Using fiber-reinforced polymer (FRP) reinforcing bars as the mainreinforcement for concrete structures in severe environments isbecoming a widely accepted solution to overcome the problem ofsteel corrosion and the related deteriorations. Due to the relativelylower cost of glass FRP (GFRP) bars compared to the othercommercially available FRP bars, the use of GFRP bars in rein-forced concrete (RC) structures has been widely investigated in thelast few years. This paper reports experimental data on the shearstrength of concrete beams reinforced with GFRP stirrups. A totalof four large-scale RC beams with a total length of 7000 mm(276 in.) and a T-shaped cross section were constructed and testedup to failure. The test variables were type and ratio of shear reinforce-ment (stirrups). The test beams comprised three beams reinforcedwith sand-coated GFRP stirrups of 9.5 mm (3/8 in.) diameterspaced at d/2, d/3, and d/4 (where d is the beam depth), and areference beam reinforced with conventional steel stirrups of 9.5 mm(3/8 in.) diameter spaced at d/2. As designed, the beams failed inshear due to GFRP stirrup rupture or steel stirrups yielding. ACI440.1R-06 and the updated version of CAN/CSA S6-06 are able topredict the shear strength of beams reinforced with GFRP stirrupswith a reasonable accuracy. The analytical approach usingResponse 2000 (R2K), which is based on the modified compressionfield theory (MCFT), predicted well the shear capacity of thebeams reinforced with GFRP stirrups, but overestimated theirshear crack width.
INTRODUCTIONThe use of concrete structures reinforced/prestressed with
fiber-reinforced polymer (FRP) composite materials hasbeen growing to overcome the common problems caused bycorrosion of steel reinforcement. The climatic conditionswhere large amounts of salts are used for ice removal duringwinter months may contribute to accelerating the corrosionprocess. These conditions normally accelerate the need forcostly repairs and may lead to catastrophic failure. Therefore,replacing the steel reinforcement with the noncorrosive FRPreinforcement eliminates the potential of corrosion and theassociated deterioration. The direct replacement of steel withFRP bars, however, is not possible due to various differencesin the mechanical properties of the FRP materials compared tosteel, especially the higher tensile strength, the lower modulusof elasticity, bond characteristics, and the absence of a yieldingplateau in their characteristic stress-strain relationships.
Extensive research programs have been conducted toinvestigate the flexural behavior of concrete members rein-forced with FRP reinforcement.1-4 The shear behavior ofFRP reinforced concrete (RC) beams without shear rein-forcement has also been studied;5 however, the use of FRPas shear reinforcement (stirrups) for concrete members hasnot been sufficiently explored to provide a rational model
and yield satisfactory guidelines to predict the shear strengthof concrete members reinforced with FRP stirrups.
Due to the unidirectional characteristics of FRP materials,bending of FRP bars into stirrup configuration significantlyreduces the strength at the bend portions.6-8 The reducedstrength of the FRP stirrup at the bend is attributed to localstress concentration at the bend due to curvature and theintrinsic weakness of fibers perpendicular to their axis. Thebend capacity of FRP bars is influenced by the bendingprocess, the ratio of bend radius to bar diameter (rb/db), andtype of reinforcing fibers.9 The recent editions of the ACI440.1R-069 guidelines and the CAN/CSA S6-0610,11 code,along with the commercially available FRP bent bars,encouraged the use of FRP stirrups.
Through a collaboration project between the University ofSherbrooke, the Ministry of Transportation of Quebec(MTQ), and an FRP manufacturer, new FRP (carbon andglass) stirrups have been recently developed and characterizedaccording to B.5 and B.12 test methods of ACI 440.3R-04.12
The behavior of these stirrups in large-scale beam specimens,however, had not been investigated. To achieve this, anexperimental program was conducted to investigate the shearperformance of FRP stirrups in large-scale beam specimens.The first phase evaluated the structural performance ofcarbon FRP (CFRP) stirrups in beam specimens.13 There is arecent increase in demand for glass FRP (GFRP) bars becauseof its many successful applications, including bridge deckslabs,14,15 barrier walls,16,17 parking garages,18 continuouspavement,19 and other concrete structures. Furthermore,considering the lower costs of GFRP bars in comparison toCFRP and aramid FRP (AFRP), GFRP reinforcement isbecoming more attractive for the construction industry. There-fore, a second phase was conducted to study the shear behaviorof concrete beams reinforced with GFRP stirrups. The results ofthis phase are presented and discussed herein.
