Setting Bar-Bending Requirements for High-Strength · PDF fileSetting Bar-Bending Requirements...
Transcript of Setting Bar-Bending Requirements for High-Strength · PDF fileSetting Bar-Bending Requirements...
i
SettingBar-BendingRequirementsforHigh-StrengthSteelBars
StephenD.ZhaoWassimM.GhannoumSponsoredby:TheCharlesPankowFoundationTheConcreteReinforcingSteelInstituteTheAmericanConcreteInstitute’sFoundation,ConcreteResearchCouncilJune30,2016
ii
SettingBar-BendingRequirementsforHigh-StrengthSteelBars
CPFResearchGrantAgreement#01-15
Fundedby
CHARLESPANKOWFOUNDATIONP.O.Box820631
Vancouver,Washington98682Co-fundedby
TheConcreteReinforcingSteelInstitute’s,andTheAmericanConcreteInstitute’sFoundation
PrincipalInvestigator: Dr.WassimM.Ghannoum
GraduateResearchAssistant: StephenZhao
IndustrySupport:
IndustryChampions: MikeMota,VPEngineering,CRSI
AdvisoryPanel: SalemFaza,MMFX
DenisHunter,Gerdau
ErikNissen,NUCORSteelSeattle
JacobSeltzer,CMC
iii
Acknowledgements
This projectwasmade possible by funding from the Charles Pankow Foundation, the
ConcreteReinforcingSteelInstitute,andtheAmericanConcreteInstitute’sFoundation.
ThesteeldonationsofCMC,Gerdau,MMFX,andNUCORSteelInc.Seattlearegratefully
acknowledged.Thebendingwasperformedatnocosttothisprojectbythefabrication
facilityatHarrisRebarinNewBraunfels.ThetechnicalcontributionsofMikeMota,the
project’sindustrychampion,DavidMcDonald,CRSIPresidentandCEO,andtheadvisory
panelisgratefullyacknowledged.
iv
Abstract
SettingBar-BendingRequirementsforHigh-StrengthSteelBars
The reinforcing steel industry is currently developing high-strength
reinforcingbarswithspecifiedyieldstrengthsof80and100ksiduetoincreased
demandforsuchgrades inconcreteconstruction.However,noneofthehigher
steelgradesareabletomatchthebenchmarkmechanicalpropertiesofgrade60
steel; with each high-strength variant diverging from benchmark behavior in
different ways. There is concern that the less ductile higher grade reinforcing
barsmayfractureatthebendsandmayrequirelargerbenddiameters.Limited
testsareavailablethatinvestigatetherelationbetweenbenddiameterandthe
ductility,orconverselythebrittleness,ofreinforcingbarsatbends.Nosuchtests
existforthenewlydevelopedhigh-strengthreinforcementhavingyieldstrengths
exceeding 80 ksi. Bend/re-bend (or re-straightening) tests were conducted on
grade60andhighergradereinforcingbarstoinvestigaterelationsbetweenbend
diametersandbendperformance.Thetestsweremonitoredusingdigitalimage
correlation technology from which never-before recorded comparative
measureswere obtained. Test results indicated significant differences in bend
performance betweenbars of varying grades, such thatwider bend diameters
maybenecessaryforcertainhighergradebars.
v
TableofContents
ListofTables ........................................................................................................ viii
ListofFigures ......................................................................................................... ix
CHAPTER1:INTRODUCTION 1
1.1Motivation ......................................................................................................... 1
1.2ObjectivesandScope ........................................................................................ 1
CHAPTER2:BACKGROUND 3
2.1Metallurgy ......................................................................................................... 3
2.1.1QuenchingandTempering(QT) ............................................................ 3
2.1.2Micro-Alloying(MA) .............................................................................. 4
2.1.3PatentedMicrostructureManipulation(MMFX) ................................. 4
2.2StrainAging ....................................................................................................... 4
2.3BendTests ......................................................................................................... 6
CHAPTER3:EXPERIMENTALPROGRAM 9
3.1OverviewofProgram ........................................................................................ 9
3.1.1Bend/re-bendTests .............................................................................. 9
3.1.1.1SpecimenDetailsandPreparation ........................................... 9
3.1.1.2ControlledTestParameters .................................................... 11
3.1.1.3FixedParameters .................................................................... 14
3.1.1.4Instrumentation ...................................................................... 15
3.1.2StrainAgingTests ................................................................................ 18
3.1.3MonotonicTests ................................................................................. 18
vi
3.2SpecimenNomenclature ................................................................................. 18
CHAPTER4:TESTRESULTSANDGENERALOBSERVATIONS 20
4.1MonotonicTests ............................................................................................. 20
4.1.1SummaryofObservations .................................................................. 28
4.2StrainAgingTests ............................................................................................ 29
4.2.1StrainAgingTestData ......................................................................... 29
4.2.2StrainAgingPerformanceMeasures .................................................. 33
4.2.3StrainAgingResults ............................................................................ 34
4.2.3.1EffectsofStrainAgingDuration .............................................. 34
4.2.4.2EffectsofVanadiumonStrainAging ...................................... 37
4.3Bend/re-bendTests ........................................................................................ 39
4.3.1TypicalStressvs.StrainRelationsinBend/re-bendTests .................. 41
4.3.1TypicalStressvs.RemainingBendAngleRelationsinBend/re-bendTests ............................................................................................................. 43
4.3.2SummaryofResultsforBend/re-bendTests ...................................... 45
4.3.3EffectsofBarYieldStrengthonRe-bendPerformance ...................... 48
4.3.4EffectsofBarSizeonRe-bendPerformance ...................................... 53
4.3.6EffectsofBendDiameteronRe-bendPerformance .......................... 58
CHAPTER5:RECOMMENDATIONSFORMINIMUMBENDDIAMETERS 70
5.1PerformanceObjective ................................................................................... 71
5.2RelationbetweenInsideBendDiameterandThresholdStrainRatio(αf) ...... 72
5.3MinimumBendDiametersbasedonMinimumASTMElongations ............... 74
5.4MinimumBendDiametersbasedonCRSIMillDatabaseElongations ........... 80
5.4.1ProbabilitiesofFailureofBendsBasedonGrade60ProductionData82
5.4.2RequiredBendDiameterstoAchieveTargetProbabilitiesofFailureBasedonProductionData ............................................................................. 85
vii
CHAPTER6:SUMMARYANDCONCLUSIONS 88
References ............................................................................................................ 92
viii
ListofTables
Table1:Measuredβforvariousbarsizesvsβfrompinusedforbending...........................13
Table2:Re-bendtestloadingrates.......................................................................................17
Table3:Summaryofmeanmaterialpropertiescalculatedfrommonotonictensiontests.21
Table4:Ratioofεf/εun.........................................................................................................27
Table5:Summaryofstrainagingtestresults.......................................................................34
Table6:Bend/re-bendResultsfor#8and#11Bars..............................................................46
Table7:Bend/re-bendResultsfor#5Bars............................................................................47
Table8:TheoreticalStrainsatBends....................................................................................63
Table9:ASTMA615FractureElongationRequirements......................................................75
Table10:ASTMA706FractureElongationRequirements....................................................76
