Numerical analysis of multilayered CFRP retrofitted RC beams with partial interaction

This paper presents a theoretical model to simulate the behaviour of RC beams strengthened with multilayered CFRP matrix allowing for inter-layer slip. An element of the composite beam is assumed to be subjected to a system of forces that satisfy equilibrium and compatibility of deformations. The inter-layer slip is allowed for by relating the differential strain at the interfaces between the CFRP layers and the concrete to the longitudinal shear flow at the corresponding interface through the shear stiffness of the adhesive layer. The basic differential equations are derived in terms of displacement variables and solved numerically using finite differences. The results of the numerical simulation included slip values along the interfaces, maximum slip values, stresses and strains and deflections. The results compare reasonably well with experimental findings.     

Flexural behavior of reinforced concrete (RC) beams retrofitted with hybrid fiber reinforced polymers (FRPs) under sustaining loads

This paper reports experimental studies of reinforced concrete (RC) beams retrofitted with new hybrid fiber reinforced polymer (FRP) system consisting carbon FRP (CFRP) and glass FRP (GFRP). The objective of this study is to examine effect of hybrid FRPs on structural behavior of retrofitted RC beams and to investigate if different sequences of CFRP and GFRP sheets of the hybrid FRPs have influences on improvement of strengthening RC beams. Toward that goal, 14 RC beams are fabricated and retrofitted with hybrid FRPs having different combinations of CFRP and GFRP sheets. The beams are loaded with different magnitudes prior to retrofitting in order to investigate the effect of initial loading on the flexural behavior of the retrofitted beam. The main test variables are sequences of attaching hybrid FRP layers and magnitudes of preloads. Under loaded condition, beams are retrofitted with two or three layers of hybrid FRPs, then the load increases until the beams reach failure. Test results conclude that strengthening effects of hybrid FRPs on ductility and stiffness of RC beams depend on orders of FRP layers.     

Fatigue crack propagation behavior of RC beams strengthened with CFRP under cyclic bending loads

A fatigue crack propagation equation of reinforced concrete (RC) beams strengthened with a new type carbon fiber reinforced polymer was proposed in this paper on the basis of experimental and numerical methods. Fatigue crack propagation tests were performed to obtain the crack propagation rate of the strengthened RC beams. Digital image correlation method was used to capture the fatigue crack pattern. Finite element model of RC beam strengthened with carbon fiber reinforced polymer was established to determinate J‐integral of a main crack considering material nonlinearities and degradation of material properties under cyclic loading. Paris law with a parameter of J‐integral was developed on the basis of the fatigue tests and finite element analysis. This law was preliminarily verified, which can be applied for prediction of fatigue lives of the strengthened RC beams.     

Effect of clamping force on the delamination onset and growth in bolted composite laminates

Clamping force is a key element that alters the mechanism and sequence of failure in bolted joints of composite laminates. The mode of failure in bolted joints can be controlled by geometrical parameters and the preferred fail safe mode of failure is ‘bearing’ which generally consists of matrix cracks, delamination and fibre microbuckling. Three-dimensional (3-D) pinned (without clamping force) and bolted (1 kN clamping force) joint models were developed in [0/90]_s carbon fibre reinforced plastic (CFRP) laminates to show the clamping force effect on the onset and growth of delamination. It is shown that delamination was resulted from the shear stress components (Mode II & III) at the interface and the contribution of the out-of-plane component (Mode I - opening), so the clamping force, was negligible without modelling the in-plane failure modes and their coupling with delamination, which will be considered in future work.     

