554 ACI Structural Journal/September-October 2010ACI STRUCTURAL
JOURNAL TECHNICAL PAPERACI Structural Journal, V. 107, No. 5,
September-October
2010.MSNo.S-2008-398.R3receivedAugust14,2009,andreviewedunderInstitutepublicationpolicies.Copyright2010,AmericanConcreteInstitute.Allrightsreserved,including
the making of copies unless permission is obtained from the
copyright
proprietors.Pertinentdiscussionincludingauthorsclosure,ifany,willbepublishedintheJuly-August
2011 ACI Structural Journal if the discussion is received by March
1,
2011.Laboratorytestsofreinforcedconcretebeamswithoutshearreinforcementhaveshownthattheshearstrength(intermsofaverage
shear stress) decreases as the size (depth) of the
memberincreases.Thispaperdiscussestheresultsofexperimentalresearchperformedtotestthehypothesisthattheeffectivedepthinfluencestheshearstrengthofreinforcedconcreteflexuralmembersthatdonotcontainwebreinforcementintherangeofoverall
depth between 12 to 36 in. (610 to 900 mm) where ACI
318-08doesnotrequireskinreinforcement.Theresultsoftestsoneightsimply
supported reinforced concrete beams without shear and
skinreinforcementaredescribed,discussed,andcorrelatedherein.Thelongitudinalreinforcementratiowasapproximately1.25%.Thetarget
concrete compressive strength was 10,000 psi (70 MPa). Thebeam
width varied between 8 and 24 in. (203 and 610 mm). All
ofthebeamsweresimplysupportedandmonotonicallyloadedinincrementsatmidspanuptodestruction.Theshearspan-depthratio
was maintained at 3.0. Test results show a reduction in
shearstrengthwithincreasingeffectivedepth;however,significantdifferences
in behavior were observed between the 12 in. (305
mm)specimensandthelargerspecimensintermsoftheamountofflexuralcracking,crackprogression,load-displacement,andload-strainmeasurementsdespiteholdingothertraditionallyconsideredinfluentialparametersconstant.Thesedifferencessuggestthatthereductioninshearstrengthwasinfluencednotonly
by a size effect but also by differences in behavior and
modeofsheartransferatfailure(beamactionversusarchaction).Forthe
beams tested in this study, flexural crack spacing did not
scalewithbeamsize.ThechangeinACI318-08restrictingisolatedbeams
without minimum shear reinforcement to heights not greaterthan 10
in. (250 mm) is supported by the findings of this study.Keywords:
cracking; reinforced concrete beams; shear strength tests;
sheartransfer
mechanisms.INTRODUCTIONTheshearstrengthoflargeconcretebeamshasbeeninvestigated
by researchers such as Taylor1 and Kani2
sincethe1960sandhasbeenthefocusofmuchrecentresearch.3-6Earlier
research has warned of a potential size effect on theshear strength
of these members; that is, the shear
strengthtendstodecreaseasthedepthofthebeamincreases.Additional
research has indicated that the shear
strengthofconcretebeamsisalsoafunctionofotherimportantparameters,
including the concrete compressive strength,longitudinal
reinforcement ratio, shear span-depth ratio, andmaximum aggregate
size.7 Collins and Kuchma5 found thata reduction in shear strength
at failure was also related to
themaximumspacingofthelayersofhorizontallongitudinalsteel.Thereisarelativelylimitedamountofexperimentaldata8
pertaining to concrete beams with an overall depth inthe range of
24 to 36 in. (610 to 900 mm), however, whereACI 318-089 does not
require skin reinforcement. (Skinreinforcement in the context of
this paper is the
well-distributedhorizontalreinforcementrequiredinbeamswithheightsgreater
than 36 in. [900 mm] and specified in Section 10.6.7of ACI 318-08.)
Therefore, more data on such members
areneededtosystematicallyexaminetheeffectofmemberdepth on the shear
strength of concrete beams without shearreinforcement and without
skin
reinforcement.Resultsoftestsoneightsimplysupportedreinforcedconcretebeamswithoutshearandskinreinforcementsubjectedtoaconcentratedloadatmidspanaredescribed,discussed,
and correlated herein. The major variables
studiedweretheoverallmemberheightandwidth.Thebeamsranged in overall
height from 12 to 36 in. (305 to 915 mm),as shown in Fig. 1. Values
for other key parameters shown toinfluence the shear strength
(namely, concrete
compressivestrength,percentageoflongitudinalsteel,maximumaggregate
size, type of loading, and shear span-depth
ratio)werestrategicallyselectedinanattempttominimizetheshearstrengthintermsofaverageshearstressandwereheld
constant.7RESEARCH SIGNIFICANCETests1-5 have shown that the average
shear stress requiredto cause failure in reinforced concrete beams
without shearand skin reinforcement decreases as the size of the
memberincreases.ThedatabaseofshearstrengthtestsonconcretebeamswithoutshearandskinreinforcementpresentedbyReinecketal.,8however,containslimiteddataonbeamswithanoveralldepthinthecriticalrangeof24to36in.(610to900mm)whereskinreinforcementintheformofwell-distributed
horizontal longitudinal steel is not requiredby ACI 318-08. Thus,
more test data, such as those presentedin this study, are needed to
study the effect of depth on theshear strength of concrete beams
without shear reinforcementin this critical range of overall depth.
