Bond strengthening of lap spliced reinforcement using external FRP jackets: An effective technique for seismic retrofit of rectangular or circular RC columns

Confinement of concrete at the critical hinging regions is one of the most effective means for improving the seismic behavior of reinforced concrete (RC) members. Confinement reduces the bond degradation of the steel reinforcement and limits the concrete damage within the confined zone leading to increased energy absorption and dissipation capacity of the structure. Recent experimental and analytical studies undertaken on the use of FRP composites for seismic upgrading of RC members [FRPRCS08 Proceedings. In: Triantafillou TC, editor. 8th International symposium on fiber-reinforced polymer reinforcement for concrete structures. Patrace, Greece: University of Patrace; July 2007. p. 16–8] have clearly identified the advantages of this technology when compared to conventional strengthening methods. However, unfortunately, no guidelines have yet been developed by code committees for seismic retrofit using FRP composites. This paper provides a synthesis of the results of a series of experimental and analytical studies undertaken in the main part by the writer and in part by other investigators on the use of external FRP jackets for bond strengthening of developed/spliced steel bars in tension and its implications on the static and seismic response of concrete members. Results of the experimental programs are briefly discussed, and design expressions for evaluating the minimum thickness of FRP jacket required for seismic bond strengthening are presented and compared. The accuracy of the design expressions was verified against experimental data. In addition, a generalized model of the local bond stress–slip response of steel bars embedded in FRP confined concrete corresponding to splitting mode of bond failure is described. The model is composed of a monotonic envelope curve and bond degrading curve and can be used for evaluating the seismic behavior of the hinging zones in reinforced concrete members when confined externally with FRP jackets in comparison with the response of unconfined concrete.     

Modeling short-term tension stiffening in reinforced concrete prisms using a continuum-based finite element model

Tension stiffening is most often included in models of reinforced concrete by modifying the constitutive laws of the tensile concrete. In reality, tension stiffening is caused by the bond stress that develops at the steel–concrete interface between the primary cracks. In this paper, a modified CEB–FIP bond model is incorporated into a non-linear finite element program to accurately model tension stiffening at the serviceability limit states. The bond–slip relationship at any point along the reinforcement bar is modified to account for the local damage of the surrounding concrete, as well as the level of steel stress. A non-local analysis is undertaken to adjust the constitutive law of the bond interface element at each load step. The proposed model is shown to accurately predict the crack spacing, stresses and deformation in axially loaded tension members at typical in-service load levels.     

纤维增强塑料筋混凝土粘结滑移本构模型

纤维增强塑料筋与钢筋性能的差异 ,使纤维增强塑料筋混凝土的粘结性能与钢筋混凝土的粘结性能存在明显不同 ,因此 ,研究塑料筋混凝土粘结滑移本构模型 ,对推广塑料筋混凝土结构在工程中的应用具有重要的理论意义和实用价值。在总结国内外已有的纤维增强塑料筋与混凝土粘结滑移本构模型的基础上 ,提出了粘结滑移的连续曲线本构模型。该模型以粘结滑移曲线的三个关键点为基础 ,物理概念明确、光滑连续 ,并与试验结果吻合良好     

Modeling of debonding failure for RC beams strengthened in shear with NSM FRP reinforcement

The shear capacity of reinforced concrete members can be successfully increased using near-surface mounted (NSM) fiber-reinforced polymer (FRP) reinforcement. Tests conducted thus far have shown that failure is often controlled by diagonal tension associated to debonding between the NSM reinforcement and the concrete substrate. In absence of steel stirrups and/or when the spacing of the NSM reinforcement is large, debonding involves separately each of the bars crossed by the critical shear crack. In order for shear strengthening of beams with NSM reinforcement to be safely designed, an analytical model able to encompass the failure mode mentioned above must be developed. This paper presents two possible approaches, a simplified and a more sophisticated one, to predict the FRP contribution to the shear capacity. In the first approach, suitable for immediate design use, an ideally plastic bond–slip behavior of the NSM reinforcement is assumed, which implies a complete redistribution of the bond stresses along the reinforcement at ultimate. The second approach, implemented numerically, accounts for detailed bond–slip modeling of the NSM reinforcement, considering different types of local bond–slip laws calibrated during previous experimental investigations. It also takes advantage of an approach developed by previous researchers to evaluate the interaction between the contributions of steel stirrups and FRP reinforcement to the shear capacity. The paper illustrates the two models and compares their predictions, with the ultimate goal to evaluate whether the first simple model can be used expecting the same safety in predictions of the second model.     

