Assessment of Eurocode-like design equations for the shear capacity of FRP RC members

Fibre reinforced polymer (FRP) bars represent an interesting alternative to conventional steel as internal reinforcement of reinforced concrete (RC) members where some properties such as durability, magnetic transparency, insulation, are of primary concern. The present paper focuses on the assessment of Eurocode-like design equations for the evaluation of the shear strength of FRP RC members, as proposed by the guidelines of the Italian Research Council CNR-DT 203 [CNR-DT 203/2006. Guide for the design and construction of concrete structures reinforced with fiber-reinforced polymer bars. National Research Council, Rome, Italy; 2006]. Both the concrete and the FRP stirrups contributions to shear are taken into account: the new equations derived with reference to Eurocode equations for shear of steel RC members are verified through comparison with the equations given by ACI, CSA and JSCE guidelines, considering a large database of members with and without shear reinforcement failed in shear.     

Assessment of available prediction models for the strength of FRP retrofitted RC beams

A reinforced concrete beam retrofitted with fibre reinforced polymer composites (FRP) to enhance its flexural capacity can experience several failure modes, namely flexural failure, end debond and midspan debond. The mechanism of those failures and available prediction models are first identified in this paper. The models are then assessed with an up to date database of beams reported in literature together with beams tested by the authors. The study verifies that beam theory can predict flexural failure well. The credibility of several methods to predict end debond and mid-span debond is also proved.     

IR thermography for interface analysis of FRP laminates externally bonded to RC beams

Non-destructive (ND) evaluation by thermographic analysis was applied to reinforced concrete (RC) beams strengthened with CFRP laminates, to assess the quality of the interface between reinforcement and substrate before and under loading, during laboratory bending tests. The proper algorithm for processing data acquired from the thermographic system was first selected by testing reduced-scale fiber reinforced polymer (FRP)-strengthened concrete slabs with artificial defects and anomalies, deliberately placed at the interface. Portable heating equipment was purposely set-up to allow continuous scanning along the loaded beams. Results showed that infrared thermography (IRT) can supply significant qualitative and quantitative information on bonding of FRP materials applied to structural substrates, for both preliminary and in-situ investigations, by means of a reliable low-time-consuming procedure. Cross-evaluation of crack patterns during bending tests and thermographic results are also presented.     

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.     

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.     

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.     

Evaluation of corrosion activity in FRP repaired RC beams

This paper presents the results of an experimental study to evaluate the corrosion activity in reinforced concrete beams repaired with fibre reinforced polymer (FRP) sheets. Ten beam specimens (152 × 254 × 3200 mm) were constructed. One specimen was neither strengthened nor corroded to serve as a reference. Three specimens were corroded and not repaired. The remaining six beams were corroded and repaired with FRP sheets. The FRP sheets were applied after the main reinforcing bars were corroded to a 5.5% mass loss. Following the FRP repair, some specimens were subjected to further corrosion to investigate their post-repair performance. The corrosion activity was evaluated using non-destructive and destructive techniques. The non-destructive techniques included half-cell potential measurements. The destructive techniques included evaluation of the mass loss of the main reinforcing bars. The experimental results showed that the corrosion potential decreased with the progress of corrosion, and the FRP repair caused a higher rate of decrease in the corrosion potential with time than that observed when FRP was not provided. Results showed that mass loss of the main reinforcing bars due to corrosion was reduced by up to 16% because of FRP repair.     

Prediction of the behavior of RC Beams Strengthened with FRP Plates

Epoxy-bonding a composite plate to the tension face is an effective technique to repair reinforced concrete beams since it increases their strength and rigidity. In this paper, the structural behavior of reinforced concrete beams with fibre reinforced polymer (FRP) plates is studied numerically. For it, a numerical damage model is used in order to predict their strength, stiffness and failure modes observed in experimental tests taking into account the influence of different variables such as the amount of steel reinforcement, the type and amount of external reinforcement, the plate length, etc. The consideration of concrete cracking and the yielding of the steel rebars allows to predict in a realistic way the behavior of the strengthened beams and especially the debonding failure mode. In that sense both end and midspan debond can be represented since the model is able to reproduce the tension stiffening phenomenon.     

Failure of RC beams strengthened in bending with unconventionally arranged CFRP laminates

This paper describes the experimental tests made on RC beams retrofitted by unconventionally arranged CFRP strips and on a reference, not retrofitted one. Diagonal CFRP strips were applied on the lateral faces of the specimens and connected to the longitudinal ones in order to improve the anchorage length of the latters. The experimental outcomes prove that this CFRP strips distribution can improve the load carrying capacity of the retrofitted beams, provided that the diagonal strips are long enough and that the longitudinal reinforcement is arranged along the whole beam. Comparison with the predictions based on CNR-DT 200 and ACI 440.2R-02 guidelines is finally displayed.     

