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Composite Structures 88 (2009) 497–508

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Composite Structures

journal homepage: www.elsevier .com/locate /compstruct

Flexural behaviour of reinforced concrete beams strengthenedwith prestressed carbon composites

Dong-Suk Yang a, Sun-Kyu Park b, Kenneth W. Neale a,*

a Department of Civil Engineering, University of Sherbrooke, 2500 boul. de I’Université, Sherbrooke, Quebec, Canada, J́1K 2R1b Department of Civil Engineering, Sungkyunkwan University, 300 Chunchun-Dong, Jangan-Gu, Suwon, Gyeonggi-Do 440-746, South Korea

a r t i c l e i n f o

Article history:Available online 7 July 2008

Keywords:Anchorage systemCFRP platesDuctility,Finite element analysisFlexural testsPrestressing

0263-8223/$ - see front matter � 2008 Elsevier Ltd. Adoi:10.1016/j.compstruct.2008.05.016

* Corresponding author. Tel.: +1 819 821 7752; faxE-mail address: [email protected] (K

a b s t r a c t

In this study, a total of 13 FRP-strengthened reinforced concrete beams were tested in flexure andanalyzed using the finite element method. The various variables included bonding or no bonding ofthe FRP, the anchorage system, the amount of prestressing, and the span length. The experimentsconsisted of one control beam, two non-prestressed FRP-bonded beams, four prestressed FRP-unbondedbeams, four prestressed FRP-bonded beams, and two prestressed FRP-unbonded beams with differentspan lengths. All the beams were subjected to three-point and four-point bending tests under deflectioncontrol, with the loading, deflection and failure modes recorded to the point of failure. A nonlinear finiteelement analysis of the tested beams was also performed using the DIANA software; this analysisaccounted for the nonlinear concrete material behaviour, the reinforcement, and an interfacial bond-slipmodel between the concrete and CFRP plates.

The aim of this investigation was to study the flexural performance of reinforced concrete membersstrengthened using CFRP plates, employing different FRP bonding and prestressing methods. The failuremode of the prestressed CFRP-plated beams was not debonding, but FRP rupture. For the reinforcedconcrete members strengthened with externally bonded prestressed CFRP plates, debonding of thecomposite laminates occurred in two stages. After the debonding of the CFRP plates that occurred inthe bonded cases, the behaviour of the bonded CFRP-plated beams changed to that of the unbondedCFRP-plated beams due to the effect of the anchorage system. The flexural test results and analyticalpredictions for the CFRP-strengthened beams were compared and showed very good agreement in termsof the debonding load, yield load, and ultimate load. The ductility of the beams strengthened with CFRPplates having the anchorage system was considered high if the ductility index was above 3.

� 2008 Elsevier Ltd. All rights reserved.

1. Introduction

The bonding of steel plates for the strengthening and rehabilita-tion of reinforced concrete structures was a popular strengtheningmethod in the past. In recent years, there has been extensive re-search on the use of fibre reinforced polymer (FRP) compositesfor the replacement of steel plates in plate bonding. FRPs have alsobeen widely used as external wrapping for column strengtheningand prestressed bonding for reinforced concrete members. Indeed,there is considerable interest worldwide in the field of FRPs for ci-vil engineering infrastructure and much research has been carriedout on a variety of important topics [1–18].

The widely used strengthening method of simply bonding FRPs,such as carbon fibre, aramid and glass fibre, for strengthening astructure generally produces a debonding failure prior to theattainment of the tensile strength of the FRP being used [6,11,

ll rights reserved.

: +1 819 821 7974..W. Neale).

13]. In fact, the debonding strain of the composite differs accordingto the material used, and this debonding occurs at about 30–50% ofthe FRP tensile strength [8].

A reinforced concrete member strengthened with prestressedFRPs is a combination of the FRP bonding and external prestressingmethods. This leads to a more efficient use of the FRP; the methodcan be used to compensate for prestressing losses of existing rein-forced concrete or prestressed concrete members, to enhance thestrengthening performance, and to improve the serviceability ofcracked or deflected members.

