Chen 2003

Construction and Building Materials 17(2003) 27–41

0950-0618/03/$ - see front matter� 2002 Elsevier Science Ltd. All rights reserved.PII: S0950-0618Ž02.00091-0

Shear capacity of FRP-strengthened RC beams: FRP debonding

J.F. Chen *, J.G. Tenga, b

Institute for Infrastructure and Environment, School of Engineering and Electronics, Edinburgh University, The King’s Buildings,a

Edinburgh EH9 3JN, UKDepartment of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hong Kong, PR Chinab

Abstract

Many studies have been undertaken on shear strengthening of reinforced concrete(RC) beams by externally bonding fibre-reinforced polymer(FRP) composites. These studies have established clearly that such strengthened beams fail in shear mainlyin one of two modes: FRP rupture; and FRP debonding, and have led to preliminary design proposals. This paper is concernedwith the development of a simple, accurate and rational design proposal for the shear capacity of FRP-strengthened beams whichfail by FRP debonding. Existing strength proposals are reviewed and their deficiencies highlighted. A new strength model is thendeveloped. The model is validated against experimental data collected from the existing literature. Finally, a new design proposalis presented.� 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Fibre reinforced polymer; Fibre reinforced plastic; FRP; Debonding; Reinforced concrete beams; Shear design; Shear strength; Shearstrengthening

1. Introduction

A recent innovation for the shear strengthening ofreinforced concrete(RC) beams is to externally bondfibre-reinforced polymer(FRP) composite plates orsheets. This method has become popular because of theadvantages of FRP composites such as their highstrength-to-weight ratio, good corrosion resistance, andversatility in coping with different sectional shapes andcorners. Many studies on this theme have been carriedout since the early 1990sw1–24x. These studies haveestablished clearly that such strengthened beams fail inshear mainly in one of the two modes: tensile ruptureof the FRP; and debonding of the FRP from the sidesof the RC beam, depending on how the beam isstrengthenedw25x.Common methods of strengthening include side bond-

ing, U-jacketing and wrapping(Fig. 1). Both FRP stripsand continuous sheets have been used. The fibres in theFRP may also be oriented at different angles.The combination of different bonding configurations,

fibre distributions and fibre orientations can result inmany different strengthening schemes. Symbolic repre-sentations are used here as in Chen and Tengw7x when

*Corresponding author.

presenting the test database so that each shear strength-ening scheme is identified by a set of clearly definedsymbols. Each of the shear strengthening schemes canbe denoted by one symbol representing the bondingconfiguration (S for side bonding,U for U jacketingand W for wrapping), followed by a second symbolrepresenting the fibre distribution(S for strips andP forplatesysheets) and followed by two sets of numbersrepresenting the first and second fibre orientations(Fig.1). For example, US45y135 represents U jacketing withFRP strips at 45 and 1358. A more detailed discussionis given in Teng et al.w25x.Available experimental data indicate that almost all

beams strengthened by wrapping failed due to FRPrupture (although debonding most likely occurs first,FRP rupture controls the shear capacity in this case).Some beams strengthened by U jacketingw6x also failedin this mode. A predictive strength model and a designproposal for this failure mode are given in Chen andTeng w7x. In contrast, almost all beams strengthened byside bonding only, and most strengthened by U jacket-ing, failed due to FRP debonding. Fig. 2 shows thepossible debonding zones for both U jackets and sideplates. Once the FRP starts to peel off, the beam canfail very quickly. The ductility of beams failing in thismode is usually very limited.

28 J.F. Chen, J.G. Teng / Construction and Building Materials 17 (2003) 27–41

Fig. 1. FRP shear strengthening schemes.

Fig. 2. Shear failure due to FRP debonding:(a) side-bonded FRP; and(b) FRP U jacket.

It may be noted that pure interfacial debonding failurealong the FRPyadhesive interface or the adhesiveyconcrete interface and failure within the adhesive havebeen rarely reported. Debonding failures almost alwaysoccur in the concrete at a small distance from theconcreteyadhesive interface with some concrete attachedto the debonded FRP. Although such failures are notdebonding failures in a strict sense, the term ‘debondingfailure’ has, nevertheless, been commonly used and isthus also adopted here. Because the failure actuallyoccurs in the concrete, the properties of the concreteplay a key role in this failure mode.This paper is concerned with the development of a

simple, accurate and rational design proposal for theshear capacity of FRP-strengthened beams which fail byFRP debonding. Existing design proposals are firstbriefly reviewed, and their deficiencies highlighted. Anew shear strength model is then developed, whichmakes use of the best bond strength model currentlyavailable for FRP-to-concrete bonded joints. The newshear strength model is validated against experimentaldata collected from the existing literature. Finally, a newdesign proposal is presented.

