Fibre reinforced polymer shear reinforcement for concrete members: behaviour and design guidelines

Emile Shehata, Ryan Morphy, and Sami Rizkalla

859

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 beams included four beams reinforced with carbon fibre reinforced polymer (CFRP) stirrups, four beams reinforced with glass fibre reinforced polymer (GFRP) stirrups, one beam reinforced with steel stirrups, and one control beam without shear reinforcement. The variables were the material type of stirrups, the material type of the flexural reinforcement, and the stirrup 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 by the kinking action due to inclination of the diagonal shear crack with respect to the direction of the stirrups. A total of 52 specially designed panel specimens were tested to investigate the bend and kinking effect on the capacity of FRP stirrups, 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, shear design 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 en polymere renforce de fibres (PRF) pour Ie renforcement en cisaillement de structures en beton. Un total de dix poutres en beton arme a grande echelle ont ere examinees pour etudier la contribution d'etriers en PRF dans Ie mecanisme d'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 renforcee d'etriers en acier et une poutre de controle sans renforcement en cisaillement. Les variables furent Ie type de materiau des 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 la resistance en ten­sion paralU:le aux fibres, est introduite en flechissant les barres de PRF en une configuration d'etrier, et par I'action de desequilibre due a I'inclinaison de la fissure de cisaillement diagonale par rapport a la direction des etriers. En meme temps que deux specimens de controle renforces d'etriers en acier, un total de 52 specimens de panneaux specifique­ment con';US ont ere 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, et Pangle des etriers. Base sur les resultats de cette etude, des equations de conception pour Ie cisaillement pour des pou­tres en beton renforcees de PRF, con venables 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 par d'autres.

Mots eMs : 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, Canada. S. 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 by the Editor until February 28, 2001.

lAuthor to whom all correspondence should be addressed (e-mail: rizkall@cc.umanitoba.ca).

Can. J. Civ. Eng. 27: 859-872 (2()()(}) <9 2000 NRC Canada

860

Introduction

With an estimated 80 000 Canadian bridges and 230 000 bridges in the United States in need of serious repair (Bedard 1992), a new emphasis on building bridges that last longer with a minimum of maintenance is emerging. Fibre­reinforced polymers (FRPs) are a corrosion-free material and have recently been used as flexural reinforcement to overcome the deterioration of concrete structures due to cor­rosion of steel reinforcement. Stirrups used for shear rein­forcement are normally located as an outer reinforcement with respect to the flexural reinforcement and, therefore, are more susceptible to severe environmental effects due to the minimum concrete cover provided. The use of FRP as shear reinforcement for concrete structures has not yet been ex­plored enough to establish a rational model to predict the shear behaviour and strength of concrete members rein­forced with FRP stirrups. This paper summarizes an experi­mental program conducted at The University of Manitoba, Canada, to examine the structural performance of FRP stir­rups. The first phase of the experimental program evaluates the strength of a single FRP stirrup as influenced by the bend and the crack angle. The second phase of the experi­mental program investigates the modes of failure, shear strength, and behaviour of concrete beams reinforced with FRP stirrups. Based on the findings of this investigation, de­sign guidelines for concrete beams reinforced with FRP as shear reinforcement are proposed. The shear design equa­tions are formulated to suit the Canadian Standards Associa­tion design code, CSA A23.3 (CSA 1994). Expression for the minimum FRP shear reinforcement ratio is proposed. The reliability of the proposed equations is evaluated using measured values of 116 beams tested by others. Strain limits for the FRP stirrups to control the shear crack width in con­crete beams are proposed

Research significance

The study provides design guidelines for the use of CFRP and GFRP stirrups as shear reinforcement for concrete struc­tures. Findings of the research are presented in a format of design equations proposed to the CSA design code to predict the strength capacity of FRP stirrups and the shear strength of concrete beams reinforced with FRP. The information is valuable for designers using FRP for shear reinforcement in concrete structures and for the development of the Code cur­rently undertaken by the CSA Technical Committee for de­sign of concrete structures reinforced with FRP.

Material properties /

Two types of FRP stirrups were used as shear reinforce­ment, CFRP and GFRP. Steel and CFRP strands were used as flexural reinforcement. The characteristics of the CFRP, GFRP, and steel reinforcement used in this study are sum­marized in Table 1. CFRP Leadline bars, produced by Mitsubishi Chemical Corporation, Japan, have a rectangular cross section (lOx 5 mm) with a I-mm epoxy-resin coat to protect the fibre core from ultraviolet (UV) radiation or chemical attack. The CFRP Leadline stirrups were delivered prefabricated. The carbon fibres were pre-bent in the form of stirrups prior to the curing process. Two different configura-

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

tions of the Leadline stirrups were used in this program, as shown in Fig. 1.

The carbon fibre composite cables (CFCC), produced by Tokyo Rope, Japan, have three different sizes: 7.5-mm 7-wire cable, 5-mm solid cable, and 5-mm 7-wire cable. The CFCC stirrups were delivered prefabricated. It was reported that the pre-pregnated strands were bent over metal bars to the required bend radius and then the epoxy-resin matrix was heated to harden. This process was evidenced by the flattened zone at the bend location. The configuration of the CFCC stirrups used in this program is shown in Fig. 1.

GFRP stirrups, commercially known as C-BAR, were also used in this program. C-BAR stirrups, produced by Marshall Industries Composites Inc., Lima, Ohio, have a nominal di­ameter of 12 mm. The mechanical properties of the 12-mm C-BAR reinforcing bar are given in Table 1. The C-BAR stirrups were delivered prefabricated. The C-BAR bars were bent during the curing process of the impregnated glass fibres. Curing included a heating process that could affect the strength capacity of the bend section. The configuration of the C-BAR stirrups used in this program is given in Fig. 1. The steel stirrups used in this program as shear rein­forcement in the control specimens were made of 6.35-mm diameter deformed steel bars.

