Shear strength of fibre-reinforced polymerreinforced concrete deep beams without webreinforcement

Ahmed K. El-Sayed, Ehab F. El-Salakawy, and Brahim Benmokrane

Abstract: This paper describes an experimental investigation to evaluate the shear strength and behavior of concrete deepbeams reinforced with fibre-reinforced polymer (FRP) bars. A total of ten full-scale reinforced concrete beams without webreinforcement were constructed and tested in four-point bending. The test variables were the reinforcement ratio and themodulus of elasticity of the longitudinal reinforcing bars as well as the shear span to depth ratio. The test beams includedfive beams reinforced with glass FRP bars and five beams reinforced with carbon FRP bars. The behavior of the deepbeams is described in terms of load–deflection response, cracking patterns and modes of failure, strains in reinforcementand concrete, inclined cracking, and ultimate shear strengths. All ten beams showed significant reserve strength after the in-clined cracking was fully developed. The test results also indicated that the ultimate shear strength of the tested beams con-siderably increased with the decrease of the shear span to depth ratio. In addition, the ultimate shear strengths of the testedbeams were predicted using the shear design provisions recommended by the new version of the Canadian Standard CSA-S806-11 and compared with the experimental results, showing good agreement.

Key words: deep beams, experimental results, fibre-reinforced polymer, shear strength.

Résumé : Cet article présente une étude expérimentale servant à évaluer la résistance en cisaillement et le comportement depoutres-cloisons en béton armées de tiges en polymère renforcé de fibres (PRF). Un total de 10 poutres en béton armé àpleine échelle sans armature d’âme a été construit et mis à l’épreuve sous flexion à quatre points. Les variables d’essaiétaient le rapport d’armature et le module d’élasticité des tiges d’armature longitudinales ainsi que le rapport portée en ci-saillement – profondeur. Les poutres à l’essai comprennent cinq poutres armées de tiges en polymère renforcé de fibres enverre (PRFV) et cinq poutres armées de tiges en polymère renforcé de fibres en carbone (PRFC). Le comportement despoutres-cloisons est décrit en termes de la réponse en déformation en raison de la charge, les motifs de fissuration et les mo-des de défaillance, les contraintes dans l’armature et le béton, la fissuration inclinée ainsi que les résistances à la rupture encisaillement. Les 10 poutres ont montré de bonnes réserves de résistance une fois la fissuration inclinée pleinement dévelop-pée. Les résultats des essais ont également indiqué que la résistance à la rupture en cisaillement des poutres mises à l’é-preuve a considérablement augmenté avec la diminution du rapport portée en cisaillement – profondeur. De plus, lesrésistances à la rupture en cisaillement des poutres à l’essai ont été prédites en utilisant les dispositions de calcul du cisaille-ment recommandées dans la nouvelle version de la norme canadienne CSA-S806-11 et elles montraient une bonne concor-dance lorsque qu’elles étaient comparées aux résultats expérimentaux.

Mots‐clés : poutres-cloisons, résultats expérimentaux, polymère renforcé de fibres, résistance en cisaillement.

[Traduit par la Rédaction]

Introduction

The use of fibre-reinforced polymer (FRP) bars is gainingacceptance as an alternative to conventional steel reinforce-ment in structural members subjected to severe environmentalexposure. FRPs are non-corrodible materials with the potentialof reducing life-cycle costs in applications where corrosion ofsteel reinforcements causes costly maintenance. Applications

of FRP bars, however, are not limited only to cases where cor-rosion is the main concern. FRP bars can also be used as pri-mary reinforcements for concrete members where magnetictransparency is required. In addition to these superior proper-ties, FRP bars have a high strength to weight ratio that makesthem attractive as reinforcement for concrete structures.The shear strength of reinforced concrete beams is well es-

tablished to be influenced significantly by the shear span to

Received 14 May 2011. Revision accepted 21 March 2012. Published at www.nrcresearchpress.com/cjce on 25 April 2012.

A.K. El-Sayed. Center of Excellence for Concrete Research and Testing, Department of Civil Engineering, King Saud University, P.O.Box 800, Riyadh 11421, Kingdom of Saudi Arabia.E.F. El-Salakawy. Department of Civil Engineering, University of Manitoba, Winnipeg, MB R3T 5V6, Canada.B. Benmokrane. NSERC Research Chair in Innovative FRP Composite Materials for Infrastructures, Department of Civil Engineering,University of Sherbrooke, Sherbrooke, QC J1K 2R1, Canada.

Corresponding author: Ahmed K. El-Sayed (e-mail: ahelsayed@ksu.edu.sa).

Written discussion of this article is welcomed and will be received by the Editor until 30 September 2012.