2. Existing design proposals

In all existing design proposalsw5,21,26,27x, the shearstrength of an FRP-strengthened RC beam,V , is eval-n

uated from

V sV qV qV (1)n c s frp

whereV is the contribution of the concrete,V is thec s

contribution of the steel stirrups and bent-up bars andV is the contribution of the FRP.V and V may befrp c s

calculated according to provisions in existing designcodes, so the main differences between available pro-posals lie in the evaluation of the FRP contributionV . As this paper is concerned with failure due to FRPfrp

debonding, the following brief review only deals withhow debonding was treated in these models. A fullerreview is given in Chen and Tengw7x.Chaallal et al.w5x proposed a model by assuming that

the bonded FRP contributes to the shear capacity in thesame way as that of internal steel shear reinforcement.Debonding was dealt with by limiting the design averageshear stress between the FRP and the concrete to halfthe value expected at debonding. However, the debond-ing strength model used by them for limiting the stresslevel in the FRP does not fit well with experimentaldata w28x. Furthermore, the debonding strength of thismodel is in terms of the average shear stress betweenthe FRP and the concrete. This implies that the tensilestrength of the FRP can always be fully utilised if thereis a sufficiently long bond length(e.g. the beam depthis large enough), while in reality the stress level in the

29J.F. Chen, J.G. Teng / Construction and Building Materials 17 (2003) 27–41

Fig. 3. Notation for a general shear strengthening scheme.

FRP at debonding does not increase with bond length ifthe bond length is already longer than the effective bondlength w28x.Triantafillou w21x proposed to limit the strain in the

FRP to an effective strain which was obtained fromregression of experimental data. The model fails todistinguish between different strengthening schemes andfailure modes. At the late stage of preparing the presentpaper, Triantafillou and Antonopoulosw26x proposed anextension of Triantafillou’sw21x model in which differ-ent effective strain expressions were proposed for CFRPwrapping and other strengthening schemes, but no dis-tinction was made between side bonding and U jacket-ing. The International Federation for Structural Concrete(fib) report on externally bonded FRP reinforcement forRC structuresw29x recommended the use of Triantafillouand Antonopoulos’w26x effective strain with a reductionfactor of 0.8 for design. However, a close examinationof the data presented in Triantafillou and Antonopoulosw26x reveals that their model is statistically not satisfac-tory for safe practical designw7x.Khalifa et al. w27x proposed a modification to Trian-

tafillou’s w21x effective strain model in which the ratioof effective stress(or strain) in the FRP to its ultimatestrength(or strain) is used instead of the effective stress(or strain) itself. In particular, they proposed a bondmechanism design approach based on the bond strengthmodel of Maeda et al.w30x, which led to a stressreduction factorR of

2y30.0042f9 wŽ .c frpffrp,eRs s F0.5 (2)0.58f E t ´ dŽ .frp frp frp frp,rup frp,e

where f is the effective stress of frp at failure,ffrp,e frp

and´ are the ultimate tensile strength and strain offrp,rup

FRP,E is the elastic modulus of FRP,w and t arefrp frp frp

the width and thickness of FRP strips, andd is thefrp,e

effective depth of FRP reinforcement which they definedas the depth from the upper edge of the shear reinforce-ment to the centroid of the steel tension reinforcement.The units in Eq.(2) are in Newtons and millimetresexcept thatE is in giga-Pascals. This model featuresfrp

two deficiencies. First, the effective strain approach isempirical and no satisfactory explanation is availablefor the small effective strain ratioR (which has an upperlimit of 0.5) obtained from experimental data. Second,the bond strength model of Maeda et al.w30x adoptedin deriving the design proposal cannot correctly predictthe effective bond length, which can be misleading fordesign usew28x.The report from the Concrete Society in the UKw31x

which provides design guidance for FRP strengtheningof concrete structures adopted Khalifa et al.’sw27xmodels. It also recommended that the maximum strainin the FRP should not exceed 0.004.Recognising the deficiencies of the existing models,

the present authors have developed two rational shearstrength models for the FRP rupture failure mode andfor the debonding failure mode, respectively. The formeris presented in Chen and Tengw7x and the latter ispresented in this paper.

3. A new shear strength model for FRP debonding

3.1. A general shear strengthening scheme

A general shear strengthening scheme for a beamwith a critical shear crack inclined to its longitudinalaxis by an angleu is considered here(Fig. 3). It isassumed that the FRP strips are bonded on both sidesof the beam, have the same widthw (perpendicularfrp

to fibre orientation, Fig. 9) and thicknesst , and arefrp

evenly distributed with a centre-to-centre spacing ofs measured along the longitudinal axis. The FRP mayfrp

contain fibres at several different angles, but only themain fibres at an angle ofb measured from the longi-tudinal axis of the beam are considered to be active inresisting the shear force.For continuous uni-directional FRP platesysheets,

s and w have a relationship ofs sw ysinb w7x.frp frp frp frp

Therefore,s sw if and only if bs908. It may befrp frp

noted thats sw has been used by some researchers,frp frp

and even in design guidancew31x, for continuous sheetswithout giving due consideration to the fibre orientation.


