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.     

Influence of FRP anchor fan configuration and dowel angle on anchoring FRP plates

To enhance the strain capacity of fibre-reinforced polymer (FRP) plates which have been bonded onto reinforced concrete (RC) members for strengthening purposes, FRP anchors can be utilised. Research on the characterisation of FRP anchors is still quite limited though despite the increasing use of FRP anchors in practice. In order to reduce such a knowledge gap, this paper reports the results of 30 single-shear FRP-to-concrete joint tests of which 26 joints were anchored with FRP anchors of differing geometric configurations and four joints were unanchored controls. More specifically for the anchored joints, the connection of the FRP anchor to the FRP plate via so called fan fibres was varied in addition to the angle of anchor insertion and these test parameters represent fundamentally important anchor components which have not been researched to date. Failure modes, joint strengths, load–slip responses as well as FRP plate strain distributions are reported and a relationship relating the influence of anchor insertion angle to joint strength is provided. A maximum increase in joint strength of 160% on average above the unanchored control joints was achieved. In addition, the maximum strain resisted by the FRP plate, relative to its elongation capacity, was increased on average from 25% for unanchored control joints to 67% for some anchored joints.     

Effect of imperfections in the bond on the strength of FRP wrapped cylindrical concrete columns

Effect of imperfections at the interface between concrete and FRP on the strength of FRP confined axially loaded cylindrical concrete columns is investigated, experimentally and numerically. It is seen that the presence of imperfections facilitates localization of deformation, adversely affects the confining capacity of FRP, and reduces the failure load. The influence of size, location and orientation of imperfection on failure load is studied: the orientation and location are found to be more important than size. Critical locations and orientations of the imperfection are found and explained in terms of the mechanics of shear banding in pressure-sensitive elasto-plastic materials.     

FRP-to-concrete joint assemblages anchored with multiple FRP anchors

Mechanical anchorage can enhance the strain capacity of externally bonded fibre-reinforced polymer (FRP) composite plates which are used for the strengthening of concrete members. Anchors made from FRP, which are known as FRP anchors or spike anchors, are an effective anchorage because they can be applied to a wide variety of FRP-strengthened structural elements such as beams and slabs. Limited research and understanding of FRP anchors in isolation or in groups is, however, hindering their rational design. As a result of such a knowledge gap, a series of tests is reported in this paper on forty-one FRP-to-concrete joints anchored with single as well as multiple FRP anchors in addition to two unanchored control joints. Apart from the number of anchors, the location of the anchors is investigated in addition to the method of anchor installation. The displacement controlled nature of the tests has enabled the complete load-slip responses of the joints to be captured, as well as FRP plate strains, and such results facilitate valuable insights to be gained in behaviour and understanding. The optimal arrangement of anchors tripled the strength of anchored joints relative to the unanchored control joint average. In addition, the slip capacity was generally increased at least five fold. Finally, a simple analytical model is also presented which is shown to compare reasonably well with the test results.     

U型FRP加固钢筋混凝土梁受剪剥离性能的有限元分析

采用FRP布对梁进行抗剪加固,可以有效的解决梁因配箍率不足而导致的受剪承载力偏低的问题。根据文献[1]中7根试验梁的参数,针对工程中常用的U型FRP受剪加固形式,建立三维有限元分析模型,采用商业有限元计算软件ANSYS,数值模拟了加载全过程和受剪剥离受力性能,根据试验结果确定了FRP-混凝土界面粘结剥离强度,并建议了合适的裂面剪力传递系数。根据有限元分析结果,作者又进一步研究了U型FRP布的应变分布、分担剪力的贡献、剥离破坏的过程,以及加固量、FRP类型和粘贴面积率对加固梁受剪承载力的影响。在有限元分析的基础上结合试验结果,建议了U型粘贴加固的受剪剥离承载力计算方法。     

Shear design of reinforced concrete beams with FRP longitudinal and transverse reinforcement