The focus of this paper is to study the flexural performance ofreinforced concrete members strengthened by CFRP plates, usingFRP bonding and prestressing methods. Flexural tests were per-formed with respect to the bonding method, the anchorage system,the amount of prestressing, and the span length as experimentalvariables. A total of 13 beams, including a control beam, were sub-jected to flexural tests. A nonlinear finite element analysis of thebeams was also performed for each flexural test using the DIANAsoftware package, incorporating the plasticity of concrete and

Table 1Details of the tested beams

Beams Variables ofexperiment

Content Spanlength

Control – Not strengthened 240 cmNFCB1 No anchorage 1 laminate

498 D.-S. Yang et al. / Composite Structures 88 (2009) 497–508

interface elements between the FRP and concrete. The analyticalresults for the CFRP-strengthened reinforced concrete are com-pared to the flexural test results. The strengthening effect, failuremode, and load-deflection behaviour were considered for eachexperiment, and the ductility was evaluated as the ratio of the ulti-mate load for each tested beam to the deflection at yielding.

systemNFCBW2 2 laminate of width directionPFCU1-0R Prestressing No

bondPrestressing 0% + anchorage

PFCU1-2R Prestressing 20% + anchoragePFCU1-4R Prestressing 40% + anchoragePFCU1-6R Prestressing 60% + anchoragePFCB1-0R Bond Prestressing 0% + anchoragePFCB1-2R Prestressing 20% + anchoragePFCB1-4R Prestressing 40% + anchoragePFCB1-6R Prestressing 60% + anchoragePFCU1-4L L/hf Unbond + prestressing 60% + anchorage 450 cmPFCU1-6L Unbond + prestressing 60% + anchorage 600 cm

2. Experimental program for reinforced concrete beamsstrengthened with CFRP plates

2.1. Variables of the experiments and beams

In this investigation, flexural tests were performed with theexperimental variables being bonding or no bonding of the FRPs,the anchorage system, the amount of prestressing, and the spanlength (240 cm, 450 cm and 600 cm). Flexural tests were con-ducted on a control beam without strengthening, on beamsstrengthened with bonded CFRP plates with one and two laminatesin the width direction, and on beams strengthened with CFRPplates prestressed with 0%, 20%, 40%, and 60% of the ultimate ten-sile strength of the CFRP plates.

A total of 13 beams were subjected to flexural tests. Rectangularnormal-weight concrete beams were cast with dimensions of200 mm (b) �300 mm (h). The characteristics of all the beams, aswell as their steel reinforcement details, are shown in Fig. 1 andTable 1.

2.2. Materials

The type of concrete used in the flexural tests was a ready-mixed concrete, which had been aged for 28 days, with a specified

(a) Beams of span length 240cm

(b) Beams of span length

(c) Beams of span

2,700

HD3-HD10

150 2,4003-HD13

CFRP Plate

1,900145

4, 800

3- HD

150

CFRP Plate

4, 000

2, 4501, 025

6,300

150

CFRP Plate

5,500

1, 500 3, 000

Fig. 1. Beam detail

concrete strength of 18.0 MPa, measured compressive strength of16.4 MPa, and slump of 120 mm. All the beams were reinforcedwith three D13 bars (diameter of 13 mm) and three D10 bars(diameter of 10 mm) in the compression and tension zone, respec-tively. The beams were provided with 10 mm diameter shear rein-forcements, with a 100 mm spacing; they were all designed toprevent shear failure. The design yield stress of the 10 mm and13 mm diameter reinforcing bars were 475.2 MPa and 466.2 MPa,respectively.

The composite material used in this test program consisted of athree-layer component with a bi-directional CFRP sandwiched be-tween two unidirectional CFRP plates. This was done during thegeneral moulding process so as to prevent cracking in the unidirec-tional layers due to the prestressing load. The material propertiesof the CFRP used in the flexural tests are given in Table 2.

450cm

length 600cm

10@100

1503-HD13

3-HD10

200

300

HD10@100

HD 10@ 10010

150

3- HD 13

1, 025

HD10@1003-HD10

150

3-HD13

1, 500

s (units: mm).