Fatigue lives of RC beams strengthened with CFRP at different temperatures under cyclic bending loads

Fatigue performance of reinforced concrete (RC) components strengthened with fibre reinforced polymer (FRP) is largely improved. However, temperature changes of service environment have a great effect on the fatigue behaviour of RC components strengthened with FRP. Concerning about temperature variations in subtropical areas such as South China, this paper analyses the fatigue behaviour of RC beams strengthened with carbon fibre laminate (CFL) from experimental studies and theoretical analysis under four different temperatures (5 °C, 20 °C, 50 °C, 80 °C) and five different stress levels (0.60, 0.66, 0.72, 0.78, 0.84). The paper discusses temperature fatigue behaviour of RC beams strengthened with CFL under cyclic bending loads in different service environments, and proposes a calculation formula of fatigue lives of RC beams strengthened with CFL under environmental temperatures and external forces coupling. Experimental results show that the formula not only effectively predicts the fatigue lives of the RC beams strengthened with CFL under environmental temperatures and bending loads coupling but also estimates the fatigue limits.     

Finite element modelling of multiple cohesive discrete crack propagation in reinforced concrete beams

This paper presents a finite element (FE) model for fully automatic simulation of multiple discrete crack propagation in reinforced concrete (RC) beams. The discrete cracks are modelled based on the cohesive/fictitious crack concept using nonlinear interface elements with a bilinear tensile softening constitutive law. The model comprises an energy-based crack propagation criterion, a simple remeshing procedure to accommodate crack propagations, two state variable mapping methods to transfer structural responses from one FE mesh to another, and a local arc-length algorithm to solve system equations characterised by material softening. The bond-slip behaviour between reinforcing bars and surrounding concrete is modelled by a tension-softening element. An example RC beam with well-documented test data is simulated. The model is found capable of automatically modelling multiple crack propagation. The predicted cracking process and distributed crack pattern are in close agreement with experimental observations. The load-deflection relations are accurately predicted up to a point when compressive cracking becomes dominant. The effects of bond-slip modelling and the efficiency and effectiveness of the numerical algorithms, together with the limitations of the current model, are also discussed.     

碳纤维束铆钉锚固下CFRP布加固梁的力学性能

粘贴碳纤维布(CFRP)加固梁时,通常需对其进行锚固,避免发生因CFRP布过早剥离而无法充分利用其抗拉强度。但当梁施工空间较小,梁侧面形状不规则时,CFRP布锚固较困难,采用新型碳纤维束铆钉锚固的方式能够很好地解决这一弊端。本文通过对四组不同锚固方式下的CFRP布加固梁进行四点受弯承载力试验,对比分析加载过程中各梁的力学性能和破坏规律,研究表明碳纤维束铆钉锚固下CFRP布加固梁强度和刚度都有显著增强。进一步对碳纤维束铆钉锚固方法优化,得到最佳碳纤维束铆钉锚固深度约为80mm,最佳锚固间距约为200mm。     

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.     

Numerical optimization of strengthening disturbed regions of dapped-end beams using NSM and EBR CFRP

This paper presents a parametric investigation, based on non-linear finite element modeling, to identify the most effective configuration of carbon fiber-reinforced polymers (CFRP) for strengthening reinforced concrete (RC) dapped-end beams. Following a field application and laboratory tests, it focuses on effects of 24 externally bonded (EBR) and near surface mounted reinforcement (NSMR) configurations on yield strain in steel and the capacity and failure mode of dapped-end beams. The investigated parameters were the mechanical properties of the CFRP, the strengthening procedure and the inclination of the fibers with respect to the longitudinal axis. Two failure scenarios were considered: rupture and debonding of the FRP. The results indicate that high-strength NSM FRPs can considerably increase the capacity of dapped-end beams and the yielding strains in reinforcement can be substantially reduced by using high modulus fibers.     

Fatigue performance of RC beams strengthened with CFRP under coupling action of temperatures and vehicle random loads

Considering significant influence of servicing environments and vehicle random loads on fatigue performance of main load‐bearing members of bridges, in this paper, fatigue performance of reinforced concrete bridge structures strengthened with carbon fibre–reinforced polymer under coupling action of environmental temperatures and vehicle random loads was studied. A vehicle random loading spectrum for fatigue tests was simulated and compiled. A fatigue testing method with coupling action of random loads and temperatures was proposed, and 3‐point bending fatigue tests of the reinforced concrete beams strengthened with carbon fibre–reinforced polymer under coupling action of temperatures and vehicle random loads were performed. Effects of temperatures and loading form on the fatigue damage mechanism were preliminarily discussed. A modified Palmgren‐Miner rule and semiempirical fatigue equations were proposed and proved effective.     