Fifteen-millimetre, seven-wire CFCC and steel strands were used as flexural reinforcement for the beam specimens tested in this program and their geometrical and mechanical properties are given in Table I. Concrete was provided by a commercial supplier (perimeter Concrete Ltd.) and all of the test specimens were cast in place in the laboratory. The tar­get compressive strength of the concrete was 35 MPa after 28 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 each beam. 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. The average tensile strength, based on the split-cylinder test, ranged from 3.0 to 4.0 MPa.

Experimental program

Panel specimens A total of 42 specially designed specimens, using differ­

ent types of CFRP, GFRP, and steel stirrups, were tested to study the bend effect on the strength of FRP stirrups. The configutation and dimensions of a typical specimen are shown in Fig. 2. The specimens were designed to represent the variation of the bend radius, rb, for standard hook stir­rups (Type A) and continuous stirrups (Type B), as shown in Fig. 2. For Type A stirrups, the anchored end was debonded to simulate the performance of standard hook stirrups as shown in Figs. 1 and 2b. In Type B, the stirrups were debonded at the continuous end as shown in Figs. I and 2b. The debonding length of the stirrups within the blocks was achieved by using plastic tubes secured in place using duct tape. Other variables considered in this phase are the mate­rial type, the effective bar diameter, de (de = i4Ab/1t), and the tail length, J;, as defined in Fig. 2. Detaile information about the bend specimens is given in Table 2. The test setup consisted of a hydraulic jack, used to apply the relative dis-

to 2000 NRC Canada

Shehata et al. 861

Table 1. Properties of FRP and steel bars used in the experimental program.

CFRP CFRP CFCC Steel

Leadline U - 5.0 7-wire 7-wire 7-wire GFRP Bar Strand

Shear Shear Shear Shear Flexure Shear Shear Flexure Diameter, db (mm) 5xlO 5.0 5.0 7.5 15 12.0 6.35 15 Area, Ab (mm2) 38.48 15.20 10.10 30.40 113.6 113 31.67 140 Effective diameter, d. (mm) 7.0 4.40 3.59 6.22 12.0 12.0 6.35 13.4 Strengtha (MPa) 1800 1842 1782 1875 1750 713 600b 1590b

Ultimate strengthC (MPa) 1730 2170 1810 1910 2200 640 660b 1860 Elastic modulus, E (GPa) 137 143 137 137 137 41 206 200 Maximum En (%) 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.

Fig. 1. Configuration of FRP stirrups used in the experimental program.

placement between the two concrete blocks, and a load cell to measure the applied load. Concrete used for all specimens had an average compressive strength of 50 MPa at 28 days.

Ten specially designed specimens using different types of CFRP Leadline and GFRP were tested to study the kink ef­fect on the strength of FRP stirrups. Two additional speci­mens reinforced with steel stirrups were tested as control specimens. Each specimen was reinforced with two stirrups located at an angle e with the central axis of the panel. The variables considered in this experimeIit3l phase were the ma­terial type (CFRP or GFRP) and the angle of inclination, e, varying between 0° and 60°. The test setup consisted of two hydraulic jacks connected to the same air pump to apply equal load on both sides of the specimen. The configuration and test setup of a typical specimen are shown in Fig. 3.

Beam specimens A total of ten reinforced concrete beams were tested: four

beams reinforced with CFRP Leadline stirrups, four beams with GFRP C-BAR stirrups, one beam with steel stirrups, and one beam without shear reinforcement as a control spec-

imen. The tested beams had a T cross section with a total depth of 560 mm and a flange width of 600 mm, as shown in Fig. 4. Eight beams were reinforced for flexure with six 15-mm, 7-wire steel strands. Two beams were reinforced for flexure using seven 15-mm, 7-wire CFCC strands. All beams were designed to fail in shear while the flexural steel tendons 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 the concrete contribution to the shear resistance, including the dowel action of the steel strands used for flexural reinforce­ment, which are normally weaker than conventional steel bars. Each beam consisted of a 5.0-m simply supported span with 1.0-m projections from each end to avoid bond-slip failure of the flexural reinforcement. Only one shear span was reinforced with FRP stirrups, while the other shear span was reinforced using two 6.35-mm diameter closely spaced steel stirrups, as shown in Fig. 4. The variables considered were the material type of stirrups, stirrup spacing, s, and the material type of flexural reinforcement. Detailed information about the tested beam specimens is given in Table 3. The

© 2000 NRC Canada

862

Fig. 2. Details and test setup of bend specimens: (a) plan, (b) stirrup anchorage configuration, and (c) photo.

(a)

(b)

(c)

E~ ~g N­o

200

Type A - standard hook

200

Type B - continuous end

beams were tested in four-point bending, with 2.0-m con­stant moment region. A closed-loop MTS cyclic loading testing machine was used to apply the load. Instrwnentation of the beam included linear voltage displacement transduc­ers (LVDTs) for deflection measurement. Electrical strain gauges were used to measure the strain in the stirrups. PI gauges with 200 mm gauge length were mounted on the web surface in three directions at different locations in the shear span, as shown in Fig. 5, to evaluat~ the shear deformations in terms of the shear crack width· and the slide along the crack.

Test results

Strength of FRP stirrups

Effect of bend radius The strength ofFRP stirrups may be as low as 35% of the

strength parallel to the fibres,ffuV' depending on the bend ra­dius, rb, and tail length, l~, as given in Table 2. In general, test results indicate that a decrease in the bend radius, rb, re-

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

Fig. 3. Details and test setup of kink specimens: (a) plan and (b) photo.