Table 2Material properties of the CFRP plates

Tensile strength(MPa)

Modulus of elasticity(MPa)

Remarks

CFRP Plates 2350 1.73 � 105 Width 5 cm thickness0.13 cm

Epoxy resin 33.5 1500–3500 Bond strength 4.3 MPa

D.-S. Yang et al. / Composite Structures 88 (2009) 497–508 499

2.3. Anchorage system and prestressing

The reinforced concrete beams were provided with prestressedCFRP plates anchored to the tension face in order to obtain the re-quired strengthening capacity. As shown in Fig. 2, an anchorage

Ro

Base Plate

Bearing Plate

M 16 bolt

M12 anchorbolt

Concrete

End section

Fig. 2. Details of the a

Fig. 3. Prestress

Fig. 4. Location of CFRP

system is necessary for fixing the prestressed CFRP plates. Therough surface of the anchorage system is processed, and then fixedto the beam with anchor bolts. In order to prevent a load concen-tration, the anchorage system of the CFRP plate was attached to aGFRP tab. The device for prestressing the beams with the CFRPplates is shown in Fig. 3.

2.4. Loading equipment and arrangement of strain gauges

During loading, a strain gauge was attached to the CFRP platesto measure the strain. The flexural members strengthened withprestressed CFRP plates were tested under three and four-pointloading, over spans of 240 cm, 450 cm and 600 cm.

As shown in Fig. 4, the strain gauges were attached to the bot-tom edge and the mid-depth point of the CFRP plates at the middle

ugh surface

GFRP Tab

CFRP

Center section

nchorage system.

ing device.

plate strain gauges.

constant tension cut- off

tf

2f

2f

tf

crnnf

crnn

constant shear retention

Multi linear tension softening

Fig. 6. Concrete model for the finite element analysis.


of each shear span, as well as at the middle of the beam span in thelongitudinal direction. To obtain an accurate deflection reading, aLinear Variable Differential Transducer (LVDT) was also mountedat the mid-span and connected to a data logger. Crack initiationand propagation were monitored by visual inspection during test-ing, and the crack patterns were marked.

3. Nonlinear finite element analysis

3.1. General

The numerical analysis of the experimentally tested FRP-platedconcrete beams was conducted with a full 2D nonlinear finite ele-ment analysis of the experimental set-up using the commercialprogram DIANA.

Fig. 5 shows the mesh geometry for the control and prestressedFRP-plated beams. The Drucker–Prager criterion was used for theconcrete in compression, and the combined smeared crack modelfor the tensile behaviour of the concrete.

The general finite element model was as follows: the bond-slipbetween the concrete and steel rebars was not considered in thispaper. The concrete and CFRP plates were modelled using planestress elements, with smeared elements for the steel reinforce-ment, and interface elements between the concrete and bondedCFRP laminates.

3.2. Material models

As shown in Fig. 6, the commonly used concrete analysis modelconsisted of the traditional plasticity model for the compressionconcrete, while the tensile behaviour consisted of a smeared crackmodel, which assumes micro-cracking.

As shown in Fig. 7a, the reinforcing rebars had an elasto-plasticbehaviour, defined by its yield strength, with a typical elastic mod-ulus of 200 GPa. A yield plateau, whose range depends on the class

(a) Reinforced concrete beam

(b) Reinforced concrete beams str

concrete model compression bar model

concrete model compression bar model

Bond-Slip modeAnchorage system

model

Fig. 5. Mesh geometry for the

of steel, is followed by a strain-hardening behaviour up to failure.In this model the reinforcing bars are modelled as steel layers ofequivalent thickness.

The CFRP plates have a very high unidirectional tensile strength,but with a stiffness close to that of steel. The behaviour was

s without CFRP plates

engthened with CFRP plates

Stirrup model

Tension bar model

CFRP Plates modell

Stirrup model

Tension bar model

finite element analysis.

(a) Reinforcement (b) CFRP Plates

y

x

1

1'2

3

4

2'

(c) Interface element (4-nodes)

sf

uf

yf uE

sE

yε uε sε

εfu

ε f

θ

ηϖ

ϑξ

Fig. 7. Reinforcement and CFRP plate models for the finite element analysis.