RESEARCH SIGNIFICANCEExtensive research in recent years has been undertaken to
investigate the performance of FRP as primary reinforcementfor concrete members; however, limited studies were conductedon the shear behavior of concrete members reinforced withFRP stirrups. This paper evaluates the shear performance andstrength of large-scale RC beams reinforced with GFRP stirrupsconsidering different shear reinforcement ratios. In addition,the paper examines the accuracy of the recently publisheddesign provisions concerning FRP as shear reinforcement.
Title no. 107-S06
Performance Evaluation of Glass Fiber-Reinforced Polymer Shear Reinforcement for Concrete Beamsby Ehab A. Ahmed, Ehab F. El-Salakawy, and Brahim Benmokrane
ACI Structural Journal/January-February 201054
SHEAR DESIGN PROVISIONSTable 1 summarizes some of the shear design provisions
for RC members reinforced with FRP stirrups. These designprovisions are based on the traditional equation that estimatesthe shear strength of a concrete member as a summation ofthe concrete and stirrup contributions (Vc + VFRP) to theshear-carrying capacity. However, the stress level in the FRPtransverse reinforcement (stirrups) is generally limited tocontrolling shear crack widths, maintaining shear integrity ofthe concrete, and avoiding failure at the bent portion of theFRP stirrup.9 Therefore, the tensile strain in FRP transversereinforcement is limited to ensure that such an approachis applicable.9-11 The design provisions listed in Table 1were used to predict the shear-carrying capacity of the testspecimens and then compared to the experimental results.
EXPERIMENTAL INVESTIGATIONTest specimens
A total of four large-scale RC beams, including threebeams reinforced with GFRP stirrups and one with steelstirrups, were constructed and tested. The 7.0 m (275.6 in.)long beams had a T-shaped cross section (simulating the NewEngland Bulb Tee (NEBT) beams that are being used by theMinistry of Transportation of Quebec [MTQ], Canada)
measuring a total height of 700 mm (27.6 in.), a web widthof 180 mm (7.1 in.), a flange width of 750 mm (29.5 in.), anda flange thickness of 85 mm (3.3 in.). In addition, all beamswere provided with the same longitudinal reinforcement(three layers of three 15.4 mm [0.6 in.] diameter seven-wiresteel strands) to keep the dowel effect and the longitudinalstiffness unchanged. The high-strength steel strands and theT-shaped cross section were selected to make the flexuralcapacity greater than the shear strength of the beam. In thiscase, shear failure is expected, which allows the use of thefull capacity of the stirrups. Figure 1 shows the geometry andreinforcement details of the test specimens.
The transverse reinforcement consisted of 9.5 mm (3/8 in.)diameter GFRP stirrups for three beams—SG-9.5-2, SG-9.5-3,and SG-9.5-4—and 9.5 mm (3/8 in.) diameter steel stirrupsfor the fourth beam, SS-9.5-2. The stirrups’ spacing for thethree beams reinforced with GFRP stirrups were 300, 200,and 150 mm (11.8, 7.9, and 5.9 in.), which represent d/2, d/3, and
ACI member Ehab A. Ahmed is a Doctoral Candidate in the Department of CivilEngineering, University of Sherbrooke, Sherbrooke, QC, Canada. He received his BScand MSc in civil engineering from the University of Menoufiya, Menoufiya, Egypt. Hisresearch interests include structural analysis, design, and testing of fiber-reinforcedpolymer reinforced concrete structures.
Ehab F. El-Salakawy is an Associate Professor and Canada Research Chair inAdvanced Composite Materials and Monitoring of Civil Infrastructures in theDepartment of Civil Engineering at the University of Manitoba, Winnipeg, MB,Canada. His research interests include large-scale experimental testing andfinite element modeling of reinforced concrete structure.
Brahim Benmokrane, FACI, is an NSERC Research Chair Professor in InnovativeFRP Composite Materials for Infrastructures in the Department of Civil Engineeringat the University of Sherbrooke. He is a member of ACI Committee 440, FiberReinforced Polymer Reinforcement.
Fig. 1—Dimensions and reinforcement details of test specimens.(Note: 1 mm = 0.0394 in.)
d/4, where d is the effective beam depth. The steel stirrups forBeam SS-9.5-2, however, were spaced at 300 mm (11.8 in.)(d/2). Because those beam specimens are part of an extensiveresearch program, the specimen designation can be explainedas follows. The first letter, S, indicates longitudinal reinforcementtype (S for steel), while the second letter indicates the material ofthe stirrups (G for GFRP, and S for steel). The number in themiddle, 9.5, indicates the diameter of the stirrups, and thelast number represents the spacing of the stirrups (2 for d/2;3 for d/3; 4 for d/4). Table 2 presents the flexural and shearreinforcement details of the test specimens.
