ACI Structural Journal/January-February 2011 1

ACI Structural Journal, V. 108, No. 1, January-February 2011.MS No. S-2008-327.R2 received January 13, 2010, and reviewed under Institute

publication policies. Copyright © 2011, American Concrete Institute. All rights reserved,including the making of copies unless permission is obtained from the copyright proprietors.Pertinent discussion including author’s closure, if any, will be published in the November-December 2011 ACI Structural Journal if the discussion is received by July 1, 2011.

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

This paper presents the results of an investigation of shear strengthof large-sized concrete beams reinforced with ASTM A1035 Grade 100bars. The performance of these beams is compared to that ofsimilar beams reinforced with ASTM A615 Grade 60 bars. Theresults indicate that by using the higher yield strength of ASTM A1035bars with a reduced reinforcement ratio, the beams can achievesimilar shear strengths as the beams reinforced with Grade 60bars. The results also show that cracking and deflection underservice load of the beams with a reduced reinforcement ratio arewithin acceptable limits.

Keywords: beam; cracking; deflection; high-strength reinforcement; shearstrength; stirrup; web reinforcement.

INTRODUCTIONReinforcing bars conforming to ASTM A10351 are

characterized by their high tensile strength and enhancedcorrosion resistance in comparison to ASTM A6152 Grade 60bars. The use of these high-strength steel bars offers severaladvantages, such as the reduction of the reinforcement ratio,less cost for reinforcement placement, reduced reinforcementcongestion, better concrete placement, and an increase inservice life due to enhanced corrosion resistance. The high-strength reinforcing bars used in this investigation3 exhibit anonlinear stress-strain curve without a distinct yield plateaureaching a stress of 100 ksi (690 MPa) at 0.35% strain. Onemajor concern with using this high-strength steel bar iswhether the larger induced steel strains under service loadcould cause unacceptably large cracking and deflection ofthe reinforced concrete (RC) beam and whether the beamwould achieve adequate ductility under ultimate load.

The objective of this research is to examine the behaviorof concrete beams reinforced with different reinforcementratios of high-strength steel stirrups up to yield strength of100 ksi (690 MPa) and to evaluate the serviceability andeffectiveness of using high-strength steel as transverse reinforce-ment in flexural members. The paper also examines the abilityof current codes to predict the contribution of transverse steelto the shear capacity of RC flexural members.

RESEARCH SIGNIFICANCEThere are no experimental data or design guidelines for the

use of high-strength steel as shear reinforcement with a yieldstrength of 100 ksi (690 MPa) for RC flexural members. Mostof the research currently available in the literature focuses onthe use of high-strength steel as flexural reinforcement.4-9 Thispaper will provide much-needed information on the behaviorof high-strength steel stirrups designed for a yield strengthof 80 and 100 ksi (550 and 690 MPa) for RC members. Italso provides an evaluation of the current ACI 318-08,10 CSAA23.3-04,11 and AASHTO12 code provisions in predicting the

contribution of transverse steel to the shear capacity of RCflexural members.

EXPERIMENTAL PROGRAMThe experimental program included 18 tests using nine

large-sized RC beams tested under static loading up tofailure. All beams were 22 ft (6.7 m) long and were designedusing a nominal concrete compressive strength of 4000 psi(28 MPa). The beam length was chosen such that each beamcould be tested twice, thus doubling the amount of collecteddata. The shear span-depth ratio (a/d) of all specimens waskept constant.

The nine beams were classified into three groups based ontheir shear resistance. The spacing of the shear reinforcementwas varied to reflect a minimum and maximum level of shearresistance allowed by ACI 318-08.10 Test specimens weredesigned to induce stresses of 80 and 100 ksi (550 and 690 MPa)in the high-strength stirrups. Within each group, the beamswere geometrically similar and the shear reinforcement wasdesigned to achieve the same nominal shear capacity. Hookswere provided at both ends of the longitudinal tensionreinforcement to prevent anchorage failure. The transversereinforcement consisted of No. 3 and No. 4 (No. 10 and No. 13)closed stirrups designed according to ACI 318-0810

