fibre reinforced polymer shear reinforcement for concrete member

8/12/2019 Fibre Reinforced Polymer Shear Reinforcement for Concrete Member

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Fibre reinforced polymer shear reinforcement forconcrete members: behaviour and designguidelinesEmile Shehata Ryan Morphy and Sami Rizkalla

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Abstract: This paper describes an experimental program conducted to examine the structural perfonnance of fibre reinforced polymer (FRP) stirrups as shear reinforcement for concrete structures. A total of ten large-scale reinforced concrete beams were tested to investigate the contribution of the FRP stirrups in a beam mechanism. The ten beamsincluded four beams reinforced with carbon fibre reinforced polymer (CFRP) stirrups, four beams reinforced with glassfibre reinforced polymer (GFRP) stirrups, one beam reinforced with steel stirrups, and one control beam without shearreinforcement. The variables were the material type of stirrups, the material type of the flexural reinforcement, and thestirrup spacing. Due to the unidirectional characteristics of FRP, significant reduction in the strength of the stirrup relative to the tensile strength parallel to the fibres is introduced by bending FRP bars into a stirrup configuration and bythe kinking action due to inclination of the diagonal shear crack with respect to the direction of the stirrups. A total of52 specially designed panel specimens were tested to investigate the bend and kinking effect on the capacity of FRPstirrups, along with two control specimens reinforced with steel stirrups. The variables considered in the panel specimens are the material type of the stirrups, the bar diameter, the bend radius, the configuration of the stirrup anchorage,the tail length beyond the bend portion, and the angle of the stirrups. Based on the findings of this investigation, sheardesign equations for concrete beams reinforced with FRP, appropriate for the Canadian Standards Association (CSA)code, are proposed. The reliability of the proposed equations is evaluated using test results of 118 beams tested by others.Key words shear, fibre-reinforced polymers, CFRp, cracks, GFRP, kink, stirrups, bend capacity.Resume: Cet article decrit un programme experimental dirige afin d examiner la perfonnance structurale d etriers enpolymere renforce de fibres (PRF) pour Ie renforcement en cisaillement de structures en beton. Un total de dix poutresen beton arme agrande echelle ont ere examinees pour etudier la contribution d etriers en PRF dans Ie mecanismed une poutre. Les dix poutres inc1uaient quatre poutres equipees d etriers en polymere renforce de fibres de carbone(pRFC), quatre poutres equipees d etriers en polymere renforce de fibres de verre (pRFV), une poutre renforceed etriers en acier et une poutre de controle sans renforcement en cisaillement. Les variables furent Ie type de materiaudes etriers, Ie type de materiau pour Ie renforcement en flexion, et I espacement des etriers. A cause des caractenstiques unidirectionnelles du PRF, une reduction significative dans la resistance de I etrier, relative a a resistance en tension paralU:le aux fibres, est introduite en flechissant les barres de PRF en une configuration d etrier, et par I action dedesequilibre due a I inclinaison de la fissure de cisaillement diagonale par rapport a la direction des etriers. En memetemps que deux specimens de controle renforces d etriers en acier, un total de 52 specimens de panneaux specifiquement con ;US ont r examines pour etudier Ie flechissement et l effet de desequilibre sur la capacire des. etriers en PRF.Les variables considerees pour les specimens de panneaux sont Ie type de materiau des etriers, Ie diametre des barres,Ie rayon de flechissement, Ia configuration de l ancrage des etriers, la longueur du bout depassant la partie flechie, etPangle des etriers. Base sur les resultats de cette etude, des equations de conception pour Ie cisaillement pour des poutres en beton renforcees de PRF, convenables pour Ie code de Ia Canadian Standard Association (CSA), sont proposees.La fiabilire des equations proposees est evaluee en utitisant des resultats de tests sur 118 poutres examinees pard autres.Mots e s : cisaiUement, polymeres renforces de fibres, PRFC, fissures, PRFV, desequilibre, etriers, capacite en flechissement. /[Traduit par la Redaction]

Received July 30, 1999. Revised manuscript accepted Decenlber 22, 1999.E. Shehata. Wardrop Engineering Inc., Winnipeg, MB R3C 4M8, Canada.R. Morphy. Crosier Kilgour Partners, Winnipeg, MB R3C IM5, CanadaS. Rizkalla.1 The Canadian Network of Centres of Excellence on Intelligent Sensing for Innovative Structures (ISIS Canada),The University of Manitoba, Winnipeg, MB R3T 5V6, Canada.Written discussion of this article is welcomed and will be received y the Editor until February 28, 2001.lAuthor to whom all correspondence should be addressed (e-mail: [email protected]).