Additionally, this studywas unique because the effect of depth was
studied in a
seriesofbeamsdesignedinanattempttominimizetheoverallshear strength
(in terms of average shear stress) by
selectingcriticalvaluesofkeyparametersbasedonresultsfromprevious
research studies.EXPERIMENTAL PROGRAMSpecimen designThe concrete
beams in this experimental program
rangedinheightfrom12to36in.(305to915mm)10.Theupperbound of the
height range of 36 in. (900 mm) was
selectedsuchthatlongitudinalskinreinforcementwouldnotbeTitle no.
107-S54Influence of Effective Depth on Shear Strength of Concrete
BeamsExperimental Studyby Lesley H. Sneed and Julio A. Ramirez555
ACI Structural Journal/September-October 2010required by the Code9
because skin reinforcement has
beenshowntoinfluencethecrackingbehaviorandincreasetheshear
strength, particularly in beams without shear reinforce-ment.5
Additionally, the height range was selected based
onthepaucityofdataontheshearstrengthofbeamswithoutshearandskinreinforcementinthedatabasedevelopedbyReineck
et al.8Two series of test specimens (Fig. 1) were fabricated
andtested. Beams in Series 1 (Specimens 1-1, 1-2, 1-3, and
1-4)varied in height from 12 to 36 in. (305 to 915 mm) and had
awidth of 12 in. (305 mm). Beams in Series 2 (Specimens 2-1,2-2,
2-3, and 2-4) varied in height from 12 to 36 in. (305 to915 mm) and
varied in width from 8 to 24 in. (203 to 610 mm).The beams in
Series 1 were intended to evaluate the effect
ofheightusingspecimensofconstantwidth,whereasthebeamsinSeries2wereintendedtoevaluatetheeffectofheightinspecimenswithaconstantwidth-to-heightratio.FurthercomparisoncanbemadebetweenSeries1and2beams
of the same height but different width (Specimens 1-1and 2-1, for
example).Thedesignloadingconsistedofaconcentratedloadlocated at the
center of the span, in addition to the self
weightofthespecimen.Eachbeamwasdesignedsuchthattheapplied load
corresponding to the nominal flexural
strengthMn,calculatedinaccordancewithACI318-08,was15to26% higher
than the load corresponding to the nominal shearstrength Vc
estimated by Eq. (1). Values for Vc and Mn aregiven in Table
1.(1a)(1b)Other parameters assumed to influence the shear
strengthofconcretebeamswithoutshearandskinreinforcement7were held
constant. Values of these parameters were selectedin an attempt to
minimize the overall shear strength (in
termsofaverageshearstress)basedontheireffectsonthebasicmechanismsofsheartransfer,namely:1)shearstressinuncracked
concrete (flexural compression zone); 2)
interfacesheartransfer(aggregateinterlock);3)dowelshearaction;and
4) arch action. A shear span-to-effective depth ratio, av/d,of 3.0
was chosen in an attempt to preclude deep beam actionand to
diminish the contribution from arching action,
basedonresultsbyKani.2Kanis2researchindicatedthatthedecrease in
average shear stress with increasing av/d tends tominimize at av/d
greater than approximately 3 for longitudinalreinforcement ratios
in the range of those used in this study(1.2 to 1.3%). The beams
had a target uniaxial concrete
cylindercompressivestrengthof10,000psi(70MPa)atthetestdate.The
value of 10,000 psi (70 MPa) was selected becauseSection 11.1.2.1
of ACI 318-08 limits the value of fcto 100 psi(8.3 MPa) in beams
without minimum web reinforcement. TheVc2 fc bwd(psi) =Vc0.166 fc
bwd(MPa)
=ACImemberLesleyH.SneedisanAssistantProfessorofcivilengineeringattheMissouriUniversityofScienceandTechnology,Rolla,MO.SheisanAssociatemember
of Joint ACI-ASCE Committee 445, Shear and Torsion. Her research
interestsincludedesign,rehabilitation,andstrengtheningofreinforcedandprestressedconcrete
structures.Julio A. Ramirez, FACI, is a Professor of civil
engineering and NEEScomm CenterDirector at Purdue University, West
Lafayette, IN. He is a member of ACI Committee318, Structural
Concrete Building Code, and Joint ACI-ASCE Committees 408, Bond
andDevelopment of Reinforcement, and 445, Shear and Torsion. He is
Chair of the ACIBoard Task Group on Joint Committees. He received
the ACI Delmar Bloem Awardin 2000 and the ACI Joe W. Kelly Award in
2006.Fig. 1Test specimen details. (Note: dimensions in inches; 1
in. = 25.4 mm.)556 ACI Structural Journal/September-October
2010maximum aggregate size in the concrete was limited to 3/8
in.(9.5 mm). The maximum aggregate size tends to influence
theinterfaceshear-transfermechanismasindicatedbyTaylor,1whoconcludedthattheshearstrengthofconcretedecreasesslightly
with decreasing maximum aggregate size. The use of
arelativelysmallmaximumaggregatesizeintheconcretemixture was used
to obtain a practical lower bound with respectto the effects of
aggregate size on the concrete shear strength.The longitudinal
reinforcement in each beam consisted ofa single layer of ASTM A615