requirements, with a bend radius equal to six times the bardiameter and an extension of six times the bar diameter past the90-degree bend. Figure 1 shows the elevation and crosssection of the beams in Groups 1, 2, and 3. The cross sectionsand reinforcement details of all of the specimens are summarizedin Table 1. The beams shown in Table 1 are identified by threeparameters: the first two characters indicate the group towhich the beam belongs; for example, G1 is Group 1. Thesecond parameter specifies the longitudinal and transversesteel type, using C for conventional steel and M for high-strength steel. The third parameter is the specified designyield strength in the stirrup; 0 indicates no transversereinforcement, 60 indicates 60 ksi (415 MPa), 80 indicates80 ksi (550 MPa), and 100 indicates 100 ksi (690 MPa)design stress in the stirrup based on ACI 318-08.10 Thebeams were tested with a targeted a/d = 3. For the first fourbeams of Group 1 with a target shear capacity of 3 bd,the beams were tested with a loaded span equal to 19.0 ft (5.8m) as detailed in Table 2 and shown in Fig. 2. The same fourbeams were then rotated and tested with a loaded span equal to13.2 ft (4 m) while maintaining the same a/d of 3. This set oftests is identified as Group 2. With the smaller sectional

fc′

Title no. 108-S04

Behavior of Concrete Beams Reinforced with ASTM A1035 Grade 100 Stirrups under Shearby Aruna Munikrishna, Amr Hosny, Sami Rizkalla, and Paul Zia

ACI Structural Journal/January-February 20112

dimensions of the remaining five beams compared to thefirst four beams, it was possible to test these beams twiceusing the same setup configuration. For the replicate tests, anadditional letter “R” was added at the end of the identification todifferentiate the second test from the first test of the specimen. Ineach group, the beams reinforced with high-strength stirrups werecompared with beams reinforced with Grade 60 steel stirrups.Also, Beams G1-M0, G2-M0, G3-C0, and G3-M0 weredesigned without shear reinforcement and were used todetermine the nominal concrete contribution to the shearstrength Vc. Details of the experimental program can befound elsewhere.13

MATERIAL PROPERTIESLocal ready mixed concrete using Type I cement and a

maximum aggregate size of 3/8 in. (9.5 mm) was used toconstruct all specimens. Three 4 x 8 in. (102 x 204 mm)concrete cylinders were used to determine the compressivestrength of concrete in accordance with ASTM C39 at thetime of testing, as shown in Table 3.

Tension coupons from the reinforcing steel were used todetermine the stress-strain characteristics. Samples of No. 3and No. 4 Grade 100 and Grade 60 bars were taken from thesupply used to fabricate the beams. The stress-strain relationshipsfor No. 3 and No. 4 Grade 100 bars and Grade 60 bars areshown in Fig. 3. The Grade 60 bars used in this researchprogram had yield strengths greater than 60 ksi (415 MPa) anddid not exhibit a typical yielding plateau. The No. 3 bars had ayield strength of 80 ksi (550 MPa) compared to 69 ksi (475 MPa)for the No. 4 bars. Both bars had an ultimate strength ofapproximately 100 ksi (690 MPa), as shown in Fig. 3.

In general, the Grade 100 bars exhibit a linear stress-strainrelationship up to a stress level of 95 ksi (655 MPa) for No. 3and No. 4 bars. This linear behavior is followed by anonlinear behavior and reduction in the modulus of elasticityup to an ultimate strength of 155 ksi (1070 MPa) for No. 3bars and 160 ksi (1105 MPa) for No. 4 bars. The stress of 100 ksi(690 MPa) at a strain of 0.35% was taken as the yield strengthaccording to the recommendations of ACI 318-08,10

Section 3.5.3.2.

TEST SETUPThe test setup was designed to allow each beam to be

tested twice to replicate test data. Table 2 shows the testsetup details, including the location of the load from twosupports, the effective depth of beams, and the a/d for eachgroup. All beams were instrumented to measure applied

ACI member Aruna Munikrishna is a Practicing Engineer in the Raleigh, NC area.She received her BE from R.V. College of Engineering, Bangalore, India, in 2005, andher MSc from North Carolina State University, Raleigh, NC, in 2008.

ACI member Amr Hosny is a PhD Candidate in structural engineering at NorthCarolina State University, where he also obtained his MSc in 2007. He received hisBSc from Ain Shams University, Cairo, Egypt, in 2004.

Sami H. Rizkalla, FACI, is a Distinguished Professor of civil and constructionengineering in the Department of Civil, Construction, and Environmental Engineeringat North Carolina State University, where he also serves as the Director of the ConstructedFacilities Laboratory and NSF I/UCRC in Repair of Structures and Bridges.

