Improving shear capacity of existing RC T-section beams usingCFRP composites

Ahmed Khalifa, Antonio Nanni *

224 Engineering Research Laboratory, Department of Civil Engineering, University of Missouri at Rolla, Rolla, MO 65409, USA

Received 10 May 1999; accepted 8 December 1999

Abstract

This paper presents the shear performance of reinforced concrete (RC) beams with T-section. Di�erent con®gurations of ex-

ternally bonded carbon ®ber-reinforced polymer (CFRP) sheets were used to strengthen the specimens in shear. The experimental

program consisted of six full-scale, simply supported beams. One beam was used as a bench mark and ®ve beams were strengthened

using di�erent con®gurations of CFRP. The parameters investigated in this study included wrapping schemes, CFRP amount, 90°/

0° ply combination, and CFRP end anchorage. The experimental results show that externally bonded CFRP can increase the shear

capacity of the beam signi®cantly. In addition, the results indicated that the most e�ective con®guration was the U-wrap with end

anchorage. Design algorithms in ACI code format as well as Eurocode format are proposed to predict the capacity of referred

members. Results showed that the proposed design approach is conservative and acceptable. Ó 2000 Elsevier Science Ltd. All

rights reserved.

Keywords: Bond; Carbon ®ber; Composites; Externally bonded reinforcement; Fiber-reinforced polymer (FRP); Reinforced concrete; Repair; Shear

strength; Strengthening; T-section

1. Introduction

Recently, innovative composite materials known as®ber-reinforced polymers (FRP) have shown greatpromise in rehabilitation of existing reinforced concrete(RC) structures. Rehabilitation of these structures canbe in the form of strengthening of structural members,repair of damaged structures, or retro®tting for seismicde®ciencies. In any case, composite materials are anexcellent option to be used as external reinforcing be-cause of their high tensile strength, light weight, resis-tance to corrosion, high durability, and ease ofinstallation.

Externally bonded FRP reinforcement has beenshown to be applicable for the strengthening of manytypes of RC structures [1,2] such as columns, beams,slabs, walls, tunnels, chimneys, and silos, and can beused to improve ¯exural and shear capacities, and also

provide con®nement and ductility to compressionmembers.

In order to take full advantage of the potential duc-tility of the RC member, it is desirable to ensure that¯exure rather than shear govern ultimate strength. Shearfailure is catastrophic and occurs with no advancewarning of distress. Many of the existing RC beamshave been found to be de®cient in shear strength and inneed of strengthening. De®ciencies occur due to severalreasons such as insu�cient shear reinforcement or re-duction in steel area due to corrosion, increased serviceload construction defects. In these situations, it has beenshown that externally bonded FRP reinforcement canincrease the shear capacity [3±11].

The objectives of this program are to:1. Investigate the shear behavior and modes of failure of

T-section RC beams with shear de®ciencies afterstrengthening with CFRP sheets.

2. Address the factors that a�ect shear strength, such aswrapping schemes, CFRP amount, 90°/0° ply combi-nation, and CFRP end anchorage.

3. Increase the database on shear strengthening.4. Improve and validate the design approach previously

proposed by the authors [8].

Cement & Concrete Composites 22 (2000) 165±174

* Corresponding author. Tel.: +1-573-341-4553; fax: +1-573-341-

6215.

E-mail address: nanni@umr.edu (A. Nanni).

0958-9465/00/$ - see front matter Ó 2000 Elsevier Science Ltd. All rights reserved.

PII: S 0 9 5 8 - 9 4 6 5 ( 9 9 ) 0 0 0 5 1 - 7

For these objectives, six full-scale, T-section RCbeams with shear de®ciencies were strengthened in dif-ferent con®gurations and tested.

2. Experimental program

In this experimental program, the selected parametersare:

(a) CFRP amount and distribution (continuoussheets versus series of strips); (b) bonded surface (twosides versus U-wrap);

(c) ®ber direction combination (90°±0° ®ber directioncombination versus 90° direction);

(d) end anchorage (U-wrap without end anchor ver-sus with end anchor).

2.1. Test specimens and materials

The experimental program consisted of six full-scaleRC beams with a T-shaped cross-section. The specimenswere reinforced with longitudinal steel bars with no steelshear reinforcement in the test region to favor shearfailure. Specimen details and dimensions are shown inFig. 1. The materials used for manufacturing the test

specimens and their mechanical properties are listed inTable 1.