(a)

(b)

E E 8

steel stirrups @4Omm

3-

"'I <f--_____ .L7.><oo"-m=m'--_____ .... _1

1OM

14 240 mm _I

xI+ Section x-x

duces the bend capacity. The strength reduction is attributed to the residual stress concentration at the bend zone. The ra­dii of the bend used in this study range from 3.0 to 7.0 times the effective bar diameter, de. Figure 6 indicates that the bend capacity,fbend, varies greatly for the same type of rein­forcing fibre. The Japanese Society of Civil Engineers (JSCE 1997) recommends the use of the following equation to evaluate the strength capacity of an FRP bent bar:

[1] fbend = 0.05 rb + 0.30 ffuv de

Test results indicate that eq. [1] provides conservative pre­diction for both the CFCC and GFRP stirrups with sufficient tail length, I;, presented in the following section. However, it was found that eq. [1] overestimates the bend capacity of the CFRP Leadline stirrups even with large bend radius, rb'

Therefore, it is recommended to use a minimum bend radius not less than four times the effective bar diameter or 50 mm, whichever is greater, for FRP stirrups in order to achieve a

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Shehata et at. 863

Table 2. Details and test results of bend specimens.

Stirrup Stress at Stirrup Yb l~

l~/d; anchorage failure Mode of

material type (mm) yb/de (mm) type Ifv (MPa) Irvllfuv failure

CFRP 20 3 21 3 A 632 0.35 S-RB Leadline 20 3 42 6 A 639 0.35 S-R stirrups 20 3 63 9 A 737 0.41 S-RB

20 3 84 12 A 728 0.40 S-RB 20 3 120 18 A 793 0.44 S-R 20 3 B 715 0.40 R-B 50 7 21 3 A 1057 0.59 R-B 50 7 42 6 A 1235 0.69 R-B 50 7 63 9 A 1062 0.59 R-B 50 7 84 12 A 1053 0.58 R-B 50 7 120 18 A 962 0.53 R-B 50 7 B 981 0.55 R-B

CFCC 15 4.2 45 9 A 916 0.51 R-B 7-wire 15 4.2 B 1455 0.82 R-B 5-mm

CFCC 15 3.4 45 9 A 983 0.53 R-B U-5mm 15 3.4 B 1187 0.64 R-B

CFCC 20 3.2 45 6 A 798 0.43 R-B 7-wire 20 3.2 22.5 3 A 789 0.42 R-B 7.5-mm 30 4.8 45 6 A 1159 0.62 R-B

30 4.8 67.5 9 A 1475 0.79 R-B 30 4.8 90 12 A 1846 0.98 R-B 30 4.8 150 20 A 1902 1.01 R-B 30 4.8 B 1798 0.96 R-B

GFRP 50 4 72 6 A 400 0.56 R-S C-BAR 50 4 145 12 A 345Q 0.48 R-B

50 4 B 347b 0.49 R-B

Steel 20 3 40 6 A 593 0.99 Y-B 20 3 B 669 1.12 Y-B

Note: 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 bend .

• Average of six specimens. hAverage often specimens.

stirrup capacity of at least 50% of the strength parallel to the fibres (Shehata 1999).

Effect of stirrup anchorage and tail length . Significant reduction in the CFCC stirrup capacity was

observed in Type A anchored with a ,standard tail length of 6db, as compared to Type B anchored, as shown in Table 2. The strength reduction is attributed to possible slip at the bend, leading to initiation of failure at a lower stress level. An increase in the tail length, I;, resulted in an increase in the stirrup capacity, as given in Table 2. For a tail length to effective diameter ratio, I;/de, equal or higher than 12, the capacity of Type A anchored CFCC stirrups is as high as that of Type B anchored stirrups. For Leadline stirrups, an increase in the tail length, I;, resulted in a slight increase in the capacity. A tail length of 70 nnn (lOde) is sufficient to develop the bend capacity of the stirrups using rtJde of 7.0. The tail length of the GFRP stirrups tested in this study was

either 6de or 12de. The bend capacity of such a minimum tail length of 6de was found to be equal to or higher than 48% of the guaranteed tensile strength parallel to the fibres, which almost equals the average bend capacity of Type B stirrups. Therefore, it is reconnnended to use a tail length of 6de or 70 nnn, whichever is greater.

Effect of crack angle All kink specimens failed either by rupture of FRP stir­

rups or yield of steel stirrups at the crack location. The rela­tionship between the measured stress in the direction of the fibres ofFRP stirrups at failure,ftv> and the stirrup angle, e, is shown in Fig. 7. There is no clear trend for an increase or decrease in the stress at failure with the variation of the an­gle e within the range used in this study for both GFRP and CFRP stirrups. The average failure stress to ultimate strength parallel to the fibres ratio was found to be 0.81 with a standard deviation of 0.06. Figure 7 shows that for kink

<C 2000 NRC Canada

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

Fig. 4. Details of beam specimens.

PI2

SOOOmm I

i 600mm 600mm

1135 1 1135 1

Table 3. Details and test results of beam specimens.

Shear illtimate Average Ebdld = cracking shear Max stirrup stirrup

Beam Stirrup fbeniEfy Spacing fl force Vcr Vtcst strain at strain at Mode of Tn" material (%) s (MPa) (kN) (kN) failure (%) failure (%) failurec

SN-O 54 67.5 186.5 DT SS-2 Steel dt2h 54 70.0 272.5 0.95 0.44 SY SC-2 CPRP dl2 54 75.0 277.5 1.05 0.77 SR SC-3 Leadline 0.63 dt3 54 75.0 341.0 1.04 0.71 SR SC-4 dt4 51 75.0 375.5 0.80 0.55 SR SG-2 GFRP dl2 54 75.0 292.0 1.20 0.91 SR SG-3 12 mm 0.85 d/3 33 65.0 312.5 0.83 0.53 SC SG-4 dt4 33 65.0 311.5 0.78 0.48 SC CC-3 Leadline 0.63 dt3 50 67.5 305 0.90 0.65 SR CG-3 GFRP 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; C, CFRP; G, GFRP).

bd 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

SC, shear compression failure.

specimens the stress in a FRP stirrup at failure could be as low as 65% of the guaranteed tensile strength parallel to the fibres. Meanwhile, it was observed for" bend tests (Table 2) that the stress at failure could be as low as 35% of the guar­anteed tensile strength parallel to the fibres. Therefore, it was concluded that the bend effect on strength capacity of FRP stirrups is more critical than the kink effect.