Table 3Comparison of results for concrete beams strengthened with CFRP plates

Beams Cracking load (kN) Yield load Ultimate load Failure mode

Test (a) (kN) Anal. (b) (kN) (b)/(a) Test (a) (kN) Anal. (b) (kN) (b)/(a)

Control 18.2 40.4 41.0 1.01 49.4 49.5 1.00 FlexuralNFCB1 13.7 56.3 59.0 1.05 77.0 83.4 1.08 DebondingNFCBW2 – 98.4 99.5 1.01 98.4 104.0 1.06 DelaminationPFCU1-0R 18.9 43.0 47.4 1.10 115.0 114.2 0.99 FRP rupturePFCU1-2R 33.5 56.4 61.0 1.08 119.8 112.6 0.94 FRP rupturePFCU1-4R 47.0 75.9 83.9 1.11 120.7 124.2 1.03 FRP rupturePFCU1-6R 54.1 83.6 92.6 1.11 122.5 123.6 1.01 FRP rupturePFCB1-0R 24.5 55.4 56.4 1.02 121.5 117.8 0.97 Debonding–rupturePFCB1-2R 26.4 71.6 75.5 1.05 123.0 108.0 0.88 Debonding–rupturePFCB1-4R 42.4 85.2 91.6 1.08 125.2 114.8 0.92 Debonding–rupturePFCB1-6R 51.8 100.5 105.9 1.05 122.8 121.7 0.99 Debonding–rupturePFCU1-6L2 25.7 101.3 98.4 0.97 121.4 125.5 1.03 FRP rupturePFCU1-6L3 33.6 62.4 65.0 1.04 71.8 76.8 1.07 FRP ruptureMean 1.05 1.00C.O.V (%) 3.91 5.71


essentially linearly elastic up to the tensile strength limit. Once thetensile strength has been reached, it is assumed to suddenly fail ina perfectly brittle mode (Fig. 7b). The interface model between theCFRP plates and concrete used 4 node elements, in the same loca-tion as the perpendicular 2 nodes, as shown in Fig. 7c. As an inter-face model between CFRP plates and concrete, a bond-slip modelwas applied.

4. Results and discussion

4.1. Load-carrying capacities

A total of 13 beams were subjected to flexural tests, and lateranalyzed using the finite element approach described above. Bond-

ing or no bonding, the anchorage system, the amount of prestress-ing and the span length were the experimental variables. Table 3summarizes the results of the flexural behaviour of all the beamsin terms of their flexural loading capacities.

From the flexural tests and analytical results, the load capacityof the beam strengthened with one laminate (5 cm of width) was40–60% higher than that of the control beam, and the beamstrengthened with two laminates in the width direction (10 cmin width) was 100% or greater than that of the control beam. Incomparison to the control beam, as the stiffness of the beamsstrengthened with bonded CFRP plates increased, so did the crack-ing load of the beams increase.

Whether bonded or not, the ultimate load of the beamsstrengthened with prestressed CFRPs remained almost constant.


It was seen that the failure mode of the prestressed CFRPplated-beams was not debonding, but FRP rupture. However, thecracking and yield loads of the bonded prestressed CFRP plated-beams were greater than those of the unbonded prestressed CFRPplated-beams, as a result of the increased stiffness due to the com-posite bonding.

As shown in Table 3, the average ratio of the test and analyticalvalues for the yield load was 1.05, with a coefficient of variation of3.91%. As for the ultimate load, the average ratio was 1.00, with acoefficient of variation of 5.71%. Thus, the analytical results forthe reinforced concrete beams strengthened with CFRP platesshow a very good agreement with those obtained experimentallyfor the yield and ultimate loads.

4.2. Cracking modes for the beams

Fig. 8 shows the cracking modes of the beams. The failure modeof the bonded non-prestressed beam (NFCB1) strengthened withonly one laminate was induced by brittle intermediate crack-in-duced debonding from the mid- to end-span when the strain ofthe CFRP plates reached about 6500–7000 l. However, that ofbeam (NFCBW1) strengthened with two laminates in the widthdirection was a result of plate-end debonding when the CFRP platestrain reached about 5200 l. Therefore, it can be seen that thestrengthening efficiency of the member strengthened with one

Fig. 8. Beam cracking modes.

laminate was better than that of the member strengthened withtwo or more laminates.