Table11:ASTMA1035FractureElongationRequirements..................................................76
Table 12: Comparison between minimum bend diameters to achieve the yield strength
performanceobjectiveandACI318-14minimumbenddiameters(assumingthesameACI318-
14benddiametersapplytohigh-strengthbars)..........................................................................77
Table13:Summaryof fractureelongationvalues fromCRSIMillDatabase forASTMA615
bars...............................................................................................................................................81
Table14:Summaryof fractureelongationvalues fromCRSIMillDatabase forASTMA706
bars...............................................................................................................................................81
Table 15: Summary of fracture elongation values fromCRSIMill Database for dual grade
ASTMA615/A706bars..................................................................................................................81
Table 16: Minimum required fracture strains for bars bent to current ACI 318-14 bend
diameters......................................................................................................................................83
Table 17: Probabilities of failing the performance objective for bars in production today
benttoACI318-14insidediameters.............................................................................................84
Table18:Targetbenddiameterratiosrequiredtoachieveagivenprobabilityoffailingthe
yieldperformanceobjective.........................................................................................................86
Table19:Recommendedtargetbarbenddiameterratios...................................................87
ix
ListofFigures
Figure1:Typical stress-straincurvesshowingtheeffectsofstrainaging (G.TVanRooyen,
1986)...............................................................................................................................................5
Figure2:Pictureofbend/re-bendtestcoupons(NISTGCR13-917-30).................................8
Figure3:RMSArnoldBenderusedtobendspecimens........................................................10
Figure4:Verifyingbendspecimentolerance........................................................................10
Figure 5: Specimen dimensions for #11, #8 and #5 barswith ACI 318-14minimum bend
diameter(db=barnominaldiameter)..........................................................................................11
Figure6:Exampleofbend/re-bendspecimenundertestingwithtargets...........................16
Figure7:Stress-straincurvesfrommonotonictestsofgrade60A706bars........................22
Figure8:Stress-straincurvesfrommonotonictestsofgrade60A615bars........................23
Figure9:Stress-straincurvesfrommonotonictestsofgrade80A615bars........................24
Figure10:Stress-straincurvesfrommonotonictestsofgrade80A706bars......................25
Figure11:Stress-straincurvesfrommonotonictestsofgrade100bars..............................26
Figure 12: Stress-strain curves for grades 60 and 80 A706 and grade 100MA bars from
Manufacturer1,notagedandstrainaged1month.....................................................................30
Figure 13: Stress-strain curves for grade 60 and 80 A706 bars fromManufacturer 4, not
agedandstrainaged1month......................................................................................................31
Figure14:Stress-straincurvecomparisonsbetweengrade80QTfromManufacturer4and
grade100MAfromManufacturer1,notagedandstrainaged3months...................................32
Figure15:Apparentyieldpointandlossofelongationafterstrainaging............................33
Figure16:Normalized∆!vsstrainagingduration...............................................................35Figure17:Normalized!fractureA.vsstrainagingduration........................................................36Figure18:∆!/!"vs%Vanadium..........................................................................................37
Figure19:Normalized!fractureAvs%Vanadium......................................................................38
Figure20:Photographofabarthatfracturedinthe90obendafterlimitedstraightening..40
Figure21:Typicalstressvsstrainrelationsfornon-straightenedbars.................................42
Figure 22: Typical stress vs strain relations for straightened bars exhibiting high ductility
duringre-bending.........................................................................................................................42
x
Figure23:Typicalstressvs.remainingbendanglerelationsfornon-straightenedbars......44
Figure24:Typicalstressvs.remainingbendanglerelationsforstraightenedbars.............44
Figure25:Normalizedre-bendstressatfracturevsmeasuredbaryieldstrength...............49
Figure26:Normalizedre-bendstressatfracturevsmeasuredbaryieldstrength...............50
Figure27:Normalizedre-bendstrainatfracturevsmeasuredbaryieldstrength...............51
Figure28:Remainingbendangleatfracturevsmeasuredbaryieldstrength.....................52
Figure 29: Comparison of normalized stress at fracture vs measured yield strength for
variousbarsizes............................................................................................................................54
Figure 30: Comparison of normalized strain at fracture vs measured yield strength for
variousbarsizes............................................................................................................................55
Figure 31: Re-bend stress at fracture normalized by tensile strength vs measured yield
strengthfor#5bars.......................................................................................................................57
Figure32:NormalizedRe-bendFractureStressvsTargetBendDiameter...........................59
Figure33:NormalizedRe-bendFractureStrainvsTargetBendDiameter...........................60
Figure34:NormalizedRe-bendFractureAnglevsTargetBendDiameter............................61
Figure35:MaxTheoreticalStrainDerivation........................................................................62
Figure 36: Bar uniform strain vs measured yield strength overlaid with the estimated
maximumbendstrains(εma).........................................................................................................65
Figure37:Normalizedfracturestressvsnormalizedtheoreticalbendstrain......................67
Figure38:Normalizedfracturestress(fub/ft)vsnormalizedtheoreticalbendstrain............68
Figure39:Normalizedfracturestrainvsnormalizedtheoreticalbendstrain.......................69
Figure40:Normalizedfracturestressvsnormalizedtheoreticalbendstrain......................71
Figure 41: Relation between βTH and bar fracture strain (εf) for various threshold strain
ratios(αf).......................................................................................................................................73
Figure 42: βASTM,ADJ and bar fracture strain (εf) for various threshold strain ratios (αf) for
ASTMA615#5bars.......................................................................................................................78
1
CHAPTER1:Introduction
1.1Motivation
Thereisanincreasingneedforhigherstrengthreinforcingsteelinseismicandnon-
seismic applications. A main driver for higher strengths is the need to reduce bar
congestion in seismic designs and reduce material quantities generally. Steel
manufacturersintheUnitedStatesarecurrentlydevelopingreinforcingbarswithyield
strengths reaching 120 ksi andwith varyingmechanical and chemical properties. The
newhigh-strengthbarsarebeingproducedusingvaryingmethods,themostcommonof
whicharequenchingand tempering,andmicro-alloying.However,noneof thehigher
steelgrades inproductionareable tomatch thebenchmarkmechanicalpropertiesof
grade60 steel;witheachhigh-strengthvariantdiverging frombenchmarkbehavior in
differentways.Thereisconcernthatthelessductilehighersteelgradesmayfractureat
the bends and may require larger bend diameters. Anecdotal evidence has been
reported of high-strength bars (HSRB) fracturing at the bends when dropped at a
constructionsite(particularlyincoldweather).