Behaviour of FRP stirrups in beam action All the tested beams failed in shear before yielding of the

flexural steel strands or rupture of CFRP strands. No slip of the flexural reinforcement was observed during any of the beam tests. Shear failure of beams reinforced with FRP stir­rups was initiated either by rupture of the FRP stirrups at the

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

Contribution of FRP stinups The shear capacity of a concrete beam without shear rein­

forcement, V = is determined as the applied load that causes the initiation of the first shear crack. The contribution of the FRP stirrups to the shear carrying capacity of concrete beams was evaluated based on the difference between the measured shear strength, f;;est, and the measured shear at the initiation of the first crack, Vcr-Based on a traditional 45°

IC 2000 NRC Canada

Shehata et al.

Fig. 5. Instrumentation for shear cracks and deformation.

Fig. 6. Effect of bend radius, rb' on strength capacity of the bend, fbcnd'

1AI---;-----==-~==================J

~ d.= ~ [L·_L_e_ad_'_in_e ___ -_C_F_C_C ____ A_G __ FR_P~)

1.2

" 08 ~.

~ 0.6

OA

0.2

t\.. db . ~7 r rh

..... - ............ ····························T·-·····~··········-·····-................... .

I- • • .j.

... •

0+----+----~--~--~----4_--_+----+---~

o 2 6 8

truss model, stress in the stirrup at failure, ffv, was deter­mined as follows:

[2] I' _ (f';est - v"as Jfv - Afvd

where Afv is the area of the FRI' ~tirrups, s is the stirrup spacing, and d is the effective depth of the beam. Figure 9 shows the effective stress in FRP stirrups at failure for the different spacings, s, used in this study. Test results. indicate that the effective capacity of FRP stirrups in beam action might be as low as 50% of the strength parallel to the fibres, provided that shear failure occurs due to rupture ofFRI' stir­rups. For closely spaced stirrups, there is a higher chance for the diagonal cracks to intersect the bend zone of the stirrups, leading to possible lower contribution of the FRP stirrups, as evident in Fig. 9. For beams reinforced with CFRP strands for flexure, the shear capacity is less than fOf the corre-

865

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

O+-~~-+-+~~~r-+-;-~~_+_+_+--~~~

o 10 20 30 40 50 60 70 80 90

II

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, as will be discussed in the following section.

Effect of FRP longitudinal reinforcement The use of CFRP strands as flexural reinforcement in two

beams resulted in a reduction in the shear capacity, com­pared to similar beams reinforced with steel strands. The contribution of FRP stirrups, V. f , at any load level is deter­mined based on the average strain in stirrups measured by the strain gauges. The concrete contribution for members with CFRP flexural reinforcements, Vcf, is calculated as VCf = Va - V.f, where Va is the applied shear. The relationship between the applied shear and the components of the shear resisting mechanism Vcf and V.f is presented in Fig. 10 for the beams reinforced with steel or CFRP strands for flexure and CFRP stirrups spaced at d/3. Test results indicate that the concrete contribution, Vc' for the beam reinforced with steel strands, at any load level up to failure, is higher than

© 2000 NRC Canada

866

Fig. 8. Beam specimen at failure.

Fig. 9. Effect of stirrup spacing on effective capacity of FRP stirrnps.

I·· CFRP

0.7

:J. 0.5 ~

-------------------~:-f------------------------------------------­\._~.\

0.25-j.-

t 0+

0,2

Beams with CFRP flexural strands

0.3 0.4

sId

0.5 0.6

the concrete contribution, Vcr, for (he corresponding beam reinforced with CFRP strands. Similar behaviour was ob­served for beams reinforced with GFRP stirrups (Shehata 1999). This behaviour indicates that the use of FRP flexural reinforcement in concrete beams results in smaller depth of the compression zone, wider cracks, and less dowel contri­bution, leading to reduction in the concrete contribution to the shear carrying mechanism, VCf'

Shear cracking The shear cracking load was monitored by three tech­

niques in addition to the visual observation of cracks. The

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

Fig. 10. Effect of flexural reinforcement on shear resisting com­ponents.

400~--------------------------------------~

~ ~ 300 II) c o a. E g 200 Ol c

'W 'r;; 1!? :;; 100 .,

.s::. (/)

Vc = shear resisting force provided by conorete ./ __ //

V'-f = shear resisting force provided by concrete in /.<

beams reinforced with FRP for flexure /' V, = shear resisting force provided by steel stirrups //

V" = shear resisting force provided by FRP stirrup~/ ,/

,,-///*//

100 200

Applied shear [kN]

Beam reinforced with steel slrands

/

300 400

crack width for three beams reinforced with CFRP, GFRP, and steel stirrups using stirrup spacing of dl2 is shown in Fig. 11. It can be seen that large crack widths were observed for the beam with CFRP stirrups, even though the stiffuess index EfvPfv is higher for this beam than for the one rein­forced with GFRP stirrups. For the beam reinforced with GFRP stirrups, it is evident that the beam with equivalent shear reinforcement ratio, pfv(EfvIEs), of 0.15% behaves sim­ilarly to the one with steel stirrups ratio, Psv' of 0.40%. This indicates that an increase in the shear reinforcement ratio, Pfv, of 80% minimizes the effect of the low modular ratio (HfvlHs = 0.21) due to the good bond of GFRP stirrups. In

© 2000 NRC Canada

Shehata at al.