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ith an estimated 80 000 Canadian bridges and 230 000in need of serious repairon building bridges that lastof maintenance is emerging. Fibrepolymers FRPs) are a corrosion-free material

ome the deterioration of concrete structures due to corof steel reinforcement. Stirrups used for shear rein

of FRP as shear

of concrete members reinan experiof Manitoba,of FRP stir-first phase of the experimental program evaluates

of a single FRP stirrup as influenced by theof the experiof failure, shearof concrete beams reinforced with

on the findings of this investigation, de

CSA A23.3 CSA 1994). Expression foris proposed.of the proposed equations is evaluated usingof 116 beams tested by others. Strain limits

in con

he study provides design guidelines for the use of CFRPd GFRP stirrups as shear reinforcement for concrete strucof the research are presented in a format ofons proposed to the CSA design code to predictof FRP stirrups and the shear strengthconcrete beams reinforced with FRP. The information isinof the Code cur

by the CSA Technical Committee for deof concrete structures reinforced with FRP.properties /

wo types of FRP stirrups were used as shear reinforceof th CFRP,

in this study are sum1. CFRP Leadline bars, produced bylOx 5 mm) with a I-mm epoxy-resin coat toUV) radiation or

ated. The carbon fibres were pre-bent in th form ofTwo different configura-

Can. J. Civ. Eng. Vol. 27 2tions of the Leadline stirrups were used in this program, asshown in Fig. 1.The carbon fibre composite cables CFCC), produced byTokyo Rope, Japan, have three different sizes: 7.5-mm 7-wire cable, 5-mm solid cable, and 5-mm 7-wire cable. TheCFCC stirrups were delivered prefabricated. It was reportedthat the pre-pregnated strands were bent over metal bars tothe required bend radius and then the epoxy-resin matrixwas heated to harden. This process was evidenced by theflattened zone at the bend location. The configuration of theCFCC stirrups used in this program is shown in Fig. 1.GFRP stirrups, commercially known as C-BAR, were alsoused in this program. C-BAR stirrups, produced by MarshallIndustries Composites Inc., Lima, Ohio, have a nominal diameter of 12 mm. The mechanical properties of the 12-mmC-BAR reinforcing bar are given in Table 1. The C-BARstirrups were delivered prefabricated. The C-BAR bars werebent during the curing process of the impregnated glassfibres. Curing included a heating process that could affectthe strength capacity of the bend section. The configurationof the C-BAR stirrups used in this program is given inFig. 1. The steel stirrups used in this program as shear reinforcement in the control specimens were made of 6.35-mmdiameter deformed steel bars.Fifteen-millimetre, seven-wire CFCC and steel strandswere used as flexural reinforcement for the beam specimenstested in this program and their geometrical and mechanicalproperties are given in Table I. Concrete was provided by acommercial supplier perimeter Concrete Ltd.) and all of thetest specimens were cast in place in the laboratory. The target compressive strength of the concrete was 35 MPa after28 days. Nine concrete cylinders were cast from each batch.Six cylinders were tested in compression, three cylinders after 28 days and three cylinders on the day of testing of eachbeam. The average compressive strength of the concrete cylinders ranged between 33 and 54 MPa at the time of testing.The remaining three cylinders were tested in tension. Theaverage tensile strength, based on the split-cylinder test,ranged from 3.0 to 4.0 MPa.