It is further assumed that the shear crack ends at adistance of 0.1d below the compression face of thebeam(Fig. 3) so that the expression for the contributionof FRP to shear resistance and that for the contributionof steel stirrups given in the Eurocode have the sameform. Here, d is the effective depth of the beammeasured from the compression face to the centre ofsteel tension reinforcement. Employing a downward-oriented co-ordinate originating from the upper tip ofthe shear crack(Fig. 3), the effective height of the FRPh is expressed as:frp,e

h sz yz (3)frp,e b t

where z and z are the co-ordinates of the top andt b

bottom ends of the effective FRP, which may beexpressed as

z sd (4a)t frp,t

w xz s d y(hyd) y0.1ds0.9dy(hyd ) (4b)b frp frp

in which d is the distance from the compression facefrp,t

to the top edge of the FRP,h is the height of the beam,andd is the distance from the compression face to thefrp

lower edge of the FRP(thus,d sh for U jackets).frp

Noting that the origin of thez-coordinate is 0.1dbelow the compression face(Fig. 3), Eq. (4a) meansthat the upper edge of the effective FRP is always takento be at 0.1d below the actual upper edge. The effectiveupper edge thus starts from the crack tip if FRP isbonded to the full height, leading to significant simpli-fication of the resulting equations. The allowance of anextra bond length of 0.1dysinb above the effectiveupper edge is a conservative and consistent measure forall cases.The lower end of the effective FRP is taken to be at

the centroid of the steel tension reinforcement if theFRP terminates at the base of the RC beam(hsd infrp

Eq. (4b)) for simplification of expressionsw7x. Thismeans that the effective lower end is(hyd) above theactual lower edge of FRP. For consistency, the lowerend of the effective FRP is also taken to be(hyd)above the actual lower edge if the FRP terminates abovethe base(Eq.(4b)). This treatment is again conservative.Fig. 3 shows an example where the side plates terminateslightly above the base of the RC beam.

3.2. FRP contribution to shear capacity

In the debonding failure mode considered in thispaper, the stresses in the FRP intersected by the criticalshear crack are likely to be non-uniform primarilybecause the bond length of the FRP depends on the

location of the shear crack relative to the ends of theFRP. Assuming that the average(or effective) stress inthe FRP intersected by the critical shear crack at theultimate limit state isf for a strengthened beam asfrp,e

shown in Fig. 3, the contribution of FRP strips to theshear capacity can be expressed as

h cotuqcotb sinbŽ .frp,eV s2f t w (5)frp frp,e frp frp sfrp

Taking the non-uniformity of stresses in the FRPintersected by the critical shear crack into consideration,the effective or average stress in the FRP at the ultimatelimit state, f , can be defined asfrp,e

f sD s (6)frp,e frp frp,max

in which s is the maximum stress in the FRP andfrp,max

D is termed here the stress distribution factor whichfrp

is defined as

zb

s dzfrp,z|zt

D s (7)frp h sfrp,e frp,max

wheres is the stress in the FRP at the ultimate limitfrp,z

state at the location where the intersecting critical shearcrack is at a coordinatez. In deriving Eq.(7), it hasbeen assumed that discrete FRP strips can be treated asan equivalent FRP continuous sheetyplate. As a result,this model is applicable to beams strengthened witheither discrete strips or continuous sheetsyplates, withcontinuous sheetsyplates being a special case of discretestrips. The smearing approach for strips involves somesimplification and for it to have reasonable accuracy, astrip spacing limitation needs to be applied as discussedlater in the paper.For shear failures controlled by FRP debonding con-

sidered in this paper, stresses in the FRP at failure arecontrolled by the ultimate bond strength between theFRP and the concrete. Therefore, boths andDfrp,max frp

are related to this bond strength. The bond behaviourbetween FRP and concrete in RC beams shear-strength-ened with bonded FRP may be closely represented bysimple shear tests(Fig. 4). In the following sub-sections,s and D are evaluated based on an FRP-to-frp,max frp

concrete bond strength model developed for these typesof testsw28x.

3.3. Maximum FRP stress along a shear crack

Substantial research has been carried out on simpleshear testsw6,28,30,32–42x. A very important aspect ofthis bond behaviour is that there exists an effective bond


Fig. 4. Single and double shear tests.

length beyond which an extension of the bond lengthcannot increase the bond strength. This is a fundamentaldifference between externally bonded FRP reinforcementand internal reinforcement. For the latter, a sufficientlylong bond length can always be found so that the fulltensile strength of the reinforcement can be achieved,provided there exists a sufficient concrete cover.The authors have recently developed a simple, rational

and accurate model for predicting the bond strength andthe effective bond length for this type of FRP-to-concrete jointw28x. This model has been shown to bein closer agreement than any other existing models withtest data covering a wide range of parameters collectedfrom the literature. This bond strength model is thusadopted here, to derive the maximum stress in the FRPand the stress distribution factor along the critical shearcrack.At debonding failure, the maximum stress in the FRP

occurs at the location where the FRP has the longestbond length. The maximum stress in the FRPs isfrp,max

thus limited by the ultimate bond strength unless FRPrupture controlsw28x:

SffrpT

s smin (8)frp,max UyE f9frp cT0.427b bw Ly

V tfrp

whereb reflects the effect of bond length andb theL w

effect of FRP-to-concrete width ratio(b yb ) of thefrp c

shear test specimen. The maximum stresss , thefrp,max

elastic modulus of FRPE and the concrete cylinderfrp

compressive strengthf 9 are all in megaPascals whilec

the thickness of FRP stripst is in millimetres.frp

For shear strengthening considered here, the maxi-mum stress in the FRP intersected by the critical shearcrack may be obtained from Eq.(8) using appropriategeometric parameters as follows. Clearly, this maximumstress occurs in the fibre with the longest bond length.Assuming that the critical shear crack is a straight line,the maximum bond length for the FRP occurs at thelower end of the shear crack for an FRP U jacket but islocated at the mid-height of the FRP for side plates(Fig. 3). Therefore, the maximum bond lengthL ismax

given by

Shfrp,e for U jacketsT sinbUL (9)max

hfrp,eT for side platesV2sinb

Replacing the bond lengthL in the bond strengthmodel of Chen and Tengw28x with L here, the bondmax

length coefficientb can be expressed asw28xL

S1 if lG1T

b s (10)L U

plTsin if l-1V 2

in which the normalised maximum bond lengthl isdefined as

Lmaxls (11)

Le

whereL is the effective bond lengthe

E tfrp frpL s (12)e y yf9c

Similarly, the FRP plate widthb and concrete prismfrp

width b defined in Chen and Teng’sw28x bond strengthc

model for simple shear lap tests may be replaced herewith the FRP strip widthw and the centre-to-centrefrp

spacing (perpendicular to the fibres) between thems sinb. The strip width coefficientb w28x can thus befrp w

expressed as

2yw y s sinbŽ .frp frpb s (13)w y1qw y s sinbŽ .frp frp


It may be noted thatb s for continuous sheetsyy2y2w

plates becausew y(s sinb)s1 in this case.frp frp

3.4. Stress distribution in FRP along a shear crack

Because an FRP-to-concrete bonded joint generallyexperiences some slip after reaching the ultimate bondstrength (i.e. it shows some pseudo-plastic behaviourw43x, it may be assumed that all the FRP intersected bythe critical shear crack has developed the full bondstrength at the ultimate limit state. Note that the bondstrength of a particular partystrip, however, depends onthe location of the shear crack relative to the ends ofthis partystrip.Under this assumption, for a beam strengthened by

U-jacketing, the stress in the partystrip of FRP inter-sected by the critical shear crack at a coordinatez atfailure can be obtained from Eq.(8) by replacingLmax

with L szysinb in Eq. (9):z

SffrpT

s smin (14)frp,z UyE f9frp cT0.427b bw Lzy

V tfrp

where

S1 if l G1z

L zT zb s andl s s (15)Lz zU L L sinbe eplzTsin if l -1z

V 2

When s calculated according to Eq.(8) isfrp,max

smaller thanf , the stress distribution factorD canfrp frp

be obtained by substituting Eqs.(8) and (14) into Eq.(7):

S p1ycos l

2 2T if lF1pl pU sin lD s (16)frp 2

py2T1y if l)1V pl

Note that the condition for Eq.(16) that sfrp,max

obtained from Eq.(8) is less thanf is almost alwaysfrp

satisfied in practice. Even if this is not satisfied, Eq.(16)may still be used as it is slightly on the conservativeside.Following the same procedure, the expression for the

stress distribution factor for side bonding can be foundto be exactly the same as Eq.(16). Therefore, Eq.(16)is applicable to both U jackets and side stripsyplates.

However, the actual calculated values are different forthese two cases even if the bond geometry is the sameon the beam sides because the maximum bond lengthL for U jackets is twice that for side stripsyplatesmax

(Eq. (9)).Fig. 5a shows the variation ofD with l. A morefrp

detailed picture ofD within 0-l-5 is shown in Fig.frp

5b. The figure shows thatD increases from 0.5 aslfrp

increases from 0 and approaches unity whenl approach-es infinity. For the same bonding geometry on the sidesof a beam,D is larger for U jacketing than for sidefrp

bonding, because the values ofl are different for thetwo cases. Similarly, the maximum FRP stress along theshear crack(Eq. (8)) for U jacketing is larger than orat least equal to that for side bonding. These reflect thefact that U jacketing is more effective in shear strength-ening than side bonding.Fig. 6 shows the FRP contribution to shear capacity

for two example RC beams calculated using the aboveequations. The two beams havehs150 and 350 mmand ds120 and 310 mm, respectively, withf 9 s40c

MPa. Both are bonded over the full height with CFRPstrips oft s1 mm,E s200 GPa andf s3500 MPa.frp frp frp

It is clear that U jacketing is more effective than sidebonding. Fig. 6 also shows that the FRP contribution toshear capacity increases as the strip-to-spacing ratiorises(w ys sinbs1 for continuous plateysheets), butfrp frp

this increase is non-linear. This reflects the non-linearrelationship betweenb andw ys sinb in Eq. (13).w frp frp

The fact that the stress in the FRP varies along theshear crack and the maximum stress is limited by theultimate tensile strength of FRP, explains why thecontribution of externally bonded FRP shear reinforce-ment to the shear capacity of a beam is less than thatof internal steel shear reinforcement of equivalent totaltensile capacity. For most beams which fail by FRPdebonding, the maximum stress the FRP reaches issubstantially smaller than the ultimate tensile strengthof FRP, reducing the FRP contribution further belowthat obtained by treating it as equivalent steel shearreinforcement.