Fig. 11. Applied shear versus crack width for beams reinforced with stirrups spaced at d12.

400

300

100

CFRP.p.=0.24%

p"tE"IE.) =0.16%

Beams reinforced wi1h steel strands for flexure

O+-----~-----+------~----+-----~----~ o 2

Shear crack width {mmJ

Fig. 12. Shear crack width versus average strain in stirrups: (a) beams reinforced with CFRP stirrups and (b) beams rein­forced with GFRP stirrups.

3

(a) 3.------------------,

0.2 0.4 0.6 0.8

Average strain In stirrups (%]

(b) 3.------------------.

'-'- s=dl4

U U /'M M Average strain In stlnups [%]

1- Beams with steel strands .--- Beam with CFRP strilnds

general. it was observed that the beams reinforced with GFRP stirrups perfonned well despite the low elastic modu­lus of the GFRP material.

Shear crack width versus stirntp strain The relationship between the shear crack width and the

average strain in stirrups is shown in Figs. 12a and 12b for

867

Fig. 13. Shear crack width versus average strain in stirrups -serviceability requirement.

0.8 E g .c 0.6 :§ ;r; ... l!l 0.4 0

lii 1! Cf.)

0.2

... CFRP

GFRP //

!// ~,;{.L... ... ___ . ___ . _________ 7.__,.,~~·..J---

0.1 0.2 0.3 0.4 0.5

Average strain in stirrups [%]

Table 4. Classification of tested beams failed in shear.

Reinforcement No. of Group Flexure Shear beams A FRP None 20 B FRP FRP 72 C Steel FRP 28 D FRP Steel 6 Total 126

beams reinforced with CFRP stirrups and for beams reinforced with GFRP stirrups with different stirrup spacing. respectively. Test results indicate an insignificant effect of the shear reinforcement ratio and the material of the longitu­dinal reinforcement on the relationship between the crack width and the corresponding strain in the stirrups. Using an average curve. the relationship between the shear crack width and the strain in the stirrup for CFRP. GFRP. and steel stirrups is shown in Fig. 13. Figure 13 indicates that for a given strain level in stirrups. the crack widths of the beams reinforced with GFRP stirrups are smaller' than those of beams reinforced with steel and CFRP stirrups. This behav­iour clearly reflects the effect of the low elastic modulus of GFRP in comparison to CFRP and steel materials.

Proposed design provision

This section introduces a design provision for concrete beams reinforced with FRP shear reinforcement and FRP or steel longitudinal reinforcement. The equations are conve­niently formulated to suit possible adoption by the CSA code for concrete design. The primary parameters affecting the shear strength of concrete beams reinforced with FRP are investigated using extensive test data accumulated by the authors (Shehata 1999). Based on the influence of each pa­rameter. appropriate modifications to the shear design equa­tions in the current CSA 23.3-94 code are suggested. The proposed equations account for the influence of the various parameters and shear failure modes of concrete beams rein­forced with FRP. A rational approach is also proposed for

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the minimum FRP shear reinforcement required for concrete beams.

Available experimental results In addition to the beams tested in the current investiga­

tion, a total of 118 beams were collected from experimental programs carried out by Nagasaka et a1. (1993), Tottori and Wakui (1993), Yonekura et a1. (1993), Zhao et al. (1995), VJjay et al. (1996), Alsayed et a1. (1996, 1997), and Duranovic et al. (1997). The selected beams were reinforced with FRP as shear and (or) flexural reinforcement. The beams were classified into four groups, as given in Table 4.

The following are the ranges of the parameters of test data used to establish the proposed model: effective depth of the member, 150 < d < 500 mm; shear span to depth ratio, 1.2 < aid < 4.3; concrete compressive strength, 23 < Fe < 84 MPa; flexural reinforcement ratio, 0.5% < PI < 4.6%; elastic modulus of flexural reinforcement, 29 < Eft < 200 GPa; shear reinforcement ratio, 0.04% < PlY < 1.5%; elastic modu­lus of shear reinforcement, 31 < ElY < 145 GPa; and shear reinforcement capacity, 0.7 < PIY/fuv < 20 MPa.

All selected beams failed in shear, either by rupture of the stirrups (shear rupture) or by concrete crushing (shear com­pression). The detailed dimensions, material properties, maximum shear force at failure, Vtest, and observed mode of failure for the 126 beams can be found elsewhere (Shehata 1999).

The different parameters considered in the statistical anal­ysis are (i) the strength reduction of FRP stirrups due to bending of bars into a stirrup configuration; (ii) the presence of diagonal cracks with respect to the direction of the fibres; (iii) the low elastic modulus of the longitudinal reinforce­ment, Eft; and (iv) the low elastic modulus of the shear rein­forcement, ElY'

The effect of using FRP as flexural reinforcement is based on the results of Group A beams. The effect of using FRP stirrups is based on the results of Group C beams. The effect of longitudinal reinforcement on the concrete contribution, Vc, is based on groups B and D. Based on the proper separa­tion of the foregoing parameters, the following equations for the factored shear resistance, V rf' is proposed:

[3]

[4]

[5]

/

where A. = 1.0 for normal density concrete; 4>c = 0.60 is the material factor for concrete; and 'f is a reduction factor for FRP (values of 0.85 and 0.75 for CFRP and GFRP, respec­tively, are recommended (CHBDC 1998)).

Reliability of the proposed provisions The proposed equations have been used to predict the

shear strength of Group B and Group C beams. The pre­dicted nominal shear stress, Vn, based on eq. [3] is compared to the measured shear strength. ViesI'> in Fig. 14a for Group B. The calculated shear stress, v n' was based on the nominal

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

shear strength, Vn, using material and a reduction factor of 1.0 in eq. [3]. Predictions according to the current CSA 23.3-94 for steel-reinforced concrete, JSCE (1997), and CHBDC (1998) are given in Figs. 14b, 14c, and 14d, respec­tively. The 45° dotted lines in Fig. 14 correspond to the ex­act prediction, while the two solid lines represent the vleslvn ratios that statistically bound 90% of the data points.