Material propertiesThe test specimens were cast in the laboratory at the
University of Sherbrooke using ready mixed normalweightconcrete (concrete Type V, MTQ) with a 28-day targetcompressive strength of 35 MPa (5.08 ksi). Table 2 alsopresents the concrete properties of test specimens.
GFRP stirrups, No.10 (9.5 mm [3/8 in.] diameter), made ofcontinuous longitudinal glass fibers preimpregnated in athermosetting vinyl ester resin and winding process with afiber content of 78.8% (by weight), were used as shearreinforcement. The GFRP stirrups had a sand-coated surfaceto enhance bond performance between bars and surroundingconcrete. The stirrups have an overall height of 640 mm(25.2 in.), width of 140 mm (5.5 in.), and bend radius rb of38.1 mm (1.5 in.) (4db where db is the bar diameter). Figure 2shows the stirrups’ details. The tensile capacity and modulus ofelasticity of the straight portions, directly cut from the GFRPstirrups, were 664 ± 25 MPa (96.31 ± 3.63 ksi) (COV =3.8%) and 45 ± 2 GPa (6526 ± 290 ksi) (COV = 4.4%),respectively. The bend capacity of the stirrups was determinedusing the B.5 test method specified by ACI 440.3R-04.12 Themeasured strength of the GFRP stirrups at the bend was 387 ±15 MPa (56.13 ± 2.18 ksi) (COV = 3.9%), which represents58% of the tensile strength of GFRP straight portions.
Deformed steel bars, No. 15M (15.9 mm [5/8 in.] diameter)and No. 10M (11.3 mm [0.44 in.] diameter), were used forthe top of the web and flange reinforcement, respectively (Fig. 1).The yield stress and modulus of elasticity for those steel barswere 450 MPa and 200 GPa (65.27 and 29,007 ksi), respectively.Additionally, 9.5 mm (3/8 in.) diameter plain steel bars wereused to fabricate the stirrups for the control beam (Fig. 2).The yield stress and modulus of elasticity were 576 MPaand 200 GPa (83.54 and 29,007 ksi), respectively. The tensilestrength and modulus of elasticity of the seven-wire strands(15.4 mm [0.6 in.] diameter) were 1860 MPa and 200 GPa(269.77 and 29,007 ksi), respectively.
Instrumentation, test setup, and procedureThe strains in the flexural reinforcement, concrete, and
stirrups located in the shear span were measured using electricalresistance strain gauges. The deflection of the beam wasmeasured using four LVDTs placed at the midspan, and atmidshear span. The shear crack width was monitored duringthe test by visual inspection until the first crack appeared,which was initially measured using a hand-held microscopewith a magnifying power of 50×. Then, six high-accuracyLVDTs (±0.001 mm) were installed in the position of theshear crack (three at each shear span). The formation andpropagation of the cracks on each beam and correspondingloads were marked and recorded during the test.
Fig. 2—Details of GFRP and steel stirrups: (a) GFRP stirrups;and (b) steel stirrups. (Note: 1 mm = 0.0394 in.)
Table 2—Concrete properties and reinforcement details of test specimens
SG-9.5-4 33.5 2.65 18,861 GFRP 9.5 150 45 ± 2 0.526 664 ± 25 387 ± 15 0.120*Based on 150 × 300 mm cylinder testing, where fc′ is concrete compressive strength; fcr is concrete tensile strength; and Ec is concrete modulus of elasticity.†Efv is modulus of elasticity of shear reinforcement; ffuv is ultimate tensile strength parallel to fiber direction; fbend is strength of FRP stirrup at bend; and fy is yield strength of steel.Note: 1 mm = 0.0394 in.; 1 kN = 0.225 kips; 1 MPa = 0.145 ksi.
ρfvEfv
Es
------
Fig. 3—Details of test setup.