Grade 60 deformed reinforcingbars. The longitudinal reinforcement
ratio was held constantat approximately 1.25% and met the minimum
requirementsofACI318-08,Section10.5.1.Concretecovertothelongitudinal
reinforcement ranged from 2.5 to 3.0 in. (64 to76 mm), and the
relevant cover requirements in Chapter 7 ofACI 318 were met. In
Specimen 1-4, bar spacing
requirementswereslightlylessthanthosespecifiedinACI318-08;however,becausethemaximumaggregatesizeintheconcrete
was limited to 3/8 in. (9.5 mm) and the concrete wasproperly
consolidated, the concrete was able to flow readilybetween the bars
as it was being placed. Longitudinal reinforcingbars were anchored
at the specimen ends using mechanicalanchors. Additionally,
full-height ties (confining
reinforcement)wereplacedaroundthelongitudinalreinforcementintheanchorage
zones from the interior face of the support plate
tothefreeendofthelongitudinalreinforcingbarstohelpconfine the
concrete in this region. The detailing of the
reinforce-mentisshowninFig.1.Table2summarizestheas-builtdimensions
and material properties for each test specimen.Material
propertiesNormalweight concrete was produced by a local ready
mixsupplier with Type 1 portland cement and aggregates local tothe
region. Average values of concrete compressive
strengthtestsandsplittingtensilestrengthtests,eachusingtheaverage
of three 4 x 8 in. (100 x 200 mm) concrete
cylindersatthetestdate,aregiveninTable2.ReinforcingbarsTable 1Test
specimen design and test values summarySpecimenVc(Eq. (1)),kips
(kN)Mn,*kip-in. (kN-m)Ptest,kips (kN)Vtest,kips (kN)Mtest,kip-in.
(kN-m)vtest= Vtest/bwdpsi (MPa)vtest,fc Vtest/VcMtest/MnSeries
11-121.5(95)718(81.1)58.5(260)29.5(131)809(91.4)269(1.86)2.75 1.38
1.131-249.3(219)4116(465.0)60.7(270)31.4(140)1937(218.8)125(0.86)1.28
0.54
0.471-362.5(279)6975(788.1)63.3(282)33.2(148)2629(297.0)103(0.71)1.06
0.53
0.381-478.1(347)10,779(1217.9)70.6(314)37.7(168)3595(406.2)97(0.67)0.93(0.97)0.47
0.33Series
22-114.7(65)567(64.1)25.5(113)12.9(57)354(40.0)175(1.21)1.76 0.88
0.622-264.8(288)5424(612.9)67.4(300)35.0(156)2161(244.1)105(0.72)1.08
0.64
0.402-3107.1(476)12,267(1386.0)112.2(499)58.8(262)4650(525.4)109(0.75)1.10
0.55
0.382-4155.8(693)21,527(2432.2)149.3(664)79.3(353)7582(856.6)102(0.70)0.99(1.02)0.49
0.35*Values calculated using stress block approach.Values reported
include specimen self weight and are calculated at distance d from
face of support plate.Values indicate specimen self weight.Values
in parentheses indicate calculation is based on limitation of 100
psi (8.3 MPa) for value of fcin accordance with ACI 318-08.Table
2Test specimen as-built dimensions and material properties
summarySpecimenL,in. (mm)bw,*in. (mm)h,*in. (mm)d,in.
(mm)av/dAs,in.2 (mm2),%fc ,psi (MPa)ft,psi (MPa)fy,psi
(MPa)Loadedplate width,in. (mm)Supportplate width,in. (mm)Series
11-155.00(1397)12.00(305)12.06(306)9.13(232)3.011.32(852)1.209580(66.1)690(4.75)62,500(431)3.0(76)3.0(76)1-2124.50(3162)12.06(306)24.06(611)20.88(530)2.983.16(2039)1.259580(66.1)655(4.50)65,700(453)7.0(178)6.0(152)1-3160.00(4064)12.00(305)30.00(762)26.81(681)2.984.00(2581)1.249430(65.0)650(4.50)68,700(474)10.5(267)6.0(152)1-4194.00(4928)12.06(306)36.00(914)32.37(822)3.005.08(3277)1.3010,840(74.8)725(5.00)68,900(475)14.0(356)6.0(152)Series
22-155.00(1397)8.00(203)12.06(306)9.19(233)2.990.93(600)1.269940(68.6)605(4.20)70,000(483)3.0(76)3.0(76)2-2124.50(3162)16.06(408)23.94(608)20.81(529)2.994.00(2581)1.209400(64.8)660(4.55)68,700(474)7.0(178)6.0(152)2-3160.00(4064)20.00(508)30.00(762)26.94(684)2.977.00(4516)1.309880(68.1)670(4.65)68,700(474)10.5(267)6.0(152)2-4194.00(4928)24.13(613)36.00(914)32.37(822)3.0010.16(6555)1.3010,570(72.9)640(4.40)68,900(475)14.0(356)6.0(152)*Values
reported are minimum values measured within shear span, av, of
specimen.Width is in direction of span.ACI Structural
Journal/September-October 2010
557meetingASTMA615Grade60wereused.Yieldstrengthresults from
standard coupon tests are also given in Table 2.Fabrication and
curingSpecimenswereconstructedandtestedintheKettelhutStructuralEngineeringLaboratoryatPurdueUniversity.Reinforcing
steel cages were assembled in the lab and weresupported from the
soffit by steel bar supports. Concrete wasbatched and delivered by
a local concrete ready mix supplier.All of the beams were moist
cured for 3 to 4 days and, afterformwork removal, were stored in
the laboratory until theywere tested. The age of concrete at the
test date was at least59 days after casting.Test setup and
instrumentationEach beam was simply supported, with the north
support apinandthesouthsupportaroller.Inallcases,thesupportplates
were at least the full width of the specimen.