The four design methods are also compared in Table 5, using the ratio of measured-to-calculated shear strength, vtest"vn, for Group B beams.

It was observed that direct application of the current CSA code equations to available test date results in an unsafe pre­diction for the shear strength of concrete beams reinforced with FRP. Both JSCE and CHBDC models greatly underesti­mate the shear strength. The proposed equation results in better distribution for the measured-to-calculated ratio, as shown in Fig. 140.

Minimum shear reinforcement Minimum shear reinforcement is required to prevent sud­

den shear failure upon formation of the first diagonal tension cracking. Tt is also required to provide adequate control of the diagonal tension cracks at the service load level. Exami­nation of Group A beams showed that the cracking shear strength of beams without shear reinforcement is the same for beams reinforced with steel ·or FRP reinforcement (Shehata 1999). However, the use ofFRP in reinforced con­crete beams may result in a concrete contribution, VCf, less than the shear cracking strength. Therefore, for beams rein­forced with FRP flexural reinforcement, a minimum amount of shear reinforcement is required to provide shear strength higher than the cracking load. The following recommenda­tion for the minimum shear reinforcement ratio is proposed:

[6a] for Eft <E.

[6b] _ 0.06$

PIYm" - 0 4fr • fuv

where Vc is the factored shear resistance attributed to con­crete according to CSA 23.3-94. Equation [6] was examined with-the available test results of Group B beams reinforced with FRP as longitudinal and shear reinforcement. Using the factored shear resistance according to CSA 23.34-94, the di­agonal tension cracking stresses, vcr> for beams with FRP shear reinforcement ratio PlY > PlY _ were calculated and compared to the measured ultimate' shear stress, vtest, in Fig. 15. It is evident from Fig. 15 that the measured shear strength, exceeded the predicted diagonal tension cracking load for all beams with reinforcement ratio higher than the minimum value specified in eq. [6].

A minimum amount of FRP shear reinforcement should be provided where factored shear force, V II' exceeds one-half of the concrete contribution in beams reinforced with FRP, Vcr, based on eq. [6].

© 2000 NRC Canada

Shehata et al. 869

Fig. 14. Measured ultimate shear stress versus calculated from design equations based on (a) proposed design equation [3], (b) the simplified method in the eSA 23.3-94 code, (e) JSCE method (1997). and (d) CHBDC code (1998) for beams reinforced with FRP for shear and flexure and tested by many researchers.

(a) ftj' 6-r----.---...,.,...---, (b) ;---~--__r_----:t 0-

~

O~--~~---+--~--+-~ o 2 4 6 o 246

Calculated shear strength, V n [MPa] Calculated shear strength, v n [NlPa]

I. Vljay • Alsayed • Zhao <II. Duranvic ox Nagasaka x Nakamura IBI Tottor! + Shehata 1

Table 5. Comparison between measured, v_ and calculated, vn• shear strength for Group B beams - CSA and CHBDC design approaches.

Proposed JSCE CHBDC Design method equations CSA23.3-94 (1997) (1998)

Total no. of beams 72 72 72 72 Average (avg.) 1.16 0.62 2.73 2.68 Standard deviation 0.24 0.14 0.79 0.82

(std. dev.) COY 0.21 0.23 029 0.31

(= std. dev./avg.) Range /

Low 0.73 0.34 1.36 1.11 High 2.12 1.08 4.96 4.67 High/low 2.90 3.18 3.65 4.21

No. of unconservative IS 71 0 0 predictions· «LO)

*fndicates the number of beams (out of the total numbert for which v_ < vn•

C 2000 NRC Canada

870

Fig. 15. Requirement of minimum shear reinforcement.

6.-------------------------------~

Beams with P.tv > P .Ii'min ,// ./

5

1

_________________________________________________ ~ ____ ----..011--------" ,

V <V,'"

~~-=~-~~=~~~.:~:~~==~--,/ V >V

,," test cr ------------------------'------------------------------------------------

,,/" 'Y "".. ..

--------;:;.£~-~~-~!-~~!!~~-~---~-~:!--------!--" ,

,

o ~'-4--4_-4~4_--~~--~~--~~--~-4 o 1 2 3 4 5 6

Viesl [MPa]

Proposed serviceability limits

Control of crack widths at the service load level is an im­portant serviceability criterion for reinforced concrete struc­tures. The current ACI code (1995) limits the crack width for members reinforced with steel to 0.33 mm (0.013 in.). As FRP reinforcement is generally considered to be non­corroding, the maximum crack width could be increased for FRP reinforcement. In the current drafts of CHBDC (1998) and ACI Committee 440 Design Guidelines (1999), as well as JSCE (1997), the maximum allowable crack width was increased to 0.51 mm (0.20 in.) for concrete members rein­forced with FRP. It was observed for beams reinforced with CFRP stirrups that the average strain in the stirrups corre­sponding to a shear crack width of 0.51 mm is 0.2%, as shown in Fig. 13. The corresponding strain value for beams reinforced with GFRP stirrups is 0.35%, as also shown in Fig. 13. It should be noted that for beams reinforced with steel stirrups, the average strain in the stirrups corresponding to a crack width of 0.51 mm is 0.18%.