Model for post-yield tension stiffening and rebar rupture in concrete members

A tension stiffening model is presented which enables the calculation of average tensile stresses in concrete, after yielding of reinforcement, in reinforced concrete elements subjected to uniaxial tension, shear or flexure. To determine the average tensile stress-strain relationship for concrete, a crack analysis approach is employed taking into account the bond mechanism between concrete and deformed reinforcing bars, and numerical analyses are conducted to determine the tensile behavior of reinforced concrete members including post-yield response. Analytical parametric studies are conducted to determine the influence of various parameters including concrete compressive strength and reinforcement yield strength, ultimate strength, hardening stress, and hardening strain. Analysis results obtained from the proposed model, when compared to experimental results for uniaxial members, indicate good agreement for structural behavior after yielding of reinforcement. The proposed model makes it possible to accurately calculate reinforcement stresses at crack locations and, thus, average strain conditions which result in rupture of reinforcement. This leads to more realistic predictions of the uniaxial, flexural, and shear ductility of reinforced concrete members.     

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.     

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.     

Numerical Analysis of Debonding Mechanisms in FRP-Strengthened RC Beams

Abstract:   Fiber-reinforced polymer (FRP) composites have been increasingly used as externally bonded reinforcement in lieu of their steel counterpart in the rehabilitation and retrofit of existing concrete structures. Without proper understanding of interfacial fracture behavior and failure mechanisms, it is impossible to efficiently develop an effective and rational FRP bonding technique. This article is mainly focused on clarifying the debonding behavior and failure mechanisms caused by different types of flexural crack distributions in FRP-strengthened R/C beams, which has not been solved so far. Using a discrete crack model for concrete crack propagation and a bilinear bond–slip relationship with softening behavior to represent FRP–concrete interfacial behavior, a nonlinear fracture mechanics-based finite-element analysis is performed to investigate the effects of crack spacing and interfacial parameters such as stiffness, local bond strength, and fracture energy on the initiation and propagation of the debonding and the structural performance. It is shown that the debonding behavior and load-carrying capacity are significantly influenced by two important factors: interfacial fracture energy and crack spacing in relation to the effective transfer length of FRP sheets. Based on the numerical results, some suggestions concerning the effect of interfacial properties are made as practical design aids.     

HB FRP加固混凝土结构组合界面黏结特性

为揭示HB-FRP(hybrid bonded fiber reinforced polymer)加固混凝土结构多作用组合工作机制,设计了5组黏结作用组合试验.基于实测荷载-滑移关系、应变分布、黏结-滑移关系开展了界面黏结特性研究,提出组合界面黏结-滑移统一模型和黏结荷载表达式.结果表明:HB-FRP加固混凝土组合作用可拆分为FRP黏结混凝土、侧压力和FRP黏结钢板;组合界面的黏结应力发展不同步,FRP板下表面与混凝土的剥离早于FRP板上表面与钢板的剥离,叠合工作时序不同;由侧压力引起的界面摩擦应力随界面应力的发展而增加并趋于稳定;理论模型结果与试验结果具有较好的一致性,可用于计算组合界面的黏结荷载.     

基于扰动应力场模型的ABAQUS二次开发及其与塑性损伤模型的比较

扰动应力场模型（DSFM）由于考虑了裂缝间的剪切滑移效应,融合了转动裂缝模型和固定裂缝模型的思想,可以更真实地模拟钢筋混凝土构件的受剪性能。通过大型通用有限元软件ABAQUS的二次开发接口,开发了基于DSFM模型思想的用户子程序UMAT,重点介绍将剪切滑移应变从总应变中分离出来的算法,并给出能够适应UMAT开发要求的编程方法和流程。利用所开发的UMAT子程序和ABAQUS内置的塑性损伤（CDP）模型对多伦多大学完成的多块钢筋混凝土平板试验进行分析。结果表明,所开发的子程序能够准确反应不同配筋形式的钢筋混凝土单元在不同受力状态下的响应,而ABAQUS内置的CDP模型由于无法反应钢筋混凝土单元斜裂缝出现后的剪应力强化效应,不能用于钢筋混凝土的受剪性能分析。     