The crack width of the control beam under ultimate load wasalso observed to be wider than that of the prestressed beams.The crack propagation of the prestressed beams with bonded CFRPplates was similar to that of the control beam. However, as theprestressing of the beams strengthened with CFRP plates in-creased, the crack width of the beams decreased. Also, the crackingmode of the prestressed beams with bonded CFRP plates was con-centrated within the constant moment region. Thus, it can be seenthat beams strengthened with prestressed CFRP plates had betterperformance in terms of crack control than those strengthenedwith non-prestressed CFRP plates.

4.3. Beams strengthened with bonded CFRP plates

Fig. 9a shows the load-deflection relationships for the controland strengthened beams (NFCB1, NFCBW2). With regard to thestrengthening efficiency, the beam strengthened with one lami-nate was 40–60% higher than that of the control beam, and thebeam (NFCBW1) strengthened with two laminates in the widthdirection was 100% or greater than that of the control beam.

In comparing the test and analytical results, we observe thatboth gave almost identical results for the control beams, but thebeams strengthened with CFRP plates (NFCB1, NFCBW2) displayedabout a 5–10% greater stiffness than their analytical values. How-ever, the analytical and test values for the deflection were almostidentical when the beams strengthened with one and two lami-nates in the width direction experienced debonding.

Fig. 9b displays the CFRP plate strain of the NFCB1 beam ob-tained from the flexural and analytical results. The initial strainof the CFRP plate, as determined by the analysis, was greater thanthe test value, but the stiffness after cracking load was almost iden-tical. In addition, the strain of the CFRP plate rapidly increased afterabout 50 kN, the reinforcement yielding point, in both the test andanalytical results.

As mentioned above, the bonded non-prestressed beam(NFCB1) strengthened with only one laminate failed due to deb-onding when the strain of the CFRP plate reached about 6500–7000 l. Therefore, it can be seen that the prestressing amount ofthe CFRP plate was an extra strain excluding the debonding strain(=6500–7000 l), to maximize the strengthening efficiency of theCFRP plate.

4.4. Beams strengthened with unbonded prestressed CFRP plates

As the prestressing of the CFRPs increased, the load capacity ofthe beams strengthened with unbonded prestressed CFRP platesalso increased. Also, because the FRP was not bonded, failure wasinduced by rupture of the CFRP plates. Even after the steel barsyielded, the load capacity of the beams continuously increased,and the ductility of the prestressed beams increased more thanthat of the non-prestressed beams.

With regard to the cracking load, the values for the controlbeam and non-prestressed beam (PFCU1-0R) were similar, butthose of the prestressed beams were a maximum of twice that ofthe control beam. The ultimate load of the prestressed beamswas about 130–150% greater than that of the control beam, butthose of the prestressed beams were similar regardless of theamount of prestressing.

Fig. 10a shows that the beam (PFCU1-0R) strengthened withunbonded non-prestressed CFRP plates, when under the initialload, had approximately 10% stiffness differences between the ana-lytical and test values; however, there was no stiffness differenceafter the cracking load. With regard to specimens PFCU1-4R andPFCU1-6R, the analytical values for the stiffness were generally

Deflection(mm)

Loa

d(kN

)

Control (test) Control (analysis)

NFCB1 (test) NFCB1 (analysis)

NFCBW2 (test) NFCBW2 (analysis)

(a) Load−deflection relations

0

10

20

30

40

50

60

70

80

90

0

20

40

60

80

100

120

0 1000 2000 3000 4000 5000 6000 7000 8000

0 10 20 30 40 50 60 70 80

Microstrain

Loa

d(kN

)

Test

Analysis

(b) Load−CFRP plate strain relations

Fig. 9. Comparison of results for reinforced concrete beams strengthened with bonded CFRP plates.


greater than the test values; for the PFCU1-2R beam the analyticalvalues for the stiffness became smaller than the test value underthe ultimate load.