To control shear crack widths of concrete beams rein­forced with FRP stirrups, it is recommended to use unified limit of 0.002 (0.2%) for the strain in stirrups at the service load level. The average strain in the stirrups at the service load level, Vs"" can be estimated based on the 45° truss model as follows:

[7] e = s(V ser - v.,f) :s; 0.002 / fvo« ArvEfvd

Summary and conclusions

Fifty-two specially designed panel specimens and ten large-scale reinforced T-section concrete beams reinforced with FRP stirrups were tested. The effects of the bend ra­dius, the crack angle, the stirrup anchorage, the stirrup spac­ing, and the material type of flexural reinforcement were investigated. Based on the test results and an additional 1 t 8 beams tested .by others, design guidelines are proposed for

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

the use of FRP as shear reinforcement in concrete structures. The fonowing specific conclusions can be drawn: (1) The bend effect on the strength capacity ofFRP stirrups

is more critical than the kink effect and, therefore, lim­its the strength of FRP stirrups in the beam action.

(2) The following limitations are proposed for detailing of FRP stirrups to achieve a capacity of at least 50% of the guaranteed strength parallel to the fibres: (a) The bend radius, rb, should not be less than four

times the effective bar diameter or 50 mm, which­ever is greater.

(b) The tail length, I;, should not be less than six times the effective bar diameter or 70 mm, which­ever is greater.

(3) The FRP stirrups should be designed for 40% of the guaranteed strength parallel to the fibres under the ef­fect of factored applied load according to the CSA 23.3-94 code.

(4) Beams reinforced with CFRP strands for flexure showed less concrete contribution, Vc' than beams rein­forced with steel strands. This is attributed to the wide cracks, small depth of the compression zone and poor dowel action associated with the use of FRP as longitu­dinal reinforcement.

(5) Shear defonnations are affected by the bond character­istics and the elastic modulus of the stirrup material. The beams with GFRP stirrups showed better perfor­mance than those with CFRP stirrups for the same rein­forcement index ratio.

(6) The proposed design equation provides better predic­tion of experimental data and, therefore, is recom­mended for code implenlentation.

(7) A minimum shear reinforcement ratio is recommended for concrete beams reinforced with FRP to ensure that the shear strength exceeds the shear cracking load.

(8) Limiting strain of 0.002 is recommended for both CFRP and GFRP stirrups to control the shear crack width in concrete beams.

An example for shear design of a concrete beam rein­forced with FRP is given in Appendix 2.

Acknowledgements

The authors are members of the Network of Centres of Excellence on Intelligent Sensing for Innovative Structures (ISIS Canada) and wish to acknowledge the support of the Network of Centres of Excellence Program of the Govern­ment of Canada and the Natural Sciences and Engineering Research Council. The writers gratefully acknowledge sup­port provided by Tokyo Rope Mfg. Co. Ltd., Japan, Mitsubishi Chemical Corporation, Japan, and Marshall In­dustries Composites Ltd., United States, for providing the materials used in the test program. Special thanks are ex­tended to Mr. M. McVey for his assistance during fabrication and testing of the specimens.

References

ACI Committee 440. 1999. Provisional design recommendations for concrete reinforced with FRP bars. Draft 4, ACT Fall Con­vention, American Concrete Institute, Baltimore, Md.

© 2000 NRC Canada

Shehata et al.

Alsayed, S., Al-Salloum, Y., AlmusaIlam, T., and Amjad, M. 1996. Evaluation of shear stresses in concrete beams reinforced by FRP bars. Proceedings of the Second International Conference on Advanced Composite Materials for Bridges and Structures (ACMBS-II), Montreal, Que., pp. 173-179.

. Alsayed, S., AI-Salloum, Y., and Almusal1am, T. 1997. Shear de­sign of GFRP bars. Proceedings of the Third International Sym­posium on Non-Metallic (FRP) Reinforcement for Concrete Structures, Sapporo, Japan, Vol. 2., pp. 285-292.

Bedard, C. 1992. Composite reinforcing bars: assessing their use in construction. Concrete International, 14(1): 55-59.

CHBDC. 1998. Fiber reinforced structures. In Canadian highway bridge design code. Section 16, Final Draft. Technical Commit­tee of the Canadian Highway Bridge Design Code.

CSA. 1994. Design of concrete structures for buildings. Standard A23.3-94, Canadian Standards Association, Rexdale, Ont.

Duranovic, N., Pilakoutas, K., and Waldron, P. 1997. Tests on con­crete beams reinforced with glass fibre reinforced plastic bars. Proceedings of the Third International Symposium on Non­Metallic (FRP) Reinforcement for Concrete Structures, October 1997, Sapporo, Japan, Vol. 2, pp. 479-486.

JSCE. 1997. Recommendation for design and construction of con­crete structures using continuous fibre reinforcing materials. in Concrete Engineering Series 23. Edited by A. Machida. Japa­nese Society of Civil Engineers, Tokyo, Japan, pp. 1-80.

Nagasaka, T., Fukuyama, H., and Tanigaki, M. 1993. Shear perfor­mance of concrete beams reinforced with FRP stirrups. In ACI SP-138. Edited by A. Nanni and C. Dolan. American Concrete Institute, Detroit, Mich., pp. 789-811.

Rizkalla, S., AbdelraInnan, A., McVey, M., Mahmoud, Z., Morphy, R., Fam, A., Williams, B., Rizkalla, N., and Liu, S. 1997. Mate­rial properties of C_BARfM reinforcing rods. Research report submitted to Reichhold Chemicals Inc., ISIS Canada, The Uni­versity of Manitoba, Winnipeg, Man.

Shehata, E. 1999. FRP for shear reinforcement in concrete struc­tures. Ph.D. thesis, Department of Civil and Geological Engi­neering, The University of Manitoba, Winnipeg, Man.

Tottori, S., and Wakui, H. 1993. Shear capacity of RC and PC beams using FRP reinforcement. In ACI SP-138. Edited by A. Nanni and C. Dolan. American Concrete Institute, Detroit, Mich., pp. 615-631.