An experimental and numerical investigation on torsional strengthening of solid and box-section RC beams using CFRP laminates

The issue of maintenance and repair/upgrading of existing structures has become a major issue, particularly extending the service lifespan of bridges. Fibre reinforced polymer (FRP) has shown great promise as a state-of-the-art material in flexural and shear strengthening as external reinforcement. However, little attention has been paid to torsional strengthening in terms of both experimental and numerical research. This paper reports the experimental work in an overall investigation of torsional strengthening of solid and box-section reinforced concrete beams with externally-bonded CFRP. This was found to be a viable method of torsional strengthening. Numerical work was carried out using non-linear finite element (FE) modelling. Good agreement in terms of torque–twist behaviour, steel and CFRP reinforcement responses, and crack patterns was achieved. The unique failure modes of all the specimens were modelled correctly as well.     

CFRP布端绕双杆自锁加固混凝土窄梁抗弯试验

为了抵抗粘贴碳纤维增强聚合物基复合材料（CFRP）加固钢筋混凝土结构中常见的剥离破坏,发明了将CFRP布端部以特定方式绕平行双杆实现自锁的方法。鉴于窄梁截面宽度有限,提出将CFRP布贴梁受拉底面布置后,用安装在梁侧面的双L形端锚装置固定双杆,形成侧锚底贴加固方案。完成了5根混凝土强度较低的矩形截面梁四点弯曲试验,其中4根采用上述锚固方式抗弯加固,检验了锚固效果,考察了CFRP布宽度及其沿全长与梁底面是否粘结对加固效果的影响。试验结果表明,采用本文方法进行加固后,端部剥离得以避免,中部剥离即使发生,或在无粘结加固梁受力后期,CFRP布仍能承担较大拉力,因此,极限荷载较对比梁有明显提高。比较而言,CFRP布与梁底有粘结时加固效果更好,CFRP布宽度加大也对提高承载力有益。     

Numerical model for CFRP confined concrete elements subject to monotonic and cyclic loadings

Uniaxial cyclic and monotonic compression tests were carried out on partially and fully wrapped concrete cylinders with Carbon Fibre Reinforced Polymer (CFRP) wet lay-up sheets. The influence of the concrete compressive strength, CFRP stiffness, geometric confinement arrangement and loading type on the compressive behaviour of reinforced concrete column elements of circular cross-section up to their failure was assessed. A uniaxial stress–strain constitutive model is proposed, and the results obtained from the experimental tests were used to calibrate some of the parameters of this model, and to appraise the model performance. This model allows the simulation of reinforced concrete members by using Timoshenko one-dimensional elements, in the context of the finite element method (fibre model). Good agreement was obtained between numerical simulations and experimental results for both monotonic and cyclic loading tests.     

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.     

Structural response of hyperstatic concrete beams reinforced with GFRP bars: Effect of increasing concrete confinement

The design of concrete structures reinforced with glass fibre reinforced polymer (GFRP) bars is influenced by their reduced stiffness and brittleness. In hyperstatic structures, the methodology used in force analysis depends on the ductility of the structural systems, which in this case, being essentially provided by the concrete, can be potentially increased by confining concrete in critical zones. This paper presents experimental and numerical investigations about the flexural behaviour of continuous beams reinforced with GFRP bars, namely of their service and failure responses, and the effect of increasing concrete confinement in critical cross-sections. A calculation procedure to quantify the confinement effect in beams due to the reduction of the spacing between shear stirrups is first presented. The experimental investigations comprised a comparative study in which two-span concrete beams reinforced with either GFRP or steel bars were tested in bending. In the former, the effect of reducing the shear stirrups spacing was analyzed together with the under- and over-reinforcement at the central support and midspan cross-sections, respectively. The development of a crack hinge in the continuity support zone highlighted the better performance of beams under-reinforced on the top layer with GFRP bars compared to “equivalent” beams reinforced with steel, namely at the resistance level. In addition, the confinement at critical zones increased significantly the strength and ductility. The numerical investigations included the development of non-linear finite element models for all beams tested - numerical results are in good agreement with test data and seem to confirm the confinement effect observed in the experiments.     