Fig. 10b displays the load-strain relationships for the unbondedprestressed CFRP plates (0%, 60%). The beams PFCU1-0R andPFCU1-6R showed approximately 10% stiffness differences be-tween the analytical and test values during the initial stiffness,but after cracking, the analytical values approached those obtainedin the tests.

4.5. Beams strengthened with bonded prestressed CFRP plates

From the experimental observations, for the beams withbonded prestressed CFRP plates, debonding occurred in two stagesup to the anchorages and then, due to the anchorage system, theCFRP plates ultimately ruptured. Also, due to external bonding ofthe CFRP plates, the beams with bonded prestressed CFRP platesmaintained their stiffness from the initial to the debonding loads.After the two debonding phases, the load capacity of the beamstemporarily decreased. However, the behaviour of the bondedCFRP-plated beams changed into that of the unbonded CFRP-platedbeams due to the presence of the anchorage system. Thus, the CFRPplates of the bonded prestressed beams ruptured in a similar

fashion to the unbonded prestressed beams under the ultimateload.

As shown in Table 3, with regard to the cracking load for thebonded non-prestressed beam (PFCB1-0R) with the anchorage sys-tem, it increased by about 35%, 30%, respectively, compared to thecontrol beam and the unbonded non-prestressed beam (PFCU1-0R)with the anchorage system. The cracking load of the bonded pre-stressed CFRP-plated beams increased by a maximum of 180%compared to the control beam. The yield loads of beams with theanchorage system and bonded CFRP plates were 35–150% higherthan that of the control beam.

In Fig. 11a, the analytical values obtained for the beams PFCB1-0R were generally similar to the test values, with the exception ofthe debonding load; however, the analytical values for the load anddeflection under the debonding load were about 20% different fromthose of the test values. The ultimate load of all the beams, withthe exception of the 20% prestressed beam (PFCB1-2R), were al-most the same, 120 kN. Thus, the analytical results for the rein-forced concrete beams with bonded prestressed CFRP platesshow good agreement with those obtained experimentally for boththe yield and ultimate loads.

Fig. 11b shows the relationship between the load and CFRPplate strain for the externally bonded prestressed beams. Both

0

20

40

60

80

100

120

140

0 20 40 60 80 100 120

Deflection(mm)

Loa

d(kN

)

PFCU1-0R (test) PFCU1-0R (analy.)




CONTROL (test) CONTROL (analy.)


0

20

40

60

80

100

120

140

0 2000 4000 6000 8000 10000 12000 14000

Microstrain

Loa

d(kN

)




Fig. 10. Comparison of results for reinforced concrete beams strengthened with unbonded prestressed CFRP plates.


beams show about 10% strain differences between the analyticaland test values for the initial and debonding loads, but after thetwo stages of FRP debonding, the analytical values are similar tothose obtained in the tests.

4.6. Beams strengthened with prestressed CFRP Plates in terms of L/hf

effect

The failure mode, according to the length-to-depth (L/hf) effect,of beams strengthened with externally unbonded prestressed CFRPplates was the same as for those strengthened using the bondedprestressed system. That is, the stiffness until the initial crackingload was the same regardless of prestressing or bonding. In com-parison to the bonded system beams, those with unbonded sys-tems showed a significantly increased ductile behaviour from theyield to the ultimate loads. The flexural behaviour was observedto be the same, even if the span length of the member wasincreased.

Fig. 12a shows the relationships between the loads and deflec-tions according to the beam span length. According to the analyt-ical values for the 60% prestressed unbonded beam (PFCU1-6L2)with a 450 cm span length, the analytical values for the deflection

under ultimate load differed by about 10 mm compared to the testvalues, but in the cracking and yield loads they were similar. Addi-tionally, the load results obtained for the beams PFCU1-6L3 weregenerally 10% higher than the test values, but were similar in rela-tion to the deflection.

Fig. 12b compares the analytical and test values obtained for theCFRP plate strains. Beams strengthened by external unbondedprestressed CFRP plates, according to the L/hf value, showed simi-lar failure modes to the beams mentioned: the analytical resultsobtained for the reinforced concrete beams with bonded pre-stressed CFRP plates showed good agreement with those obtainedexperimentally in relation to the load capacities and CFRP platestrains.