The shear resisting mechanisms of reinforced concrete (RC) beams with longitudinal and transverse FRP reinforcement can be affected by the mechanical properties of the FRP rebars. This paper presents a mechanical model for the prediction of the shear strength of FRP RC beams that takes into account its particularities. The model assumes that the shear force is taken by the un-cracked concrete chord, by the residual tensile stresses along the crack length and by the FRP stirrups. Failure is considered to occur when the principal tensile stress at the concrete chord reaches the concrete tensile strength, assuming that the contribution of the FRP stirrups is limited by a possible brittle failure in the bent zone. The accuracy of the proposed method has been verified by comparing the model predictions with the results of 112 tests. The application of the model provides better statistical results (mean value V_test/V_pred equal to 1.08 and COV of 19.5%) than those obtained using the design equations of other current models or guidelines. Due to the simplicity, accuracy and mechanical derivation of the model it results suitable for design and verification in engineering practice.     

Fracture mechanic modeling of fiber reinforced polymer shear-strengthened reinforced concrete beam

A numerical method is developed to model shear-strengthening of reinforced concrete beam by using fiber reinforced polymer (FRP) composites. Tensile crack is simulated by a non-linear spring element with softening behavior ahead of the crack tip to model the cohesive zone in concrete. A truss element is used, parallel to the spring element, to simulate the energy dissipation rate by the FRP. The strain energy release rate is calculated directly by using a virtual crack closure technique. It is observed that the length of the fracture process zone (FPZ) increases with the application of FRP shear-strengthening. The present model shows that the main diagonal crack is formed at the support in the control beam while it appears through the shear span in the shear-strengthened beam. Another important observation is that the load capacity increases with the number of CFRP sheets in the shear span.     

预应力FRP加固混凝土结构技术研究与应用

介绍了笔者进行的预应力芳纶纤维布和碳纤维筋加固混凝土结构的一些主要研究成果,内容包括:预应力芳纶纤维布永久锚具的开发;预应力芳纶纤维布的应力松弛损失研究;预应力芳纶纤维布加固混凝土梁的受弯、受剪性能研究;温度对芳纶纤维布配套粘结材料的力学性能影响研究;体外预应力碳纤维筋局部加固混凝土梁的力学性能研究;碳纤维筋预应力粗纤维混凝土梁的抗震性能研究;预应力纤维布加固混凝土结构的工程应用等。     

Analytical solution for the pull-out response of FRP rods embedded in steel tubes filled with cement grout

Fiber-reinforced plastic (FRP) tendons have been widely used for ground anchors in civil engineering. Although various pull-out tests of FRP rods from grout-filled steel tubes have been conducted to simulate ground anchors in rock, there are relatively few theoretical studies reported in the literature for this type of bonded anchorages. The intention of this paper is to present an analytical solution for predicting the maximum pull-out load of FRP rods embedded in steel tubes filled with cement grout. First, the expression of the shear stress along the thickness direction of the grout layer is obtained analytically. The tensile stress in the rod and the interfacial shear stress at the rod–grout interface are formulated at different loading stages. By modeling interfacial debonding as an interfacial shear crack, the pull-out load is then expressed as a function of the interfacial crack length. Finally, based on the Lagrange multiplier method, the maximum pull-out load and the critical crack length are determined. The validity of the proposed analytical solution is verified with the experimental results obtained from literature. It can be concluded that the proposed analytical solution can predict the maximum pull-out load of spiral wound and indented rods embedded in steel tubes filled with cement grout with reasonable accuracy. The proposed solution can be also applied in predicting the pull-out capacity of steel bars from concrete.     

Standardised double-shear test for determining bond of FRP to concrete and corresponding model development

Bond stress – slip characteristics play a major role in the behaviour of EBR FRP strengthened RC beams. These characteristics are normally determined by using experimental data from small-scale bond tests. However, the research community is yet to agree on a unified experimental set-up and testing procedure for these tests. The lack of standard tests leads to high variability in published results and hinders the development of reliable design models. The testing programme presented herein was part of an international Round Robin Test (iRRT) exercise, aimed at assessing the suitability of double shear tests to characterise the bond behaviour of FRP strengthening systems. A total of 20 tests were performed on different FRP plates. Recommendations on how to improve the iRRT methodology are given. Based on the results, an improved capacity model that accounts for concrete surface preparation is proposed and validated against an extensive database of published results. The outcome of the current research is expected to provide engineers with more confidence in designing safely strengthening applications whilst making the best use of the FRP materials.     