Specimenswereloadedwithanappliedconcentratedloadatthemidspan. For
Specimens 1-1, 1-2, 1-3, 1-4, 2-1, 2-2, and 2-3,the load was
applied through a single load cell located at thecenter (midwidth)
of the beam. A swivel-head ball-bearingsystem was placed between
the load cell and the load platewhen testing Specimens 1-2, 1-3,
1-4, 2-2, and 2-3 (shown inFig. 2(a)). For Specimen 2-4, the load
was applied throughtwo load cells aligned in the beam width
direction.
Specimens1-2,1-3,1-4,2-2,2-3,and2-4wereloadedunderloadcontrol using
a 600 kip (2700 kN) capacity hydraulic
testingmachine(refertoFig.2(a)).Specimens1-1and2-1wereloaded using
a 30 ton (270 kN) hydraulic ram connected to
a10,000psi(70MPa)handpump.Theramwaslocateddirectly under and
reacted off the 600 kip (2700 kN) capacityhydraulic testing machine
used in testing the other specimens(refer to Fig. 2(b)).Uniaxial
electrical resistance strain gauges were
attachedtothelongitudinalreinforcingbarsatlocationsselectedtostudythevariationoflongitudinaltensilestrainsalongthelengthofthereinforcementshowninFig.3.Straingaugeswerealsoattachedtotheconfiningreinforcementtostudythe
behavior of the confining reinforcement, both before
andafterthemaximumloadwasachieved.Displacementwasmeasuredwithlinearlyvariabledifferentialtransformers(LVDTs)attachedalongthefaceofeachbeamatthesupports,midspan,andthequarterpointsalongthespan.Rotation
transducers were located at each support.Test resultsFailure loads,
given as Ptest, and shear force calculated ata distance d away from
the interior face of the support plates,given as Vtest, for each
beam are given in Table 1. (Note thatthe values for applied load
and shear force in Table 1 includeweights of equipment not
registered by the load cells. Valuesfor shear force also include
the self weight of the
specimens.)Figure4showstheaverageshearstressatfailureforeachbeam
tested, Vtest/bwd, graphed on the vertical axis
againstthecorrespondingeffectivedepthdalongthehorizontalaxis. For
comparison, Vc/bwd calculated by Eq. (1) for fc=10,000 psi (70 MPa)
is also shown in the figure.DISCUSSION OF TEST RESULTSGeneral
behaviorTwodistinctmodesoffailurewerenoted.Inallofthebeams except
for Specimen 1-1, the peak load was reachedwhen the inclined crack
penetrated the compression zone
ofthebeamneartheloadingplatepriortoyieldingofthelongitudinalreinforcement.InSpecimen1-1,atied-archdeveloped,
and the mode of failure was associated with
thefailureofthedirectstrutthatformedbetweentheappliedload and the
supports.The load-displacement history for all beams measured
atthemidspanisshowninFig.5.Inthefigure,theload-displacement
behavior of beams with the same overall heightis shown in the same
graph to study the effect of width for
agivenheight.TheverticalaxisofFig.5showsthetotalappliedload-displacementrelationshipsofeachpairofspecimens
of the same height after dividing the applied loadfor each specimen
by its corresponding width bw. With theexception of the 12 in. (305
mm) deep beams (Specimens
1-1and2-1),thepairsdisplaysimilarload-displacementrelationships and
reached their maximum load at a
similarlevelofdisplacement.Theload-displacementrelationshipsof the
12 in. (305 mm) deep beams, however, are similar upto Point C noted
in Fig. 5 and are significantly different
attheirrespectivemaximumdisplacementlevels,withtheFig. 3Test
specimen instrumentation.Fig. 2(a) Test Specimen 2-3: second major
inclined crack,south support, west face (applied load P = 112.2
kips [499
kN]);and(b)TestSpecimen1-1:crackpatternatfailure,northsupport, west
face (applied load P = 58.5 kips [260
kN]).Fig.4Averageshearstressatfailure,vtest=Vtest/ bwd,versus
effective depth d.558 ACI Structural Journal/September-October
2010displacementofSpecimen1-1morethantwicethatofSpecimen
2-1.InSpecimen1-1,thechangeintheslopeoftheload-displacement
relationship at Point A in Fig. 5 corresponds toflexural cracking.