ACI Honorary Member Paul Zia is a Distinguished University Professor Emeritus atNorth Carolina State University. He served as ACI President in 1989 and is a member ofseveral ACI committees, including ACI Committee 363, High-Strength Concrete; JointACI-ASCE Committees 423, Prestressed Concrete, and 445, Shear and Torsion; theConcrete Research Council; and the TAC Technology Transfer Committee, serving asChair of ITG-6.

Fig. 1—Typical cross sections for beams of Groups 1, 2, and 3.

Fig. 2—Typical section and test setup of beams.

ACI Structural Journal/January-February 2011 3

loads, deflections, crack widths, and steel strain. For eachbeam, a strain gauge was placed on one bar of the bottomlayer of the tension reinforcement at the location of theapplied load to measure strains. Weldable strain gauges wereused to measure strains in stirrups. The location of the weld-able strain gauges was determined by estimating the locationof the compressive strut acting from the point of load applicationto the support. The weldable strain gauges were attached tothe stirrups using a spot welder as recommended by themanufacturer. Three strain rosettes were attached to the frontface of the beam to measure the crack widths and the strainin the stirrups after cracking. The rosette consisted of three7.87 in. (200 mm) calibration test pressure gauges placed

horizontally, vertically, and inclined at 45-degree angles. Inaddition to the rosettes, six 3.94 in. (100 mm) calibrationtest pressure gauges were attached to the back face of thebeams to measure strain in a stirrup. Crack comparators werealso used to measure the crack width at different load levelsin addition to the rosettes. All instruments were connected toan electronic data acquisition system to continuously recordthe data. Figure 4 shows pictures of the instrumentation.

LOAD-DEFLECTION BEHAVIORThe applied shear versus deflection at the load point up to

failure for beams in Group 1, 2, and 3 is shown in Fig. 5. Theresults indicate that the precracking stiffness of the beams in

Table 1—Reinforcement details of beams

Group ID Target shear capacityCross section,

in. a/dDesign flexural

stress

Flexural steel Design stirrup stress Stirrup size

Spacing, in. ρtrTensile Compressive

1

G1-M0

Minimum 3 bd 24 x 28 3.1

100 ksi Four No. 11 Two No. 9 — — — —

G1-C60 CONV. 60 ksi Six No. 11 Two No. 9 CONV. 60 ksi No. 3 8.0 0.11

G1-M80 100 ksi Four No. 11 Two No. 9 80 ksi No. 3 10.0 0.09

G1-M100 100 ksi Four No. 11 Two No. 9 100 ksi No. 3 13.0 0.07

2

G2-M0

Minimum 3 bd 24 x 28 3.1

100 ksi Four No. 11 Two No. 9 — — — —

G2-C60 CONV. 60 ksi Six No. 11 Two No. 9 CONV. 60 ksi No. 3 8.0 0.11

G2-M80 100 ksi Four No. 11 Two No. 9 80 ksi No. 3 10.0 0.09

G2-M100 100 ksi Four No. 11 Two No. 9 100 ksi No. 3 13.0 0.07

3

G3-C0

Maximum 7 bd 16 x 22 3.0

CONV. 60 ksi Seven No. 11 Four No. 10 — — — —

G3-M0 100 ksi Five No.11 Four No. 10 — — — —

G3-C60 CONV. 60 ksi Seven No. 11 Four No. 10 CONV. 60 ksi No. 4 4.5 0.31

G3-M80 100 ksi Five No. 11 Four No. 10 80 ksi No. 4 5.5 0.25

G3-M100 100 ksi Five No. 11 Four No. 10 100 ksi No. 4 7.0 0.20

Note: 1 in. = 25.4 mm; 1 ksi = 6.895 MPa.

fc′

fc′

fc′

Table 2—Load location and a/d details

Group

Target shear

capacity

Cross section Loaded

span,ft

Test configuration Effective

depth, in. a/db, in. h, in. l1, in. l2, in. l3, in. l4, in.

1 3 bd 24 28 19.0 15 79 155 15 25.4 3.1

2 3 ′ bd 24 28 13.2 3 79 85 97 25.4 3.1

3 7 ′ bd 16 22 14.8 15 54 129 66 18.0 3.0

Note: 1 in. = 25.4 mm; 1 ft = 304.8 mm.

fc′

fc′

fc′

Fig. 3—Stress-strain relationship for No. 3 and No. 4 high-strength and Grade 60 steel. Fig. 4—Instrumentation.