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Can. J. Civ. Eng. 39: 546–555 (2012) doi:10.1139/L2012-034 Published by NRC Research Press

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depth ratio, a/d. Based on this ratio, the reinforced concretebeams are divided into two categories with different shear be-havior and strength (Zsutty 1968, 1971). The first category is“slender beams,” having a shear span to depth ratio, a/d,greater than or equal to 2.5, while the second category is“short or deep beams,” having a shear span to depth ratio,a/d, less than 2.5. In slender concrete beams the behavior ofthe beams is governed by the beam action, and the contribu-tion of the arch action to the strength and behavior of suchbeams is insignificant. On the other hand, the arch action sig-nificantly contributes to the shear strength and behavior ofdeep concrete beams.Because FRP and steel bars have different properties, in-

cluding the modulus of elasticity, transverse strength, andbar surface and bonding characteristics, the shear behavior ofconcrete beams reinforced with FRP bars is expected to differfrom that of concrete beams reinforced with steel bars. Re-cent investigations conducted on concrete slender beams(a/d ≥ 2.5) reinforced longitudinally with FRP bars reportedreduced shear strength for such members compared withthose with similar reinforcement ratios of steel (El-Sayed2006; El-Sayed et al. 2005, 2006a, 2006b; Razaqpur et al.2004; Gross et al. 2004; Tureyen and Frosch 2002; Yost etal. 2001). This reduced shear strength of FRP-reinforcedbeams is attributed mainly to the relatively low modulus ofelasticity of FRP bars. However, the influence of using FRPbars as longitudinal reinforcement on the shear strength andbehavior of concrete deep beams (a/d < 2.5) has not yetbeen explored. This lack of test data relevant to the shearstrength of concrete deep beams reinforced with FRP bars ex-plains why the shear design provisions in most recently pub-lished design codes, manuals, and guides (ACI 440.1R-062006; CSA S806 2011; ISIS-M03-07 2007; JSCE 1997) ad-dressing FRP bars as primary reinforcement are establishedfor designing the shear strength of reinforced concrete slenderbeams. In addition, the shear strength of slender beams repre-sents the lower bound values in comparison with those of re-inforced concrete deep beams.Reinforced concrete deep beams have a wide range of ap-

plications in structural engineering, such as pile caps, founda-tions, bridge girders, offshore structures, and transfer girdersin tall buildings (Teng et al. 2000). According to span todepth ratio, the strength of deep beams is usually controlledby shear rather than flexure if normal amounts of longitudi-nal reinforcement are used (Oh and Shin 2001). This investi-gation focuses on evaluating the shear strength of concretedeep beams without web reinforcement and reinforced withFRP bars as the main tensile reinforcement.

Research significanceThe use of FRP materials as reinforcement for concrete

structures is rapidly increasing. However, the behavior andshear strength Vc of concrete deep beams (a/d < 2.5) rein-forced with FRP bars as main tensile reinforcement have notyet been explored. The present experimental investigation is apart of an extensive research program (El-Sayed 2006; El-Sayed et al. 2005, 2006a, 2006b) undertaken at the Univer-sity of Sherbrooke to examine the effect of using FRP barson the shear capacity Vc of reinforced concrete beams with-out web reinforcement. This study provides experimental

data on the behavior and shear strength of concrete deepbeams considering the effect of the reinforcement ratio andthe modulus of elasticity of the longitudinal reinforcing barsas well as the shear span to depth ratio.

Experimental investigationThe experimental program described in this paper included

testing of ten reinforced concrete deep beams. Carbon FRP(CFRP) and glass FRP (GFRP) bars were used in reinforcingthe concrete beams. No top compression or web shear rein-forcement was used in the beams. The overall dimensions ofthe beams were designed to be consistent with the ACI 318code (ACI 318 2011) definition of deep beams. Accordingto the ACI 318 code (ACI 318 2011), deep beams are de-fined as members loaded on one face and supported on theopposite face, so that compression struts can develop be-tween loads and supports. Moreover, deep beams have either(a) ln/h ≤ 4.0 or (b) a/h ≤ 2.0, where ln is the clear span ofthe deep beams, h is the overall depth, and a is the shearspan length. The details of the materials used, test specimens,instrumentation, test setup, and test procedure are describedbelow.

MaterialsThe CFRP and GFRP bars employed in this study had a

sand-coated surface to enhance bond and force transfer betweenbars and concrete. The bars were made of continuous longitu-dinal fibres impregnated in a thermosetting vinylester resinwith a fibre content of 73% by weight (Pultrall Inc. 2005).The size of CFRP and GFRP bars used was No. 13, with a di-ameter, db, of 12.7 mm. The mechanical properties of the rein-forcing bars were determined by tensile tests on representativespecimens in accordance with ACI 440.3R-04 (ACI 440.3R-042004). The tensile properties of the CFRP and GFRP reinforce-ment used in this study are summarized in Table 1. The beamswere constructed using ready-mixed normal-weight concretewith a target compressive strength of 35 MPa after 28 days.The mixture proportions per cubic meter of concrete were asfollows: coarse aggregate content of 1051 kg with a size rang-ing between 10 and 20 mm, fine aggregate content of 672 kg,cement content of 430 kg, water–cement ratio of 0.39, air en-trainer of 301 mL, and water-reducing agent of 860 mL. Theactual slump measurement prior to casting was 80 mm. Theaverage compressive strength of concrete, based on testingstandard concrete cylinders (150 mm × 300 mm), ranged be-tween 39.4 and 40.5 MPa at the time of beam testing. Also,the average tensile strength obtained by performing split cylin-der tests was 3.0 MPa.