4. Comparison with experimental observations

4.1. Experimental data

An extensive literature review has been carried out tocollect test data of RC beams shear-strengthened withbonded FRPs. Table 1 includes 46 beams that failed byFRP debonding, including 13 beams strengthened byFRP U jacketing and 33 beams strengthened by FRPside bonding. Only the geometric and material propertiesrequired to determine the contribution of FRP to theshear capacity by the strength model presented in theprevious section are shown. Further details can be foundfrom the original sources. Tests that were not sufficiently


Fig. 5. Stress distribution factor for side bonding and U jacketing:(a) 0-l-20; (b) 0-l-5.

well documented have been excluded. The geometricparameters of cross-section are given in terms of a Tbeam, with the flange thicknessT s0 for rectangularf

beams. The beams were tested under symmetric three-point bending or four-point bending, or anti-symmetricalmoment conditionsw15x.The test data listed in Table 1 have the following

parameter ranges: beam heighths110–475 mm; webthickness b s70–200 mm; cylinder compressivew

strength of concretef 9 s20.5–59 MPa; steel tensionc

reinforcement ratios0.3–4.1%; shear spanayds1.1–4.7; and steel shear reinforcement ratios0.07–0.42%.

4.2. Experimental FRP contribution to shear capacity

Reference data of unstrengthened beams with thesame geometry and internal reinforcement are availablefor all the specimen groups. However, differences existbetween strengthened and un-strengthened referencespecimens in concrete strength. To take these differencesinto account, the following simple procedure was usedin this study.The shear capacity of the un-strengthened reference

beam,V , may be calculated using one of the well-pre,ref

known design codes for concrete structures. The exper-


Fig. 6. Effect of strip width-to-spacing ratio on shear capacity of sam-ple beams.

imental shear capacity of the reference beam,V , isexp,ref

most likely much higher than the predicted value. Theirratio is denoted byk, that is

Vexp,refks (17)Vpre,ref

It may be assumed that the same ratiok applies tothe contribution to the shear capacity of the strengthenedtest beam by the concrete and the internal reinforcement.This experimental contribution is thuskV , wherepre,RC

V is the contribution by the concrete and thepre,RC

internal reinforcement calculated according to the samecode as forV . Therefore, the contribution of FRPpre,ref

to the shear capacity of a strengthened test beam can beobtained by

V sV ykV (18)frp exp pre,RC

where V is the experimental shear capacity of theexp

strengthened beam.In the present study,V andV were calculatedpre,ref pre,RC

according to BS 8110w44x but any other codes may beused which would lead to little difference for thededucedV . It may be noted thatk is a combinedfrp

scaling factor for concrete and steel shear reinforcement(all test specimens had the same steel shear reinforce-ment as their respective reference beam). This simpleapproach was adopted in the present study, because thealternative approach of separating the contributions fromconcrete, steel and FRP based on the assumption thatsteel reinforcement crossing the critical shear crack withthe assumed angle reached yielding led to little differ-ence to the deduced FRP contribution.The shear crack angleu has a significant effect on

the shear capacity(see Eq.(5)), but the actual value isseldom reported in the literature. The majority of thevalues listed in Table 1 was estimated from pictures,sketches or text descriptions presented in the original

sources. No such information is available to make suchestimates for a few groups of specimens, so a singleangle for all beams of the same study, which made theirresults the best fit for the present model, was assumedin this case. This assumption may appear less than ideal,but it should be noted that in the final design proposalpresented later in the paper, a single angle of 458 isused, so the validity of the final design proposal is notat all affected by this assumption.

4.3. Comparison of experimental observations with theo-retical predictions

The new model is compared with the test data givenin Table 1. Table 2 shows that the new shear strengthmodel has a good agreement with experimental obser-vations for both side bonded and U jacketed beams. Onaverage, the test data are approximately 10% higherthan the predictions of the model. This may be areflection of the fact that the effective FRP edges weretaken to be at a small distance(0.1d) below the actualupper edge and a small distance(from the tension faceto the centroid of the steel tension reinforcement) abovethe actual lower edge. The good agreement between thenew model and the experimental data is shown graphi-cally in Fig. 7.

5. A new design proposal

5.1. Design equations

For shear strengthening using side stripsyplates, theshear capacity needs only to be evaluated for the FRPdebonding failure mode as given here. For U jacketing,the smaller of the predictions of the FRP rupture modew7x and the debonding mode shall be taken as theultimate shear capacity.For practical design, it can be assumed thatus458.

The contribution of FRP to the shear strength is thus

h sinbqcosbŽ .frp,effrp,edV s2 t w (19)frp frp frpg sb frp

in which g is the partial safety factor in a limit stateb

design approach.g s1.25 is suggested here. The designb

effective FRP stressf is defined asfrp,ed

f sD s (20)frp,ed frp frp,max,d

where the maximum design stress in FRPs mayfrp,max,d

be obtained by using the 95th percentile characteristicvalue of the bond strength given by Chen and Tengw28x, i.e.

Efrp ys s0.315b b f9 Ff (21)frp,max,d w L c frpy tfrp

35J.F.