4.7. Behaviour of bonded and unbonded systems

As shown in Fig. 13a, the CFRP plate strains for all spans show alinear strain distribution in the bonded system and, after steelyielding, the gradient of the CFRP plate strains increased with theincreasing portion of the load on the CFRP plates. Therefore, whenthe CFRP plate strain in the mid-span exceeds 6500 l, this will bethe debonding strain.

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100 120

Deflection (mm)

Loa

d (k

N)

PFCB1-0R (test) PFCB1-0R (analy.)




CONTROL (test) CONTROL (analy.)


0

20

40

60

80

100

120

140

160

0 2000 4000 6000 8000 10000 12000 14000

Microstrain

Loa

d (k

N)




Fig. 11. Comparison of results for reinforced concrete beams strengthened with bonded prestressed CFRP plates.


After debonding of the CFRP plates occurred in a bonded sys-tem, the behaviour of the bonded CFRP-plated beams changed tothat of the unbonded CFRP-plated beams due to the effect of theanchorage system. Therefore, it was predicted that a redistributionof stress affects in the whole span of the CFRP plate, which is madeuniform by debonding, as shown in Fig. 13b. However, the CFRPplate strain after debonding is not uniform over the whole span.Because of the friction with the epoxy resin bonded to the CFRPplate surface and concrete paste, it seems that uniform strain dis-tributions cannot occur.

As shown in Fig. 13c, the CFRP plate strain distribution in theunbonded system was uniform over the whole span, and main-tained an identical pattern with increasing load. In other words,the CFRP plate strain of the mid-span in the bonded system wassimilar to that of the steel bar until the yield load. However, theincrement of the CFRP plate strain in the unbonded system wasvery small until the yield load.

The strain of the CFRP plates in the bonded system increasedlinearly. However, the CFRP plate strains in the unbonded systemwere less than those in the member due to the distribution ofthe CFRP plate stress. Moreover, the rupture strain for the CFRP

plates in the unbonded system decreased compared to that inthe bonded system.

4.8. Estimation of ductility

In this paper, the safety of the members is assessed by usingductility indices, which are expressed as the ratio of the deflectionswhen a member is subject to the ultimate load to that when ityields.

The ductility index for each beam is shown in Table 4. Beamswith bonded CFRP plates without the anchorage system showed alower ductility index than the control beam, due to brittle failurecaused by debonding failure between the concrete and CFRPplates. Disregarding the 60% prestressed CFRP-plated beams(PFCB1-6R, PFCU1-6R), the ductility index of the prestressedCFRP-plated beams was greater than that of the control beam.Therefore, the ductility index was increased with a decreasedprestressing. However, the ductility of beams strengthened byCFRP plates with an anchorage system was considered high whenthe ductility index was above 3. Generally, the ductility indices ofthe beams in a bonded system were less than that of those in an

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100 120 140 160 180 200

Deflection(mm)

Loa

d(kN

)

PFCU1-6L2 (test) PFCU1-6L2 (analy.)



0

20

40

60

80

100

120

140

0 1000 2000 3000 4000 5000 6000 7000

Microstrain

Loa

d (k

N)



(b) Load−CFRP Plate strain relations

Fig. 12. Comparison of results for reinforced concrete beams strengthened with prestressed CFRP plates in terms of the L/hf effect.


unbonded system. That is, the load and the deflection at the yieldload of beams in a bonded system, which is a composite sectionwith CFRP plates, were more than those of beams in an unbondedsystem. The average ratio of the test and analytical deflectionvalues for the yield and ultimate loads were 0.96 and 1.06, witha coefficient of variation of 12.91% and 11.81%, respectively. Thus,the analytical results for reinforced concrete beams strengthenedby CFRP plates show good agreement with those obtainedexperimentally for the deflection under the yield and ultimateloads.

5. Conclusions

In this paper, flexural tests and a finite element method analy-sis, using the DIANA program, were performed for reinforced con-crete beams strengthened by prestressed CFRP plates.