ACI Structural Journal/January-February 201056
The beams were tested in four-point bending over a simplysupported clear span of 6000 mm (236 in.), leaving 500 mm(20 in.) at each end to prevent any premature anchoragefailure of the longitudinal reinforcement. The point load waslocated at a distance of 2000 mm (78.7 in.) from the support,which corresponds to a shear span-depth ratio of 3.33. Theload was applied through a 1000 kN (224.81 kip) capacity
actuator and a spreader beam. A load-controlled rate of5.0 kN/min (1.12 kips/min) was used up to 90% of theexpected failure load. Thereafter, the load was applied ata displacement-controlled rate of 0.6 mm/min (0.023 in./min) toavoid any accidental problems associated with the suddenand brittle shear failure. The complete test setup is shownin Fig. 3. During the test, loads, strain gauges, and LVDT
Table 3—Summary of test results
Test specimen
Shear cracking load,* Vcr,kN (kips)
Ultimate shear, Vtest , kN (kips)
Angle of major crack, θ, degrees
vtest =Vtest/bd,MPa (ksi)
Maximum stirrup strain, microstrain Average stirrup
strain at failure, microstrain Mode of failure†Straight portion Bend
SG-9.5-4 56 (12.59) 416 (93.52) 44 3.85 (0.56) 13,100 8000 8350 GR*Corresponding to appearance of first shear crack. Determined from slope changing of shear-concrete strain relationship and verified using strain gauge readings.†SY is steel stirrup yielding; and GR is GFRP stirrup rupture.‡Gauge reading at connection between straight and bend portions.Note: Both shear cracking load and ultimate shear did not include self-weight of beam.
Fig. 4—Failure of test specimens: (a) SG-9.5-2 (GFRP @ d/2); (b) SG-9.5-3 (GFRP @ d/3);(c) SG-9.5-4 (GFRP @ d/4); and (d) SS-9.5-2 (steel @ d/2).
ACI Structural Journal/January-February 2010 57
readings were recorded using two data acquisition systems.More details on test specimens, materials, instrumentation ofthe specimens, and test procedure can be found elsewhere.19
Test results and discussionThe summary of the test results regarding the shear
capacity of test specimens, maximum strains, angle of themajor shear crack, and mode of failure are summarized inTable 3. Detailed analysis and discussion of the results,however, are introduced in the following section.
Capacity and mode of failureBecause the test specimens were designed to fail in shear,
the ultimate shear strength of the test specimens wasgoverned by the stirrup’s strength. Despite the difference inthe load level at which shear failure of beams reinforced withGFRP stirrups (SG-9.5-2, SG-9.5-3, and SG-9.5-4) tookplace, a similar failure mechanism was observed. Diagonaltension failure occurred suddenly for the three beams due tothe rupture of GFRP stirrups. The test specimens failed at acorresponding applied shear force equal to 259, 337, and 416 kN(58.23, 75.76, and 93.52 kips) for SG-9.5-2 and SG-9.5-3,and SG-9.5-4, respectively. Even though the SS-9.5-2 beam(with steel stirrups) also failed in shear, the shear failure wasinitiated by stirrup yielding. Then, the shear cracks started towiden rapidly as the applied load increased due to the post-yielding plastic behavior of the steel bars. Finally, a concrete
crushing at the top flange of the beam near the loading pointoccurred at a shear force of 272 kN (61.15 kips). Figure 4shows photographs of the test specimens at failure, while Fig. 5schematically shows the final crack patterns of the testedbeams at failure with the failure shear plane and its inclina-tion angle highlighted. The failure plane of Beam SG-9.5-2was the closest to the loading point with the steepest inclina-tion angle. The other two beams reinforced with higher ratios ofGFRP stirrups (SG-9.5-3 and SG-9.5-4) failed at a plane close tothe midshear span. The main difference in final crack patternsbetween the three beams was the number and spacing of diagonalcracks developed in the shear span. The higher the failureload, the greater the number of induced shear cracks.
DeflectionAs expected, the shear failure was the dominant mode of
failure and all specimens failed in shear prior to reachingtheir flexural capacity. Figure 6 shows the applied shearforce-deflection relationship for the tested beams at twolocations: at midspan and in the middle of the shear span. Thebeams showed similar behavior and there was no significantdifference between the beams with different GFRP stirrupsspacing and the reference beam with steel stirrups, exceptSG-9.5-2, which showed higher deflection values thanother beams.
Flexural strainsThe relationships between the applied shear force and the
flexural strains (longitudinal reinforcement and concrete) atthe midspan of all beams are shown in Fig. 7. As noticed inthe deflection curves (Fig. 6), there was no significant differencein flexural strains among the tested beams. There was also noevidence of the yielding of longitudinal reinforcement orcrushing of concrete.
Strains in GFRP stirrupsThe maximum stirrup strains for different beams are
included in Table 3, whereas Fig. 8 shows the applied shearforce-average stirrup strain relationships considering thestrains from the stirrup located in the beam end where theshear failure occurred. The average strains were calculatedfrom the stirrups located within a distance equal to 0.7 theshear span a, measured from the loading point (four, six, andeight strain gauges for the beams with stirrup spacing equalto d/2, d/3, and d/4, respectively). The stirrups close to the
Fig. 5—Cracking pattern at failure for test specimens. (Note:1 mm = 0.0394 in.)