Test specimens and instrumentationA total of ten large-scale reinforced concrete deep beams

were constructed and tested to investigate their shear strengthand behavior. Five beams were reinforced with CFRP bars,and five beams were reinforced with GFRP bars. The testedbeams were 2600 mm long, 250 mm wide, and 400 mmdeep, as shown in Fig. 1. As the anchorage of the longitudi-nal bars is one of the critical details affecting the behavior ofdeep beams, the ends of all beams were extended 500 mmbeyond the supports to provide adequate anchorage for thelongitudinal bars in the concrete. To ensure shear failure, all

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the beams were reinforced with adequate amounts of longitu-dinal reinforcement to prevent flexural failure.The test beams were divided into five series: A, B, C, D,

and E, as given in Table 2. Each series included two beams:

one reinforced with CFRP bars and one reinforced withGFRP bars. The beams of the first three series (Series A, B,and C) were tested to investigate the effect of the reinforce-ment ratio and the modulus of elasticity of the longitudinal

Table 1. Properties of reinforcing bars.

Bar type Diameter (mm) Area (mm2) Tensile strength (MPa) Modulus of elasticity (GPa) Ultimate strain (%)Carbon FRP 12.7 127 986 ± 50 134 ± 9 0.74 ± 0.05Glass FRP 12.7 127 749 ± 27 42 ± 1 1.8 ± 0.04

Fig. 1. Details of test beams.

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bars on the concrete shear strength of deep beams. The rein-forcement ratios were 0.78%, 1.24%, and 1.71%, respectively,for the beams of Series A, B, and C. The shear span of thesix beams of the first three series was kept constant at550 mm, giving a shear span to depth ratio, a/d, of 1.69. Onthe other hand, Series D and E included beams having thesame reinforcement ratio as beams of Series B, rf = 1.24%,but with different shear spans. The shear spans of the beamsof Series D and E were 425 mm and 300 mm, respectively,corresponding to shear span to depth ratios, a/d, of 1.30 and0.92. Series B, D, and E were devoted to studying the effectof the shear span to depth ratio, a/d, on the concrete shearstrength of the test beams with either CFRP or GFRP longi-tudinal bars. The ten beams had two bottom layers of rein-forcements with a clear spacing of 30 mm apart. In eachlayer, the spacing between two bars was at least 29 mm. Theside clear concrete cover was kept constant at 30 mm for allbeams, while the vertical clear cover ranged between 46 and51 mm to maintain a constant effective depth, d, of 326 mmfor all beams. The designation of the beams uses the firstcharacter C or G, which refers to the two types of reinforce-ment used — carbon FRP or glass FRP bars, respectively.The number before the slash, 0.7, 1.2, or 1.7, indicates thereinforcement ratio of the longitudinal reinforcement, whilethe number after the slash, 1.6, 1.3, or 0.9, indicates theshear span to depth ratio of the beam. The details of the testspecimens are given in Table 2 and shown in Fig. 1.To monitor the behavior of the test beams, electrical resist-

ance strain gages were attached to the reinforcing bars andconcrete. The strain gages were attached to the reinforcingbars in two different patterns. For all beams, two electricalstrain gages were bonded on the longitudinal reinforcingbars at mid-span to measure tensile strains. To monitor thestain profile along the reinforcement, the beams of Series Cwere additionally instrumented with strain gages attached tothe reinforcing bars at the locations of the two concentratedloads, at the middle of each shear span, and at the inner faceof each support-bearing plate. For all beams, two electricalstrain gages were bonded on the concrete top surface of thebeam at mid-span to measure the concrete compressivestrains. The mid-span deflections were measured using twolinear voltage differential transducers (LVDTs) fastened ateach side of the beam. Two high-accuracy LVDTs(±0.001 mm) were installed at the positions of the firstcracks to measure crack width. During loading, the formation

of the cracks on the sides of the beams were also marked andrecorded.

Test setup and procedureThe beams were tested in a four-point bending setup over

a simply supported span of 1600 mm, as shown in Fig. 1.Each tested beam was loaded directly on the top compressiveface, with two equally concentrated loads according to thespecified a/d, and supported at the bottom. Two 500 kNclosed-loop MTS actuators were used to apply the load.Each actuator was supported by a steel frame, and the twoactuators were connected together with a rigid steel spreaderI-beam. Applied loads and reactions were transmitted to thetested beams by means of 250 mm × 100 mm × 25 mm steelplates to prevent premature crushing or bearing failure atthese locations. To ensure uniform contact between loadingor supporting plates and the concrete surface of the speci-men, a thin layer of neoprene strips was used.During testing, load was monotonically applied at a stroke-

controlled rate of 0.6 mm/min. The applied load was meas-ured by the internal load cells on the actuators. The loadingwas stopped when the first two cracks appeared, and the ini-tial crack widths were measured manually using a hand-held50× microscope. Then, the two high-accuracy LVDTs wereinstalled to measure crack width with increasing load. Theapplied load, displacements, crack widths, and strain readingswere electronically recorded during the test using a data ac-quisition system monitored by a computer.

Test results and discussion

All ten beams of this investigation reached failure underloading except beam C-1.2/0.9 in Series E. This beam wasreinforced with CFRP bars and was tested under a shearspan to depth ratio, a/d, of 0.92. The loading capacity of1000 kN of the two MTS actuators was reached before thatbeam failed. The remaining nine beams failed at load levelslower than the capacity of the two MTS actuators. The ninebeams failed in shear before reaching the design flexural ca-pacity, except beam G-1.2/0.9, which failed in flexure. Asummary of the beam test results is presented in Table 3.One can note that each beam was symmetrically loaded withtwo concentrated loads, and, consequently, the shear forceequals half the total applied load.