xperimental programanel specimensA total of 42 specially designed specimens, using different types of CFRP, GFRP, and steel stirrups, were tested to

study the bend effect on the strength of FRP stirrups. Theconfigutation and dimensions of a typical specimen areshown in Fig. 2. The specimens were designed to representthe variation of th bend radius, rb, for standard hook stirrups Type A) and continuous stirrups Type B), as shown inFig. 2. For Type A stirrups, the anchored end was debondedto simulate the performance of standard hook stirrups asshown in Figs. 1 and 2b In Type B, the stirrups weredebonded at the continuous end as shown in Figs. I and 2bThe debonding length of the stirrups within the blocks wasachieved by using plastic tubes secured in place using ducttape. Other variables considered in this phase are the material type, the effective bar diameter, de de = i4Ab/1t , andthe tail length, J; as defined in Fig. 2. Detaile informationabout the bend specimens is given in Table 2. The test setupconsisted of a hydraulic jack, used to apply the relative dis-

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t al. 86

of FRP and steel bars used in the experimental program.CFRP CFRP CFCC SteelLeadline U - 5.0 7-wire 7-wire 7-wire GFRP Bar StrandShear Shear Shear Shear Flexure Shear Shear Flexure

db (mm) 5xlO 5.0 5.0 7.5 5 12.0 6.35 5b (mm2) 38.48 15.20 10.10 30.40 113.6 113 31.67 140

d (mm) 7.0 4.40 3.59 6.22 12.0 12.0 6.35 13.4a (MPa) 1800 1842 1782 1875 1750 713 6

b 59 bC (MPa) 1730 2170 1810 1910 2200 640 66 b 1860

modulus, (GPa) 137 143 137 137 137 4 206 200En (%) 1.26 1.52 1.32 1.40 1.60 1.56 2.0 4.0

Guaranteed strength according to the manufacturer.byield strength.Based on tension tests.

of FRP stirrups used in the experimental program.

and a load cellall specimensan average compressive strength of 5 MPa at 28 days.Ten specially designed specimens using different types ofon the strength of FRP stirrups. Two additional speci

as controlmens. Each specimen was reinforced with two stirrupsat an angle ewith the central axis of the panel. Thees considered in this experimeIit3l phase were the ma-

of inclination, eof two

of the specimen. The configurationtest setup of a typical specimen are shown in Fig. 3.

A total of ten reinforced concrete beams were tested: fourbeam with steel stirrups,one beam without shear reinforcement as a control spec-

imen. The tested beams had a T cross section with a totaldepth of 560 mm and a flange width of 600 mm as shownin Fig. 4. Eight beams were reinforced for flexure with six15-mm, 7-wire steel strands. Two beams were reinforced forflexure using seven 15-mm, 7-wire CFCC strands. Allbeams were designed to fail in shear while the flexural steeltendons are designed to remain in the elastic range to simulate the linear behaviour of FRP. The beam without shear reinforcement was used as a control beam to determine theconcrete contribution to the shear resistance, including thedowel action of the steel strands used for flexural reinforcement, which are normally weaker than conventional steelbars. Each beam consisted of a 5.0-m simply supported spanwith 1.0-m projections from each end to avoid bond-slipfailure of the flexural reinforcement. Only one shear spanwas reinforced with FRP stirrups, while the other shear spanwas reinforced using two 6.35-mm diameter closely spacedsteel stirrups, as shown in Fig. 4. The variables consideredwere the material type of stirrups, stirrup spacing, s and thematerial type of flexural reinforcement. Detailed informationabout the tested beam specimens is given in Table 3. The

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of bend specimens: a) plan,stirrup anchorage configuration, and c) photo.

~~ g o

200

Type A - standard hook

200

Type B - continuous end

MTS cyclic loadingf the beam included linear voltage displacement transduc

in the stirrups. PIin three directions at different locations in the shear5 to e v l u t ~ the shear deformationsof the shear crack width and the slide along the

est resultsof FRP stirrups

ffect o bend radiusThe strength ofFRP stirrups may be as low as 35 of therb, and tail length, as given in Table 2. In general,rb, re-

Can. J. Civ Eng. Vol 27, 2000Fig. 3. Details and test setup of kink specimens: a) plan andb) photo.a)

(b)

EE8

steel stirrups@4Omm

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at 863able 2. Details and test results of bend specimens.

