to appropriately simulate all the cracks in an entire strengthened beam and consequently to carry out a parameter study, a beam segment between two major adjacent flexural cracks in a flexural-shear zone of a strengthened beam was taken as a new simple mechanical model. The new simple “beam segment model” was validated to be rational by using Saint–Venant Principle and a numerical study. In the light of this, a parameter study was performed through a three dimensional nonlinear FE analysis of the proposed beam segment model. The influences of the load level, the bond-slip (δ–τ) relationship of FRP-to-concrete interface, and the geometry of the beam segment on the IC induced debonding were investigated. The numerical analysis shows that the influence of δ–τ relationship of FRP-to-concrete interface on debonding is fairly more significant than that of crack spacing of strengthened beams. Comparisons between analytical and experimental results show that the proposed beam segment model is appropriate for estimating the IC induced debonding.     

Debonding of FRP in bending: Simplified model and experimental validation

Reinforced concrete members strengthened in bending by bonding of surface-mounted fiber-reinforced polymer (FRP) may present several failure modes: failure of material (reinforcing steel, concrete and composite material) or failure of the interface between concrete-adhesive or adhesive-FRP. Nevertheless, experience gained from testing confirms that in most cases delamination prevails over the other possible rupture modes. Delamination in FRP strengthened sections is difficult to model because it involves multiple parameters such as FRP stiffness, adhesive material properties, presence of cracks in concrete, among others. A simplified model to predict strain of FRP at failure is presented in this paper. The experimental validation is presented as well. With this purpose carbon FRP and aramid strengthened specimens and large scale bridge models are considered. The types of bridge models tested include externally-prestressed segmental box-girder and monolithic RC continuous girders.Based on the results of the proposed model, an equation for the prediction of the ultimate force per unit width in the FRP to prevent FRP debonding is proposed. The equation has been experimentally checked with beams of small and large size, representative of real structures. In comparison to other available models, the equation is very simple to apply.     

Analytical model for the torsional behaviour of reinforced concrete beams retrofitted with FRP materials

An analytical approach for the prediction of the torsional response of reinforced concrete (RC) beams strengthened with fibre-reinforced-polymer (FRP) materials is described. The analysis method employs the combination of two different theoretical models: a smeared crack model for plain concrete in torsion for the elastic till the first cracking response and a properly modified truss model for the post-cracking response. The proposed method addresses the contribution of the externally bonded FRP materials to the torsional capacity of RC beams using specially developed equations in the well-known truss theory and utilizes softened and FRP-confined concrete stress–strain relationships. Detailed verification of this methodology is achieved through extensive comparisons between analytically predicted behaviour curves and experimentally obtained ones. The experimental data comprise a series of 12 tests in pure torsion and an additional database of experimental information for 24 specimens compiled from works around the world. These comparisons demonstrated that the proposed model is capable of adequately describing the full torsional response and of predicting with satisfactory accuracy the torsional moment at cracking and the ultimate torque capacity of FRP strengthened RC beams. Applications of the developed method as an assessment tool to strengthened beams with U-shaped FRP configurations and some first design examples that demonstrate the contribution of the FRP materials on the torsional response are also included.     

Strengthening of one-way spanning RC slabs with cutouts using FRP composites

This paper reports the results of tests on fibre reinforced polymer (FRP) strengthened one-way spanning reinforced concrete (RC) slabs with central cutouts. Four wide slabs with cutouts were tested in addition to two narrow slabs without cutouts. Different positions of applied line loads for the slabs with cutouts resulted in different slab bending action and hence different FRP behaviour for the strengthened slabs. All FRP-strengthened slabs achieved a higher load-carrying capacity than their unstrengthened control counterparts. In addition, all strengthened slabs failed by debonding initiating at intermediate cracks (IC debonding) and in the case of the slabs with cutouts, the critical cracks were diagonal and originated from the corners of the cutout. The ability of the FRP to redistribute stresses around the cutout, the failure mechanisms, as well as pre- and post-debonding behaviour of the strengthened slabs was therefore assessed for different load application positions. Strains on the FRP, concrete and internal steel reinforcement, as well as deflections at different positions on the slab surfaces are also reported. An analytical model, which is based on the ultimate moment of resistance about critical crack lines, is also reported and it its predictions are found to correlate well with the experimental results. The analytical model is able to capture the different slab bending actions in addition to the debonding failure of the strengthened slabs.     

Unified analytical approach for determining shear capacity of RC beams strengthened with FRP

This paper presents a rational model to predict the ultimate load capacity of reinforced concrete (RC) beams strengthened by a combination of longitudinal and transverse fiber reinforced polymer (FRP) composite plates/sheets (flexure and shear strengthening system). The model is based on the truss analogy and the theory of plasticity and is opportunely refined in order to incorporate some critical aspects, such as variable angle crack, non-uniform FRP stress distribution over the shear crack, shear span/depth ratio. It is a general and unified model that allows consideration of all the main possible failure mechanisms of strengthened RC beams, related to flexural-shear interaction, shear web-crushing and pure flexural mechanisms. The model is validated against a large number of beam tests reported in the literature, involving a wide range of geometrical and mechanical characteristics. The numerical investigation shows a very satisfactory correlation between predicted and experimental data.     

碳纤维增强复合网格-聚合物水泥砂浆加固RC梁的抗弯性能试验研究

为研究碳纤维增强复合(CFRP)网格和聚合物水泥砂浆(PCM)复合加固钢筋混凝土(RC)梁的抗弯性能,对5个RC梁试件进行抗弯性能试验,分析CFRP网格-PCM复合加固RC梁的抗弯破坏机理,研究网格不同层数和不同单位加固量对RC梁抗弯性能的影响。基于抗弯承载力的既有计算模型,引入剥离应变建立改良计算模型,并采用其他学者的9根FRP网格加固RC梁的受弯试验数据,验证改良计算模型的准确性。研究结果表明：CFRP网格-PCM对RC梁的抗弯加固效果明显,单位加固量较高的试件具有更高的承载能力,但其更易发生剥离破坏;在单位加固量相当的条件下,单层网格与双层网格呈现出相同的抗弯性能,双层网格重叠布置的加固方式是有效的;抗弯承载力的既有计算模型对试验结果拟合效果较差,所建立的改良计算模型拟合程度较好,能更好地反映CFRP网格-PCM复合加固层的实际受力状态。