Table 2. Details of test beams.

BeamShear span todepth ratio, a/d

Longitudinal reinforcement

Reinforcingmaterial

FRP reinforcementratio, rf (%)

Axial stiffness,EfAf (N × 106)

Series A C-0.7/1.6 1.69 CFRP 0.78 85.1G-0.7/1.6 GFRP 0.78 26.7

Series B C-1.2/1.6 1.69 CFRP 1.24 136.1G-1.2/1.6 GFRP 1.24 42.7

Series C C-1.7/1.6 1.69 CFRP 1.71 187.2G-1.7/1.6 GFRP 1.71 58.7

Series D C-1.2/1.3 1.30 CFRP 1.24 136.1G-1.2/1.3 GFRP 1.24 42.7

Series E C-1.2/0.9 0.92 CFRP 1.24 136.1G-1.2/0.9 GFRP 1.24 42.7

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Load–deflection responseThe total applied load versus mid-span deflection plots for

Series A, B, and C beams are shown in Fig. 2a. The beamsof these series had a constant shear span to depth ratio, a/d =1.69, but had different types and amounts of reinforcing ma-terials. Figure 2b shows the total applied load versus mid-span deflection plots for the beams having identical rein-forcement ratio (rf = 1.24%) but with different a/d ratios(beams of Series B, D, and E). Table 3 gives also the mid-span deflection at failure for each beam. For all ten beams,the load–deflection relationship was approximately bilinear.For each series, the first part of the load–deflection plot upto flexural cracking was similar, representing the behavior ofthe uncracked beam utilizing the gross moment of inertia ofthe concrete cross section. The second part, post-cracking upto failure, represents the cracked beam with reduced momentof inertia. In this part, the flexural stiffness of the testedbeams was dependent on the axial stiffness (EfAf) of the rein-forcing bars.Figures 2a and 2b show that for each series of test beams,

the post-cracking flexural stiffness for the beam reinforcedwith GFRP bars is lower than the flexural stiffness of thecounterpart beam reinforced with CFRP bars, indicating theeffect of modulus of elasticity. Figure 2a also shows the ef-fect of the reinforcement ratio on the load–deflection re-sponse of the tested beams. The figure indicates that as theamount of reinforcement was increased, for the same type ofreinforcing material, the post-cracking flexural stiffness in-creased. Thus, the flexural behavior of the tested beams, interms of load–deflection response, seems to be a function ofthe axial stiffness of the reinforcing bars.The influence of a/d on the load–deflection relationship is

shown in Fig. 2b. The figure shows that the lower the a/d,the steeper the load–deflection plot, indicating that the beambecomes more rigid. This behavior was observed for thebeams reinforced with either CFRP or GFRP bars, as shownin Fig. 2b.

Crack patterns and modes of failureIn the early stages of loading, flexural cracks were ob-

served in the region of pure bending as the applied load wasincreased. With a further increase of load, additional flexuralcracks were developed in the mid-span, and new flexuralcracks were formed on the shear span between the loading

point and support. Inclined cracks were formed within theshear span independently of the flexural cracks. The inclinedcracks started near the mid-height of the beam web, almosthalfway between the loading and support points, and propa-gated toward these points with the increasing load. Theflexural cracks had formed earlier, then stabilized andstopped propagating. All beams exhibited significant reservestrength after the diagonal cracks were fully developed, asexpected because of the arching action.The failure modes of the nine beams tested to failure are

given in the last column of Table 3. No premature failuredue to anchorage failure of the tension reinforcement or dueto bearing failure at the supports or at the loading points wasobserved. Three failure modes were obtained: diagonal split-ting failure, shear-compression failure, and flexural failure.

Table 3. Summary of test results.

BeamLoad atfailure (kN)

Inclined crackingshear Vcr exp (kN)

Ultimate shearVu exp (kN)

Vcr exp/Vu exp(%)

Mid-span deflectionat failure (mm)

Max. strain (m3) FailuremodeBars Concrete

C-0.7/1.6 359 85 179.5 47.4 9.9 4680 1879 DSG-0.7/1.6 329 71 164.5 43.2 17.6 9730 2081 DSC-1.2/1.6 390 100 195.0 51.3 8.0 3310 1355 DSG-1.2/1.6 350 77 175.0 44.0 12.0 7610 1880 DSC-1.7/1.6 467 110 233.5 47.1 6.3 3070 1700 DSG-1.7/1.6 392 80 196.0 40.8 12.0 6240 2030 DSC-1.2/1.3 744 135 372.0 36.3 10.6 5220 2320 SCG-1.2/1.3 538 95 269.0 35.3 13.7 9050 1960 DSC-1.2/0.9 —* 200 —* —* —* —* —* —*G-1.2/0.9 901 151 450.5 33.5 15.2 11000 2700 FL

Note: DS is diagonal splitting failure; FL is flexural failure; SC is shear-compression failure.*Failure not reached.

Fig. 2. Load–deflection relationships: (a) for beams having a/d =1.69 and (b) for beams having rf = 1.24%.