Stirrup Stress atStirrup Yb l ~ d ; anchorage failure Mode ofmaterial type mm) yb/de (mm) type Ifv MPa) Irvllfuv failureCFRP 20 3 21 3 A 632 0.35 S-RBLeadline 20 3 42 6 A 639 0.35 S-Rstirrups 20 3 63 9 A 737 0.41 S-RB20 3 84 12 A 728 0.40 S-RB20 3 120 18 A 793 0.44 S-R20 3 B 715 0.40 R-B50 7 21 3 A 1057 0.59 R-B50 7 42 6 A 1235 0.69 R-B50 7 63 9 A 1062 0.59 R-B50 7 84 12 A 1053 0.58 R-B50 7 120 18 A 962 0.53 R-B50 7 B 981 0.55 R-BCFCC 15 4.2 45 9 A 916 0.51 R-B7-wire 15 4.2 B 1455 0.82 R-B5-mmCFCC 15 3.4 45 9 A 983 0.53 R-BU 5mm 15 3.4 B 1187 0.64 R-BCFCC 20 3.2 45 6 A 798 0.43 R-B7-wire 20 3.2 22.5 3 A 789 0.42 R-B7.5-mm 30 4.8 45 6 A 1159 0.62 R-B

30 4.8 67.5 9 A 1475 0.79 R-B30 4.8 90 12 A 1846 0.98 R-B30 4.8 150 20 A 1902 1.01 R-B30 4.8 B 1798 0.96 R-BGFRP 50 4 72 6 A 400 0.56 R-SC-BAR 50 4 145 12 A 345Q 0.48 R-B

50 4 B 347b 0.49 R-BSteel 20 3 40 6 A 593 0.99 Y-B20 3 B 669 1.12 Y-BNote: Failure modes: R-S, rupture along the straigbtportion between the concrete blocks; R-B, rupture at the bend; R-D,rupture at the end of the debonded length inside the concrete block; S, slippage of the bonded part of the .stirrup; S-RB,l lippage of the bonded part of the .stirrup, followed by rupture at the bend; R-BD, rupture of some fibres at the bend zone

and others at the end of the debonded length; Y-S, yield along the straight portion; and Y-B, yield at the bendAverage of six specimens.hAverage often specimens.of at least 50% of the strength parallel to the

o stirrup anchorage and tail length .Significant reduction in the CFCC stirrup capacity wasin Type A anchored with a ,standard tail length of

b as compared to Type B anchored, as shown in Table 2.to possible slip at theof failure at a lower stress level.n increase in the tail length, I; resulted in an increase inin Table 2. For a tail length toI de equal or higher than 12, theof Type A anchored CFCC stirrups is as high asof Type B anchored stirrups. For Leadline stirrups, anI; resulted in a slight increase inof 70 nnn (lOde) is sufficient to

of the stirrups using rtJde of 7.0.of the GFRP stirrups tested in this study was

either 6de or 12de. The bend capacity of such a minimum taillength of 6de was found to be equal to or higher than 48% ofthe guaranteed tensile strength parallel to the fibres, whichalmost equals the average bend capacity of Type B stirrups.Therefore, it is reconnnended to use a tail length of 6de or70 nnn whichever is greater.Effect o crack angleAll kink specimens failed either by rupture of FRP stirrups or yield of steel stirrups at the crack location. The relationship between the measured stress in the direction of thefibres ofFRP stirrups at failure,ftv> and the stirrup angle, eis shown in Fig. 7. There is no clear trend for an increase ordecrease in the stress at failure with the variation of the angle ewithin the range used in this study for both GFRP andCFRP stirrups. The average failure stress to ultimatestrength parallel to the fibres ratio was found to be 0.81 witha standard deviation of 0.06. Figure 7 shows that for kink

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Can. J. Civ. Eng. Vol. 27, 2of beam specimens.