Inthisreport,high-strengthreinforcingbars(HSRB)aredefinedassteelreinforcing
barswithyieldstrengthsof80ksiorhigher(i.e.,grade80orhigher).
1.2ObjectivesandScope
Efforts are underway to produce newASTM specifications for HSRB to give steel
mills a clear target to aim for in their production of HSRB. To complete the ASTM
specifications for HSRB, bar bending requirements need to be revisited given recent
evidence of HSRB fracturing at bends. Limited tests are available that investigate the
relation between bend diameter and the ductility, or conversely the brittleness, of
2
reinforcing bars at bends. No such tests exist for the newly developed high-strength
reinforcementhavingyieldstrengthsexceeding80ksi.
Themain objectives of this study are to evaluate the performance under load of
bends satisfying ACI 318-14 (2014) in HSRB, and compare that performancewith the
benchmarkperformanceofgrade60barsbentinthesamewayandtosamediameters.
To achieve project objectives, bend and re-bend tests, such as those specified in
New-Zealand and United-Kingdom standards (AS/NZS 4761:2001; BS
4449:2005+A2:2009),wereconductedonHSRBandgrade60bars.Thetestsprovideda
measureof thereservestrengthandductilityofbarbends,whichcannotbeobtained
usingvisualinspectionofbendcracking,asdescribedinASTMstandardsforreinforcing
bars (ASTMA615, A706, A1035).HSRBwith varyingmanufacturing processes, grades,
diameters,andbenddiametersweretested.Therangeofparameterswasselectedto
represent the most typical bar properties and manufacturing processes currently in
production or development in theUnited States. All barswere fully strain-aged after
bending and prior to re-bending, to represent typical conditions of bar bends in
concretestructures.Strainagingtestswereconductedtoevaluatetheeffectsofstrain
agingonallbar types considered,and todetermine the requiredwait timeafterpre-
strainingorbendingbeforere-bendingcouldbeperformed.
3
CHAPTER2:Background
2.1Metallurgy
ThreemainproductionmethodsarecurrentlyusedintheUnitedStatestoproduce
HSRB.Eachof thesemethodsgeneratesHSRBwithdifferingmechanical and chemical
properties. The three processes are quenching and tempering, micro-alloying, and
manipulation of the microstructure using alloying and heat treatment. Steel bars
produced through quenching and tempering typically exhibit relatively low tensile to
yieldstrength(T/Y)ratiosandrelativelyhighstrainsatfracture.Steelbarsproducedby
micro-alloying have a relatively high tensile to yield strength ratio and relatively high
strainsatfracture.HSRBproducedusingthethirdproductionmethodaretheonlyones
withASTMspecifications(ASTMA1035(2011)).Thesebarstypicallyhavelargetensileto
yieldstrengthratiosbutrelatively lowstrainsatfracture.Thedifferencesbetweenthe
threeproductionmethodsandthebarpropertiestheyproducearebrieflydiscussedin
thissection.
2.1.1QuenchingandTempering(QT)
The process of quenching and tempering (QT) consists of quenching the steel
immediately after rolling and then allowing the bar to be tempered by the heat
remaininginthecorewhilegraduallycooling.Asaresult,theQTprocessproducessteel
withmechanical properties that vary significantlybetween its inner core layer and its
outer skin layer,with the inner core having a lower yield strength andmoreductility
thantheouterlayer.QTtreatedbarsretaintheiryieldplateausincetheyhavenotbeen
strainhardenedand,sincetheoverallchemicalcompositionhasnotbeenaltered,they
canbeweldableiftheirchemistrysatisfiesASTMA706requirements.QTsteeltypically
exhibitsa lowT/Yratioontheorderof1.15forgrade100reinforcingbars.Slavinand
Ghannoum(2015)providesmoredetailsabouttheQTprocess.
4
2.1.2Micro-Alloying(MA)
Micro-alloying is a process that involves introducing small amounts of alloys in
ordertoachievethedesiredpropertiesinsteelbars.Vanadiumisoneofthealloysmost
commonlyused to increase the strengthof reinforcingbars. It increases strengthand
fracture toughness primarily due to inhibition of grain growth during heat-treatment
and the precipitation of carbides and nitrides. The use of Vanadium can reduce the
amount of carbon needed to achieve higher strengths and is therefore useful for
achievingweldableHSRB.Micro-alloying can produce amarked yield point and a T/Y
ratio larger than that from quenched and tempered steels (on the order of 1.25 for
grade100reinforcingbars).SlavinandGhannoum(2015)providesmoredetailsabout
themicro-alloyingprocess.