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.     

Increasing durability of lightweight concrete through FRP wrap

The purpose of this study was to investigate the effects of Fiber Reinforced Polymer (FRP) wraps on reducing chloride ingress and increasing the durability of lightweight concrete. Several prior studies have dealt with FRP application on normal weight concrete. However, the literature on externally bonded FRP application on lightweight concrete is sparse. This study involved an accelerated testing to determine concrete degradation and decrease in chloride ingress and associated increased durability that FRP wrapping can provide to lightweight concrete. Forty two cylinders were subjected to electricity induced accelerated testing in a saline solution for 50 days. Samples were removed from the immersion tank after specific failures and analyzed for chloride content and failure modes. Both lightweight and normal weight concrete greatly benefited from FRP wrapping in terms of increased time to failure and reduced concrete chloride. Lightweight concrete generally performed better with Carbon FRP (CFRP), and normal weight concrete with Glass FRP (GFRP). CFRP wraps produced the best overall protection. Multiple wraps were more effective at reducing chloride ingress than single wraps. Lightweight concrete had greater chloride permeability reductions, whereas normal weight concrete benefited more from FRP confinement effects. The majority of sample failures were caused by cracking in the concrete substrate.     

Behavior and modeling of confined concrete cylinders in axial compression using FRP rings

This study suggests a secondary dense lateral reinforcement for reinforced concrete (RC) columns that are located between the primary lateral reinforcement and concrete surface, which are used to delay the buckling of longitudinal reinforcement and increase the ductility of RC columns. ‘Dense’ means that the spacing of the lateral reinforcement is smaller than the maximum gravel size. This study conducted axial compressive tests on concrete cylinders confined by dense reinforcement in order to improve the effectiveness of the dense lateral reinforcement. FRP (Fiber Reinforced Polymer) rings were used for the reinforcement since they are corrosion resistant. The dense reinforcing method with FRP rings can successfully increase the peak strength of the concrete and the failure strain. The stress–strain curves of the confined concrete became almost bilinear with hardening behavior, which were similar to that of the concrete confined by the jackets of FRP sheets. This study also provides models of stress–strain in an axial direction and lateral strain. Based on the models, this study analyzes the confining effectiveness of the FRP rings on concrete.     

Shear strengthening of reinforced concrete beams with PBO-FRCM composites

The work analyses the functioning of reinforced concrete beams which are shear reinforced with FRCM (Fibre Reinforced Cementitious Matrix) composite mesh on mineral mortar. The analysis of previous tests provides an overview on the efficiency of the related FRP (Fibre Reinforced Polymers) system used for strengthening the beams against shearing forces. The information gathered on the functioning of FRCM strengthened concrete elements show that the key factor in this technology is ensuring appropriate carrying capacity of anchoring of the mesh. The tests were carried out on reinforced concrete beams with different design of lateral reinforcement. The beams differed in terms of the angle of inclination of the reinforcement to the longitudinal axis, as well as in terms of the manner of anchoring the mesh at the top and bottom surface of beams. The destruction mechanisms of beams were analysed and described. Value of deflection measured at the maximum load for all of the beams is significantly greater than the allowable value. The distribution of strains is presented as a function of the load, where the phases of operation in relation to shear of FRCM reinforced beams are visible.     

A modified pull-out test for bond of near-surface mounted FRP rods in concrete

Among the strengthening techniques based on fiber-reinforced polymer (FRP) composites, the use of near-surface mounted (NSM) FRP rods is emerging as a promising technology for increasing flexural and shear strength of deficient concrete, masonry and timber members. In order for this technique to perform effectively, bond between the NSM reinforcement and the substrate material is a critical issue. Aim of this project was to investigate the mechanics of bond between NSM FRP rods and concrete, and to analyze the influence of the most critical parameters on the bond performance. Following up to previous investigations, a different type of specimen was designed in order to obtain a test procedure as efficient and reliable as possible. Among the investigated variables were: type of FRP rod (material and surface pattern), groove-filling material, bonded length, and groove size. Results of the first phase of the project are presented and discussed in this paper.     

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.     