2.2. Strengthening schemes and test setup

Specimen BT1 was the reference beam. Specimen BT2was strengthened using continuous surface bonded U-wraps throughout the beam span. The wraps were madeof single-ply CFRP sheets with the ®ber direction ori-ented perpendicular to the longitudinal axis of the beam

Notation

a shear spanAf area of CFRP shear reinforcement� 2tfwf

bw width of the beam cross-sectiond depth from the top of the section to the tension

steel reinforcement centroiddf e�ective depth of the CFRP shear reinforcement

(usually equal to d for rectangular sections andd ) ts for T-sections)

Ef elastic modulus of FRP (GPa)f 0c nominal concrete compressive strength (MPa)ffe e�ective tensile stress in the FRP sheet in the

direction of the principal ®bers (stress level inthe FRP at failure)

ffu ultimate tensile strength of the FRP sheet in thedirection of the principal ®bers

Le e�ective bond length (mm)R reduction coe�cient (ratio of e�ective average

stress or strain in the FRP sheet to its ultimatestrength or elongation)

sf spacing of FRP stripstf thickness of the FRP sheet on one side of the

beam (mm)Vc nominal shear strength provided by concrete

Vf nominal shear strength provided by FRP shearreinforcement (ACI format)

Vn nominal shear strength (ACI format)Vs nominal shear strength provided by steel shear

reinforcement (ACI format)Vfd design shear contribution of CFRP to the shear

capacity (Eurocode format)VRd1 design shear capacity of concrete (Eurocode

format)VRd2 maximum design shear force that can be carried

without web failure (Eurocode format)Vwd design contribution of steel shear reinforcementwf width of FRP stripwfe e�ective width of FRP sheet (mm)b angle between the principal ®ber orientation and

the longitudinal axis of the beamefe e�ective strain of FRPefu ultimate tensile elongation of the ®ber material

in the FRP composite/ strength reduction factor (ACI format)cf partial safety factor for CFRP materials

(Eurocode format)qf FRP shear reinforcement ratio��2tf=bw�

�wf=Sf�

Fig. 1. Beam specimens detailing and dimensions.

166 A. Khalifa, A. Nanni / Cement & Concrete Composites 22 (2000) 165±174

(90°). No end anchors were used for specimen BT2.The CFRP wraps were applied following the manu-facturerÕs recommendations [12]. Prior to strengthen-ing, the concrete surface was prepared using waterblasting and allowed to dry. It was then coated with alayer of epoxy-based primer, which penetrates theconcrete pores and provides better bond properties.After the primer became tack-free, a layer of putty, athick paste epoxy, was applied to level the surface andpatch small holes. A ®rst coat of saturant resin wasthen applied followed by the ®ber sheets. A ribbedroller was used on the sheets to ensure impregnation ofthe ®bers by the saturant. The sheet was then coatedwith a second layer of saturant resin and the excessiveresin was removed.

Specimen BT3 was strengthened with two perpen-dicular ®ber direction plies of CFRP sheets (90°/0°). The®rst ply was the same as beam BT2. The second ply wasbonded to the two beam sides with ®ber direction par-allel to the beam axis (i.e., 0° direction). The purpose ofadding a horizontal ply in 0° direction was to investigateif it had any e�ect on increasing the beam shear capacityby increasing the shear friction strength along the po-tential diagonal crack between the load and reaction.The horizontal ply may strengthen the contribution ofconcrete but will not a�ect the shear strength of the trussmechanism. In addition, the horizontal ply may act toarrest propagation of vertical cracks starting at thebottom of the section.

Specimen BT4 was strengthened with one-ply CFRPstrips in the form of a U-wrap with 90° ®ber orientation.The strip width was 50 mm with center-to-center spacingof 125 mm.

Specimen BT5 was strengthened with CFRP stripsattached only on the two beams sides with 90° ®berorientation. The strip width and spacing were similar tospecimen BT4.