Point B marks an increase in the
magnitudeofthelongitudinalstrainsinthereinforcementattheinteriorface
of the south support. This can be seen in Fig. 6 at the Gauge
9location, where the ordinate of Point B in Fig. 5 corresponds toan
ordinate value of approximately 40 kips (180 kN). Point Cindicates
a load level where a significant increase in the
strainrateattheinteriorfaceofthenorthsupportwasnoted.Theauthors
assign these changes to the presence of fully
developedinclinedcracksandaredistributionofthesheartransfermechanismstakingplace.Afinalslopechangeintheload-displacementrelationshipcanbeseenatPointD,whichisattributedtoyieldingofthelongitudinalreinforcementcorre-sponding
to an ordinate value of approximately 58 kips (260 kN).Cracks were
observed and marked on the west face of
eachbeamatloadincrementsstartingfromtheloadatwhichflexuralcrackingwasfirstobserveduntilclosetofailure.Before
the appearance of the first flexural cracks, all of
thebeamsexhibitedlinearelasticbehaviorasindicatedbytheload-displacementrelationshipsinFig.5.Afterflexuralcracks
appeared in the region of high moment, the behaviorof the beams
under increasing load varied according to
theeventualmodeoffailure.Crackpatternsweredrawntoscale,asshowninFig.7.AscanbeseenfromFig.7,theflexuralcrackspacingalongthelongitudinalaxisofthebeam
measured at the level of the longitudinal reinforcementwas
approximately the same in all of the beams, despite thevariation in
the overall beam height of 300%. In other
words,theflexuralcrackspacingmeasuredatthelevelofthelongitudinalreinforcementdidnotchange(orscale)withbeam
height.After the flexural cracks developed vertically up to a
certainpoint,theirgrowthsloweddownandinsomeinstancescompletelystopped.Atthisstage,underfurtherincreaseinapplied
load, inclined cracks began to appear. In most cases, theinclined
cracks were continuations of existing flexural cracks.Under further
increase in the applied load, the inclined
cracksprogressedupwardtowardtheappliedloadanddownwardalong the
longitudinal reinforcement, producing localized
splittingtowardthesupport(Fig.7).Inmostofthespecimens,somelocalizeddebondingalongthelengthofthelongitudinalFig.6Measuredlongitudinalbarstrainsalonglength.(Note:
1 kip = 4.45 kN.)Fig. 5Comparison of load-midspan displacement
curves forspecimens with same depths (applied load has been
normalizedwith respect to specimen width, bw, in each graph).ACI
Structural Journal/September-October 2010 559reinforcement occurred
within the shear span, as indicated bythe presence of localized
horizontal splitting cracks.The crack progression of Specimens 1-1
and 2-1
supportsthenotionoftheformationofadirectcompressivestrutmechanismassociatedwithhorizontalsplittingalongthelongitudinalreinforcementandtheconsequentlocalizeddebondingofthisreinforcementinamanneranalogoustotied-archbehavior.AscanbeseeninFig.7,theinclinedcrack
pattern, particularly in Specimen 1-1 and on the northshear span of
Specimen 2-1, was more linear than curvilinear, asobserved in the
other specimens. Also, more
localizedsplittingwasobservedinthesetwospecimensthanintheothers.Further,
Specimens 1-1 and 2-1 each had only a single flexuralcrack in each
shear span, whereas the larger specimens hadmultiple flexural
cracks in each shear span. In Specimen 1-1, thefailure crack
extended diagonally from the load plate to thesupport plate, and
several inclined cracks formed before themaximum load was achieved,
indicating that the redistribution ofinternal forces was taking
place.It must be noted that for the beams tested in this program,
theinclinedcrackingload,evenwiththeaidofthestrainmeasurements,wasdifficulttodetermineprecisely.Despitethe
lack of precision in determining the corresponding load,
theinitiation of the inclined crack signals a definite change in
thebehaviorofthebeamwithoutwebreinforcement.Forthebeams in this
study, the initiation of the inclined crack did notresult in the
immediate collapse of the beam. This behavior hasbeen observed by
many different researchers and is explainedin ACI 445R,7 where the
initiation of an inclined crack
resultsinacomplexredistributionofforcesthatchangesthecontributionsofthedifferentmechanismsofsheartransfer.Theappliedload-longitudinalstrainrelationshipissuddenlyalteredbecausetheinclinedcrackintroducesadditionaldeformation
without a corresponding increase in load. In thebeams tested, for
loads smaller than the inclined cracking load,the longitudinal
reinforcing steel strain distribution
measuredalongthespancorrespondedcloselytotheshapeofthemoment
diagram. When inclined cracks were fully developed,however, the
strain measured in the longitudinal reinforcementat the section
where the inclined crack intersected the reinforce-ment changed
suddenly to a much higher
value.Figure6showsthestrainmeasuredinthelongitudinalreinforcement