Fatigue behavior of RC T-beams strengthened in shear with EB CFRP L-shaped laminates

The use of externally bonded carbon fiber-reinforced polymer (EB-CFRP) to strengthen deficient reinforced concrete (RC) beams has gained in popularity and has become a viable and cost-effective method. Fatigue behavior of RC beams strengthened with FRP is a complex issue due to the multiple variables that affect it (applied load range, frequency, number of cycles). Very few research studies have been conducted in shear under cyclic loading. The use of prefabricated CFRP L-shaped laminates (plates) for strengthening RC beams under static loading has proven to be technically feasible and very efficient. This study aimed to examine the fatigue performance of RC T-beams strengthened in shear for increased service load using prefabricated CFRP L-shaped laminates. The investigation involved six laboratory tests performed on full-size 4520 mm-long T-beams. The specimens were subjected to fatigue loading up to six million load cycles at a rate of 3 Hz. Two categories of specimens (unstrengthened and strengthened) and three different transverse-steel reinforcement ratios (Series S0, S1, and S3) were considered. Test results were compared with the upper fatigue limits specified by codes and standards. The specimens that did not fail in fatigue were then subjected to static loading up to failure. The test results confirmed the feasibility of using CFRP L-shaped laminates to extend the service life of RC T-beams subjected to fatigue loading. The overall response was characterized by an accelerated rate of damage accumulation during the early cycles, followed by a stable phase in which the rate slowed significantly. In addition, the strains in the stirrups decreased after the specimens were strengthened with CFRP, despite the higher applied fatigue loading. Moreover, the addition of L-shaped laminates enhanced the shear capacity of the specimens and changed the failure mode from brittle to ductile under static loading. Finally, the presence of transverse steel in strengthened beams resulted in a substantially reduced gain in shear resistance due to CFRP, confirming the existence of an interaction between the transverse steel and the CFRP.     

Genetic algorithm model for shear capacity of RC beams reinforced with externally bonded FRP

A variety of on-site construction applications using FRP materials have been realized worldwide. However, this technology is currently at a stage where its future widespread implementation and competitiveness will depend on the development of reliable design guidelines based on sound engineering principles. This paper presents simple, yet improved, equations to calculate the shear capacity of FRP bonded-reinforced concrete beams based on the genetic algorithms (GAs) approach applied to 212 experimental data points available in the open literature. The performance of the proposed equations was compared to that of commonly used shear design methods, namely the ACI 440, Eurocode (EC2), the Matthys Model, Colotti model and the ISIS Canada guidelines. Results demonstrate that the proposed equations better agree with the available experimental data than the existing models investigated. Moreover, a sensitivity analysis was carried out to investigate the effect of the shear span-to-depth ratio on the shear capacity contributed by concrete, the ultimate effective strain in FRP sheets, and the ultimate effective stress in transverse rebars. Results indicate that the shear span-to-depth ratio has a significant effect on the shear behaviour of FRP bonded-reinforced concrete beams.     

Experiments and analytical comparison of RC beams strengthened with CFRP composites

This paper deals with strengthening, upgrading, and rehabilitation of existing reinforced concrete structures using externally bonded composite materials. Five strengthened, retrofitted, or rehabilitated reinforced concrete beams are experimentally and analytically investigated. Emphasis in placed on the stress concentration that arises near the edge of the fiber reinforced plastic strip, the failure modes triggered by these edge effects, and the means for the prevention of such modes of failure. Three beams are tested with various edge configurations that include wrapping the edge region with vertical composite straps and special forms of the adhesive layer at its edge. The last two beams are preloaded up to failure before strengthening and the ability to rehabilitate members that endured progressive or even total damage is examined. The results reveal a significant improvement in the serviceability and strength of the tested beams and demonstrate that the method is suitable for the rehabilitation of severely damaged structural members. They also reveal the efficiency of the various edge designs and their ability to control the characteristic brittle failure modes. The analytical results are obtained through the Closed-Form High-Order model and are in good agreement with the experiment ones. The analytical and experimental results are also used for a preliminary quantitative evaluation of a fracture mechanics based failure criterion for the strengthened beam.     