2.1.3PatentedMicrostructureManipulation(MMFX)
ThepatentedMMFXprocess involvesmanipulating themicrostructureof steel to
obtainthedesiredmechanicalpropertiesandstrength.Theprocessgeneratesbarswith
stress-stainrelationsthatdonothaveawell-definedyieldpoint,exhibitarelativelyhigh
T/Yratio,buthaverelativelylowfractureelongations.TheMMFXsteelbarssatisfythe
ASTMA1035specifications.TheA1035specificationsmaintainthesamebenddiameter
for testing bar bends as in the ASTMA615 andA706 specifications used for the vast
majorityofbarscurrently inproductionintheUnited-States.ACI318-14(2014)allows
theuseofA1035grade100bars inconfinementapplicationsandrequiresthemtobe
bentatthesamediameterasothersteelgradesincludinggrade60.
2.2StrainAging
Strainagingisdefinedastheprocessbywhichsteelstrainedbeyonditselasticlimit
undergoes time dependent changes in itmechanical properties. Typically, reinforcing
bars strainedbeyond theirelastic limitwill,over time, seean increase in their tensile
5
strengthandadecrease in theirductilityas illustrated inFigure1. Strainaging isalso
proven to affect the brittle transition temperature in steel (G.T. Van Rooyen, 1986).
Factorsaffectingstrainagingincludethesteelcomposition,temperature,andthetime
elapsedsince largestrainswere incurred.Strainaging ismostlyattributed tonitrogen
reallocation within the steel matrix (G.T. Van Rooyen, 1986). Higher temperatures
accelerate this process; hence strain aging occurs much faster in warmer regions.
Typically,mostoftheeffectsofstainaging insteelreinforcingbarswilloccurwithina
fewmonthsafterinelasticstrainsareincurred(G.T.VanRooyen,1986).
Figure1:Typicalstress-straincurvesshowingtheeffectsofstrainaging(G.TVanRooyen,1986)
Asreinforcingbarsarebent,theyexperiencelargeinelasticstrains.Barbendsare
therefore prone to strain aging embrittlement, which may cause them to fracture
prematurely and limit their ability to sustain inelastic deformations during structural
loading.
6
ResearchdonebyG.TVanRooyen (1986) andRashid (1976) suggests thatmicro-
alloyedsteel includingtitaniumandvanadiumcan lowertheeffectsofstrainagingon
steelbars.Suchalloyshavepropertiesthatallowthemtobondwiththenitrogeninthe
composition to form nitrides. These reactions limit the amount of free nitrogen
throughoutthesteelthatisattributedtostrainagingeffects.
2.3BendTests
Three main categories of experimental tests are useful for investigating the
behaviorofbends in reinforcingbars,witheachcategoryof testsgeared toanswera
particularsetofquestions:
1-Visualinspectionsofbends(ASTMbendtests)
2-Bend/re-bendtests
3-Bendtestsinconcrete
1-ASTMreinforcingbarspecifications(suchasA615,A706,andA1035)specifythe
following bending requirement “The bend test specimen shall withstand being bent
aroundapinwithoutcrackingontheoutsideofthebendportion.”Therequiredbend
test therefore involves bending bars to 180o (or 90o for #14 and larger bars) at a
specifiedpinbenddiameter.Avisualinspectionisthenperformedtoidentifycrackingat
thebend. If no cracking is visually observed, a specimen is deemed topass thebend
test. The pin diameters specified in ASTM bend tests are tighter than those used in
construction,as specifiedbyACI318-14or theCRSIhandbook,and thereforeprovide
some degree of safety against observing cracking in bends during bar fabrication.
However, while this test is simple to perform, it does not provide ameasure of the
reservestrengthandductilityofbarbends,asaload-testcan.Itispossiblethatmicro-
crackingnotvisibletotheeyemaycompromisetheperformanceofbarsin-situ.
7
2 - Bend and re-bend tests have been performed in New-Zealand (AS/NZS
4761:2001;HopkinsandPoole(2008)andtheUnited-Kingdom(BS4449(2005)).Inthese
tests, bar coupons are bent to the required angle and bend diameter (Figure 2), and
then straightened at either quasi-static or dynamic loading rates. For grade 60 bars,
workhardeningincreasessteelstrengthatthebendsandtypicallycausesthecoupons
to fracture away from the bends in a ductile manner. However, if bars have limited
ductilitysuchasHSRB,straindemandsatthebendsmaycausecracks,whichcanmake
bends weaker than the unbent portions of the bars and more susceptible to brittle
fracture. Ifabar fails inabrittlemanneratabend, it isconsideredtohavefailedthe
bend/re-bendtest.If,however,abarfailsinaductilemanner,thenitisdeemedtohave
passedthetest.Thistypeoftesthastheadvantageofputtingbar-bendsunderloadand
thereforeprovidesadirectmeasureof the strengthandductilityperformanceofbar-
bends.
HopkinsandPoole(2008)conductedbendandre-bendtestsonnewly introduced
grade500E(~72ksi)barsinNewZealandandAustralia.Thestudyaccountedforstrain
agingandexploredtheeffectsofcoldtemperatureontheperformanceofbends.The
study tested bars produced using micro-alloying (MA), as well as quenching and
tempering (QT). Test results confirmed that current bar bend diameters used inNew
Zealandwereadequateforthatgradeofsteel,regardlessofthemanufacturingprocess.
Amarkedworsening of the performanceof bar-bendswas observed at temperatures
below-10oCelsius.
It should be noted that the bend/re-bend tests apply larger demands on the bar
bendsthantheywouldnormallyseeinaconcretestructure.Forthisreason,itisbestto
comparethebend/re-bendperformanceofHSRBtothatofgrade60bars,whichhave
beenusedfordecadesandhaveshownadequateperformanceinconcretemembers.