at key locations along the beam length givenin Fig. 3 at increments
of applied load between first flexuralcracking and peak load for
Specimens 1-1, 2-1, and 2-3. Thedistribution shown for Specimen 2-3
is representative of thelarger specimens. At the higher load
levels, Specimens 1-1and 2-1 were the only beams in which strains
were measuredin the longitudinal reinforcement at the supports
where themoment is zero (Gauges 2 and 3 at the North Support,
andGauges 9 and 10 at the South Support in Fig. 6). Specimen
1-1wastheonlybeaminwhichyieldingwasrecordedinthelongitudinalreinforcementanywherewithinthespan.Infact,bythetimethefailure(peak)loadwasachieved,thelongitudinalreinforcementhadyieldedacrosstheentireclearspan(Fig.6),indicatingthatthespecimenwasbehavingasatiedarch.Thetieportionofthetied-archconsistedofthelongitudinalreinforcement,mostlydebondedduetolocalizedsplittingalongtheentireclearspan
and well-anchored in the anchorage zones beyond
thesupports.Thetied-archbehaviorinSpecimen1-1allowedthemembertocarryadditionalloadwellbeyondtheloadattributed
to the presence of fully developed inclined
cracks(diagonalcracking).ThelongitudinalstrainsmeasuredinSpecimen
2-1 at the peak load, particularly in the south
shearspan,showadistributionsimilartothatofSpecimen1-1;however, full
yielding and tied-arch behavior did not occur. ACI Committee 42611
explained that arch compression inbeams is resisted in part by
dowel forces in the longitudinalreinforcement, which results in
horizontal splitting along
thebars.Itmustbenotedthattheformationofthearchmechanismintheformofasinglestrutbetweentheloadplateandthesupportplatestartsgraduallyintheformofcompression
fans at both load and support plates. These fansrequire the dowel
forces for equilibrium as they intersect
thelongitudinalreinforcementinbeamswithoutstirrups.Specimens1-1and2-1weretheonlyspecimenswheretensile
strains were recorded in the confining
reinforcementintheanchoragezonesbeforethemaximumloadwasachieved.
Figure 8 shows the applied load-strain relationshipsmeasured in the
confining reinforcement near the level of
thelongitudinalreinforcement.Specimen2-3,whichisrepresentative of
the larger specimens, shows no
measuredtensilestrainsintheconfiningreinforcement.Incontrast,Specimens
1-1 and 2-1 both show tensile strains measured inthe confining
reinforcement starting to increase at the
sameloadatwhichmeasuredtensilestrainsinthelongitudinalreinforcement
at the support started to increase. The role
oftheconfiningreinforcementintheanchoragezonescanbeunderstoodasassistinginthedowelmechanismbyproviding
support to the longitudinal reinforcement
togetherwiththesupportreaction-inducedcompressionandatthesametimeresistingthetransversetensilestrains(outofFig.
7Final crack patterns, west face (drawn to scale).560 ACI
Structural Journal/September-October 2010plane) in the concrete
induced by the same support
reactioncompression.TheauthorspostulatethatthedifferenceindowelshearstrengthbetweenSpecimens1-1and2-1mayalsoexplainthedifferenceinshearstrengthbetweenthesetwo
specimens and why the direct strut was able to reach thesupport in
Specimen 1-1 but not in Specimen
2-1.Inbeamswithoutstirrups,mechanicalendanchorageappears to have
little, if any, effect on resistance to diagonaltension, as was the
case in these tests. In all beams, strainsmeasured in the
longitudinal reinforcement at the end of
thebars,thatis,immediatelyinfrontofthemechanicalanchoragelocationsshowninFig.3,werenegligibleuntilafterthefailureloadwasachieved,indicatingthatthemechanical
anchors were not engaged before failure and
thusdidnotcontributetotheresistance.Abrams12foundexperimentallythatbarsanchoredbyvarioustypesofbearinganchoragestendtogivehighvaluesofbond,butonlyafterconsiderableendslipoccurs.Becausenoslipofthelongitudinalreinforcementoccurredintheanchoragezones,
it can be concluded that the end anchorage conditiondid not
influence the magnitude of the failure load.Shear strengthAs can be
seen from Fig. 4, in the range of overall heightfrom 24 to 36 in.
(610 to 915 mm), the average shear
stressatfailurerangedfromalowof97psi(0.67MPa)inSpecimen 1-4 to a
high of 125 psi (0.86 MPa) in Specimen1-2. For the 24 to 36 in.
(610 to 915 mm) beams, the rate
ofshearstrengthreductionwithincreasingheightwasapproximately
linear, and a 50% increase in overall
height(55%increaseind)correspondedtoa14%reductioninaverageshearstrength.Whenthe12in.(305mm)deepbeamsareincludedinthecomparison,therateofshearstrength
reduction with increasing height is no longer linearand is more
significant. Comparing the 12 to 36 in. (305 to915 mm) beams, the
reduction in average shear strength
was64%and44%fortheSeries1andSeries2specimens,respectively.Withrespecttopairsofbeamsofthesameoverallheight,Fig.4showsthattheshearstrengthofSpecimens1-4and2-4wasnearlythesame(intermsofaverage
shear stress), despite a difference in width-to-heightratio.