Fig. 6—Applied shear force-deflection relationship for testspecimens.
58 ACI Structural Journal/January-February 2010
support were excluded from the average because their strainwas very small in comparison with the remaining stirrups inthe shear span. Besides, any shear cracks intersecting thesestirrups usually appeared at loading stages close to failure.Generally, the larger the stirrup spacing, the higher thestirrup strain at all loading levels. The maximum stirrupstrain in the straight portion of the GFRP stirrup, measuredat failure, was 13,400, 13,600, and 13,100 microstrains forSG-9.5-2, SG-9.5-3, and SG-9.5-4, respectively. Thesestrain values correspond to approximately 92% of the GFRPstraight portion’s strength. The maximum strain at the bend,however, was 8000 microstrain from Beam SG-9.5-4, whichcorresponds to 93% of the bend strength. This is in goodagreement with the bend strength of the GFRP stirrupsdetermined based on the B.5 test method,12 which was387 MPa (56.13 ksi) (corresponding to 8600 microstrain). Itis worth mentioning that although all test conditions for allbeams were identical, there was a small difference betweenthe average stirrup strains in the two shear spans of the samebeam. Herein, the average stirrup strains obtained from theshear span where the shear failure occurred was considered.
From the comparison presented in Fig. 8, it can be noticedthat all beams showed the same behavior at early loadingstages. Following shear cracking and with increasing loads,Beam SS-9.5-2 (with steel stirrups at d/2) showed thesmallest average strain values compared to the other beamsreinforced with GFRP stirrups. This may be referred to thehigher shear reinforcement index (ρfyEfy/Es) for that beamcompared to the others with GFRP stirrups. The shearreinforcement index of SG-9.5-4 was approximately 50% ofthe SS-9.5-2 (0.12 and 0.26 for SG-9.5-4 and SS-9.5-2,respectively), but it did not show a significant difference in
the average strain values until the yielding of the steel stirrups. Thisindicates the dependency of the shear behavior not only on themodulus of elasticity, but also on other mechanical propertiessuch as the bond characteristics of the shear reinforcement.This issue should be further investigated.
Corresponding to an average strain in the GFRP stirrupsequalling 2500 microstrain (the strain limit specified by theCHBDC, CSA S6-0610), the applied shear forces were 173,185, and 218 kN (38.89, 41.56, and 49.01 kips) for SG-9.5-2,SG-9.5-3, and SG-9.5-4, respectively (Fig. 8). These valuesrepresent 67%, 55%, and 52% of the observed failure loadsof the test specimens, respectively. They also represent122%, 116%, and 122%, respectively, of the predicted shearcapacity using CHBDC provisions.10 On the other hand, thecalculated stirrup strains based on the CHBDC CSA S6-06(2006)10 (Eq. (17)) are 2500 (the code upper limit), 2104,and 2013 microstrain corresponding to average stresses of112.5, 94.7, and 90.6 MPa (16.32, 13.74, and 13.14 ksi),respectively. These average stresses represent 17%, 14%,and 14% of the GFRP stirrup strength parallel to the fiberdirection and 30%, 24%, and 23% of the bend strength ofthe stirrups for SG-9.5-2, SG-9.5-3, and SG-9.5-4, respec-tively. Therefore, limiting the ultimate strain in an FRPstirrup to 2500 microstrain leads to unduly conservativepredictions of the shear capacity of concrete members rein-forced with GFRP stirrups.
Increasing this limit strain to 4000 microstrain, asrecommended by ACI 440.1R-069 and the updated CHBDCCSA S6-06 (2009),11 the observed applied shear force was193, 225, and 257 kN (43.39, 50.58, and 57.78 kips), corre-sponding to 75%, 67% and 62% of the failure load for SG-9.5-2, SG-9.5-3, and SG-9.5-4, respectively. The aforemen-tioned strain limit represents approximately 25% of thestrain capacity of the majority of the commercially availableGFRP products.
The strain distribution in the shear span, where failureoccurred, is plotted using the strain gauge reading versus thestirrup position for Beam SG-9.5-2, as shown in Fig. 9. It canbe noticed that the strain in the stirrups along the shear spanis affected by the cracking pattern and the position of boththe stirrup and strain gauge with respect to the crack. Near a
Fig. 8—Applied shear force-average stirrup strain relationship.Fig. 9—Stirrup strain distribution along shear span of SG-9.5-2beam (GFRP @ d/2). (Note: 1 mm = 0.0394 in.)
ACI Structural Journal/January-February 2010 59
crack, the measured strain is higher than the average. Someof the stirrups did not show a very high stress level at earlyloading stages until the shear cracks were stabilized. Thehighest stress levels were measured in the GFRP stirrupslocated at the middle third of the shear span with an averagestrain of 8890 microstrain.
