RC beams strengthened with composite material: a limit analysis approach and experimental study

This paper deals with the flexural strengthening of reinforced concrete beams by means of thin carbon fibre reinforced plastic (CFRP) plates. A simplified laminated plate model is used to describe the behaviour of three-layered plate in cylindrical bending which were subjected to third-point line loads. The upper bound theorem of limit analysis is used to approximate the ultimate load capacity for multi-layered plates and identify different collapse mechanisms. A reinforced concrete beam strengthened by CFRP is designed as a three-layered plate. Experimental results are obtained and a comparison with theoretical predictions made.     

化爆作用下FRP加固RC板的试验研究及动力响应分析

我国20世纪60年代、70年代修建的大量防护工程抗力等级较低,急需进行加固补强。进行了化爆作用下,外贴FRP条带加固钢筋混凝土(RC)双向板抗爆性能的试验研究。按介质-结构相互作用理论确定结构的爆炸冲击荷载,建立了加固板的三折线弯曲抗力模型,利用虚功原理建立了加固RC板的运动微分方程,按数值方法求解了外贴FRP加固双向板在化爆冲击波作用下的动力响应时程,分析结果与试验结果吻合较好。研究结果表明:外贴FRP条带加固可以有效延缓混凝土的开裂、限制裂缝的开展,提高RC双向板的刚度,减小结构位移,减轻结构破坏程度,外贴FRP加固RC双向板的抗爆炸冲击波能力得到了明显提高,外贴FRP条带在极限状态时发生了剥离破坏和断裂破坏。     

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.     

Failure diagrams of FRP strengthened RC beams

Amongst various methods developed for strengthening and rehabilitation of reinforced concrete (RC) beams, external bonding of fibre reinforced plastic (FRP) strips to the beam has been widely accepted as an effective and convenient method. The experimental research on FRP strengthened RC beams has shown five most common modes, including (i) rupture of FRP strips; (ii) compression failure after yielding of steel; (iii) compression failure before yielding of steel; (iv) delamination of FRP strips due to crack; and (v) concrete cover separation. In this paper, a failure diagram is established to show the relationship and the transfer tendency among different failure modes for RC beams strengthened with FRP strips, and how failure modes change with FRP thickness and the distance from the end of FRP strips to the support. The idea behind the failure diagram is that the failure mode associated with the lowest strain in FRP or concrete by comparison is mostly likely to occur. The predictions based on the present failure diagram are compared to 33 experimental data from the literature and good agreement on failure mode and ultimate load has been obtained. Some discussion and recommendation for practical design are given.     

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.     

侵蚀环境下FRP条带加固锈蚀钢筋混凝土圆柱轴心受压试验

通过侵蚀环境下碳纤维增强聚合物(CFRP)复合材料条带和玻璃纤维增强聚合物(GFRP)复合材料条带加固锈蚀钢筋混凝土圆柱试验,分析了侵蚀环境对混凝土强度、纤维增强聚合物基复合材料加固锈蚀柱的极限荷载和荷载-轴向位移曲线的影响。结果表明,混凝土强度受冻融环境影响较大,受干湿环境影响较小;纤维增强聚合物(FRP)复合材料加固锈蚀柱的轴向极限荷载与冻融循环次数、钢筋锈蚀率及FRP复合材料种类有关,随冻融循环次数分别增加到25次、50次、75次,GFRP复合材料条带和CFRP复合材料条带加固锈蚀钢筋混凝土圆柱的轴向极限荷载分别降低了10.97%、13.37%、16.04%和5.95%、4.66%、4.33%;FRP复合材料加固锈蚀柱的刚度和耗能受侵蚀环境种类、侵蚀环境作用次数、锈蚀率及FRP复合材料种类的影响。在试验研究的基础上,通过理论分析侵蚀环境下混凝土强度损伤系数和锈蚀钢筋强度退化方程,提出了侵蚀环境下FRP复合材料条带加固锈蚀钢筋混凝土圆柱轴心受压承载力计算方法。      