Similarly, the shear strength of Specimens 1-3 and 2-3was nearly
the same. Specimens 1-2 and 2-2 show an 18%difference in shear
strength, whereas Specimens 1-1 and
2-1hadthelargestdifferenceinshearstrength(42%)betweenany specimen
pairs of the same height.The behaviors of Specimens 1-1 and 2-1,
however,
weresignificantlydifferentthanthebehavioroftheothersixspecimensandarecriticaltounderstandthedifferencesinshear
strength observed in this study. Significant
differencesinbehaviorwereobservedbetweenthe12in.(305mm)specimensandthelargerspecimensintermsofamountofflexural
cracking, crack progression, load-displacement, andload-strain
measurements despite holding other traditionallyconsidered
influential parameters constant. These
differencessuggestthatthereductionwasinfluencednotonlybytheeffective
depth parameter, but also by factors that
influencedthedifferenceinbehaviorandmodeofsheartransfer.Inother
words, the effective depth parameter was not entirelyisolated;
thus, the observed reduction in shear strength wasnot entirely due
to a size effect.The nominal calculated shear strength Vc of each
specimen,computed using Eq. (1), is given in Table 1. The
calculatedshear strength is based on the measured strengths of
materialsand the as-built dimensions. The nominal calculated
flexuralstrengthofeachspecimenMn,computedbyusingtherectangular
stress block approach given in ACI 318-08 witha limit compressive
strain in the concrete of 0.003 and withthe measured strengths of
materials and the as-built dimensions,is also given in Table 1 for
each beam. Table 1 also indicatesthe applied concentrated load at
failure Ptest, and correspondingshear Vtest, at distance d from the
face of support (includingself weight). The ratios Vtest/Vc and
Mtest/Mn for each beamare also shown in the table. The ratios of
test-to-calculatedshear in accordance with Eq. (1) are shown in
Fig. 4. Figure 4shows that with the exception of Specimen 1-1, the
beams inthis study failed in shear with shear strength levels below
thevalue of Vc calculated by Eq. (1) from ACI 318-08. In fact,Vc
calculated by Eq. (1) is nearly twice the measured shearstrength
for the specimens with heights ranging from 24 to36 in. (610 to 915
mm).Therelationshipbetweentheratiooftest-to-calculatedshear force
per Eq. (1) and the effective depth d is shown
inFig.9forthebeamsinthisstudy,supplementedwiththespecimens included
in the database by Reineck et al.8
WiththeexceptionofSpecimen1-1,theresultsofthebeamsinthis test
series tend to plot at the lower bound of the test datain the
database. This observation confirmed that the strategyfollowed in
the design of the test program, which aimed atselecting the
critical parameter values so as to minimize theoverall shear
strength (in terms of average shear
stress).CONCLUSIONSTostudythepotentialeffectsofmemberdepthontheconcretecontributiontotheshearstrengthofflexuralmembers
without shear and skin reinforcement, eight beamsFig. 8Measured
strains in confining reinforcement.ACI Structural
Journal/September-October 2010 561were tested and the results are
discussed herein. The beamsrange in height from 12 to 36 in. (305
to 915 mm) based onthe paucity of available test data for specimen
heights in
thisrange.Valuesforotherparametersshowntoinfluencetheshear strength
of concrete beams (that is, fc , av/d, , type
ofloading[uniformlydistributedloadversusconcentratedload] and
maximum aggregate size agg) were held constantin an attempt to
isolate the effect of the parameter d. Basedon the behaviors
observed, the following conclusions are
made:1.Testresultsshowareductioninshearstrengthwithincreasing
effective depth; however, significant
differencesinbehaviorwereobservedbetweenthe12in.(305mm)specimensandthelargerspecimensintermsofamountofflexural
cracking, crack progression, load-displacement, andload-strain
measurements despite holding other traditionallyconsidered
influential parameters constant. These
differencessuggestthatthereductionwasinfluencednotonlybytheeffective
depth parameter, but also by factors that
influencedthedifferenceinbehaviorandmodeofsheartransfer.Inother
words, the effective depth parameter was not entirelyisolated;
thus, the observed reduction in shear strength wasnot entirely due
to a size effect.2. In the range of overall height from 24 to 36
in. (610
to915mm),theaverageshearstressatfailurerangedfromalowof97psi(0.67MPa)inSpecimen1-4toahighof125psi(0.86MPa)inSpecimen1-2.Forthe24to36in.(610
to 915 mm) beams, the rate of shear strength reduction
withincreasing height was approximately linear, and a 50%
increaseinoverallheight(55%increaseind)correspondedtoa14%reduction
in average shear strength. When the 12 in. (305
mm)deepbeamsareincludedinthecomparison,therateofshearstrength
reduction with increasing height is no longer linear andis more
significant. Comparing the 12 to 36 in. (305 to 915
mm)beams,thereductioninaverageshearstrengthwas64%and44% for the
Series 1 and Series 2 specimens, respectively.3. Despite holding
av/d constant, different mechanisms ofshear transfer were observed
at failure, which led to
significantlydifferentshearstrengths.Specimens1-1and2-1achievedhigher
shear strengths in terms of average shear stress due toarch type
behavior, as illustrated by the failure crack patternsand
distribution and magnitude of the strains measured in
thelongitudinal and confining reinforcement. This behavior wasnot
observed in the other beams tested in this study.4. Despite the
range of overall depth (12 to 36 in. [305
to915mm]),theaverageflexuralcrackspacingmeasuredatthelevelofthelongitudinalreinforcementinallthetestspecimenswasapproximately10in.(250mm);inotherwords,
flexural crack spacing did not scale with beam height.