PI

S mmIi 6 mm 6 mm

1135 1 1135 1

3. Details and test results of beam specimens.Shear illtimate Average

Ebdld = cracking shear Max stirrup stirrupStirrup fbeniEfy Spacing f l force cr Vtcst strain at strain at Mode ofmaterial (%) s (MPa) (kN) (kN) failure (%) failure (%) failurec54 67.5 186.5 DT

dt h 54 70.0 272.5 0.95 0.44 SYdl2 54 75.0 277.5 1.05 0.77 SRLeadline 0.63 dt3 54 75.0 341.0 1.04 0.71 SRdt4 51 75.0 375.5 0.80 0.55 SRdl 54 75.0 292.0 1.20 0.91 SR12 mm 0.85 d 3 33 65.0 312.5 0.83 0.53 SCdt4 33 65.0 311.5 0.78 0.48 SC0.63 dt3 50 67.5 305 0.90 0.65 SRGFRP 0.85 dt3 50 67.5 304.5 1.07 0.85 SR

The first letter irulicates flexur.u reinforcement type (S, steel; C, CFRPI; the second letter indicates SbellC reinforcement type (N, no siirrups; S, steel;CFRP; G, GFRP).is the effective beam depth, d = 470 mm.nT, diagonal tension failure; SY, shear failure initiated by yielding of the steel stirrups; SR, shear failure initiated by rupture of the FRP stirrups; and

in a FRP stirrup at failure could be asof the guaranteed tensile strength parallel to thees. Meanwhile, it was observed for bend tests (Table 2)at failure could be as low as 35% of the guarthe fibres. Therefore, it

on strength capacity of

of FRP stirrups in beam actionAll the tested beams failed in shear before yielding of therupture of CFRP strands. No slip ofduring any of theShear failure of beams reinforced with FRP stirby rupture of the FRP stirrups at the

bend (shear tension failure), as shown in Fig. 8, or bycrushing of the concrete in the shear span (shear compression failure). A summary of the beam test results is presented in Table 3.Contribution o FRP stinups

The shear capacity of a concrete beam without shear reinforcement, V= is determined as the applied load that causesthe initiation of the first shear crack. The contribution of theFRP stirrups to the shear carrying capacity of concretebeams was evaluated based on the difference between themeasured shear strength, f;;est and the measured shear at theinitiation of the first crack, Vcr-Based on a traditional 45

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al.

of bend radius, rb' on strength capacity of thefbcnd

1 A I ; = = ~ = = = = = = = = = = = = = = = = = = J~ d = ~ [L_L_e_ad_ _in_e____C_F_C_C____ _G_R _ P ~1.28

0.6OA

0.2

t\.. db . ~ 7r rh..... ............ T - ~ - - ...................I .j.

0 - - - - - - - - ~ - - ~ - - ~ - - - - 4 _ - - _ - - - - - - - ~o 2 6 8

ffv, was deterI _ (f ;est - v asJfv - Afvd

Afv is the area of the FRI' ~ t i r r u p s s is the stirrupd is the effective depth of the beam. Figure 9

of FRP stirrups in beam actionof the strength parallel to the fibres,

ofFRI stirof the stirrups,

lower contribution of the FRP stirrups, as9. For beams reinforced with CFRP strandsfOf the corre-

86

Fig 7. Effect of stirrup angle, e, on capacity of the FRP stirrups

O - ~ ~ - - ~ ~ ~ r - - ; - ~ ~ _ _ _ - - ~ ~ ~o 10 20 30 40 50 60 70 80 90II

sponding beam reinforced with steel strands. This could attribute to the reduction of the concrete contribution component due to the use of CFRI' as flexural reinforcements, awill be discussed in the following section.Effect of FRP longitudinal reinforcementThe use of CFRP strands as flexural reinforcement in twbeams resulted in a reduction in the shear capacity, compared to similar beams reinforced with steel strands. Thcontribution of FRP stirrups, V. f at any load level is determined based on the average strain in stirrups measured bthe strain gauges. The concrete contribution for memberwith CFRP flexural reinforcements, Vcf is calculated aV f = Va V f where Va is the applied shear. The relationshibetween the applied shear and the components of the shearesisting mechanism Vcf and V f is presented in Fig. 10 fothe beams reinforced with steel or CFRP strands for flexureand CFRP stirrups spaced at d/3. Test results indicate thathe concrete contribution, Vc for the beam reinforced witsteel strands, at any load level up to failure, is higher than