8
Figure2:Pictureofbend/re-bendtestcoupons(NISTGCR13-917-30)
3 - Bends in reinforcing bars can also be tested in concrete. In such tests, the
interactionbetweentheconcreteandbar-bendscanbeinvestigated.Simplifiedversions
ofthetestincludeembeddingahookedbarintoaconcreteblockandpullingonituntil
failure.Possiblefailuremodesthatcanbeexpectedinblocktestsinclude:barfracture
outside theblockwheredemandson thebar arehighest, bar failure inside theblock
closertooratthebend,orsplittingoftheconcreteblock.Suchtests,however,maynot
expose bends to the worst loading they could experience in a structure, as the
surroundingconcretecanrelievethebendsofsomeload.Incontrast,someoftheworst
loading on bar-bends can arise in confinement applications, where an expanding
concrete core partially straightens hoop bends while applying high tensile loads to
them.Anothercriticalapplicationforbar-bendsisindamagedregions,wherebondto
concrete and its beneficial effects on bends are reduced (e.g., joints under severe
seismicloading,orseverelycrackedregions).
Nevertheless, testsofbarbends in concretemembers areessential for validating
theadequateperformanceofbarbendsinHSRB.However,suchtestsareexpensiveto
conductanddonoteasily lend themselves to the taskofdeterminingminimumbend
diameterswhileexploring thenumerousvariables thataffect theperformanceofbar-
bends.
9
CHAPTER3:ExperimentalProgram
3.1OverviewofProgram
Theexperimentalprogramconsistedofthreetypesoftests.
1. Bend/re-bendTests2. StrainAgingTests
3. MonotonicTests
3.1.1Bend/re-bendTests
Objectives: Bend/re-bend testswere conducted to quantify residual strength and
elongation capacities under load in bar bends and compare high-strength reinforcing
barbendperformancewiththatofgrade60barbends.
3.1.1.1SpecimenDetailsandPreparation
Thebend/re-bendspecimensweresimilartothoseusedinNew-ZealandbyHopkins
andPoole(2008)anddescribed inBS4449:2005+A2:2009(2005).Barspecimenswere
constructedbybendingstraightcouponsintoa“V”shapehavingtwo45degreebends
andone90degreebend(Figure2).Couponswerebentbyalocalfabricatoraccording
to typical bending practices using an RMS Arnold Bender (Figure 3). Bars were bent
abouttheirweakaxis,withthelongitudinalribsfacingverticallyinthebender.Bending
wasconductedataroomtemperatureofabout20°C.Barswerethenlefttostrainage
prior to re-bending them in tension until fracture in a uniaxial testing machine.
Tolerancetemplateswereusedtoensurethatspecimenswerebentaccurately(Figure
4).The internalbenddiametersforthefirstbatchofbarspecimenswerethesmallest
specified in ACI 318-14. The dimensions of bend/re-bend coupons with those bend
diameters are presented in Figure 5. In subsequent bending, some #5 bar bend
diameterswereincreasedto5dband6db(withdb=barnominaldiameter).
10
Figure3:RMSArnoldBenderusedtobendspecimens
Figure4:Verifyingbendspecimentolerance
11
Figure5:Specimendimensionsfor#11,#8and#5barswithACI318-14minimumbenddiameter(db=bar
nominaldiameter)
3.1.1.2ControlledTestParameters
a- SteelGradeandSpecifications:A706 (highductility)andA615 (lowerductility)
grade 60 barswere tested to provide benchmark performance.Grade 60 bars
were obtained from three mills to obtain a representative sample of current
production.HSRBproducedusingthemainthreeproductionmethodsintheU.S.
were also tested: MA (Micro-Alloying), QT (Quenching and Tempering), and
12
MMFX(ASTMA1035).ThemainfocusinHSRBwasongrade100steel(havinga
yieldstrengthequaltoorhigherthan100ksi)butlimitedtestswereconducted
ongrade80barsaswell.Inall,steelbarsfromfourmanufacturersweretested:
a. Manufacturer1(M1):MicroAlloyedSteel(MA)
b. Manufacturer2(M2):PatentedMicrostructureMMFX(ASTMA1035)
c. Manufacturer3(M3):CombinationofQuenchandTemperingandMicro
Alloying(QT)
d. Manufacturer4(M4):CombinationofQuenchandTemperingandMicro
Alloying(QT)
b- BarSize:Threebarsizesweretestedinthisstudycoveringacommonrangeof
sizesusedinconstruction.Thebarssizesusedwere#5,#8,and#11.
c- Bend Diameters: Bar specimens were first bent to the current ACI 318-14
minimumbenddiameters.For#11bars,theinternalbenddiameterwasabout8
db. For #8 bars, the internal bend diameter was about 6db. For #5 bars, the
minimum bend diameter for transverse reinforcement was initially targeted,
which is4db.However,afterobservingpoorerperformance in#5HSRBat that
benddiameter,#5barswerebentandtestedwith5dband6dbbenddiameters.
The latterbenddiameterof6dbcorrespondstotheACI318-14minimumbend
diametersfor#5longitudinalorotherbarsintension.It isnoteworthythatthe
selectedbarsizes (#5,#8,and#11)correspondto the largestsizewithagiven
benddiameterbeforethenextbiggersizerequiresalargerbenddiameterinACI
318-14.
Due to bending pin availability and spring-back in the bending process, final
internal bend diameters were close to but not exactly equal to their target
values.Table1 lists thetargetACI318-14,aswellasthemeanachieved inside
13
benddiameterratiosforthe90degreebendsinthespecimens(βACI=ACI318-14
benddiameter/dbandβActual=meanmeasuredinsidebenddiameter/db).The
table also lists the pin diameters usedduring bending and its associatedbend
ratio(βPin=pindiameter/db).
Table1:Measuredβforvariousbarsizesvsβfrompinusedforbending
TargetβACI(db)
MeanMeasuredβActual(db)
PinDiameter
(in.)