5.WiththeexceptionofSpecimen1-1,thebeamsinthisstudy failed in shear
with shear strength levels below the valueof Vc calculated by Eq.
(1) from ACI 318-08. In fact, Vc calculatedby Eq. (1) is nearly
twice the measured shear strength for thespecimens with heights
ranging from 24 to 36 in. (610 to 915 mm).Specimen 1-1, which also
failed in shear, was the only specimenwith shear strength above the
value given by Eq.
(1).6.Finally,allofthebeamsinthisstudyfailedinshearcompressionataloadhigherthanthatcorrespondingtotheformationofthefullydevelopedinclinedcrack.Thisfindingsupports
the viewshared by other researchersthat the fullydeveloped inclined
cracking load should be taken as the measureof the useful shear
capacity of a reinforced concrete beam.DESIGN RECOMMENDATIONSWith
the exception of Specimen 1-1, the beams in this studyfailed in
shear with shear strength levels below the value of
VccalculatedbyEq.(1)fromACI318-08.(NotonlywasSpecimen1-1 the only
beam with shear strength greater thanVc, but it was also the only
beam that was behaving as a fullydeveloped tied arch at its peak
load.) In fact, VccalculatedbyEq.(1) is nearly twice the measured
shear strength for thespecimens with heights ranging from 24 to 36
in. (610 to915mm). It is important to note that the observed
reduction inaverage shear strength in Vc computed using Eq. (1) may
bemitigatedbyotherprovisionswithintheACI318-08.InACI318-05,13Section11.5.6.1(c)requiredtheuseofminimumshearreinforcement
in beams when Vu > 0.5Vc,except where h is not greater than the
largest of 10 in. (250 mm),2.5 times thickness of flange, or 0.5
times the width oftheweb.Modifications to Section 11.5.6.1 were
made to
ACI318-08(Section11.4.6.1)inanattempttofurthertightentheexemptionstominimumshearreinforcement.WhenVu>0.5Vc,
a minimum amount of shear reinforcement is specificallyrequired
now, except for beams withh not greater than 10
in.(250mm),orforbeamsintegralwithslabswithh not greaterthan 24 in.
(610 mm) and not greater than the larger of 2.5timesthethickness of
flange, and 0.5 times the width of theweb. The findings of this
study support this modification andsuggest that minimum shear
reinforcement be provided inallnonprestressed beams when Vu >
0.5Vc, particularly withan overall height range within the scope of
this study (that is,12 to 36 in. [305 to 915 mm]). This
recommendation is
offeredasonepossiblecourseofactiontomitigateshearstrengthdeficiencies
associated with the reduction in Vc observed in thetests conducted
in this study.ACKNOWLEDGMENTSThe research reported in this article
(PCA R&D Serial No. SN2921a) wasconducted by Purdue University
with the sponsorship of the Portland CementAssociation (PCA Project
Index 04-03).14 The contents of this paper reflectthe views of the
authors, who are responsible for the facts and accuracy of thedata
presented. The contents do not necessarily reflect the views of the
PortlandCement Association. Longitudinal reinforcing steel and
mechanical anchorsused in this work were generously provided by
ERICO, Inc.NOTATIONAs= area of nonprestressed longitudinal tension
reinforcementav= shear span, equal to distance from center of
concentrated load tocenter of supportav/d = shear span-to-effective
depth
ratioFig.9RatioofVtesttoVcalcperEq.(1)(ACI318-08Eq.(11-3))versuseffectivedepthd:resultsfromReinecket
al.8 and test specimens in this study.562 ACI Structural
Journal/September-October 2010agg = maximum aggregate sizebw= web
widthd = distance from extreme compression fiber to centroid of
longitudinaltension reinforcementfc =
compressivestrengthofconcreteattestdatedeterminedfromaverage of
three 4 x 8 in. (100 x 200 mm) control cylindersft= tensile
strength of concrete at test date determined from averageof three 4
x 8 in. (100 x 200 mm) control cylinders in splittingtensile
testsfy= yield strength of reinforcementh = heightl = span length,
measured center-to-center of supportsMn= nominal flexural strength
at sectionMtest= flexural strength corresponding to test load at
failurePtest= applied load corresponding to failureVc= nominal
shear strength provided by concreteVtest= nominal shear strength
corresponding to test load at failureVu= design factored shear
force at sectionvtest= Vtest/bwd = average shear stress
corresponding to test load at failure = ratio of As to
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