Delamination detection in laminated composite beams using hybrid elements

This investigation pursues two goals. One of them is developing a three-dimensional finite element with an embedded interface for analyzing the laminated composite structure. The composite element efficiency is numerically proven. Delaminatoin is an important failure mechanism in certain types of composite structures. Detecting this type of damage is currently a problem of interest to the structural health monitoring community. The second goal of the paper is presenting a novel and well-organized procedure for the identification of delaminatoin in laminated composite beams. The damage identification scheme is formulated by an inverse problem, where analysis data from related finite element modeling, are used to quantify the magnitude and local of delaminatoin. The inverse problem is then transformed to an optimization statement, and the optimum delaminatoin parameters are found by minimizing the objective function. In this study, a genetic algorithm is used for the optimization process. Several numerical examples are analyzed for the accuracy test, and a few of them are presented here.     

Numerical simulation of rebar/concrete interface debonding of FRP strengthened RC beams under fatigue load

The aim of this paper is to simulate the rebar/concrete interface debonding of FRP strengthened RC beams under fatigue load and also, to ascertain the influence of design parameters such as the elastic modulus, thickness and length of the FRP plate on the debonding performance. In order to simplify the simulation, some basic equilibrium equations are formulated and then the stresses of the rebar and FRP plate are numerically solved, and stress intensity factor is avoided in the simulation by fundamentals of fracture mechanics because of its complexity around the crack tip of bi-material interface. With the combination of finite element method and difference approximation, authors program the degradation model of coefficient of friction, debond criterion, propagation law and loop of load process into a commercial finite element code to investigate the fatigue debonding. The relationships between the debond length as well as other fatigue parameters and number of cyclic load are obtained and discussed.     

Buckling strength of adhesively-bonded single and double-strap repairs on carbon-epoxy structures

This work reports on an experimental and finite element method (FEM) parametric study of adhesively-bonded single and double-strap repairs on carbon-epoxy structures under buckling unrestrained compression. The influence of the overlap length and patch thickness was evaluated. This loading gains a particular significance from the additional characteristic mechanisms of structures under compression, such as fibres microbuckling, for buckling restrained structures, or global buckling of the assembly, if no transverse restriction exists. The FEM analysis is based on the use of cohesive elements including mixed-mode criteria to simulate a cohesive fracture of the adhesive layer. Trapezoidal laws in pure modes I and II were used to account for the ductility of most structural adhesives. These laws were estimated for the adhesive used from double cantilever beam (DCB) and end-notched flexure (ENF) tests, respectively, using an inverse technique. The pure mode III cohesive law was equalled to the pure mode II one. Compression failure in the laminates was predicted using a stress-based criterion. The accurate FEM predictions open a good prospect for the reduction of the extensive experimentation in the design of carbon-epoxy repairs. Design principles were also established for these repairs under buckling.     

Experimental and finite element analysis of a double strap joint between steel plates and normal modulus CFRP

Strengthening of steel structures using externally-bonded carbon fibre reinforced polymers ‘CFRP’ is a rapidly developing technique. This paper describes the behaviour of axially loaded flat steel plates strengthened using carbon fibre reinforced polymer sheets. Two steel plates were joined together with adhesive and followed by the application of carbon fibre sheet double strap joint with different bond lengths. The behaviour of the specimens was further investigated by using nonlinear finite element analysis to predict the failure modes and load capacity. In this study, bond failure is the dominant failure mode for normal modulus (240 GPa) CFRP bonding which closely matched the results of finite elements. The predicted ultimate loads from the FE analysis are found to be in good agreement with experimental values.