Effect of stirrup spacingIn general, beams with smaller stirrup spacing showed
higher shear capacity and lower transverse strain at anygiven load. Based on the traditional 45 degree truss model,stress in the FRP stirrup at failure, ffv, was determined fromthe following equation,9 considering the reduction factor φequal to 1.0
(18)
where Afv is the area of the FRP stirrups, s is the stirrupspacing, and d is the effective depth of the beam. Figure 10shows the effective stress in the FRP stirrups at failure withrespect to the ultimate strength ffuv for the different stirrupspacings s used in this study. The effective stirrup stress ffvat failure, with respect to the ultimate strength of the stirrups,ffuv, (parallel to the fiber direction) was 105%, 99%, and 95%for Beams SG-9.5-2, SG-9.5-3, and SG-9.5-4, respectively.The lesser the spacing of the FRP stirrups, the lower theeffective stirrup stresses because there is a higher probabilityfor the diagonal shear cracks to intersect the bend zones ofthe FRP stirrups, as evident in Fig. 10. This was demonstrated inthe study by Shehata et al.7 that used three other beams reinforcedwith CFRP stirrups with different spacings. The effectivestirrup stress at failure with respect to the ultimate strengthof the stirrups, ffuv, in these beams was 76%, 67%, and 56%corresponding to stirrups spacing equal to d/2, d/3, and d/4,respectively. The main reason for the difference between thetwo results (the current study versus that by Shehata et al.7)may be referred to bend strength relative to the straightportion strength. In the current study, the bend strength ofGFRP stirrups was 58% of the GFRP straight portionstrength; however, this ratio was 46% for the work done byShehata et al.7 using CFRP stirrups. It can be concluded thatproviding FRP stirrups, with a strength ratio of bend-to-straight portion fbend/ffuv ≥ 0.6, results in reaching the fullcapacity of both straight and bend portions simultaneously.In other words, using FRP stirrups with lower bend strengthresults in a failure governed by the bend strength, and thecapacity of the straight portions of the FRP stirrups could notbe used. Other factors that may have an impact on effectivestress values are the configuration of the stirrups, modulus ofelasticity, and bond characteristics.
Shear crack widthIn steel-reinforced concrete sections, the flexural crack
width is limited in most design codes to protect the steel barsfrom corrosion and to maintain the aesthetical shape of thestructure; however, there are no specified limits for the shearcrack width. Unlike steel reinforcement, FRP is noncorridible bynature and, therefore, limits for crack width of FRP reinforcedconcrete elements may be directly related to aestheticconsideration. Similar to steel design provisions, the FRPdesign provisions and guidelines specify relaxed limits forwidth of flexural cracks with no specific limits for the shear
φffvVtest φVcr–( )s
Afvd-----------------------------------=
crack width. FRP design provisions, however, limit thevalues for the strain in FRP stirrups as a method to controlthe shear crack width.
Figure 11 shows the relationship between the appliedshear force and the measured maximum shear crack width(the failure shear crack). From Fig. 11, it can be seen thatBeam SG-9.5-2 (GFRP at d/2) showed very large crackwidth in comparison to the other three beams. The lesser thespacing between the GFRP stirrups, the smaller the crackwidth at the same loading level. Although SG-9.5-3 andSS-9.5-2 do not have the same shear reinforcement index,both beams showed almost the same load-shear crack widthbehavior up to the yielding of the steel stirrup. This isreferred to the good bond performance of sand-coated GFRPstirrups as well as the closer stirrup spacing.
COMPARISON OF PREDICTIONSAND EXPERIMENTAL RESULTS
The shear design provisions listed in Table 1 were used topredict the shear strength of the tested beams. Table 4 presents acomparison between the experimentally obtained shearstrength and the predicted strengths. From Table 4, it is clearthat both CSA-S6-06 (2006)10 and JSCE21 shear provisionsgreatly underestimate the shear strength of the test specimens.This is due to the common concept used in calculating theFRP stirrup contribution (VFRP). The stirrup strength islimited to the least of the bend strength of the FRP stirrupsor the results of Eq. (16) and (17) for CHBDC CSA S6-06(2006),10 or Eq. (4) and (5) for JSCE.21 The upper limit of
Fig. 10—Effect of stirrup spacing on effective capacity ofFRP stirrups.