Specimen BT6 was strengthened in a manner similarto that of specimen BT2. The ends of the U-wraps inspecimen BT6 were anchored to the ¯anges on bothsides of the beam using the proposed U-anchor system[13]. A cross-section showing details of the U-anchor

system is given in Fig. 2. The anchoring was attained bygrooving the concrete ¯anges at the corner. The groovedimensions were about 15� 15 mm and extendedthroughout the strengthened part. The strengtheningwork was started with concrete surface preparation andpriming that includes the walls of the groove. The CFRPsheets were bonded to the concrete surface and to thewalls of the groove. After the resin impregnating thesheet (saturant) had set, the groove was ®lled half waywith a high viscosity binder (e.g., epoxy paste) com-patible with the FRP system. The high viscosity pasteensures easier ®eld execution, especially in the case ofover-head application. A 10 mm diameter Glass FRProd was then placed into the groove and was lightlypressed in place. This action forces the paste to ¯owaround the sheet and to cover simultaneously part of therod and the sides of the sheet. The rod was held in placeusing wedges at the appropriate spacing. The groovewas then ®lled with the same paste and the surface wasleveled.

Strengthening schemes and test setup of the testedbeams are shown in Fig. 3. All specimens were tested assimple beams using four-point loading with shear span-to-e�ective depth ratio (a/d) equal to 3. A loading ma-chine of 1800 kN capacity was used in order to apply a

Fig. 2. Details of the U-anchor obtained by slicing a beam.

Table 1

Beam material properties

Material Dimensions (mm) Yield point

(MPa)

Compressive strength

(MPa)

Tensile strength

(MPa)

Modulus of elasticity

(GPa)

Concrete ± ± 35 ± ±

Steel reinforcing D � 28 470 ± 730 200

D � 13 350 ± 530 200

D � 10 350 ± 530 200

CFRP sheetsa tf � 0:165 ± ± 3790 228

a Fiber only.

A. Khalifa, A. Nanni / Cement & Concrete Composites 22 (2000) 165±174 167

concentrated load on a steel distribution beam used togenerate the two concentrated loads. The load was ap-plied in progressively increasing cycles. A cycle beforecracking of concrete was done in order to verify whetherboth the mechanical and electronic equipment wereworking properly. Two or three cycles before ultimatewere done. By applying the load in cycles, the stability ofthe system can be checked. The applied load versus de-¯ection curves shown in this study are the envelopes ofthese load cycles. Four linear variable di�erential trans-formers (LVDTs) were used for each test to monitorvertical displacements at various locations as shown inFig. 3. Two LVDTs were located at mid span, one on eachside of the beam. The other two were located at thebeam supports to record support settlement. Straingauges were attached to the FRP on the sides of thestrengthened beams and oriented in the ®ber direction.Ten strain gauges were used for each beam to monitorFRP strain. Strain gauges were mounted at the expectedlocation of shear cracks (as observed in reference beamBT1 during testing). Strain gauge positions are shown inFig. 3.

3. Test results and discussions

Fig. 4 shows the experimental results in terms of totalapplied load versus mid span de¯ection for the testedbeams, while the photos in Fig. 5 show the modes offailure of those beams.

When beam BT1 was loaded, it exhibited diagonalshear cracks at a load of 110 kN. The shear cracksstarted at the center of both shear spans simultaneously.The ®rst shear crack was the critical crack in the beam.As the load increased, this crack started to widen andpropagated leading to the eventual failure at a load of180 kN.

In beam BT2, failure was initiated by debonding ofCFRP sheets (with a layer of concrete adhered to them)over the main shear crack in the same location observedin beam BT1. It was followed by shear compressionfailure at a load of 310 kN. Strengthening of beam BT2with CFRP U-wraps resulted in a 72% increase in theshear capacity. The maximum localized FRP strain was0.0045 mm/mm, which corresponds to 28% of the re-ported ultimate strain of the CFRP. If debonding couldbe prevented, a better utilization of the strengtheningmaterial and consequently a higher increase in shearcapacity of the beam would be attained.

In beam BT3 with CFRP (90°/0°), the failure modewas in a similar manner to that of beam BT2. Thefailure occurred at a total applied load of 315 kN withno signi®cant increase in shear capacity compared tobeam BT2. Adding ply in 0° direction over a ply in 90°direction had no e�ect in increasing the shear capacity ofthe beam when the failure mode control by FRP deb-onding. However, the horizontal ply may be e�ectivewhen the shear span-to-depth ratio is smaller, or whenfailure mode control by web crashing. Research intoquantifying that e�ect is currently being conducted atthe University of Missouri at Rolla (UMR).