4 ACI Structural Journal/January-February 2011

each group were almost identical, but there is a reduction inthe post-cracking stiffness of the beams reinforced with Grade 100bars using the design strength of 80 and 100 ksi (550 and690 MPa) due to the larger strains in the longitudinal reinforce-ment and the reduction of the transverse reinforcement ratios.The figures, however, show that despite the lower shear reinforce-ment ratio for beams reinforced with high-strength stirrups incomparison with a beam reinforced with conventional steelstirrups, all of the beams were capable of sustaining similarloads. This behavior is attributed to the use of the highertensile strength of high-strength steel. The use of the lowerlongitudinal reinforcement ratio for the beams reinforcedwith the high-strength steel caused higher deflectionscompared to the beams reinforced with the conventionalGrade 60 steel at the same load levels. The reduced transversereinforcement ratio results in larger crack widths andreduced stiffness of the beams reinforced with high-strengthstirrups. The beams without stirrups failed as expected in abrittle manner at a much lower load and had significantlyless deflection than the beams with transverse reinforcement.Beams reinforced for shear were capable of sustaining muchhigher loads and deflections and showed more ductile failures.

CRACK PATTERNThe general crack patterns observed for all beams within

the same group were identical. The first flexural crackoccurred at an applied load of 30 kips (133 kN) and waslocated near the location of the applied load and maximummoment. As the load increased, the flexural cracks propagatedtoward the compression zone and the number of flexuralcracks also increased. Flexural cracks tended to develop atapproximately the location of the stirrups. Therefore, thespacing of cracks was dominated by the location of the stirrups.As additional load was applied, new flexural cracks began toform toward the support, and these cracks developed intoflexural-shear cracks. For beams without transverse reinforce-ment (that is, Beams G1-M0, G2-M0, G3-C0, and G3-M0),a further increase in load resulted in the formation of a criticaldiagonal shear crack and sudden failure, as shown in Fig. 6for Beams G1-M0 and G2-M0 characterized by the formationof a single critical diagonal crack spanning from the point ofload application to the support. On the other hand, beamswith transverse reinforcement were capable of carryinghigher loads and were characterized by the initiation ofadditional flexure-shear cracks between the applied loadsand the supports. They exhibited a fairly ductile responsewithout explosive failure. As the loading continued, a well-defined shear crack formed at the middle of the shorter shearspan and propagated toward the support and the loading

Table 3—Service loads

Group ID b, in. d, in. fc′ , psi Stirrup size Spacing, in. Vc, kips Vs, kips Vn, kips Vn(avg), kips Vservice, kips θ No. of cracks

1

G1-C60

24 25

4710 No. 3 8.0 84 42 126

128 77

32 1

G1-M80 4710 No. 3 10.0 84 45 128 35 3

G1-M100 4950 No. 3 13.0 86 43 129 41 1

2

G2-C60

24 25

4710 No. 3 8.0 84 42 126

128 77

27 1

G2-M80 4710 No. 3 10.0 84 45 128 36 1

G2-M100 4950 No. 3 13.0 86 43 129 40 1

3

G3-C60

16 18

5090 No. 4 4.5 41 96 137

143 86

47 1

G3-M80 5240 No. 4 5.5 42 105 146 38 1

G3-M100 5840 No. 4 7.0 44 103 147 49 2

Note: 1 in. = 25.4 mm; 1000 psi = 6.895 MPa; 1 kip = 4.4482 kN.

Fig. 5—Applied shear versus deflection for beams ofGroups 1, 2, and 3.

ACI Structural Journal/January-February 2011 5

plates under the load. The shear crack widened and extendedtoward the supports at a faster rate than the flexure cracks.All beams failed due to crushing of concrete in the nodalzone of the compression strut connecting the nodes at thesupport and at the applied load, as shown in Fig. 6. Thefailure of Beams G3-M80 and G3-M100 was due to highstresses developed in the stirrups and the high compressionstresses in the strut, leading to crushing at the tip of the strut.