FRP-混凝土界面粘结性能有限元方法研究

分析FRP-混凝土界面的粘结性能, 是研究FRP外贴加固钢筋混凝土结构的基础问题。本文根据已有的面内剪切试验研究结果, 采用大型通用有限元程序MSC.Marc建立有限元模型并导入裂面剪力模型子程序, 进行了非线性计算分析。引入了“裂缝带模型”、“界面粘结承载力”、“有效锚固长度”等概念, 对混凝土单元开裂软化模量以及裂面剪力模型进行了优选。得到了FRP应变分布规律和界面粘结应力分布规律, 提出了全新的“粘结屈服平台”概念, 建议相关的界面性能非线性有限元分析采用本文的方法。     

FRP增强预制裂缝混凝土的断裂性能

为了探讨纤维增强复合材料(FRP)增强预制裂缝混凝土的断裂性能,得到单层FRP对不同裂缝深度混凝土的最佳增强效果,通过相同尺寸、不同初始缝高比(0.2、0.3、0.4、0.5)的FRP增强预制裂缝混凝土三点弯曲梁断裂试验,基于FRP-混凝土界面黏结滑移模型,得到了FRP增强预制裂缝混凝土三点弯曲梁的断裂性能参数.结果表明:FRP增强预制裂缝混凝土的荷载-裂缝口张开位移(P-CMOD)曲线的峰值荷载大于普通混凝土的峰值荷载,且FRP增强预制裂缝混凝土峰值荷载随着初始缝高比的增加先增大后减小;初始缝高比从0.2变化到0.5时,FRP增强预制裂缝混凝土的起裂韧度可认为是常数;随着初始缝高比的增加,FRP增强预制裂缝混凝土的失稳韧度呈先增大后减小的趋势,当初始缝高比为0.4时,失稳韧度达到最大值,表明此时增强效果最佳;相比于普通混凝土失稳荷载后的脆性断裂破坏,FRP增强混凝土断裂破坏过程中的延性得到明显提高.     

Deflection and crack-width prediction of concrete beams reinforced with glass FRP rods

Concrete beams reinforced with fiber reinforced polymer (FRP) bars exhibit large deflections and crack widths as compared to concrete beams reinforced with steel due to the low modulus of elasticity of FRP. Current design methods for predicting deflections at service load and crack widths developed in concrete structures reinforced with steel bars may not be used for concrete structures reinforced with FRP bars. Thus, the ACI 440 Committee has provided design guidelines for concrete beams reinforced with FRP bars. Verification of the ACI 440 methods for predicting deflections and crack widths for glass fiber reinforced polymer reinforced concrete beams are presented in this paper. In addition, improvement to the crack width equation was suggested to account for 2 layers of reinforcement. This study shows that ACI 440.1R-01 can be effectively used to predict deflections in concrete beams reinforced with FRP bars and crack width in beams with one-layer FRP bars. However, when FRP bars are placed in two layers, ACI 440.1R-01 can be used after some parameters are modified. Six full concrete beams reinforced with different GFRP reinforcement ratios were load tested and the measured deflections and crack widths were analyzed and compared with those predicted by the proposed models. The experimental results compared well with those proposed by the model.     

Finite element analysis of thin GFRC panels reinforced with FRP

Glass fibre reinforced concrete (GFRC) incorporating fibre reinforced polymer (FRP) bar reinforcement is potentially an ideal composite material for the manufacture of thin structural elements due to its superior durability over GFRC containing conventional steel reinforcement. GFRC without any bar reinforcement has only been used for small units and short spans due to its relatively low flexural strength. Until now, no work has been reported on the use of FRP bars in GFRC. The first part of the paper deals with the stress–strain characteristics of GFRC. In the second part the bond strength of GFRC with both steel and FRP reinforcing bars is determined from a series of 24 pullout tests from which the characteristics of the local bond stress–slip response was established. The results show that the bond of FRP bars in GFRC is, in general, better than the bond in normal concrete, and that conventional numerical models can be used to model the behaviour. The last part of the paper investigates the performance of a 3 m span thin GFRC permanent formwork panel, reinforced with FRP, both experimentally and analytically with finite element (FE) analysis. It is concluded that the behaviour of thin GFRC elements incorporating FRP reinforcement can be predicted by FE analysis in which the GFRC stress–strain characteristics and bond characteristics are modelled with robust spring elements.     