Fig. 3. Test setup and strengthening schemes.

Fig. 4. Experimental results in terms of load-mid span de¯ection.

168 A. Khalifa, A. Nanni / Cement & Concrete Composites 22 (2000) 165±174

In beam BT4 with CFRP strips in the form of U-wraps, the diagonal shear crack is observed at a totalload of 140 kN. The crack propagated as the load in-creased in a similar manner to that of beam BT1. Thefailure occurred due to debonding of CFRP over themain diagonal shear crack, with a concrete layer at-tached to them, in the area between the center of shearcrack and its upper end. This led to an instantaneous

increase in the load carried by the other strips locatedbetween the shear crack center and its lower end re-sulting in fracture of two of them followed directly byshear compression failure. The maximum-recorded localvertical strain in CFRP at ultimate was about 0.01 mm/mm which is close to twice the value recorded in the caseof continuous sheets, beam BT2. Applied load versusvertical CFRP strain for beam BT4 is shown in Fig. 6.

Fig. 5. Failure modes of tested beams.

A. Khalifa, A. Nanni / Cement & Concrete Composites 22 (2000) 165±174 169

The strain gauges sg6, sg7, sg8, sg9, and sg10 were lo-cated at distances of 200, 450, 575, 700, and 700 mmfrom support, respectively. Sudden failure of beam BT4occurred at a point load of 324 kN. The load carryingcapacity of beam BT4 with CFRP strips is relativelyclose to that of beam BT2 with continuous sheets. Thismeans that there are optimum FRP quantities, beyondwhich the strengthening e�ect cannot be increased. Incase of U-wrap continuous sheets, debonding ofCFRP sheets from concrete initially starts at the top ofdiagonal shear crack where the development length isnot su�cient. This results in instantaneous increases inload carried by the vicinity. This led to rapid propaga-tion of the debonding of CFRP sheets over the shearcrack, combined with beam failure and whatever thequantity of FRP at the vicinity if it was more than orequal to a certain amount. The ®ndings herein closelymatch those of other researchers. Based on a review ofexperimental results available in the literature, Trianta-®llou [9] shows that the contribution of FRP to the shearcapacity increases almost linearly with FRP axial ri-gidity expressed by qfEf up to approximately 0.4 GPa,beyond which the e�ectiveness of FRP ceases to bepositive.

In beam BT5 with CFRP strips attached to beamsides only, the large diagonal shear crack was formed ata total load of about 140 kN and propagated as the loadincreased in a similar manner to beams BT1 and BT4.Brittle failure occurred at a total applied load of 243 kNby debonding of CFRP strips followed directly by shearcompression failure. The location of debonding areaherein is di�erent from beam BT4. In that case, it wasbelow the main shear crack between its center and itslower end. Strengthening of beam BT5 with CFRPstrips on the two beam sides resulted in a 35% increasein the shear capacity. Unfortunately, part of the com-puter ®le which includes the strain gauge results waslost.

As a result of the use of U-anchors, a signi®cant in-crease in the shear capacity was achieved in beam BT6.Also, the failure mode at ultimate changed from CFRPdebonding (as observed in beam BT2) to ¯exural failuremode. The measured local maximum vertical strain ofthe CFRP wrap was 0.0063 mm/mm or 40% of ultimate.This value is not an absolute because it greatly dependson the location of the strain gauge with respect to acrack. Load versus CFRP strain relationships for thetwo strengthened beams BT2 and BT6 are shown inFig. 7. The strains at gauges 7, 9, and 10 are plotted. Forboth beams, shear cracking starts at the same load level;however, a much higher ultimate load (and strain) isattained for BT6. No debonding was observed in theCFRP wrap of beam BT6 at ultimate capacity. Afterthe beam failed in ¯exure, the CFRP wrap ruptured atthe end of the shear crack near the support, as shown inFig. 5(f). The load carrying capacity of beam BT6 was442 kN with 145% and 42% increments over the refer-ence beam BT1 and the equally strengthened beam BT2,respectively. Fig. 4 indicates that beam BT6 gained moresti�ness and ductility than beam BT2. The additionalductility was obtained from the ¯exural failure mode.The mid-span de¯ection of beam BT6 at failure wasabout 3 times the de¯ection of beam BT2 at failure.