Mechanical performance of composite-strengthened concrete structures

The interest of using fibre reinforced plastic (FRP) materials in rehabilitating damaged concrete structures respectively has been increased rapidly in recent years. In this paper, the structural behaviours of the glass–fibre composite strengthened concrete structures subjected to uni-axial compression and three point bending tests are discussed through experimental studies. Two types of concrete structure are used in present study, they are concrete cylinder and rectangular concrete beam. Discussion on the environmental effects of composite strengthened reinforced concrete (RC) structures is also addressed. Experimental results show that the use of glass–fibre composite wrap can increase the load carrying capacity of the plain concrete cylinders with and without notch formation. The flexural load capacity of the concrete beam increases to more than 50% by bonding 3 layers of glass–fibre composite laminate on the beam tension surface. Direct hand lay up method gives better strengthening characteristic in term of the ultimate flexural load compared with pre-cured plate bonding technique. The flexural strengths of composite strengthened RC beams submerged into different chemicals solution for six months are increased compared with the RC beams without strengthening. The strength of the concrete structure is seriously attacked by strong acids.     

纤维增强聚合物基复合材料加固锈蚀钢筋混凝土圆柱轴心受压性能

为了给纤维增强聚合物基复合材料（FRP）加固腐蚀环境下钢筋混凝土圆柱的设计和施工提供参考,促进FRP加固钢筋混凝土圆柱的应用,本文通过加速腐蚀得到类似实际环境中已锈损钢筋混凝土圆柱,采用碳纤维增强聚合物基复合材料（CFRP）条带和玻璃纤维增强聚合物基复合材料（GFRP）条带分别对锈蚀钢筋混凝土圆柱进行加固,最后对加固后圆柱进行轴心受压试验,重点研究钢筋锈蚀率、FRP层数和种类对钢筋混凝土圆柱受压承载力的影响;基于对FRP条带间隔约束效应、钢筋锈蚀对混凝土截面及钢筋力学性能影响的研究与分析,提出FRP条带间隔约束锈蚀钢筋混凝土圆柱轴心受压承载力计算模型。试验实测值与模型计算值之比的平均值为1.020,变异系数为0.063,二者符合较好。     

Homogenized limit analysis of FRP-reinforced masonry walls out-of-plane loaded

A three-dimensional (3D) homogenized limit analysis model for the determination of collapse loads of out-of-plane loaded FRP reinforced masonry walls is presented. Homogenization is performed on unreinforced masonry, whereas strips are applied at a structural level on the already homogenized material. Unreinforced masonry strength domain is obtained by means of a compatible approach in which bricks are supposed infinitely resistant and joints are reduced to interfaces with frictional-cohesive behavior and associated flow rule. A sub-class of elementary deformation modes is a-priori chosen in the representative volume element (RVE), mimicking typical failures due to joints cracking and crushing. Masonry strength domains are obtained equating power dissipated in the heterogeneous model with power dissipated in a fictitious homogeneous macroscopic plate. Afterwards, an upper bound FE limit analysis code is implemented to study entire unreinforced and FRP reinforced walls out-of-plane loaded. For unreinforced masonry, rigid infinitely resistant wedge-shaped 3D elements are used. The utilization of 3D elements is necessary to simulate the flexural strength increase induced by the introduction of FRP strips with negligible thickness, which are modeled by means of triangular rigid elements. FRP strips contribution is taken into account assuming that masonry and FRP layers interact by means of interfacial tangential actions. Internal power dissipation is possible at the interfaces between wedge adjoining elements (masonry failure), at the interfaces between triangular FRP and wedge masonry elements (delamination) and between triangular FRP adjoining elements (FRP failure). Two different structural examples are presented to validate the numerical model, namely a FRP reinforced masonry wall in cylindrical flexion and a set of masonry walls with openings in two-way bending. Results obtained with the model proposed fit well both experimental and numerical data available for all the cases analyzed, meaning that the procedure proposed can be used in building practice.     