βPin(db)
Spring-backDifference=(βActual-βPin)/
βActual
ErrorfromTarget=(βACI-βActual)/βACI
#11(8db)4Samples
8 7.82 10.0 7.30 7.1% 2.3%
#8(6db)4Samples
6 5.64 5.0 5.00 12.7% 6.1%
#5(6db)2Samples
6 5.39 3.0 4.80 12.3% 10.1%
#5(5db)3Samples
5 4.80 2.5 4.00 20.0% 4.0%
#5(4db)3Samples
4 3.59 2.0 3.20 12.3% 10.2%
As can be seen in Table 1, themean actual bend diameterswere less than 10%
lower than the target bend diameters. Bending pins were only offered in ½”
increments, hence thepindiameterswere chosen such that the final benddiameters
wereasclosetotargetdiametersaspossiblebutnotlarger.Theactualbenddiameters
werehigherthanthepindiametersby7to20%duetospring-backafterbending.
14
3.1.1.3FixedParameters
a- BendAngle:Aprimarybendangleof90°was tested in this study.Otherbend
angleswerenotincludedinthescopeofthisproject.
b- LoadingRatewasappliedquasi-staticallytore-bendtestsinthisproject.
c- #ofSpecimens:Atleast3barspecimenspertypeweretested.
d- Strain Aging: Bar types sensitive to strain aging (as determined in the strain
agingtests)werebentandallowedtostrainagepriortobeingsubjectedtothe
re-bend tests. Thiswasdone toaccount for thepossibledeleteriouseffectsof
aging on bar ductility, and to reproduce actual in-situ conditions of bends in
concretestructures.
e- Temperature:Thefocusofthisprojectwasonassessingthebendperformance
ofHSRBatrelativelywarmambienttemperatures(20to25°C).Thisevaluationis
a necessary first step prior to bending and testing bars in cold climate at or
below their brittle transition temperatures. Cold temperature bending and
testingshouldbeevaluatedinfuturework.
f- Bending Equipment: An RMSArnold Benderwith the capability to bend at 16
RPMand14RPM(RevolutionsPerMinute)wasusedforallspecimens.
g- BendingRate:Allspecimenswerebentat16RPM.
15
3.1.1.4Instrumentation
Theload-cellintheuniversaltestingmachineprovidedreadingsoftheappliedload.
Strains and deformations of the bars were obtained during testing using a high-
resolution opticalmeasurement system reported by Sokoli et al (2014). Targetswere
appliedalongthefourstraightportionsofbentbarspecimens(Figure6).Thelocations
of thetargetsweretrackedusingtheopticalsystemwhile thebarswerebeingtested
(Figure6).
16
Figure6:Exampleofbend/re-bendspecimenundertestingwithtargets
17
3.1.1.5TestProtocol
Barwere gripped at each end using hydraulic grips thatwere 6 inches long. The
loading during re-bend tests consisted of three loading rates. The loading protocol
startedwithalowloadingratetopickupinitialloadinthespecimens.Thiswasdonein
order toobtain sufficientdata in casesofbar fracture at low forces.Once specimens
carriedalargerforce(~10%ofyield)theloadingratewasincreaseduntilthebarswere
almoststraight.Thentheratewasagainloweredtoobservefractureinmoredetail.All
threebarsizeswereloadedwiththesameratespresentedinTable2.
Table2:Re-bendtestloadingrates
18
3.1.2StrainAgingTests
Objectives: Toquantify strainagingeffectsonall thebars tested in thebend/re-
bendtestsandidentifythedurationafterwhichmoststrainagingeffectsleveloff.
Strain-agingtestswereconductedonstraight#5barcouponsforallsteeltypes.All
bars,exceptthosesatisfyingASTMA1035,werestrainedintensiontoapredetermined
strain value of 0.04 in a universal testmachine and then unloaded. A1035 barswere
strainedintensiononlytoastrainof0.02duetotheirrelativelylowuniformelongation
values.Uniformelongationisdefinedasthebarelongationatpeakstress.Tensiontests
were then performed on the pre-strained bars immediately after pre-straining, one
month after pre-straining, and three months after pre-straining. Strain aging was
allowed tooccurat room temperature (~20°C). Thebarswere strained in the strain-agingtestsatthestrainrateusedinthemonotonictensiontests.
3.1.3MonotonicTests
Monotonictensiontestswereperformedonat least threestraightspecimensper
bartypetoidentifythemechanicalpropertiesofthesteelbars.Thetestsfollowedthe
procedures specified in ASTMA370 (ASTM StandardA370-15),with strainsmeasured
overagaugelengthof8inches.
3.2SpecimenNomenclature
Formonotonic and re-bend tests, the following nomenclature is used to identify
specimens:
19
Manufacturer#_Grade_Bar Type or Specification_Diameter (in eighth of an
inch)_Testuniqueidentifier
e.g.:(M1_Gr60_A706_5_01orM1_Gr100_MA_5_01)
Forstrainagingteststhefollowingnomenclatureisused:
Manufacturer#_Grade_Bar Type or Specification_Diameter (in eighth of an
inch)_MonthsAged_Testuniqueidentifier
e.g.:(M1_Gr60_A706_5_3Mo_01)
20
CHAPTER4:TestResultsandGeneralObservations
4.1MonotonicTests
Monotonictestswereconductedonthreeormorecouponsforeachbartypeused
in the bend/re-bend testmatrix. Themeanmechanical properties and typical stress-
strainrelationsofeachbar typearesummarized inTable3andFigure7toFigure11.
Uniform elongation measures were obtained by following the ASTM E8 procedures
(ASTMStandardE8/E8M-15a).