复杂应力状态对混凝土梁外贴FRP条带抗剪贡献的影响

FRP剥离是外贴FRP抗剪加固混凝土梁主要的破坏模式之一。以往研究中往往简单的将面内剪切试验得到的FRP-混凝土界面粘结滑移关系应用于外贴FRP抗剪加固梁的剥离承载力计算。外贴FRP抗剪加固梁中FRP下的混凝土的应力状态与面内剪切试验情况有较大差别,这对FRP-混凝土界面的力学性能具有较大的影响。因此,以往的方法高估了FRP条带的抗剪贡献。该文研究了混凝土多轴应力状态对FRP-混凝土界面性能的影响,并根据试验研究结果,提出了U形FRP加固混凝土梁中FRP剥离应变的折减系数。与试验结果的对比计算分析表明:使用该折减系数修正后的设计公式更加合理。     

RC members strengthened with externally bonded FRP plates: A FE-based limit analysis approach

Fiber-reinforced-polymer (FRP) strengthening systems have been increasingly studied and used as an effective strategy to rehabilitate existing reinforced concrete (RC) structures. The present paper addresses the problem of predicting the load-carrying capacity of these strengthened structural elements. To this aim, in the framework of limit analysis a numerical methodology is presented which employs iterative finite element (FE) analyses with adaptive elastic parameters and a multi-yield-criteria formulation. The latter is adopted to appropriately describe the constitutive behaviour of the three main constituent materials, namely: concrete, steel reinforcement bars (re-bars) and strengthening FRP-laminates. The effectiveness of the promoted methodology is verified by comparison between numerical results and experimental findings regarding FRP-plated RC elements. Despite being based on a simplified approach which is affected by the underlying assumptions of limit analysis theory, the numerical procedure may be useful for the assessment of the load-carrying capacity in large RC structures repaired or retrofitted by FRP plates. Potentialities and limitations of the proposed methodology are discussed carefully.     

Strengthening slabs using externally-bonded strip composites: Analysis of concrete covers on the strengthening

This study pertains to the experimental and theoretical behaviour of slabs strengthened by fibre reinforced polymer (FRP). The experimental results show that FRP significantly increases punching failure stress, resulting in a reduction of slab rotation around the loading column. The theoretical investigation presents a finite element model for the bending of strengthened slabs. The developed model considers the concrete as a 3D multi-layered non-linear material and explicitly takes into account the steel reinforcement and the FRP strips. The proposed model is then used to analyse the effects of a concrete cover on the reinforcement and repairs. In the analysed cases, the results show that an average reduction in the concrete shear modulus, between steel rod and FRP, of more than 30% leads to significant reductions of stress and slab stiffness.     

Width effect in the interface fracture during shear debonding of FRP sheets from concrete

The increasing use of carbon fiber reinforced polymer (FRP) sheets for strengthening existing reinforced concrete beams has generated considerable research interest in understanding the debonding mechanism of failure in such systems. The influence of the width of the FRP on the load-carrying capacity is investigated in this paper. The interfacial crack propagation and strain distribution during shear debonding are studied using a full-field optical technique known as digital image correlation. The results indicate the development of high stress/strain gradients at the interface as a consequence of the relative slip between the FRP and the concrete. The interface stress transfer between the FRP and concrete produces axial strain gradients in the FRP along its length. In the vicinity of the edges along the width of the FRP, edge regions comprising of both FRP and concrete are established. The edge region is characterized by high strain gradients in a direction perpendicular to the length and is of fixed width throughout the debonding process. The size of the edge regions is also found to be quite independent of the width of the FRP. Mode-II fracture condition exists in the interface directly below the FRP away from the edge regions. The interfacial crack is shown to be associated with a cohesive stress transfer zone of fixed length. During debonding, the stress transfer zone is shown to propagate in a self-similar manner at a fixed load. The interface fracture properties obtained from the portion of FRP away from the edge regions are shown to be independent of the FRP width. It is shown that when the width of concrete is larger than that required for establishing the edge regions, the nominal stress at debonding increases with an increase in the width of FRP. The scaling in the load carrying capacity during shear debonding is shown to be the result of the edge regions which do not scale with the width of the FRP.