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Table 1Test data of debonding-controlled FRP-strengthened RC beams

Ref Specimen Concrete Web Depth Effective Flange Flange FRP FRP FRP Young’s Tensile Strengthening wfrp

s sinbfrp

Vfrp Crack

strength thickness h (mm) depth thickness width type thickness effective modulus strength scheme (kN) anglef9 (MPa)c b (mm)w d (mm) T (mm)f B (mm) t (mm)frp height E (MPa)frp f (MPa)frp u (8)

h (mm)frp,e

Side bondingw2x SO 37.7 150 150 113 GFRP 3 101.7 16 200 SS90 0.40 8.2 45

SP 37.7 150 150 113 GFRP 3 101.7 16 200 SS90 0.40 7.9 45WO 37.7 150 150 113 GFRP 3 71.7 16 200 SP90 1.00 8.7 45WP 37.7 150 150 113 GFRP 3 71.7 16 200 SP90 1.00 11.9 45

w5x RS90-1 35.0 150 250 210 CFRP 1 189.0 150 2400 SS90 0.50 34.3 45

w11x C1, 2-layer 27.5 152 152 101 CFRP 0.222 90.9 230 3400 SP90 1.00 19.1 25C1, 3-layer 27.5 152 152 101 CFRP 0.333 90.9 230 3400 SP90 1.00 18.2 25C2, 3-layer 27.5 152 152 101 CFRP 0.33 90.9 230 3500 SP90 1.00 34.1 25

w24x SB1310 39.2 200 200 160 CFRP 0.097 144.0 284 3430 SP90y0 1.00 31.1 45SB1210 39.2 200 200 160 CFRP 0.097 144.0 284 3430 SP90 1.00 22.4 45SB1214 39.2 200 200 160 CFRP 0.097 144.0 284 3430 SP90 1.00 24.7 45SB1218 39.2 200 200 160 CFRP 0.097 144.0 284 3430 SP90 1.00 25.6 45

w13x BT5 35.0 150 405 360 100 380 CFRP 0.165 224.0 228 3790 SS90 0.40 31.5 45

w15x A1 28.5 150 250 220 CFRP 0.167 198.0 230 3430 SP90 1.00 40.2 40B1 28.5 150 250 220 CFRP 0.167 198.0 230 3430 SP90 1.00 43.2 40C1 28.5 150 250 220 CFRP 0.167 198.0 230 3430 SP90 1.00 34.3 40D1 28.5 150 250 220 CFRP 0.167 198.0 230 3430 SP90 1.00 55.4 40E1 28.5 150 250 220 CFRP 0.167 198.0 230 3430 SP90 1.00 37.8 40F1 28.5 150 250 220 CFRP 0.167 198.0 230 3430 SP90a 1.00 17.7 40

w18x S2 45.2 200 300 260 CFRP 0.11 234.0 230.0 3480 SS90 0.50 62.6 28S4 37.5 200 300 260 CFRP 0.11 234.0 230.0 3480 SP90 1.00 64.3 28

w21x S1a 30.0 70 110 100 CFRP 0.11 90.0 235.0 3300 SS90 0.67 27.1 20S1b 30.0 70 110 100 CFRP 0.11 90.0 235.0 3300 SS90 0.67 22.5 20S1(45) 30.0 70 110 100 CFRP 0.11 90.0 235.0 3300 SS45 0.67 28.1 20S2a 30.0 70 110 100 CFRP 0.11 90.0 235.0 3300 SS90 1.00 31.7 20S2b 30.0 70 110 100 CFRP 0.11 90.0 235.0 3300 SS90 1.00 25.8 20S2(45) 30.0 70 110 100 CFRP 0.11 90.0 235.0 3300 SS45 1.00 30.9 20S3a 30.0 70 110 100 CFRP 0.147 90.0 235.0 3300 SS90 1.00 26.4 20S3b 30.0 70 110 100 CFRP 0.147 90.0 235.0 3300 SS90 1.00 21.1 20S3(45) 30.0 70 110 100 CFRP 0.147 90.0 235.0 3300 SS45 1.00 24.3 20

w22x 5 24.1 100 200 160 CFRP 0.097 144.0 230 2454 SP90 1.00 20.1 456 26.9 100 200 160 CFRP 0.097 144.0 230 2454 SP45 1.00 31.4 457 26.9 100 200 160 CFRP 0.194 144.0 230 2454 SP90 1.00 19.2 45

U jacketingw10x S-Diag-CL 59.0 70 475 410 60 480 CFRP 0.11 199.0 230 3400 SS45b 0.47 62.0 30

36J.F.

Chen,

J.G.