CRACK WIDTHCrack widths were measured using a crack comparator

and calibration test pressure gauges at each load level. Thelatter method uses the geometry of two calibration testpressure gauges in the rosettes to determine the summationof the shear crack width within the gauge length. In theanalysis, the vertical and diagonal gauge readings wereused to calculate the summation of the crack widths usingthe Shehata14 equation

where ΔV is the PI gauge reading in the vertical direction, ΔDis the PI gauge reading in the diagonal direction, θ is themeasured crack angle to the horizontal beam axis, lg is thegauge length of the PI gauge, and εct is the maximum tensileconcrete strain taken as 0.1 × 10–3. The average crack widthw was determined based on the number of cracks within thegauge length of the rosette. According to the commentary ofACI 318-08,10 at the service load level, the acceptable crackwidth is 0.016 in. (0.41 mm). The shear at service load forthis analysis was taken as 60% of the nominal shear strengthof the beam predicted using ACI 318-0810 for the givenreinforcement. Table 3 shows the service shear load for eachgroup, the number of cracks recorded at service load for eachbeam, and the measured angle of the crack θ with respect tothe beam axis. It should be noted that all beams weredesigned to achieve the same nominal shear capacity usingdifferent stirrup spacing for the specific yield strength of thesteel. Therefore, all of the beams within each group have thesame service load. It was also observed that the crack widthsmeasured by the calibration test pressure gauge and the crackcomparator were approximately the same for the beamswithin the same group. Therefore, only the crack widthsmeasured using the crack comparators are presented in thispaper. Furthermore, at service, the measured crack width

Σw 2ΔD Δv 0.5lgεct––( ) θsin Δv 0.5lgεct–( ) θcos+=

was less than 0.016 in. (0.41 mm) for all of the beams, asshown in Fig. 7, for Groups 1, 2, and 3. Due to the selecteddesign strength of 80 and 100 ksi (550 and 690 MPa) usedin high-strength stirrups, Beams G1-M80, G2-M80, andG3-M80 had a larger crack width in comparison toBeams G1-C60, G2-C60, and G3-C60, respectively. Figure 7shows that Beam G1-M100 in Group 1 had no cracks atservice load. This is mainly due to the higher compressivestrength of concrete in Beam G1-M100 that provided greaterconcrete contribution and delayed the formation of the firstshear crack. The first measured flexural-shear crack width of0.004 in. (0.1 mm) was recorded at 76 kips (338 kN) of shear.The results suggest that using high-strength stirrupsslightly increased the crack width in comparison toconventional stirrups.

Fig. 6—Failure for beams of Groups 1 and 2.

Fig. 7—Crack width versus applied shear for beams ofGroups 1, 2, and 3.

6 ACI Structural Journal/January-February 2011

STRAIN IN STIRRUPSThe strains in the stirrups were measured using the vertical

component of the calibration test pressure gauge rosette, thecalibration test pressure gauges on the back side of thebeams, and weldable strain gauges that were attached to thestirrups at selected locations for Beams G1-M80, G2-M80, G3-C60, and G3-M80. For Group 1, the measured shear versustransverse strain is shown in Fig. 8(a). The figure shows thatthe stirrups were stressed only after first cracking. The corre-sponding shear was taken as the concrete contribution toshear strength, Vc. The concrete contribution Vc was also esti-mated from the control specimens. Figure 8(a) indicates thatBeams G1-C60 and G1-M100 have a higher Vc compared toBeam G1-M0. This difference is due to the higher compres-sive strength of the concrete used for these beams. It can beseen that at any given load, beams reinforced with high-

strength stirrups have a slightly higher strain value due to thereduced transverse reinforcement ratio in comparison withbeams reinforced with Grade 60 stirrups. The test resultsindicated that the mere yielding of the transverse reinforcementof Beam G1-C60 did not cause the failure of the beam.Instead, the failure of the beams was due to the crushing of theconcrete in the nodal zone of the compression strut.

The shear versus strain relationship for the beams ofGroup 2 is shown in Fig. 8(b). The same phenomenon wasobserved where the strains in the beams reinforced withhigh-strength stirrups were higher at any given load leveldue to the lower transverse reinforcement ratio of thesebeams. It can also be seen that the strains measured from theweldable strain gauges, Curve G2-M80-WSG, closelymatched the strains measured using the PI gauges, CurveG2-M80. These results indicate that the strains in the trans-verse reinforcement for both beams exceeded 0.0025 and0.0035 corresponding to the design stress of 80 and 100 ksi(550 and 690 MPa), respectively, as determined from thestress-strain curves of the reinforcing bars; however, thebeams continued to sustain increasing loads. Failure wascaused due to crushing of the concrete in the nodal zone ofthe compression strut. It should be noted that the results forBeam G2-M100 were not included in Fig. 8, as failureoccurred due to a diagonal shear crack that occurred in thelonger shear span of the beam where no instrumentationswere provided.