Complete nonlinear response of reinforced concrete beams under cyclic loading

Complete nonlinear analysis is carried out for cyclically loaded reinforced concrete (RC) beams made of normal‐ and high‐strength concrete. The loading stage covers not only the pre‐peak stage but also the post‐peak stage in particular. The analysis is based on a numerical method that employs the actual stress–strain curves and takes into account the stress‐path dependence of concrete and steel reinforcement. The complete nonlinear behavior of RC beams under both non‐reversed and reversed cyclic loading is studied based on the moment–curvature relationship obtained. Generally, the response under cyclic loading is found to be dependent on the loading path in bending. The variation of neutral axis depth is different for under‐ and over‐reinforced sections during cyclic loading. The Bauschinger effect of steel reinforcement is insignificant for non‐reversed cyclic loading but notable for reversed cyclic loading, especially when the loading extends into the post‐peak stage. The beneficial effects of concrete tension stiffening are only observed at the service stage and are more significant for under‐reinforced RC beams than over‐reinforced ones. Copyright © 2007 John Wiley & Sons, Ltd.     

Ductility characteristics of fiber-reinforced-concrete beams reinforced with FRP rebars

To mitigate the corrosion problem caused by steel reinforcement, a study was initiated to develop a nonferrous hybrid reinforcement system for concrete beams by incorporating continuous fiber-reinforced-polymer (FRP) rebar and fiber-reinforced-concrete (FRC) containing randomly distributed polypropylene fibers. This paper describes the flexural performance of this FRP/FRC hybrid reinforcement system as well as FRP/plain concrete beams that served as references. Test results showed that the crack widths of FRP/FRC beams were smaller than those of FRP/plain concrete beams at the proposed service load. The compressive strains at the top fiber of concrete in FRP/FRC beams were larger than 0.004 due to the added polypropylene fibers. In addition, the ductility indices evaluating the FRP reinforced members were discussed. It is found that the ductility indices for all the tested beams were above the minimum requirement of 4. The addition of fibers improved the flexural behavior by increasing the ductility level more than 30%, when compared to the companion beam.     

不同FRP增强混凝土梁断裂性能试验研究

为了探讨不同种类纤维增强复合材料（FRP）增强带裂缝混凝土的断裂性能,开展了芳纶纤维增强复合材料（AFRP）、碳纤维增强复合材料（CFRP）和玻璃纤维增强复合材料（GFRP）增强带裂缝混凝土梁的三点弯曲试验,分析了其断裂性能参数.结果表明：相对于普通混凝土梁试件,FRP对带裂缝混凝土梁的阻裂加固效果更明显;CFRP增强混凝土梁的起裂荷载和失稳荷载均大于AFRP与GFRP增强混凝土梁,CFRP的阻裂增强效果最佳;AFRP增强混凝土梁和CFRP增强混凝土梁的破坏形式均为试件底部混凝土 FRP界面的剥离破坏,GFRP增强混凝土梁的破坏形式为试件底部GFRP的拉断破坏;通过对不同FRP增强混凝土梁阻裂加固机理的分析,计算得出CFRP增强混凝土梁的起裂韧度和失稳韧度最大,且CFRP价格适中,因此使用CFRP对带裂缝混凝土梁进行增强加固的性价比最优.     

Numerical simulation of performance of near-surface mounted FRP-upgraded beam–column sub-assemblages under cyclic loading

This study deals with the performance of the upgrading schemes for the existing gravity load designed (GLD) reinforced concrete (RC) beam–column sub-assemblages using near-surface mounted (NSM) fibre-reinforced polymer (FRP) bars. In this study, exterior beam–column sub-assemblage of a general RC-framed structure has been considered. Numerical investigations of the sub-assemblages have been carried out under cyclic loading using nonlinear finite element analysis. Experimentally validated numerical models have been used for evaluating the performance of various upgrading schemes using NSM bars. Cyclic behaviour of reinforcement, concrete modelling based on fracture energy, bond–slip relations between concrete and steel reinforcement have been incorporated. The study also includes numerical investigation of crack and failure patterns, ultimate load-carrying capacity, strain comparisons and formation of plastic hinges, load–displacement hysteresis, energy dissipation and ductility. Seismic performance in terms of energy dissipation and development of strain in beam bar shows that some of the upgraded schemes are found to be comparable to the seismically designed ductile specimens. The findings of this study would be helpful to the practising and design engineers for developing detailing criteria for newly designed – or strengthening of deficient – reinforced concrete structure.