Acoustic emission monitoring and numerical modeling of FRP delamination in RC beams with non-rectangular cross-section

A case study concerning both numerical modeling and in-situ monitoring of a retrofitted RC beam with non-rectangular cross-section is presented. Before retrofitting, non-destructive techniques, such as pull-out and impact tests, were used to estimate the mechanical parameters of concrete. At the same time, a long-term monitoring with the Acoustic Emission (AE) technique was carried out in order to investigate on creep effects and microcracking phenomena. Then, after a complete removal of the overload and retrofitting with FRP sheets, an in-situ loading test was performed. At that stage, the AE technique was again profitably used for the analysis of the cracking progression leading to FRP debonding. A numerical model of the structure is then proposed in the framework of the FE discretization with mechanical parameters estimated according to an inverse analysis on the monitored mechanical behavior of the structure before retrofitting. According to this model it is shown that, when the flexural inertia of the retrofitted beam is considerably higher than that of the unrepaired beam, snap-back instabilities can take place. Finally, considering the self-similarity between the acoustic emission phenomenon and seismicity, an analogy between the snap-back instability of the FRP delamination and that occurring during fault growth is proposed.

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Résumé Une étude de cas au sujet de modeler numérique et de surveiller in-situ d’un faisceau monté en rattrapage de RC avec la section transversale non-rectangulaire est présentée. Avant l’adaptation d’un faisceau, des techniques non destructives, telles que des essais à dégagement et à choc, ont été employées pour estimer les paramètres mécaniques du béton. En même temps, une surveillance à long terme avec la technique d’émission acoustique (AE) a été effectuée afin d’étudier sur des effets de fluage et des phénomènes de microfissuration. Puis, après un déplacement complet de la surcharge et l’adaptation ultérieure avec des feuilles de FRP, un essai in-situ de chargement a été réalisé. á cette étape, la technique d’AE a été encore profitablement employée pour l’analyse de la progression de fissures menant au décollement du FRP. On propose alors un modèle numérique de la structure dans le cadre de la discrétisation FE avec des paramètres mécaniques estimés selon une analyse inverse sur le comportement mécanique surveillé de la structure avant l’adaptation ultérieure. Selon ce modèle, on le démontre que, quand l’inertie flexural␣du faisceau monté en rattrapage est considérablement plus haute que cela de la structure non réparé, les instabilités de snap-back peuvent avoir lieu. En conclusion, vu l’auto similarité entre le phénomène d’émission et la séismicité acoustiques, on propose une analogie entre l’instabilité de snap-back du décollement de FRP et cela qui se produit pendant la croissance de défaut.

     

Local stress field approach for post cracking analysis of FRP strengthened RC elements

A computational framework previously presented for nonlinear analysis of RC elements, has been developed for FRP strengthened RC elements in this study. With the aim of the developed model nonlinear behavior of strengthened RC elements can be simulated based on local stresses state at the crack surface considering all stress transfer mechanisms. Moreover, the local response of each component and its effect on the global behavior of the element can be obtained which is useful for proposing rational design relations. The versatility of the proposed method is verified by comparing the analytical and experimental results. Based on the analytical results, a simple relation is proposed for shear design and assessment of FRP strengthened RC elements and members. The accuracy of the proposed design relation is verified against available experimental results on FRP strengthened RC beams.     

Behavior and performance of RC T-section deep beams externally strengthened in shear with CFRP sheets

A series of experimental tests were carried out to investigate the behavior and performance of reinforced concrete (RC) T-section deep beams strengthened in shear with CFRP sheets. Key variables evaluated in this study were strengthening length, fiber direction combination of CFRP sheets, and an anchorage using U-wrapped CFRP sheets. A total of 14 RC T-section deep beams were designed to be deficient in shear with a shear span-to-effective depth ratio (a/d) of 1.22. Crack patterns and behavior of the tested deep beams were observed during four-point loading tests. Except the CS-FL-HP specimen, almost all strengthened deep beams showed a shear–compression failure due to partial delamination of the CFRP sheets. From the load–displacement (p–u) curves, the effects of key variables on the shear performance of the strengthened deep beams were addressed. It was concluded from the test results that the key variables of strengthening length, fiber direction combination, and anchorage have significant influence on the shear performance of strengthened deep beams. In addition, a series of comparative studies between the present experimental data and theoretical results in accordance with the commonly applied design codes were made to evaluate the shear strength of a control beam and deep beams strengthened with CFRP sheets.     