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The diagonal splitting mode is characterized by a critical di-agonal crack joining the loading point and the support. Sucha splitting shear failure takes place as a result of the trans-verse tensile stresses perpendicular to the diagonal strut.This mode of failure was the most prevalent, as seven beamsfailed in diagonal splitting. On the other hand, the beam C-1.2/1.3 failed in shear-compression by crushing of the con-crete above the upper end of the inclined crack. The flexuralcapacity of the beam G-1.2/0.9 was attained because thisbeam failed in flexure by crushing of the concrete in thecompression zone between the two concentrated loads. Thisresult indicates that the arch mechanism developed in this

beam was sufficient to sustain the shear force. Figure 3 illus-trates by photographs the three modes of failure observed inthis investigation.

Strains in reinforcement and concreteFigures 4a and 4b show the measured mid-span strains in

reinforcement as well as in concrete versus the total appliedload for the tested beams with constant a/d ratio (Series A,B, and C) and those with identical rf (Series B, D, and E),respectively. Also, Table 3 gives the measured mid-spanstrains in the reinforcement and concrete at failure for eachbeam. The maximum concrete compressive strains at failureranged from 1355 to 2700 micro-strain. In addition, the max-imum measured tensile strains in the FRP bars at failureranged between 3070 and 5220 micro-strain for carbon barsand between 6240 and 11000 micro-strain for glass bars,which are below the ultimate strains of the FRP bars used inthis investigation (Table 1).The load–strain plots for the beams in the five series of

this investigation exhibited similar characteristics. For all tenbeams, one can note that, after cracking, the strains vary al-most linearly with the increased load up to failure. For eachseries of the test beams and at the same level of applied load,the beam reinforced with GFRP bars showed the largerstrains than the beam reinforced with CFRP bars. This resultcan be clearly noted from Figs. 4a and 4b, and it is attributedto the lower modulus of elasticity of GFRP compared withCFRP bars. Also, the increase in reinforcement ratio de-creased the strains in both the bars and concrete measured atthe same load level (Fig. 4a). On the other hand, the decreasein the shear span to depth ratio decreased the strains in bothbars and concrete measured at the same load level, as shownin Fig. 4b.

Fig. 3. Modes of failure. Fig. 4. Load–strains relationships: (a) for beams having a/d = 1.69and (b) for beams having rf = 1.24%.

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The distribution of strains along the main tensile rein-forcement serves as a measure of the tied arch action experi-enced by the beams. The more uniform the distribution ofstrain along the reinforcement between the two supports, themore developed the tied arch action. To verify the develop-ment of the arching behavior in the tested beams, the strainsalong the bottom layer of the longitudinal reinforcement ofthe beams of Series C were measured symmetrically with re-spect to the beam center at seven points along the span.These points were at mid-span, the locations of the concen-trated loads, mid-shear spans, and the inner face of the twosupport-bearing plates, as shown in Fig. 5.Strain distributions at various stages of loading are pre-

sented in Fig. 5 for the two beams of Series C. The straindistributions for each plot correspond to applied load at15%, 30%, 50%, 75%, and 100% of the beam failure load.As can be seen in Fig. 5, the strain distributions for the twospecimens were similar. For each plot, there were only minordifferences in the measured strains at symmetrical sections ofthe beam. In addition, Fig. 5 shows that prior to the forma-tion of the inclined cracks the strains were distributed alongthe tension reinforcement roughly according to the distribu-tion of the bending moment, indicating the domination ofthe beam action in this stage. One can note that the inclined

cracks were formed at an applied load of 47.1% and 40.8% ofthe failure load for the beams C-1.7/1.6 and G-1.7/1.6, re-spectively (Table 3). As inclined cracks were formed, thestrains in the reinforcement near the supports increased rap-idly until they were of the same order of magnitude as themid-span strains, resulting in an approximately uniform straindistribution in the reinforcement along the beam. This resultindicates the development of the arching behavior in thetested deep beams once the inclined cracks have formed.

Inclined cracking shear strengthThe deep beams tested in this investigation experienced in-

clined cracks, which were formed within the shear span inde-pendently of the flexural cracks. In this study, the inclinedcracking shear strength, Vcr, is defined as the shear force atthe occurrence of a first major inclined crack. A major orcritical inclined crack is the crack that intersects the mid-depth of the beam, pointing toward the concentrated loadand kicking back toward the support. The experimental in-clined cracking shear strength, Vcr exp, was determined basedon the visual observation of cracks during testing accordingto this definition. Therefore, the values of Vcr exp determinedby this definition may show a large scatter because they aresensitive to the judgment of the observer (Ahmad et al.

Fig. 5. Strain distribution along the bottom reinforcement layer for beams of Series C.

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1986, Rebeiz 1999). Table 3 gives the values of Vcr exp foreach tested beam. The values of Vcr exp ranged between33.5% and 51.3% of the experimental ultimate shear strength,Vu exp, indicating substantial reserve strength after the forma-tion of the inclined crack. The effect of the test variables onVcr exp will be discussed later.