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at failure.

of stirrup spacing on effective capacity of FRP

CFRP0.7

0 5\ _ ~ \

0.25 j.t0 2

Beams with CFRPflexural strands

0 3 0 4sId

0 5 0 6

Vcr for (he corresponding beam

of FRP flexuralofin the concrete contribution to

VCf

The shear cracking load was monitored by three tech-of cracks. The

Can. J. Civ. Eng. Vol. 27 2000

Fig. 10. Effect of flexural reinforcement on shear resisting com-ponents.

4 0 0 ~ ~

~300

I I )coaEg 200Olc'Wr;;1 ?:;; 100.s::/)

c = shear resisting force provided y conorete / _/ /V -f =shear resisting force provided y concrete in / P Ii min / /

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et al.

Y., AlmusaIlam, T., and Amjad, M. 1996.of shear stresses in concrete beams reinforced by

of the Second International ConferenceAdvanced Composite Materials for Bridges and StructuresY., and Almusal1am, T. 1997. Shear de

of GFRP bars. Proceedings of the Third International Sym

1992. Composite reinforcing bars: assessing their use inIn Canadian highway

of the Canadian Highway Bridge Design Code.of concrete structures for buildings. Standard

K., and Waldron, P. 1997. Tests on conof the Third International Symposium on Non(FRP) Reinforcement for Concrete Structures, October

of coninEdited by A. Machida. Japa

of Civil Engineers, Tokyo, Japan, pp. 1-80.and Tanigaki, M. 1993. Shear perfor

of concrete beams reinforced with FRP stirrups. In ACIEdited y A. Nanni and C. Dolan. American ConcreteZ., Morphy,Fam, A., Williams, B., Rizkalla, N., and Liu, S. 1997. Mate

of C_BARfM reinforcing rods. Research reportof Manitoba, Winnipeg, Man.

strucof Civil and Geological Engiof Manitoba, Winnipeg, Man.Wakui, H. 1993. Shear capacity of RC and PCIn ACI SP-138. Edited by A.

P., Kumar, S., and GangaRao, H. 1996. Shear and ductilityof concrete beams reinforced with GFRP bars. Pro

of the Second International Conference on Advanced

andof prestressed concrete beams using FRP rods

prestressing tendons. In ACI SP-138. Edited by A. Nanni andand Suzuki, H. 1995. Shear behaviour of

by FRP rods as longitudinal and. Non-metallic FlU reinforcement for conIn Proceedings of the Second InternationalEdited by L. Taerwe. E FN

of symbolsa shear span, rom

Afv total cross-sectional area of FRP stirrup within distances rom2bw web width of the beam, romd effective depth of cross section, rom

87db diameter of the reinforcing bar, romde effective bar diameter (de = ~ 4 A b / 1 t , mmEft elastic modulus of FRP longitudinal reinforcement, MPaEfv elastic modulus of FRP shear reinforcement, MPaEs reference elastic modulus of steel, 200 GPa

f end strength capacity of the bend portion of the FRP stirrup MPaf concrete compressive strength, MPa

ffuv guaranteed tensile strength of the FRP stirrups parallelto the fibres, MPafrv stress in the FRP stirrups at failure load, MPay yield strength of steel stirrups, MPah overall depth of the beam cross section, mm

hb height of the FRP bar hb = db for Totmd bar), mmtail length beyond the bend portion of the FRP stirrup, rom

rb bend radius of FRP reinforcement, nuns spacing of the shear reinforcement, nunVa applied shear load, NVc factored shear resistance attributed to concrete for

beams reinforced by steel reinforcements for flexuraland shear according to CSA 23.3-94, NVCf factored shear resistance attributed to concrete forbeams reinforced with FRP reinforcement for flexuraland shear, N