Sensitivity analysis of reinforced concrete beams strengthened with FRP laminates

Numerical procedures are proposed to predict the failure of reinforced concrete (RC) beams strengthened in flexure with fiber-reinforced polymeric (FRP) laminates. The framework of damage mechanics was used during the modeling. Numerical results were validated against experimental data obtained from 19 beams strengthened with different types of FRP. These beams failed by concrete crushing, cover failure and plate debonding. The numerical models were capable of predicting the experimentally observed load–deflection, failure load and failure modes. The sensitivity of the numerical results was studied. In particular, the effect of the concrete constitutive behavior and different modeling considerations was evaluated. It was found that the fracture energy of the concrete–repair interface plays a central part in predicting plate-debonding failures.     

The extrinsic influence of carbon fibre reinforced plastic laminates to strengthen steel structures

The intrinsic advantages of strengthening the steel-based structures by the use of fibre reinforced plastic (FRP) material have not yet been fully exploited. In this paper, a succinct overview of recent studies made to enhance the strength of steel beams using FRP laminates is presented. The results presented and discussed in this paper were obtained by closely studying the behaviour of steel beams strengthened with carbon FRP material. An attempt is made to succinctly summarise the findings for two different types of strengthening of the steel beams using carbon FRP laminates. The first type of beams focuses on enhancing the strength of steel in flexure while the second focuses on increasing the shear strength of the beams. Three beams were designed so as to cause them to fail in flexure. Of the beams studied, two were strengthened using carbon FRP strips attached to the tension flange. One of the beams was tested to facilitate comparison of their behaviour to the two beams which are strengthened in flexure. Three other beams were designed such that they failed predominantly in shear. Of these three, two were strengthened with carbon FRP strips attached to the webs while the third beam was used as a control beam for the purpose of drawing comparisons. Preliminary results revealed a noticeable increase in the strength for both the flexure strengthened beams and the beams strengthened in shear. The observed increase in shear strength of the beams was 26% while the increase in strength for the beams tested in flexure was 15%. This study convincingly shows that it is possible to strengthen steel beams using carbon FRP laminates in both flexure and in shear.     

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.     

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.     

表层嵌贴预应力CFRP-strip加固钢筋混凝土梁的受力性能研究

体外粘贴预应力FRP技术和表层嵌贴FRP加固技术均是FRP应用于混凝土结构加固的重要技术,但存在各自的局限和不足。表层嵌贴预应力FRP技术有望结合上述两种技术的优点,进一步提高FRP加固混凝土结构的优势和效能。该文在研制成功FRP板条夹具的基础上,加固并进行了5根钢筋混凝土受弯构件的试验研究,深入考察了各试件尤其是表层嵌贴加固试件的力学行为与破坏形态,对比了体外与表层嵌贴加固试件的承载与变形性能差异,分析了预应力的存在对表层嵌贴加固构件力学性能与破坏模式的影响。试验结果表明:表层嵌贴预应力FRP板条加固显著提高了受弯构件的承载性能,其改善效果与体外粘贴预应力FRP板加固非常接近;嵌贴方式可使粘结树脂代替机械锚具锚固预应力FRP板条,但该文试验中表层嵌贴加固试件的破坏形态为粘贴端部的树脂-混凝土界面剥离和保护层混凝土撕裂,因此有需要就提高界面粘结能力和抑制保护层混凝土撕裂的构造措施开展进一步研究。     

Effect of interphase on fibre-bridging toughness of a unidirectional FRP composite thin plate

A parametric analysis of the toughening mechanisms in a uniaxially fibre reinforced polymer (FRP) thin plate with a power-law hardening shear interphase is presented. An interfacial shear-lag model is used to analyse the relationship between the crack surface traction exerted by the intact fibres and the crack opening displacement (COD). Numerical solutions of the equations governing bridge-toughening are given. Two special kinds of interphase, i.e. linearly elastic and perfect plastic, are discussed. The results demonstrate that the toughening ratio of the composite thin plate is sensitive to several parameters, e.g. the thickness of the interphase between fibre and matrix, the hardening parameter of the interphase, the interfacial shear properties (stiffness and strength), the fibre radius and the far-field load. The results of this investigation will be beneficial to the selection of constitutive materials, the improvement of mechanical behaviour and the fabrication process of FRP composites.     