Teng/

Construction

andB

uildingM

aterials17

(2003)27–41

Table 1(Continued)

Ref Specimen Concrete Web Depth Effective Flange Flange FRP FRP FRP Young’s Tensile Strengthening wfrp

s sinbfrp

Vfrp Crack

strength thickness h (mm) depth thickness width type thickness effective modulus strength scheme (kN) anglef9 (MPa)c b (mm)w d (mm) T (mm)f B (mm) t (mm)frp height E (MPa)frp f (MPa)frp u (8)

h (mm)frp,e

w24x SCD3-23 39.2 200 200 160 CFRP 0.097 144.0 284 3430 UP90c 1.00 23.7 45

w13x BT2 35.0 150 405 360 100 380 CFRP 0.165 224.0 228.0 3790 UP90 1.00 65.0 45BT3 35.0 150 405 360 100 380 CFRP 0.165 224.0 228.0 3790 UP90 1.00 67.5 45

w12x CO2 20.5 150 305 264 CFRP 0.165 237.6 228.0 3500 US90 0.40 40.0 35CO3 20.5 150 305 264 CFRP 0.165 237.6 228.0 3500 UP90 1.00 65.0 35

w14x IIGu 36.5 127 203 165 CFRP 1.68 148.5 200 105 UP45y45 1.00 49.3 35

w18x S3 41.3 200 300 260 CFRP 0.11 234.0 230.0 3480 US90 0.50 107.1 28S5 39.7 200 300 260 CFRP 0.11 234.0 230.0 3480 UP90 1.00 104.4 28

w17x No. 2 35.7 150 300 232 100 400 CFRP 0.111 108.8 230.0 3480 UP90 1.00 24.2 46

w23x BS2 35.1 200 450 390 CFRP 0.11 351.0 230 3494 US90d 0.16 41.1 30BS5 36.8 200 450 390 CFRP 0.11 351.0 230 3494 US90 0.13 33.9 25BS6 35.8 200 450 390 CFRP 0.11 351.0 230 3494 US90d 0.08 31.3 25

Treated as statistical outlier.a

I beam, lower end of FRP clamped. Treated as equivalent U jacketing here.b

FRP bonded on the full height on one side but only a very small height on the other side. Treated as half U jacketing here.c

Both U and inverted U jackets were used within a single shear span. This could be more efficient if used appropriately.d


Fig. 7. Theoretical predictions vs. experimental observations:(a) sidebonding; and(b) U jacketing.

Table 2Statistical performance of the new shear strength model

Method of strengthening Side U Allbonding jacketing

Number of valid experimental data 32 13 45Average of test-to-predicted strength ratios 1.07 1.20 1.11Standard deviation 0.226 0.226 0.231Coefficient of variation(%) 21.1 18.9 20.9

whereb andb can be obtained from Eqs.(10) andL w

(13), respectively.In the design of a shear strengthening scheme using

U jacketing or side-bonding with strips, an iterativeprocedure is required because the coefficientb in Eq.w

(13) is related to the ratio of strip width to strip spacingw y(s sinb) (b s0.707 for continuous sheetsyfrp frp w

plates). An initial value of b s1 may be used. Thew

iterative process will converge very quickly, with threeiterations being usually sufficient.If the strain reached in the FRP at the ultimate limit

state is low, yielding may have not been reached insome of the internal steel stirrups intersected by thecritical shear crack. In such cases, the contribution ofinternal steel stirrups may need to be reducedaccordingly.

5.2. Strip spacing limit

The strength model was derived by treating strips asequivalent continuous sheetsyplates. For this treatmentto be accurate, the number of strips intersected by theshear crack should be sufficient. Otherwise, the treat-ment can lead to either conservative or un-conservativepredictions, depending on the locations of the strips.Consider diagonal shear failure as an example. The

most effective position is the middle of the shear crackfor side bonding(Fig. 8a), but at the lower end for Ujacketing (Fig. 8b), because the bond length is largestin both cases. By contrast, a strip located at either endof the shear crack for side bonding(Fig. 8c) and at theupper end for U-jacketing(Fig. 8d) is completelyineffective due to the lack of any bond length. Therefore,a strengthening scheme may be completely ineffectiveif only one strip is intersected by the shear crack.For a shear strengthening scheme to be effective, the

spacing between the strips must be limited. BS 8110w44x requires that the longitudinal spacing of internalsteel shear reinforcement does not exceed the lesser of0.75d and 300 mm. However, this cannot be directlyused here because an internal steel link can be assumedto be effective as long as it intercepts the shear crackbut an FRP strip can be completely ineffective even ifit does intercept the shear crack as discussed above. TheUK Concrete Societyw31x proposed a spacing limit ofthe lesser of 0.8d andw qdy4. This spacing limit isfrp

controlled byw qdy4 for narrow strips. For verticalfrp

strips, this rule means that the gap between two stripsshall not exceeddy4 in all cases and it requires approx-imately four strips to intersect the shear crack in thecase of very narrow strips bonded to the full height ofthe beam. This may be too restrictive. Wide strips willbe controlled by the limit of 0.8d. This limit means thatstrips wider than 0.8d cannot be used, which is anunnecessary constraint. More importantly, the use ofdin the limits leads to inconsistent results for differentFRP bonding heights on the beam sides. Furthermore,


Fig. 8. Effect of FRP strip location on effectiveness of shear strengthening.