Eq. (17) is 2500 microstrain, which is very conservative, andthe equation itself often yields a strain value less than thatlimit, especially for FRP stirrups with a high modulus ofelasticity.13 On the other hand, the JSCE21 relaxed the upperlimit of this equation (Eq. (4)) to the bend capacity of theFRP stirrups; however, the equation itself still governs thedesign. On contrary, using a constant strain value for alltypes of FRP stirrups, as recommended by ACI 440.1R-06,9
yields more reasonable yet conservative results. Considering the updated version of the CHBDC CSA S6-06
(2009),11 the predicted shear strength using Eq. (17-1) (the
same as that of ACI 440.1R-069; refer to Eq. (9) in Table 1) is ingood agreement with the experimental values. The averageVexp./Vpred. is 1.77 with a standard deviation of 0.09 and aCOV of only 5% (Table 4). This indicates that the currentACI 440.1R-069 equation, which will be adopted by CHBDCCSA S6-06 (2009)11 for the FRP stirrup strain at ultimate,provides a reasonable level of conservativeness for predicting theshear capacity of RC members with GFRP stirrups. On the otherhand, the CHBDC CSA S6-06 (2006)10 underestimatesthe inclination angle of the shear crack for beams reinforcedwith GFRP stirrups.
MCFT-BASED SHEAR STRENGTH PREDICTIONThe three beams reinforced with GFRP stirrups were
modeled using the Response 2000 (R2K),22 which is basedon the modified compression field theory (MCFT).23 Bothmember response analysis and sectional analysis were usedin R2K to predict the behavior of the beams. Unlike steelreinforcement, the FRP stirrups have two different character-istic values: the tensile strength parallel to the fiber direction(straight portions), and the bend strength. When the sectionresponse analysis was used, the bend strength was defined asthe governing ultimate stress for the GFRP stirrups. Thisassumption was based on the experimentally observed strainvalues (the bend strength of the GFRP stirrups was achievedwhile the corresponding stress in the straight portions wasnot reached). On the other hand, when the full memberresponse was used, the ultimate strength of the straightportion of the GFRP stirrups was defined as the governingmaterial strength. A comparison between the predicted andexperimental values using both methods is presented in Fig.12. It can be seen that both methods are capable of predictingthe shear strength of the beams reinforced with GFRP stirrups.However, the full member response yielded a conservativeshear strength with an average Vexp./Vpred. equal to 1.15 ± 0.12and a corresponding COV equal to 10%. It is worth mentioningthat when the sectional analysis method is used, it is importantto select the section at which the calculations are performed.This is controlled through the moment/shear (M/V) ratiobecause both the initial values for moment M and shear V areuser input data. Bentz22 recommended using the sectionlocated at a distance dv from the loading point, which wasused in this study. When the full member response wasemployed, the limiting stress of the stirrups was entered as664 MPa (96.31 ksi) and, from the results corresponding tothe failure shear load, the average stress in the GFRP stirrupswas 325 MPa (47.14 ksi) while the stress in the GFRP stir-rups at the intersection with the shear crack was 664 MPa(96.31 ksi) (the stirrup capacity). On the contrary, in thesectional analysis and corresponding to stress equalling387 MPa (47.14 ksi) in the GFRP stirrups, the stress in the
Fig. 12—Comparison between experimental and analyticalprediction (MCFT) of shear strength using Response 2000.22
Table 4—Predicted shear strength of test specimens
*Using Eq. (17-1) instead of Eq. (17).†Average for beams reinforced with GFRP stirrups.Note: Both Vexp. and Vpred. include contribution of concrete and FRP stirrups (Vc + VFRP).
Fig. 13—Comparison between experimental and analyticalprediction (MCFT) of shear crack width using Response2000.22
ACI Structural Journal/January-February 2010 61
GFRP stirrups exceeded 664 MPa (96.31 ksi) at the intersectionwith the shear crack, which is the straight portion strength.The shear crack width calculated based on the MCFT analysisis shown in Fig. 13. Although the MCFT predicted well theshear strength of RC beams reinforced with GFRP beams, itwas not able to accurately predict the shear crack width.
SUMMARY AND CONCLUSIONSThe experimental results concerning the shear behavior of
large-scale beams reinforced with GFRP stirrups are presentedand discussed. The main variables were type and ratio of the shearreinforcement. GFRP stirrups, 9.5 mm (3/8 in.) in diameter andsand-coated, were used as shear reinforcement in three beamswith different stirrup spacings. For comparison, one specimenwas reinforced with steel stirrups. The GFRP stirrups had atensile strength of 664 MPa (96.31 ksi) and a modulus ofelasticity of 45 GPa (6526 ksi), and the bend strength was387 MPa (47.14 ksi). The experimental and predicted resultswere compared considering the shear design provisionsprovided by ACI 440.1R-06,9 CAN/CSA S6-06,10,11 andJSCE.21 The shear behavior of the test specimens was alsopredicted using the MCFT and was compared with theexperimental results. The main findings of this investigationcan be summarized as follows:
1. The presence of GFRP stirrups in the beam specimens,similar to steel stirrups, enhances the concrete contributionafter the formation of the first shear crack. The lesser thespacing of the GFRP stirrups, the higher the shear resistanceenhancement due to the confinement, which controls theshear cracks and improves the aggregate interlocking.