Similar observations can be made for the beams of Group 3,as shown in Fig. 8(c). At any given load level, the strains arehigher for Beam G3-M100 with the lowest transversereinforcement ratio, followed by the strains for Beam G3-M80;Beam G3-C60 had the lowest strains in the stirrups becauseit had the highest transverse reinforcement ratio. ForBeams G3-M80 and G3-M100, it was observed that,following the formation of the first shear crack, the stirrupreached very high strains without much increase in the load.It is believed that once these stirrups yielded, the increase inthe applied load was transferred to the adjacent stirrups andso on until all of the stirrups yielded. Once all of the stirrupsin the shear span yielded, the compression strut carried additionalload, and failure occurred when the concrete at the nodal zone ofthe compression strut crushed. An explosive failure was observedin Beams G3-M80 and G3-M100. Spalling of the concrete coverwas also observed during testing. All of the stirrups wereterminated with 90-degree hooks. At high stresses, these90-degree hooks were insufficient in confining the concrete andopened up, resulting in an explosive failure; however, themeasured strains were higher than the strains corresponding to100 ksi (690 MPa) prior to failure.

CODE PREDICTIONSConcrete contribution to the shear strength of each beam

was determined by three methods: Vc1, using the test resultsfrom the control specimen without transverse reinforcement;Vc2, using the shear versus transverse strain relationshipwhen the strain is first detected in the stirrups; and Vc3, basedon the initiation of the first diagonal crack. The concretecontribution determined from these three methods iscompared with the predictions according to the ACI, CSA,and AASHTO codes in Table 4. It can be seen that for largerbeams—the beams in Groups 1 and 2—the concretecontribution was overestimated by all of the codes. This islikely due to the size effect, which is not accounted for in thecode equations. For the smaller-sized beams of Group 3, the

Fig. 8—Applied shear versus transverse strain for beams ofGroups 1, 2, and 3.

ACI Structural Journal/January-February 2011 7

code equations underestimated the concrete contribution. Also,there are some differences in the concrete contribution deter-mined by the different methods. For example, for Beam G1-C60, the control specimen failed at Vc1 = 51 kips (227 kN),whereas Vc2 = 65 kips (289 kN) based on the strain first detectedin the weldable strain gauge, and Vc3 = 56 kips (249 kN) wasobserved at the first diagonal cracking. These differences aredue to the fact that the initiation of the first diagonal crack didnot always pass through the instrumented stirrups with theweldable strain gauge. In addition, the diagonal crack couldbe too small to be visible, but it can be detected by the straingauges as is the case for Beam G2-M80, where Vc2 = 63 kips(280 kN) and Vc3 = 68 kips (303 kN).

The steel contribution Vs to the shear strength is comparedto the predicted values according to ACI 318-08,10 which isbased on a 45-degree truss model; CSA and AASHTOcodes, which are based on the Modified Compression FieldTheory, as shown in Table 5. The comparisons between theexperimental and predicted values by the code equationsindicate that ACI 318-0810 is the most conservative becauseit underestimates the steel contribution Vs from stirrups, especially

when high-strength steel is used. The test results also indicatethat CSA and AASHTO codes more accurately predict thesteel contribution Vs in all cases except for Beam G3-M100,which is more heavily reinforced with stirrups using a designstrength of 100 ksi (690 MPa).

CONCLUSIONSBased on the tests of large-scale beams reinforced with

high-strength longitudinal and transverse reinforcements,the following conclusions can be drawn:

1. The shear strength of flexural members can be achievedby using a lesser amount of high-strength stirrups and alower high-strength longitudinal reinforcement ratio incomparison with using Grade 60 reinforcement.

2. The use of the lower longitudinal reinforcement ratio forthe beams reinforced with high-strength steel caused higherdeflections compared to the beams reinforced withconventional Grade 60 steel at the same load levels.