Fig. 9. Strip spacing. Fig. 10. Predictions of design proposal vs. experimental observations.

the orientation of the fibres has not been properlyconsidered.The authors had previously proposed that the strip

spacing be limited byh (1qcotb)y2, which ensuresfrp,e

that at least two strips will cross the assumed diagonalcrack w19,25x wnote that there is an error in Teng et al.w19,25x whereh (1qcotb)y2 was mistakenly givenfrp,e

as h (sinbqcosb)y2x. However, it is possible thatfrp,e

this rule cannot be met in practice if wide strips areused. A more robust proposal is thus proposed below.For a shear strengthening scheme to be effective and

for the present strength model to be accurate, it issuggested here that the clear strip spacings yw yfrp frp

sinb (Fig. 9) should not exceed half the horizontaldistance at the lower end of the effective FRP coveredby the projection of the shear crack in the direction offibres, which is given byh (1qcotb)y2. As thisfrp,e

calculated value can be still very large for large beams,it is necessary to limit it to an upper bound. The upperlimit of 300 mm for internal steel links used in BS 8110w44x may be used before better information becomesavailable. Therefore, the limit of the clear strip spacingcan be expressed as

wfrps yfrp sinbh 1qcotbŽ .frp,e

Flesser of and 300 mm (22)2

This ensures that in all situations there are fibresintercepting the more effective half(the lower half forU jackets and middle half for side plates) of the assumeddiagonal crack. For continuous sheetsyplates, Eq.(22)is automatically satisfied becauses yw ysinbs0.frp frp

Therefore, Eq.(22) applies to all cases.

5.3. Comparison with experimental observations

Fig. 10 compares the above design proposal with allthe 46 experimental data of Table 1, including the onewhich was treated as a statistical outlier. The partialsafety factorg was set to 1. The strip spacing limitb


was not imposed for the purpose of this comparison, asthis limit is taken only as a conservative design measure.The predicted value exceeds the experimental observa-tion only for the statistical outlier. The design proposalis thus suitable for practical use.

6. Conclusions

FRP rupture and FRP debonding have been the twomain shear failure modes identified for RC beams shear-strengthened with externally bonded FRP reinforcement.Separate treatments of the two failure modes are essen-tial to develop accurate shear strength models. Thispaper has been concerned with the development of anew design proposal for FRP-strengthened RC beams,which fail in shear by FRP debonding. A review ofexisting research was first presented, which identifiedthe deficiencies of all existing approaches. Based on arational bond strength model between FRP and concrete,a new shear strength model was then developed fordebonding failures in FRP shear strengthened RC beams.This new model explicitly recognises the non-uniformstress distribution in the FRP along a shear crack asdetermined by the bond strength between FRP stripsand concrete. This new model has been found tocompare well with experimental data collected from theliterature based on an extensive review. A design pro-posal, which can be directly used in practical design,was finally presented.

7. Notation

B: width of flange of a T-beamb :w width of web of a T-beamD :frp stress distribution factor for FRP intersected

by the shear crackd: distance from beam compression face to

centroid of steel tension reinforcement forflexure

d :frp,e depth from the upper edge of the shearreinforcement to the centroid of the steeltension reinforcement

d :frp distance from beam compression face to loweredge of FRP on sides

d :frp,t distance from beam compression face to topedge of FRP on sides

E :frp modulus of elasticity of FRPf 9:c concrete cylinder compressive strengthf :frp tensile strength of FRP in the main fibre

directionf :frp,e averageyeffective stress of FRP intersected by

the shear crack at beam failuref :frp,ed averageyeffective design stress of FRP

intersected by the shear crack at beam failureh: depth of beamh :frp,e effective height of FRP

k: test-to-predicted shear capacity ratio ofunstrengthened beam

s :frp centre-to-centre spacing of FRP stripsmeasured along the longitudinal axis

T :f thickness of flange of a T-beamt :frp thickness of FRP stripV: shear forceV :c contribution of concrete to shear capacityV :exp experimental shear capacity of strengthened

test beamV :exp,ref experimental shear capacity of reference

unstrengthened beamV :frp contribution of shear strengthening FRP to

shear capacityV :pre,ref predicted shear capacity of unstrengthened

reference beamV :pre,RC predicted shear capacity of strengthened test

beam excluding FRP contributionV :n shear capacity of shear strengthened beamV :s contribution of steel shear reinforcement to

shear capacityw :frp width of FRP strip(perpendicular to the fibre

orientation)z :b co-ordinate of lower edge of effective FRP on

sidesz :t co-ordinate of upper edge of effective FRP on

sidesb: angle of first fibre orientation measured

clockwise from the horizontal direction for theleft side of a shear strengthened beam

´ :frp,rup ultimate tensile strain of FRPf: angle of second fibre orientation measured

clockwise from the horizontal direction for theleft side of a shear strengthened beam

g :b partial safety factor for FRP debondingu: angle of critical shear crack to the longitudinal

axis of a beams :frp stress of FRPs :frp,max maximum stress in FRP intersected by the

shear cracks : maximum stress in FRP intersected by thefrp,max,d

shear crack for design

Acknowledgments

The work presented here is the result of collaborativeresearch between the Department of Civil and StructuralEngineering, The Hong Kong Polytechnic University,Hong Kong, China and the School of Engineering andElectronics, Edinburgh University, UK. The authorswould like to thank The Hong Kong Polytechnic Uni-versity for the financial support to their collaborativeresearch provided through the Area of Strategic Devel-opment (ASD) Scheme for the ASD in AdvancedBuildings Technology in a Dense Urban Environment.


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