21
Table3:Summaryofmeanmaterialpropertiescalculatedfrommonotonictensiontests
BarSize Manf. GradeYield
Strengthf y(ksi)
TensileStrengthf u(ksi)
T/YRatioUniformElongationεun(%)
FractureElongation
εf(%)
A70660 64.3 93.2 1.45 12.5% 21.9%A70680 81.7 111.2 1.36 10.3% 18.2%MA100 110.4 139.6 1.26 8.8% 12.7%A61560 63.2 104.0 1.64 11.2% 17.9%A61580 80.5 121.1 1.50 9.1% 14.4%
2 A1035100 125.0 162.1 1.30 4.9% 11.7%A70660 77.4 102.8 1.33 9.1% 14.5%A70680 83.1 109.7 1.32 9.1% 13.8%A61560 63.6 90.7 1.43 12.1% 17.1%A70660 67.5 95.8 1.42 11.5% 16.0%A70660 60.5 90.0 1.49 11.5% 18.9%A70680 84.4 114.1 1.35 9.8% 16.4%MA100 99.0 125.2 1.27 8.9% 13.0%A61560 63.7 101.3 1.59 10.7% 16.2%A61580 84.4 123.5 1.46 9.2% 14.6%
2 A1035100 131.4 164.3 1.25 5.2% 10.8%A70660 80.9 101.7 1.26 9.0% 14.9%A70680 81.6 104.0 1.27 8.9% 14.6%QT100 98.7 126.0 1.28 7.2% 9.9%A61560 68.1 95.8 1.41 12.0% 18.3%A70660 66.7 90.9 1.36 12.3% 18.5%A70660 65.7 93.9 1.43 10.5% 14.7%A70680 86.5 115.2 1.33 9.5% 13.8%MA100 113.0 135.1 1.20 8.2% 11.9%A61560 63.0 97.9 1.55 11.2% 16.5%A61580 81.8 112.9 1.38 9.9% 13.9%
2 A1035100 125.6 163.6 1.30 5.4% 9.5%A70660 81.6 99.7 1.22 8.8% 12.7%A70680 83.3 102.7 1.23 8.8% 12.6%QT100 90.0 129.7 1.44 6.9% 8.4%A61560 80.2 102.9 1.28 10.3% 15.0%A70660 66.0 90.8 1.38 12.1% 18.4%QT100 106.1 125.6 1.18 7.6% 10.7%
#5
1
3
4
#11
1
3
4
#8
1
3
4
22
A706Grade60
Figure7:Stress-straincurvesfrommonotonictestsofgrade60A706bars
#5 #8 #11
Manufacturer1
Manufacturer3
Manufacturer4
23
A615Grade60
Figure8:Stress-straincurvesfrommonotonictestsofgrade60A615bars
#5 #8 #11Manufacturer1
Manufacturer4
24
A615Grade80
Figure9:Stress-straincurvesfrommonotonictestsofgrade80A615bars
#5 #8 #11
Manufacturer1
25
A706Grade80
Figure10:Stress-straincurvesfrommonotonictestsofgrade80A706bars
#5 #8 #11
Manufacturer1
Manufacturer3
26
Grade100
Figure11:Stress-straincurvesfrommonotonictestsofgrade100bars
#5 #8 #11
Manufacturer1
Manufacturer2
Manufacturer3
Manufacturer4
27
Table4summarizestheratiosofεf/εunforvariousbarsgradesandsizes.
Table4:Ratioofεf/εun
#5 #8 #11
60 1.46 1.60 1.5780 1.45 1.66 1.6460 1.47 1.52 1.5180 1.40 1.59 1.57
A1035 100 1.77 2.09 2.37
A706
A615
εf/εun
28
4.1.1SummaryofObservations
Theyieldstrengthsofgrade60A706barstestedinthisstudyrangedfrom63-77ksi.The
fracturestrainsofthosebarswereintherangeof15%to22%.Theyieldstrengthsofgrade60
A615bastestedinthisstudywerearound63to64ksiwiththeexceptionofManufacturer4’s
#5bars thatcame inatyield strengthof80.2ksi.The fracturestrainsofgrade60A615bars
wereintherangeof15%to19%.
Grade80A706barshadyieldstrengthsrangingfrom81to87ksi.Thefracturestrainsof
those barswere in the range of 13% to 19%. Grade 80 A615 barswere only obtained from
Manufacturer 1 and had yield strengths ranging from 80 to 84 ksi for all sizes and fracture
elongationsrangingfrom14%to15%.
Grade 100 bar from Manufacturers 1 and 4 exhibited a yield plateau and had yield
strengthsintherangeof105to110ksi,withfracturestrainsrangingfrom11to13%.Barsfrom
Manufacturers2and3showednoyieldplateau.Yieldstrengthsforthosebarswereobtained
using a 0.2% strain offset method (ASTM A1035, 318-14). Yield strength values for
Manufacturer 2 grade 100 bars ranged from 125 to 131 ksi while those forManufacturer 3
rangedfrom90to99ksi.Manufacturer2grade100barsexhibitedfracturestrainsfrom10to
12% whereas Manufacturer 3 grade 100 bars exhibited fracture strains from 9 to 10%.
Manufacturer 2 grade 100 bars differ from other bars as they exhibited a relatively shallow
descendingrelationbetweenstressandstrainspasttheiruniformelongation.
29
4.2StrainAgingTests
4.2.1StrainAgingTestData
Strainagingtestswereconductedon#5barsofalltypesusedinbend/re-bendtests.Figure
12toFigure14presenttypicalstress-strainrelationsobtainedfromthestrainagingtests.The
arrows in the figures are used to show the difference from non-strain aged to strain aged
results.Asexpectedbasedonpast research (Rashid,1976), grade80and100barsproduced
usingmicro-alloyingwithVanadium(Manufacturer1)exhibited limitedstrainagingcompared
withgrade60barsfromthesamemanufacturer(Figure12).BarsfromManufacturer4,which
contained relatively small amounts of micro-alloys, exhibited more pronounced strain aging
effects as indicatedbyapparent gains in tensile strengthanddecreasedductility (Figure13).
Figure 14 highlights how different manufacturing processes result in different strain aging
results.
30
Figure12:Stress-straincurvesforgrades60and80A706andgrade100MAbarsfromManufacturer1,notagedandstrainaged1month
31
Figure13:Stress-straincurvesforgrade60and80A706barsfromManufacturer4,notagedandstrainaged1month
32
Figure14:Stress-straincurvecomparisonsbetweengrade80QTfromManufacturer4andgrade100MAfromManufacturer1,notagedandstrainaged3months
33
4.2.2StrainAgingPerformanceMeasures
Two parameters were used to quantify the effects of strain aging, (∆!/!!) and(!fractureA/ !fracture).∆! isthedifferencebetweentheapparentyieldpointuponreloadingafterspecimenagingandthestressatunloadingasseenintheFigure15.∆!wasnormalizedwith
respect to the measured yield strength of the bars, !!, for comparison between different
grades. The strain at bar fracture of aged bars normalized by the strain at fracture prior to
aging (!fractureA /!fracture)wasalsoused toassess the severityof strainaging.The strainsweremeasuredoveraneightinchgaugelength.