Vcr shear force at the initiation of diagonal tension crack, NVn nominal shear strength based 'on eq. [3J using materialand reduction factor of 1.0, NV f factored shear resistance for concrete beam reinforced

with FRP, NV service shear load level, NVsf factored shear resistance provided by FRP stirrups, NV est maximum shear force at failure, NVu factored shear force due to applied loads, Nvn nominal shear streSS vn = Vlbwd , MPa

vtest shear stress based on measured shear capacity, MPaw crack width, nun

Wmax maximum shear crack width, mmEfv average strain in the stirrups at service loadangle of the shear crack with the longitudinal axis of the

beamA 1.0 for normal weight concrete (CSA standards)Pc flexural reinforcement ratioPc. FRP shear reinforcement ratio Pcv = ArvlbwS)

Pfv . minimum FRP shear reinforcementp.v steel shear reinforcement ratio Psv = A,jhwSPsvm. minimum steel shear reinforcement., s resistance factors for concrete and steel, respectively

r strength reduction factor for shear design of membersreinforced with FRP

Appendix 2 Design exampleA normal weight concrete beam is designed to carry a service live load of 15 kN m and a live load of 15 kN m in addition to its own weight over a 6.7 m single span. The beamcross section and longitudinal reinforcement are given below. Determine the required amount of shear reinforcementusing GFRP C-BAR stirrups

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Dimensions: bw = 300 mm, d = 600 mm, h = 660 mm,span = 6700 mmConcrete strength: fc = 40 MPaFlexural reinforcement: An = 1988 mm2, pft = rlbwd0.01104 Eft = 44.8 GPaShear reinforcement: ffuv = 713 MPa for #10 and #12GFRP stirrups; Efv = 41 GPa

wd = 0.30 x 0.66 x 23.5 = 4.65 kN/mWu = 1.25wd + 1.5wl

= 1.25 x 4.65 + 1.5 x 30 = 50.8 kN/mmoment at critical section:

Vu = wu(span/2 - a= 50.8 x (6.7/2 - 0.70) = 134.6 kN

Mu = Wu x span/2 x a - wua2/2= 50.8 x 6.7/2 x 0.70 - 50.8 x (0.70)2/2= 106.7 kN'm

3OOx600= 0.2 x 1.0 x 0.6 x 40 x = 136.6 kN1000v f =v fi t1 = 1 3 6 6 ~ 4 4 8 =64.7 kN (eq. [2])V s 200

VCf = 64.7 kN < Vu, shear reinforcement is needed.shear reinforcement (eq. [6]):V fmin = Yc(l- .JEll/ Es

= 136.6 x (1 - .Jr-44-.8-/2-0-0 =71.9 kNPfv = Vsfm.,Ihw d = 71 900/300 x 600 = 0.00140

m OAfruv 0.4 x 713> 0.06.,jJ: = 0.06,/40 = 0.00133

O.4ffuv 0.4 x 713

/

Can. J. Clv. Eng. Vol. 27, 2Required shear reinforcement:

V.fd = Vu - Vcfd = 134.6 - 64.7 = 69.9 kNUsing eq. [5],

V f = O.4+ f ffuv AfvdsTake s = 200 nun,

Afv = 69900 x 200/(0.4 x 0.75 x 713 x 600)= 108.9 mm2

use GFRP C-BAR stirrups #10 (2 legs),Afv = 156 mm2

Check shear reinforcement ratio:156Pfv. = = 0.0026 > Pfvm; = 0.00133 o.k.- 200 x 300

Check shear compression mode:Vu = cf + (O.8 Mt.J7[hwd J.

=64.7 + (0.8 x 0.6x..[4ij x 300x 0 0 ~ 41. 200=259.7 kN > u =134.6 kN o.k.

Check serviceability requirement:Sustained service load,Wscr = Wd + O.50wl

= 4.65 + 0.50 x 30 = 19.65 kN/mVser = 19.65 x (6.7/2 - 0.70) = 52.1 kNVser = 52.1 kN < VCf = 64.7 kN o.k.

Therefore, the beam is not cracked in shear under serviceload level.Detailing of stirrups:The stirrup detailing is provided according to the proposed guidelines. The IO-mm GFRP C-BAR stirrups shouldhave a bend radius of 50 mm and a tail length of 70 mmbeyond the bend.

fibre reinforced polymer shear reinforcement for concrete member

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