Ultimate shear strengthThe experimental ultimate shear strengths, Vu exp, of the

tested beams are given in Table 3. The arching action al-lowed such deep beams to develop ultimate shear strengthssubstantially above the inclined cracking shear strengths. Theincrease in the shear strength above the inclined crackingshear strength of the tested beams ranged between 95% and198%, depending on a/d. Eight beams among the nine beamstested to failure experienced explicit shear failure, whilebeam G-1.2/0.9 failed in flexure by crushing of the concretein the compression zone. For the purpose of comparison,however, the shear at failure of this beam will be assumed asthe ultimate shear strength in the following sections.

Effect of reinforcement ratio and modulus of elasticity oflongitudinal reinforcing barsThe effect of the two components of the axial stiffness (Ef

and Af) of the reinforcing bars on the shear strength of thetested beams is shown in Fig. 6a. The vertical axis in Fig. 6arepresents the experimental shear strength either at ultimate

Vu exp or at inclined cracking Vcr exp of the beams of SeriesA, B, and C, which were tested under constant a/d = 1.69,while the horizontal axis represents the reinforcement ratio,rf. The solid lines represent Vu exp, and the dashed lines rep-resent Vcr exp. Figure 6a shows that beams reinforced withCFRP bars experienced larger Vcr exp and Vu exp in comparisonwith beams reinforced with GFRP bars, indicating the effectof Ef. The increase in Vcr exp for the CFRP-reinforced beamsover the GFRP-reinforced ones for the three reinforcement ra-tios ranged between 20% and 42%. On the other hand, thecorresponding increase in Vu exp ranged between 9% and 38%.Figure 6a also indicates that both Vcr exp and Vu exp in-

creased as the reinforcement ratio, rf, was increased. Increas-ing rf by 59% (from 0.78% to 1.24%) increased Vcr exp andVu exp by 18% and 9%, respectively, for the beams reinforcedwith CFRP bars, while the corresponding increases for thebeams reinforced with GFRP bars were 8% and 6%. Also, in-creasing rf by 119% (from 0.78% to 1.71%) increased Vcr expand Vu exp by 29% and 30%, respectively, for the beams rein-forced with CFRP bars, while the corresponding increases forthe beams reinforced with GFRP bars were 13% and 19%.

Effect of shear span to depth ratioThe variations in ultimate and inclined cracking shear

strengths, Vu exp and Vcr exp, with increasing shear span todepth ratio, a/d, are shown in Fig. 6b. The vertical axis inthis figure represents the experimental shear strengths Vu expor Vcr exp of the FRP-reinforced beams of Series B, D, and E,which had identical reinforcement ratios (rf = 1.24%), whilethe horizontal axis represents the a/d ratio. Figure 6b showsthat the ultimate shear strength, Vu exp, increased significantlywith decreasing a/d. Decreasing a/d by 23% (from 1.69 to1.30) increased Vu exp by 91% and 54%, respectively, for thebeams reinforced with CFRP and GFRP bars. In addition, de-creasing a/d by 46% (from 1.69 to 0.92) increased Vu exp by157% for the beams reinforced with GFRP bars. One cannote that beam C-1.2/0.9, reinforced with CFRP bars andtested under a/d = 0.92, had not reached its failure capacitydespite reaching the maximum loading capacity of the twoMTS actuators. Nevertheless, the shear force (500 kN) re-sisted by the beam C-0.9/1.2 at the end of testing was 156%in excess of the ultimate shear strength, Vu exp, of the beamC-1.2/1.6, which was tested under a/d = 1.69.The increase in the ultimate shear strength Vu exp with de-

creasing a/d can be attributed to the fact that the tied archingaction becomes more effective with decreasing a/d becauseof the increased angle between the inclined strut and longitu-dinal axis of the beam. The decrease in a/d decreases the dis-tance between the supports and the applied loads and henceincreases the effectiveness of the arching mechanism bytransmitting a greater part of the load directly to the supportby diagonal compression. As shown in Fig. 6b, however, theincrease in inclined shear strength Vcr exp was smaller com-pared with the variation of Vu exp with the decrease of a/d.

Analysis of test results using CanadianStandard CSA-S806-11In this section, the ultimate shear strengths of the tested

beams were predicted using the shear design provisions ofthe new version of the Canadian Standard CSA-S806-11

Fig. 6. (a) Experimental shear strength versus reinforcement ratio forbeams having a/d = 1.69 and (b) experimental shear strength versusshear span to depth ratio for beams having rf = 1.24%.

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(CSA 2011). The new version of CSA-S806-11 (CSA 2011)includes a new shear design procedure accounting for thearch action developed in deep beams. The ultimate shearstrength provided by concrete as recommended by CSA-S806-11 for sections with no axial load can be determinedaccording to the following equation:

½1� Vc ¼ 0:05lfckakmkrksðf 0cÞ1=3bwdvsuch that 0:11fc

ffiffiffiffif 0c

pbwdv � Vc � 0:22fc

ffiffiffiffif 0c

pbwdv, where l

is a factor that accounts for concrete density; fc is the resis-tance factor for concrete; f 0c is the specified compressivestrength of the concrete and shall not be taken to be greaterthan 60 MPa; bw is the web width of the beam; and dv is theeffective shear depth, taken as the greater of 0.9d or 0.72h,where d is the effective depth and h is the overall depth ofthe beam.The factors ka, km, kr, and ks can be calculated according to

the following:

½2� ka ¼ 2:5Mf

Vfd

for a=d � 2:5

1 ≤ ka ≤ 2.5 and ka = 1.0 for a/d ≥ 2.5, where Mf and Vf arethe factored moment and shear force, respectively, at the sec-tion of interest.