4. Design approach

The design approach for computing the contributionof externally bonded CFRP reinforcement to the shearcapacity of RC beams, in ACI Code [14] format, wasproposed in the previous paper [8].

The model described the two possible failure mech-anisms of CFRP reinforcement separately (either CFRPfracture or debonding). Furthermore, two limits on thecontribution of CFRP shear reinforcement were pro-posed, the ®rst limit was set to control the shear crack

Fig. 6. Load versus vertical CFRP strain for beam BT4.Fig. 7. Load versus vertical CFRP strain for beams BT2 and BT6.

170 A. Khalifa, A. Nanni / Cement & Concrete Composites 22 (2000) 165±174

width and loss of aggregate interlock and the second topreclude web crushing. Also, the concrete strength andCFRP wrapping schemes were considered as designvariables.

To quantify the average bond strength and the ef-fective bond length at CFRP debonding, the equationspresented by Maeda et al. [15] were used [8]. However,in a recent study, based on experimental and analyticalresults, Miller [16] modi®ed the model by Maeda et al.and proposed new equations to predict the e�ectivebond length and the ultimate load at CFRP debond-ing. Although both models seemed to give nearly thesame results in terms of ultimate load, a slight modi-®cation to improve the shear design algorithms hasbeen proposed [17], including Miller model instead ofMeada et al. In addition, the model was extended toprovide the shear design algorithms in Eurocode for-mat as well as ACI format. Comparing with all avail-able test results in the literature to date, the designshear model showed acceptable and conservative esti-mates [17]. The design equations for shear strengthen-ing of RC members with externally bonded CFRP arepresented below.

4.1. Shear capacity of a CFRP strengthened section ±ACI format

The nominal shear strength of an RC section (Vn) isexpressed in Eq. (1).

Vn � Vc � Vs � Vf ; �1�where Vc is the shear strength of the concrete, Vs theshear strength of the steel reinforcement, and Vf is theshear contribution of the CFRP.

The design shear strength, /Vn, is obtained by mul-tiplying the nominal shear strength by a strength re-duction factor for shear, /. The / factor for steel andconcrete contribution from ACI is 0.85, and the / factorfor CFRP contribution is suggested to be 0.70. Eq. (2)presents the design shear strength.

/Vn � 0:85�Vc � Vs� � 0:7Vf : �2�

4.1.1. Contribution of CFRP reinforcement to the shearcapacity

The expression to compute CFRP contribution isgiven in Eq. (3). This equation is similar to that for steelshear reinforcement and is consistent with ACI format.

Vf � Af ffe� sinb� cosb�df

sf

62����f 0c

pbwd

3

ÿ Vs

!: �3�

In Eq. (3), the area of CFRP shear reinforcement, Af , isthe total thickness of the sheet usually 2tf (for sheets onboth sides of the beam) times the width of the CFRPstrip wf . Fig. 8 shows the dimensions used to de®ne thearea of CFRP in addition to the spacing sf and the ef-fective depth of CFRP, df . Note that for continuousvertical shear reinforcement, the spacing of the strip, sf ,and the width of the strip, wf , are equal.

In Eq. (3), a reasonable limit on the maximumamount of additional shear strength that may beachieved is suggested in terms of the shear strength ofconcrete and steel shear reinforcement. The limit was setto provide adequate safety against web crushing causedby the diagonal compression stress. In addition to thelimit, the spacing of CFRP strips should not be so wideto allow the full formation of a diagonal crack withoutintercepting a strip. For this reason, the strips shouldnot be spaced by more than the maximum given inEq. (4)

Sf 6wf � d=4: �4�In Eq. (3), the e�ective CFRP stress, ffe, smaller than itsnominal strength, is computed by applying a reductioncoe�cient, R, to the nominal CFRP strength, ffu, asexpressed in Eq. (5).

ffe � Rffu: �5�The reduction coe�cient is dependent on the governingmode of failure. Either fracture of CFRP reinforcementat average stress level below nominal strength due tostress concentrations (failure mode 1) or debonding ofthe CFRP reinforcement from the concrete surface(failure mode 2) governs failure. In either case, an upperlimit of reduction coe�cient is established in order to

Fig. 8. Dimensions used to de®ne the area of FRP. (a) Vertical oriented FRP strips. (b) Inclined strips.