2. At shear failure, the inclination angle of the shear crackin concrete beams reinforced with GFRP stirrups was ingood agreement with the traditional 45-degree truss model.
3. The beam reinforced with steel stirrups showed the leaststrain at the same loading level in comparison with itscounterparts reinforced with GFRP stirrups. This may bedue to the high shear reinforcement index (ρfvEfv/Es) forsteel stirrups. The beam with steel stirrups, however, didnot show the smallest shear crack width. This may beattributed to the difference in bond characteristicsbetween steel and GFRP.
4. Using FRP stirrups with a strength ratio of bend-to-straight portion, fbend/ffuv, ≥ 0.6 enables using the capacity ofthe straight portions of the FRP stirrups in beam specimens.Lower ratios will cause the bend strength to govern thestirrup whatever the tensile strength of the straight portion is.
5. Limiting the ultimate strain of the FRP stirrup as specifiedby the ACI 440.1R-069 and the updated CHBDC CAN/CSA S6-06 (2009)11 enables a more accurate but stillconservative prediction of the shear strength of concretemembers reinforced with GFRP stirrups.
6. The detailed analysis using R2K,22 which is based onthe MCFT, predicted well the shear capacity of beamsreinforced with GFRP stirrups; however, it was not ableto accurately predict the crack width of these beams.
ACKNOWLEDGMENTSThe authors wish to express their gratitude and sincere appreciation to the
Natural Sciences and Engineering Research Council of Canada (NSERC),the Canadian Network of Centers of Excellence on Intelligent Sensing forInnovative Structures (ISIS Canada), Fonds québécois de la recherche sur lanature et les technologies (FQRNT), Pultrall Inc. (Thetford Mines, QC,Canada), and the Ministry of Transportation of Québec (MTQ) for financingthis research work. The authors would like to thank the technical staff in thestructural laboratory at the University of Sherbrooke for their assistance infabricating and testing the specimens.
NOTATIONAfv = total cross-sectional area of shear reinforcement, mm2 Ag = total cross-sectional area of member, mm2
As = area of cross section of steel or FRP reinforcing bars, mm2 a = shear span, mmb = beam width, mmc = neutral axis depth, mmd = distance from extreme compression fiber to centroid of tension
reinforcement, mmdb = bar diameter, mmdv = effective shear depth for longitudinal reinforcement, mmEfl = modulus of elasticity of longitudinal reinforcement, MPaEfv = modulus of elasticity of shear reinforcement, MPaEs = modulus of elasticity of steel, MPafc′ = compressive strength of concrete, MPafbend = strength of bent portion of FRP bar, MPafcr = cracking strength of concrete, MPaffuv = tensile strength of straight portion of shear reinforcement, MPaffv = vertical stress in FRP stirrups, MPaf ′mcd = design compressive strength of concrete allowing for size effect, MPah = total depth of member, mm
k =
Md = design bending moment, N·mmMf = factored moment at a section, N·mmMo = decompression moment, N·mmNd′ = design axial compression force, NNf = factored axial load normal to cross section occurring simultaneously
with Vf, including effects of tension due to creep and shrinkage, Nnf = modular ratiorb = internal bend radius of the FRP stirrups, mms = spacing of shear reinforcement, mmsz = crack spacing parametersze = equivalent crack spacing parameter; shall not be taken less
than 0.85szVc = factored shear resistance provided by concrete, NVf = factored shear force at section, NVFRP = factored shear resistance provided by FRP shear reinforcement, Nz = distance between points of action of tensile and compressive
resultant forces; equal to d/1.15, mmαs = angle between shear reinforcement and axis of beam (in degrees)εfv = strain in an FRP stirrupεx = longitudinal strain at midheight of cross sectionγb = safety factor = 1.3γmfb = safety factor for bent portion = 1.3θ = angle of inclination of principal diagonal compressive stress (in
degrees)ρfl = flexural reinforcement ratio for FRP barsρfv = shear reinforcement ratio for FRP stirrupsρs = shear reinforcement ratio for steel stirrupsσN = stress in concrete due to axial loads, MPa
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