3. The measured shear crack widths for all beams reinforcedwith high-strength stirrups designed with a yield strength of

Table 4—Code comparisons for Vc

Group ID S, in. Vc1, kips Vc2, kips Vc3, kips

ACI CSA AASHTO

Vc, kips Vc(exp)/Vc ratio Vc, kips Vc(exp)/Vc ratio Vc, kips Vc(exp) /Vc ratio

1

G1-C60 8.0 51 65 56 84 0.61 104 0.50 97 0.53

G1-M80 10.0 51 52 52 84 0.61 89 0.58 97 0.53

G1-M100 13.0 51 67 59 86 0.60 96 0.54 100 0.51

2

G2-C60 8.0 75 77 60 84 0.90 98 0.77 97 0.77

G2-M80 10.0 75 63 68 84 0.90 85 0.88 90 0.84

G2-M100 13.0 75 70 68 86 0.88 87 0.87 92 0.82

3

G3-C60 4.5 62 62 56 41 1.50 44 1.39 44 1.41

G3-C60-R 4.5 62 68 54 41 1.50 45 1.37 44 1.41

G3-M80 5.5 63 54 59 42 1.50 37 1.67 41 1.51

G3-M80-R 5.5 63 52 58 42 1.50 38 1.64 41 1.51

G3-M100 7.0 63 52 53 44 1.42 42 1.48 44 1.43

G3-M100-R 7.0 63 53 56 44 1.42 42 1.49 44 1.43

Average 1.11 1.10 1.06

Note: 1 in. = 25.4 mm; 1 kip = 4.4482 kN.

Table 5—Code comparisons for Vs

Group ID S, in. Vs(exp), kips

ACI CSA AASHTO

Vs, kips Vs(exp) /Vs ratio Vs, kips Vs(exp) /Vs ratio Vs, kips Vs(exp) /Vs ratio

1

G1-C60 8.0 82.8 50.3 1.65 71.2 1.16 76.8 1.08

G1-M80 10.0 72.5 44.7 1.62 60.1 1.21 68.3 1.06

G1-M100 13.0 61.2 43.0 1.42 58.8 1.04 65.7 0.93

2

G2-C60 8.0 78.9 50.3 1.57 69.8 1.13 76.8 1.03

G2-M80 10.0 59.8 44.7 1.34 59.1 1.01 60.3 0.99

G2-M100 13.0 61.3 43.0 1.43 56.7 1.08 58.0 1.06

3

G3-C60 4.5 149.9 108.8 1.38 129.7 1.16 156.1 0.96

G3-C60-R 4.5 145.1 108.8 1.33 130.2 1.11 156.1 0.93

G3-M80 5.5 149.4 104.7 1.43 131.9 1.13 135.1 1.11

G3-M80-R 5.5 143.0 104.7 1.37 132.8 1.08 135.1 1.06

G3-M100 7.0 126.3 102.9 1.23 133.0 0.95 132.7 0.95

G3-M100-R 7.0 129.4 102.9 1.26 132.5 0.98 132.7 0.98

Average 1.42 1.09 1.01

Standard deviation 0.13 0.08 0.06

Coefficient of variation 0.09 0.07 0.06

Note: 1 in. = 25.4 mm; 1 kip = 4.4482 kN.

ACI Structural Journal/January-February 20118

80 and 100 ksi (552 and 690 MPa) were within the allowablelimit recommended by ACI 318-08.10

4. At ultimate, failure is typically due to crushing of theconcrete strut for beams with and without stirrups. Forbeams with high-strength stirrups, the measured strains inthe stirrups were equal to or greater than the strain of 0.0035corresponding to 100 ksi (690 MPa) prior to crushing of theconcrete strut.

5. The ACI, CSA, and AASHTO LRFD design codes canall be used to predict the shear strength of concrete beamsreinforced with high-strength stirrups, with ACI 318-0810

being the most conservative. The predictions by the CSA andAASHTO codes are quite accurate and are very close to eachother. A yield strength up to 100 ksi (690 MPa) can be usedin the design of high-strength transverse reinforcement forflexural members without impairing the ultimate load-carryingcapacity and without exceeding the limits of the crack width.The stirrups, however, should have 135-degree hooks toprovide better anchorage when it is designed for such highstresses. More testing is recommended to validate this detail.

6. The ultimate load-carrying capacities recorded for all ofthe beams were at least five times the service load specifiedby ACI 318-08.10

ACKNOWLEDGMENTSThe authors would like to thank MMFX Technologies Corporation for

their financial support for this research. They are also indebted to severalmembers of the Constructed Facilities Laboratory, including J. Atkinson,B. Dunleavy, G. Lucier, and L. Nelson for their help with beam fabricationand laboratory testing.

REFERENCES1. ASTM A1035/A1035M-07, “Standard Specifications for Deformed

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