Self-equilibrating moments in FRP-reinforced continuous structures

In continuous steel or concrete structures with surface-mounted fibre reinforced polymer (FRP) plates as flexural reinforcement, self-equilibrating moments can influence the loads at first yield and at failure, the latter due to potential buckling of the FRP plate or to end-peel both on account of offsets between points of contraflexure and the nearby FRP curtailments. In this paper, expressions are derived for the total (including self-equilibrating) moments along 2-span continuous structures with differential settlement. The expressions show how moments depend on support-to-member stiffness ratios and on distributions of section stiffness for service and ultimate limit states. Thus, the analysis is generic, applicable to FRP-reinforced steel and concrete structures. This analysis is verified via test data (including observation of end-peel in FRP compression curtailment zones offset from nearby contraflexure) and is used to construct 3D plots that facilitate identification of stiffness ratios which lead to significant self-equilibrating moments and contraflexure offset effects. Use of the plots to assess influences of differential settlement on laboratory test specimens is discussed. The analysis is shown to lead to an unprecedented result, namely that a unique point of load application exists for which changes to the stiffness layout have no impact on the moment distribution.     

FRP reinforcement of stone arch bridges: Unilateral contact models and limit analysis

A method for the estimation of the limit load and the failure mode of fiber-reinforced polymer (FRP) reinforced stone arch bridges is hereby presented. Unilateral contact interfaces with friction simulating potential cracks are considered in the finite element model of the bridge. FRP strips are then applied to the intrados and/or the extrados of the arch. The possible failure modes of the reinforced structure are sliding of the masonry, crushing, debonding of the reinforcement and FRP rupture. Identical failure modes arise from the computer simulation and from experiments on reinforced arches published in the literature.     

Nonlinear numerical analysis of the debonding failure process of FRP-to-concrete interfaces

The paper analyses numerical solutions for the process leading to debonding failure of fibre reinforced polymers (FRP)-to-concrete interfaces in shear tests with the FRP plate subjected to a tensile load at one end. Any realistic local nonlinear bond–slip law can be used in the numerical analysis proposed in the present study. However, only a Popovics’ type expression is employed in the numerical process due to its use in different studies found in the literature. Effective bond length (L_eff) is discussed and an expression depending on the Popovics’ constant (n_P) is proposed to calculate it. Assuming a fracture in pure Mode II, the debonding process is analysed in detail and distributions of bond stresses and strains in the FRP plate along the interface are presented. The load–displacement behaviour is also presented and the influence of the local bond–slip law on the debonding process is discussed.     

Experimental investigation on fire endurance of insulated concrete beams strengthened with near surface mounted FRP bar reinforcement

Fiber reinforced polymer (FRP) composites are known to be susceptible to deterioration at elevated temperature. To evaluate the feasibility of achieving a fire-rated FRP system an investigation was undertaken to examine and document the performance of near surface mounted (NSM) FRP strengthened concrete beams under fire conditions. Twelve reinforced concrete beams were strengthened in flexure with NSM FRP bars and insulated with different insulation systems. The specimens were subsequently exposed to a standard fire while subjected to full service load. Tests results on fire indicated that insulated NSM FRP strengthened beams can achieve a fire endurance of at least 2 h. Moreover structural testing to failure at room temperature of the fire testes beams has shown that well insulated members are able to retain (part of) their original strengthened flexural capacity.     

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。