A. Khalifa, A. Nanni / Cement & Concrete Composites 22 (2000) 165±174 171

control shear crack width and loss of aggregate inter-lock.

4.1.2. Reduction coe�cient for failure mode 1The proposed reduction coe�cient for failure mode 1

was based on the experimental results and the workscited presented by Trianta®llou [9]. However, modi®-cations were suggested [8] due to additional experi-mental data that have become available. The proposedreduction coe�cient is a function of CFRP sti�ness andexpressed in Eq. (6) for qfEf 6 0:7 GPa.

R � 0:5622 qfEf� �2 ÿ 1:2188�qf Ef� � 0:778: �6�Although Eq. (6) has been derived from calibration of48 test results including the two modes of failure, itshowed a good agreement and ®t all of the available testresults in the literature till date (76 test results including22 in which the failure was controlled by CFRP frac-ture) [17].

4.1.3. Reduction coe�cient for failure mode 2The shear capacity governed by CFRP debonding

from the concrete surface was presented [17] as a func-tion of CFRP sti�ness, concrete strength, e�ective depthof CFRP reinforcement, and bonded surface con®gu-rations. In determining the reduction coe�cient forbond, the e�ective bond length, Le, has to be determined®rst. Based on analytical and experimental data frombond tests, Miller [16] showed that the e�ective bondlength increases as CFRP sti�ness, Ef tf , increases.However, he suggested a conservative value for Le equalto 75 mm. The value may be modi®ed when more bondtests data become available.

When a shear crack develops, only that portion of thewidth of CFRP extending past the crack by the e�ectivebonded length has been assumed to be capable of car-rying shear [8]. The e�ective width, Wfe, is based on theshear crack angle, assumed to be 450, and the wrappingscheme. The value of Wfe is expressed in Eqs. (7a) and(7b)

Wfe � df ÿ Le if the sheet is in the form of a U-wrap;

�7a�

Wfe � df ÿ 2Le if the sheet is bonded only to the sides

of the beam: �7b�The ®nal expression for the reduction coe�cient, R, forthe mode of failure controlled by CFRP debonding isexpressed in Eq. (8)

R � f 0cÿ �2=3

wfe

efu df

�738:93ÿ 4:06�Ef tf�� � 10ÿ6: �8�

Eq. (8) is applicable for CFRP sti�ness, Ef tf , rangedfrom 20 to 90 MM-GPa. Research into quantifying the

bond characteristics for sti�ness above 90 MM-GPa isbeing conducted at UMR.

4.1.4. Upper limit of the reduction coe�cientIn order to control the shear crack width and loss of

aggregate interlock, an upper limit of reduction coe�-cient �R � 0:5� was suggested [8]. This limit is such thatthe e�ective strain, efe, is of the order of 0.005 mm/mm(including the / factor) for CFRP sheets having an ul-timate strain, efu, in the order of 0.015 mm/mm. Due tothe variety of the ultimate strain of CFRP sheets avail-able in the market, a constant upper limit of e�ectivestrain was suggested [17] to be about 0.004 mm/mm (in-cluding the / factor). Using this value, the upper limit ofreduction coe�cient, R, is taken to be equal to 0.006/efu.

4.1.5. Controlled reduction coe�cientThe ®nal controlled reduction coe�cient for the

CFRP system is taken as the lowest value determinedfrom the two possible modes of failure and the upperlimit.

For the cases of U-jacket with end anchorage andtotally wrap con®gurations, the failure mode of CFRPdebonding is not to be considered. The reduction coef-®cient is only controlled by FRP fracture and the upperlimit.

4.1.6. Concrete surface preparationIt is important to mention that the mechanical con-

crete surface preparation method (sand blasting, waterblasting, or grinder) has a signi®cant e�ect on the bondbehavior of FRP. A primer study at UMR showed thatmaking a small groove using hammer and chisel in partsof the beam surface in which the bond is critical in ad-dition to using the sand blasting, may increase signi®-cantly the FRP contribution. However, research intolinking the bond behavior of FRP with the degree ofconcrete surface roughness will be conducted at UMR.Consequently, further improvement to the shear designmodel to consider that e�ect will arise.