喷射FRP加固震损钢筋混凝土柱抗震性能试验

通过12组72件喷射纤维/树脂复合材料(FRP)试样的拉伸强度试验,研究了纤维种类、树脂基体材料、纤维体积分数、纤维混杂比及纤维长度等因素对喷射FRP拉伸强度、弹性模量和断裂伸长率等性能的影响。通过8根钢筋混凝土(RC)柱试件的拟静力试验,研究了喷射玄武岩纤维/树脂复合材料(BFRP)和混杂玄武岩-碳纤维/树脂复合材料(BF-CFRP)加固震损RC柱的抗震性能,分析了喷射FRP层厚度、纤维混杂比、柱预损程度和柱轴压比等对加固试件的极限承载力、抗侧变形能力、刚度退化特征和滞回特性的影响。结果表明:玻璃纤维与乙烯基酯树脂基体的协同工作性能最优,而玄武岩纤维具有耐久性高、延性好、与乙烯基酯树脂基体协同工作性能好等优良性能,可以作为玻璃纤维的良好替代品;玄武岩纤维混杂少量比例的碳纤维作为树脂基体增强材料,可以有效提高喷射FRP的拉伸强度和变形性能;震损RC柱经喷射FRP加固后,可以基本恢复其震损前设计极限承载力,并有效提高其延性和耗能能力。该加固方法可以对地震区已震损RC柱进行快速加固,有效防止整体结构在余震中发生倒塌等严重破坏。      

Fracture-mechanics failure criteria for RC beams strengthened with FRP strips––a simplified approach

A simplified approximation approach for the evaluation of a fracture mechanics based criterion for the edge delamination failure of reinforced concrete beams strengthened with externally bonded composite materials is presented. The proposed approach is based on evaluation of the energy release rate (ERR) through the virtual crack extension method using various analytical and numerical stress analysis models. The investigated models include the high-order model, two types of “elastic foundation” or “springs” models, a simplified beam model, and finite elements analysis. The stress and displacement fields, the governing equations and their closed form solutions, and the expressions for the release rate of the total potential energy of the various models are presented. The proposed approach sets up the basis for an energetic failure criterion, in which the ERR is compared to the specific fracture energy of the bonded system. This criterion replaces the traditional allowable stress approach in describing the initiation and stable or unstable growth of the delamination crack. The capabilities of the proposed approach and its ability to evaluate the ERR through simplified and approximated models is investigated numerically. The accuracy of the simplified approach is numerically examined through comparison with the J-integral formulation. Numerical results in terms of stresses near the edge of the bonded strip, the ERR associated with initiation and growth of the interfacial crack, and the critical loads and crack lengths are presented. The paper closes with a summary and conclusions.     

FRP-混凝土界面粘结滑移本构模型

铝合金板具有轻质高强、延展性好、低温脆断敏感性小、耐腐蚀、易于成型等优点,可用于腐蚀及寒冷环境下的混凝土结构加固。该文基于双剪试验下的铝合金板-混凝土界面粘结滑移性能研究,完成了45个构件的双面纯剪试验,分析了混凝土强度等级、铝合金板表面粗糙度、铝合金板粘结长度和粘结宽度对粘结界面破坏机理、剥离承载力以及界面滑移的演化规律。研究表明：加载过程中界面应力从加载端向自由端逐步传递,且随着混凝土强度等级、铝合金板的粘结长度和宽度的增加,试件的剥离承载力也有所提高。但铝合金板的粘结长度存在一个有效粘结长度值,超过该值试件的剥离承载力将不会增加,同时铝合金板表面粗糙度对试件剥离承载力的提高没有实质影响。     

应用Monte Carlo-JC法评估FRP加固RC梁受弯承载力可靠度

将Monte Carlo随机抽样方法与JC法相结合(称为Monte Carlo-JC法), 利用Matlab软件自带的随机数发生器编制了程序, 针对ACI 440.2R-02设计指南(称为ACI指南)中的FRP抗弯加固条款进行了较为系统的可靠度评估。可靠度分析结果表明: 混凝土强度f' _c、 CFRP片材配筋率ρ_f及CFRP片材性能是影响抗力比值均值和标准差的3个主要因素; 可靠度指标的平均值随着折减系数的增大而逐步减小, 且随着荷载效应比值L_n/D_n的增大而减小。对所有可靠度指标进行统一考虑, 得到整体抗弯设计指标β₀为4.40, 可见该指南的可靠度水平偏高。基于对抗力折减系数的参数研究结果, 无论钢筋的应变水平如何, 建议取固定值0.90。在所有相关设计指南中, ACI指南最具有代表性, 对该指南的可靠度评估具有普遍意义。      

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.