Vijay, P., Kumar, S., and GangaRao, H. 1996. Shear and ductility behaviour of concrete beams reinforced with GFRP bars. Pro­ceedings of the Second International Conference on Advanced Composite Materials for Bridges and Structures (ACMBS-II), Montreal, Que., pp. 217-226.

Yonekura, A., Tazawa, E., and Nakayama, H. 1993. Flexural and shear behaviour of prestressed concrete beams using FRP rods as prestressing tendons. In ACI SP-138. Edited by A. Nanni and C. Dolan. American Concrete Institute, pp. 525-548.

Zhao, W., Maruyama, K., and Suzuki, H. 1995. Shear behaviour of concrete beams reinforced by FRP rods as longitudinal and shear reinforcement. Non-metallic (FlU» reinforcement for con­crete structures. In Proceedings of the Second International RILEM Symposium (FRPRCS-2). Edited by L. Taerwe. E & FN Spon, London, Great Britain, pp. 352-359.

Appendix 1. List of symbols

a shear span, rom Afv total cross-sectional area of FRP stirrup within distance

s,rom2

bw web width of the beam, rom d effective depth of cross section, rom

871

db diameter of the reinforcing bar, rom de effective bar diameter (de = ~4Ab/1t), mm Eft elastic modulus of FRP longitudinal reinforcement, MPa Efv elastic modulus of FRP shear reinforcement, MPa Es reference elastic modulus of steel, 200 GPa

fbend strength capacity of the bend portion of the FRP stir­rup,MPa

f: concrete compressive strength, MPa ffuv guaranteed tensile strength of the FRP stirrups parallel

to the fibres, MPa frv stress in the FRP stirrups at failure load, MPa !y yield strength of steel stirrups, MPa h overall depth of the beam cross section, mm

hb height of the FRP bar (hb = db for Totmd bar), mm ~ tail length beyond the bend portion of the FRP stir­

rup, rom rb bend radius of FRP reinforcement, nun s spacing of the shear reinforcement, nun

Va applied shear load, N Vc factored shear resistance attributed to concrete for

beams reinforced by steel reinforcements for flexural and shear according to CSA 23.3-94, N

VCf factored shear resistance attributed to concrete for beams reinforced with FRP reinforcement for flexural and shear, N

Vcr shear force at the initiation of diagonal tension crack, N Vn nominal shear strength based 'on eq. [3J using material

and reduction factor of 1.0, N V rf factored shear resistance for concrete beam reinforced

with FRP, N V... service shear load level, N Vsf factored shear resistance provided by FRP stirrups, N

V test maximum shear force at failure, N Vu factored shear force due to applied loads, N vn nominal shear streSS (vn = Vlbwd), MPa

vtest shear stress based on measured shear capacity, MPa w crack width, nun

Wmax maximum shear crack width, mm Efv average strain in the stirrups at service load

~e angle of the shear crack with the longitudinal axis of the beam

A. 1.0 for normal weight concrete (CSA standards) Pc flexural reinforcement ratio

Pc. FRP shear reinforcement ratio (Pcv = ArvlbwS) Pfv"". minimum FRP shear reinforcement

p.v steel shear reinforcement ratio (Psv = A,jhwS) Psv

m,. minimum steel shear reinforcement

%., +s resistance factors for concrete and steel, respectively +r strength reduction factor for shear design of members

reinforced with FRP

Appendix 2. Design example

A 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 beam cross section and longitudinal reinforcement are given be­low. Determine the required amount of shear reinforcement using GFRP C-BAR stirrups

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872

Given: Dimensions: bw = 300 mm, d = 600 mm, h = 660 mm,

span = 6700 mm Concrete strength: fc' = 40 MPa Flexural reinforcement: An = 1988 mm2, pft = Arlbwd =

0.01104, Eft = 44.8 GPa Shear reinforcement: ffuv = 713 MPa for #10 and #12

GFRP stirrups; Efv = 41 GPa

Design:

wd = 0.30 x 0.66 x 23.5 = 4.65 kN/m

Wu = 1.25wd + 1.5wl

= 1.25 x 4.65 + 1.5 x 30 = 50.8 kN/m

Factored shear and moment 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

Concrete contribution:

~ 3OOx600 = 0.2 x 1.0 x 0.6 x .... 40 x = 136.6 kN

1000

v"f =v" f§i.t1 =136.6~44.8 =64.7 kN (eq. [2]) V Es 200

Since VCf = 64.7 kN < Vu, shear reinforcement is needed. Minimum shear reinforcement (eq. [6]):

V.fmin

= Yc(l- .JEll/ Es)

= 136.6 x (1 - .Jr-44-.8-/2-0-0) = 71.9 kN

Pfv .= Vsfm.,Ihwd = 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, 2000

Required shear reinforcement:

V.fd = Vu - Vcfd = 134.6 - 64.7 = 69.9 kN

Using eq. [5],

V.f = O.4+f ffuv Afvd s

Take 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:

156 Pfv. = = 0.0026 > Pfv

m;. = 0.00133 o.k.

- 200 x 300

Check shear compression mode:

Vu""" = Vcf + (O.8'Mt.J7[ hwd)J¥. =64.7 + (0.8 x 0.6x..[4ij x 300x 600)~ 41

. 200

=259.7 kN > Vu =134.6 kN o.k.

Check serviceability requirement: Sustained service load,

Wscr = Wd + O.50wl = 4.65 + 0.50 x 30 = 19.65 kN/m

Vser = 19.65 x (6.7/2 - 0.70) = 52.1 kN

Vser = 52.1 kN < VCf = 64.7 kN o.k.

Therefore, the beam is not cracked in shear under service load level. Detailing of stirrups:

The stirrup detailing is provided according to the pro­posed guidelines. The IO-mm GFRP C-BAR stirrups should have a bend radius of 50 mm and a tail length of 70 mm beyond the bend.

to 2000 NRC Canada