4.2. Shear capacity of a CFRP strengthened section ±Eurocode format

The proposed design (Eq. (3)) for computing thecontribution of externally bonded CFRP reinforcementmay be rewritten in Eurocode (EC2 1992) [18] format asEq. (9)

Vfd � Af�ffe=cf��0:9df��1� cotb� sinbsf

6 VRd2� ÿ VRd1� � Vwd��; �9�where Vfd is the design shear contribution of CFRP tothe shear capacity in Eurocode format, cf the partial

172 A. Khalifa, A. Nanni / Cement & Concrete Composites 22 (2000) 165±174

safety factor for CFRP materials (suggested equal to1.3), VRd2 the maximum design shear force that can becarried without web failure, VRd1 is the design shearcapacity of concrete, and Vwd is the design contributionof steel shear reinforcement.

4.3. Comparison between test results and calculated values

The comparison between the test results and calcu-lated shear strength using the proposed design approach(ACI format) are listed in Table 2. The measurednominal CFRP shear contribution to the shear capacitywas obtained by subtracting the ultimate shear strengthof the reference beam from the non-strengthened one.Per ACI 318-95 [14, Eq. (11.5)], the nominal shearstrength provided by concrete, Vc is equal to 57 kN inEq. (11.5), the values of Vu and Mu were taken at pointof applied load). Moreover, the design shear strengthprovided by concrete, /Vc, is equal to 48.45 kN (consid-ering / � 0:85). The comparison indicated that the designapproach gives acceptable and conservative results.

5. Conclusions

In this study, the shear performance of T-section RCbeams with shear de®ciencies, strengthened with di�er-ent con®gurations of CFRP sheets were investigated.The test results indicated that the externally bondedCFRP reinforcement can be used to enhance the shearcapacity of the beams. For the beams tested in the ex-perimental program, increase in shear strength of 35±145% was achieved.

Within the indicated scope of investigation, the par-ticular conclusions that emerged from this study may besummarized as follows:· The performance of externally bonded CFRP can be

improved signi®cantly if adequate anchoring is pro-vided.

· The proposed U-anchor system is recommendedwhere bond and/or development length of FRP arecritical according to the design procedure.

· Applying CFRP on the beam sides only gives lessshear contribution compared to U-wrap.

· Although the CFRP amount in beam BT4 was 40%of that used in beam BT2, the same strengthening ef-fect was attained. The result mean that there is opti-mum FRP quantities, beyond that the strengtheninge�ectiveness is questionable.

· CFRP strips, although may be as e�ective as contin-uous CFRP sheets in the laboratory, are not recom-mended by the authors for ®eld application.Continuous sheets may be safer than strips becausethe damage to an individual strip would have moreof an impact on the overall shear capacity.T

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A. Khalifa, A. Nanni / Cement & Concrete Composites 22 (2000) 165±174 173

· No contribution to the shear strength was observedfor 0° ply in this test specimen.

· Comparing with the test results, the shear design al-gorithm provides acceptable and conservative esti-mates.

6. Suggestions for future research

· To optimize the design algorithm, more beams stillneed to be tested with di�erent CFRP amount.

· E�ect of existing transverse steel reinforcement, shearspan-to-e�ective depth ratio, and adding a ply ofFRP in 0° direction over ply in 90° on the shear con-tribution of CFRP need to be considered in the pro-posed design algorithms.

· Strengthening e�ectiveness of U-wrap with/withoutend anchor in negative moment region has to be in-vestigated for T-section RC beams.

· In order to validate the use of U-wrap with the pro-posed end anchor in seismic retro®tting situations,the strengthening e�ectiveness of this system needsto be tested under a cyclic load.

· The shear design algorithm needs to be extended toinclude strengthening with Aramid FRP and GlassFRP sheets in addition to CFRP.

Acknowledgements

This work was conducted with partial support fromthe National Science Foundation Industry/UniversityCooperative Research Center on Repair of Buildingsand Bridges with Composites based at the University ofMissouri, Rolla. The Egyptian Cultural and Educa-tional Bureau, Washington, DC provided support to the®rst author.

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