½3� km ¼ffiffiffiffiffiffiffiffiVfd

Mf

r� 1:0

½4� kr ¼ 1þ ðEfrfÞ1=3

where Ef is the modulus of elasticity of the longitudinal FRPreinforcement; and rf is the longitudinal FRP reinforcementratio.For members with effective depth, d, greater than 300 mm

and with less shear reinforcement than required by CSA-S806-11, the factor ks is calculated according to eq. [5a].

½5a� ks ¼ 750

450þ d� 1:0

For members with effective depth, d, not exceeding300 mm, the factor ks is given by eq. [5b].

½5b� ks ¼ 1:0

Equation [1] was used for predicting the ultimate shearstrengths of the test beams, with l and fc set to equal to1.0. The predicted shear strengths Vu pred of the beams werecompared with the experimental values Vu exp, as shown inTable 4. The table shows that the CSA-S806-11 method pro-vides reasonable conservative predictions for the shear ca-pacity of the beams, as the mean value of Vu exp/Vu pred was1.33, with a coefficient of variation of 12%. The table alsoshows that the level of conservatism of the predicted shearstrength for beams reinforced with GFRP bars is differentfrom that for beams reinforced with CFRP bars. The CSA-S806-11 method appears to be more conservative in predict-ing the shear capacity of GFRP-reinforced beams, while itappears to be more accurate in predicting the shear capacityof CFRP-reinforced beams.

ConclusionsThe main findings of this investigation can be summarized

as follows:

1. Eight beams, among the nine beams tested to failure, failedin shear. The prevailing shear mode of failure was the split-ting of the diagonal strut. With the decrease of the shearspan to depth ratio to lower than 1.0, the mode of failurechanged to flexural compression.

2. All beams reinforced with either CFRP or GFRP barsshowed redistribution of internal stresses after inclinedcracking by developing the arch action. The develop-ment of the arching behavior in the tested beams wasverified by the obtained result, indicating the uniformstrain distribution in the reinforcement along the beam.

3. The development of the arching action in the tested deepbeams allowed such beams to develop ultimate shearstrengths considerably higher than the inclined crackingshear strengths. The increase in the shear strength abovethe inclined cracking shear of the tested beams rangedbetween 95% and 198%, depending on the shear span todepth ratio.

4. The beams reinforced with CFRP bars showed increasedshear strength in comparison with the beams reinforcedwith the same amount of GFRP reinforcement, indicat-ing the effect of the modulus of elasticity of the FRP re-inforcing bars.

5. In general, the shear strength of the reinforced concrete deepbeams without web reinforcement was proportional to the

Table 4. Comparison of predicted and experimental shear capacities.

Beam fc′ (MPa) bw (mm) d (mm) a/d

Reinforcement

Vu exp (kN)

CSA-S806-11 (eq. [1])

rf (%) Ef (GPa) Vu pred (kN) Vu exp/Vu pred

C-0.7/1.6 39.4 250 326 1.69 0.78 134 179.5 153.9 1.17G-0.7/1.6 40.5 250 326 1.69 0.78 42 164.5 109.0 1.51C-1.2/1.6 39.4 250 326 1.69 1.24 134 195.0 177.7 1.10G-1.2/1.6 40.5 250 326 1.69 1.24 42 175.0 125.1 1.40C-1.7/1.6 39.4 250 326 1.69 1.71 134 233.5 196.0 1.19G-1.7/1.6 40.5 250 326 1.69 1.71 42 196.0 137.6 1.42C-1.2/1.3 39.4 250 326 1.30 1.24 134 372.0 261.6 1.42G-1.2/1.3 40.5 250 326 1.30 1.24 42 269.0 184.2 1.46Mean 1.33Standard deviation 0.16Coefficient of variation (%) 12

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amount of FRP longitudinal reinforcing bars. As the amountof longitudinal reinforcement was increased, the obtainedshear strength increased. This behavior was observed for thetwo different types of FRP reinforcing bars employed in thisinvestigation.

6. The shear span to depth ratio has a significant influence onthe ultimate shear strength of the reinforced concrete deepbeams without web reinforcement. As the shear span todepth ratio was decreased, the obtained ultimate shearstrength significantly increased. The increase in the in-clined shear strength, however, was less compared withthat of ultimate shear strength.

7. The ultimate shear strengths of the test beams were analyzedusing the shear design procedure prescribed by the newCSA-S806-11. The result of analysis indicated that theCSA-S806-11 design method provided reasonable conserva-tive predictions for the shear strength of the beams. How-ever, the level of conservatism of the shear strengthpredicted by the method appeared not to be constant withvarying the FRP type (glass or carbon FRP bars).

AcknowledgementsThe authors acknowledge the financial support from

NSERC, Pultrall Inc. (Thetford Mines, Quebec), ISIS-Canada,and the University of Sherbrooke.

ReferencesACI Committee 318. 2008. Building code requirements for structural

concrete (318-08) and commentary (318R-08). American ConcreteInstitute, Farmington Hills, Michigan.