The main conclusions drawn from the study were as follows:

(1) For the flexural tests performed on reinforced concretebeams strengthened with prestressed CFRP plates, whetherbonded or not, the ultimate load of the beams strengthened

with CFRP was reasonably constant. The observed failuremode of the prestressed CFRP plated-beams was not deb-onding, but FRP rupture.

(2) For reinforced concrete members strengthened with exter-nally bonded prestressed CFRP plates, two stages of FRP deb-onding occurred. After the debonding of the CFRP plates inthe bonded system, the behaviour of the bonded CFRP-pla-ted beams changed to that of unbonded CFRP-plated beamsdue to the effect of the anchorage system.

(3) A finite element analysis of the reinforced concrete beamsstrengthened with CFRP plates was performed using theDIANA program, which considered nonlinear concrete mate-rial behaviour, the steel reinforcement, and an interfacialbond-slip model between the concrete and CFRP plates.The analytical results showed good agreement with thoseobtained experimentally for the debonding load, yield load,and ultimate load.

(4) Beams with bonded CFRP plates without an anchoragesystem showed far lower ductility indices than the controlbeam, due to brittle failure caused by debonding failurebetween the concrete and CFRP plates. However, the

0

1000

2000

3000

4000

5000

6000

7000

0 15 30 45 60 75 90 105 120 135

Distance from supporting point (cm)

Mic

rost

rain

20kN

40kN

60kN

80kN

100kN

120kN

123kN

Yield load

1st debonding

2nd debonding

(a) CFRP plate strains in a bonded system

(b) CFRP plate strain of a bonded system

0

1000

2000

3000

4000

5000

6000

0 15 30 45 60 75 90 105 120 135

Distance from supporting point (cm)

CF

RP

pla

te s

trai

n (*

10-6

)

122kN

100kN

83.6kN

80kN

60kN

40kN

20kN

Yield load

CFRP plates rupture

(c) Load−CFRP plate strains of an unbonded system

Strain in CFRPPlates

Strain in CFRPPlates

(a) Before debonding failure

(b) after debonding failure

Fig. 13. Comparisons of bonded and unbonded system.


ductility of beams strengthened by CFRP plates with ananchorage system was considered high when the ductility

index was above 3. The ductility indices of the beams inthe bonded system were less than those of the unbonded

Table 4Estimates of ductility

Beams Deflection of yield load Deflection of ultimate load Ductility index

Test (a) (mm) Anal. (b) (mm) (b)/(a) Test (a) (mm) Anal. (b) (mm) (b)/(a) Test Anal.

Control 5.7 5.4 0.95 33.6 34.7 1.03 5.89 6.43NFCB1 7.2 6.5 0.90 15.4 15.5 1.01 2.14 2.38NFCBW2 7.8 7.4 0.95 16.2 15.6 0.96 2.08 2.11PFCU1-0R 5.8 4.7 0.81 55.7 53.7 0.96 9.60 11.43PFCU1-2R 4.9 4.8 0.98 43.3 43.1 1.00 8.84 8.98PFCU1-4R 5.8 4.5 0.78 34.4 34.5 1.00 5.93 7.67PFCU1-6R 5.3 5.5 1.04 29.5 24.8 0.84 5.57 4.51PFCB1-0R 6.5 6.0 0.92 58.0 55.5 0.96 8.92 9.25PFCB1-2R 7.2 7.0 0.97 49.3 31.1 0.63 6.85 4.44PFCB1-4R 5.9 7.5 1.27 32.4 34.4 1.06 5.49 4.59PFCB1-6R 8.3 8.9 1.07 32.0 30.4 0.95 3.86 3.42PFCU1-6L2 9.8 8.0 0.82 73.8 82.0 1.11 7.53 10.25PFCU1-6L3 12.8 12.6 0.98 102.0 102.1 1.00 7.97 8.10Mean 0.96 0.96C.O.V (%) 12.91 11.81


system. That is, the load and the deflection under the yieldload of the beams in a bonded system, a composite sectionwith CFRP plates, were more than those of the beams in abonded system.

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