ACI Committee 440. 2004. Guide test methods for fiber reinforcedpolymers (FRPs) for reinforcing or strengthening concretestructures. ACI 440.3R-04, American Concrete Institute, Farm-ington Hills, Michigan.

ACI Committee 440. 2006. Guide for the design and construction ofconcrete reinforced with FRP bars. ACI 440.1R-06, AmericanConcrete Institute, Farmington Hills, Mich.

Ahmad, S.H., Khaloo, A.R., and Poveda, A. 1986. Shear capacity ofreinforced high-strength concrete beams. ACI Journal, Proceed-ings, 83(2): 297–305.

CAN/CSA S806-11. 2011. Design and construction of buildingcomponents with fibre reinforced polymers. Canadian StandardsAssociation, Rexdale, Ontario.

El-Sayed, A.K. 2006. Concrete contribution to the shear resistance ofFRP-reinforced concrete beams. Ph.D. thesis, University ofSherbrooke, Sherbrooke, Quebec, Canada.

El-Sayed, A.K., El-Salakawy, E.F., and Benmokrane, B. 2005. Shearstrength of one-way concrete slabs reinforced with FRP compositebars. Journal of Composites for Construction, 9(2): 147–157.doi:10.1061/(ASCE)1090-0268(2005)9:2(147).

El-Sayed, A.K., El-Salakawy, E.F., and Benmokrane, B. 2006a.Shear capacity of high-strength concrete beams reinforced withFRP bars. ACI Structural Journal, 103(3): 383–389.

El-Sayed, A.K., El-Salakawy, E.F., and Benmokrane, B. 2006b. Shearstrength of FRP-reinforced concrete beams without transversereinforcement. ACI Structural Journal, 103(2): 235–243.

Gross, S.P., Dinehart, D.W., Yost, J.R., and Theisz, P.M. 2004.Experimental tests of high-strength concrete beams reinforced withCFRP bars. Proceedings of the 4th International Conference onAdvanced Composite Materials in Bridges and Structures(ACMBS-4), Calgary, Alberta, Canada, July 20–23.

ISIS-M03-07. 2007. Reinforcing concrete structures with fiber

reinforced polymers. The Canadian Network of Centers ofExcellence on Intelligent Sensing for Innovative Structures, ISISCanada, University of Winnipeg, Manitoba.

Japan Society of Civil Engineers (JSCE). 1997. Recommendation fordesign and construction of concrete structures using continuousfiber reinforcing materials. Concrete Engineering Series 23. Editedby A. Machida.

Oh, J.K., and Shin, S.W. 2001. Shear strength of reinforced high-strengthconcrete deep beams. ACI Structural Journal, 98(2): 164–173.

Pultrall Inc. 2005. V-RODTM – Technical Data Sheet. ADSComposites Group Inc., Thetford Mines, Quebec, Canada, http://www.pultrall.com.

Razaqpur, A.G., Isgor, B.O., Greenaway, S., and Selley, A. 2004.Concrete contribution to the shear resistance of fibre reinforcedpolymer reinforced concrete members. Journal of Composites forConstruction, 8(5): 452–460. doi:10.1061/(ASCE)1090-0268(2004)8:5(452).

Rebeiz, K.S. 1999. Shear strength prediction for concrete members.Journal of Structural Engineering, 125(3): 301–308. doi:10.1061/(ASCE)0733-9445(1999)125:3(301).

Teng, S., Ma, W., and Wang, F. 2000. Shear strength of concrete deepbeams under fatigue loading. ACI Structural Journal, 97(4): 572–580.

Tureyen, A.K., and Frosch, R.J. 2002. Shear tests of FRP-reinforcedconcrete beams without stirrups. ACI Structural Journal, 99(4)2002: 427–434.

Yost, J.R., Gross, S.P., and Dinehart, D.W. 2001. Shear strength ofnormal strength concrete beams reinforced with deformed GFRPbars. Journal of Composites for Construction, 5(4): 268–275.doi:10.1061/(ASCE)1090-0268(2001)5:4(268).

Zsutty, T. 1968. Beam shear strength prediction by analysis ofexisting data. ACI Journal, 65(11): 943–951.

Zsutty, T. 1971. Shear strength prediction for separate categories ofsimple beam tests. ACI Journal, 68(2): 138–143.

List of symbols

Af nominal cross-sectional area of FRP reinforcementa shear span (distance between concentrated load and sup-

port)bw web width of beamd effective depth of tensile reinforcementdb bar diameterdv effective shear depth, taken as the greater of 0.9d or 0.72hEf modulus of elasticity of FRP barsf 0c specified compressive strength of concreteh overall depth of memberka factor taking into account the effect of arch action on

member shear strengthkm factor taking into account the effect of moment at sec-

tion on shear strengthkr factor taking into account the effect of reinforcement ri-

gidity on shear strengthks factor taking into account the effect of member size on

its shear strengthln clear span of deep beamMf factored bending momentVc nominal shear capacity provided by concreteVcr inclined cracking shear strength

Vcr exp experimental inclined cracking shear strengthVf factored shear forceVu ultimate shear strength

Vu exp experimental ultimate shear strengthVu pred predicted ultimate shear strength

l factor to account for concrete densityfc resistance factor for concreterf FRP reinforcement ratio

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