Figure15:Apparentyieldpointandlossofelongationafterstrainaging
∆!
!fractureA !fracture
34
4.2.3StrainAgingResults
Table5summarizesthestrainagingresultsaveragedoverthecouponstestedperbartype.
Atleastthreecouponsweretestedperbartype.TheconcentrationofVanadiumwasfoundto
behighly correlatedwith strainagingeffects,namely the increase inapparent yield strength
andthereductioninfactureelongation.Table5alsosummarizestheVanadiumconcentrations
foreachbartype.
Table5:Summaryofstrainagingtestresults
4.2.3.1EffectsofStrainAgingDuration
Figure 16 and Figure 17 illustrate the variation of (∆!/!!) and (!fractureA / !fracture) withstrainagingduration.Dashed lines representgrade60bars, shaded lines representgrade80
bars and solid lines represent grade 100bars. As can be seen in the figures, themajority of
strainagingeffectsoccurwithinthefirstmonthwithlimitedchangesobservedthereafterforall
bartypes.Basedonthesefindings,bend/re-bendtestswereconductedonbarsstartingatleast
onemonthaftertheinitialbendingwasconducted.
35
Figure16:Normalized∆!vsstrainagingduration
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0
0123
36
Figure17:Normalized!fractureA.vsstrainagingduration
37
4.2.4.2EffectsofVanadiumonStrainAging
In Figure 18 and Figure 19, clear relationships can be seen between Vanadium
concentrationsandtheeffectsofstrainaging.Theapparentyieldstrengthofstrain-agedbars
decreaseswith increasingconcentrationsofVanadium,uptoaconcentrationofabout0.08%
(Figure18).Beyondthatconcentration,(∆!/!!)appearsto leveloffat0.03regardlessoftheconcentration of Vanadium. Changes in fracture elongation also appear to vary with the
concentrationofVanadiumwithstrain-agedbarsbecomingmoreductilewithhigherVanadium
concentrations. An increase in ductility post-aging was observed at relatively high
concentrationsofVanadium(inexcessof0.35%).Onlytwodatapointsareavailablehowever
withthosehighconcentrations.
Basedontheseobservations, the followingrelationsweredevelopedbetweenVanadium
concentrationsinpercentages(%V)and(∆!/!!)or(!fractureA/ !fracture).
∆! !! = −1.26 ∗ %! + 0.13 0.00≤%V≤0.08 (Equation4.2.1)
∆! !! = 0.03 0.08<%V (Equation4.2.2)
Figure18:∆!/!!vs%Vanadium
38
!!"#$%&"'( !!"#$%&"' = 0.9 ∗ %! + 0.9 0.00≤%V≤0.26 (Equation4.2.3)
!!"#$%&"'( !!"#$%&"' = 1.12 0.26<%V (Equation4.2.4)
Figure19:Normalized!fractureAvs%Vanadium
0.8
0.9
1
1.1
1.2
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
! fractureA/! fr
acture
%Vanadium
1Month
3Month
39
4.3Bend/re-bendTests
A total of 60 bend/re-bend testswere performed. The following performancemeasures
wereusedtocomparetheperformancebetweenthevariousbartypesandgrades:
a) Fracturelocation(in90obend,45obendorinstraightregions)
b) Remainingbendangleatfractureduringre-bending(θb)
c) Axialstraininbaratfracturenormalizedbyitsuniformelongationstrain(!b/!un)d) Axialstressinbaratfracturenormalizedbyitsyieldstrength(fub/fy)
e) Axialstressinbaratfracturenormalizedbyitstensilestrength(fub/ft)
Figure 20 shows a fracture in the 90 degree bend. The remaining bend angle during re-
bending was measured using the targets bracketing the 90 degree bend. Two slopes were
calculatedfromthetwostraightregionsadjacenttothe90degreebend.Usingtherelationship
between the two slopes, the remaining bend angle was calculated, which starts around 90
degrees and goes to almost zero when a bar is fully straightened. Axial strain in bars was
obtainedbyaveragingthestrainsbetweenthetargetsfurthestawayfromeachotherinthetop
andbottom straight regions as indicatedby thearrows in Figure20.Axial stress inbarswas
obtainedbydividingtheloadreadingofthetestmachinebythenominalareaofthebars.
40
Figure20:Photographofabarthatfracturedinthe90obendafterlimitedstraightening
41
4.3.1TypicalStressvs.StrainRelationsinBend/re-bendTests
Theaxialstress-strainrelationsforthreere-bendtestsinwhichfractureoccurredpriorto
fullbendstraighteningareshowninFigure21.Theaxialstress-strainrelationsforbarsinwhich
fracture occurred after straightening and after significant inelastic straining occurred in the
straightregionsareshowninFigure22.AscanbeseeninFigures21and22,theinitialportion
ofthestressstrainrelationsmeasuredarenotlinear.Thisisattributedtothebendingmoments
thatdevelopduringre-bendinginthetopandbottomstraightportionsofthespecimenswhere
thestrainsweremeasured(Figure20).Thesemomentsdieoutoncethebarsstraigthen.
42
Figure21:Typicalstressvsstrainrelationsfornon-straightenedbars
Figure22:Typicalstressvsstrainrelationsforstraightenedbarsexhibitinghighductilityduringre-bending
0
0.2
0.4
0.6
0.8
1
1.2
0 0.002 0.004 0.006 0.008 0.01 0.012
f ub/f "
!b
M1_60_A615_5_01
M1_60_A615_5_02
M1_60_A615_5_03
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 0.02 0.04 0.06 0.08 0.1
f ub/f "
!b
M1_60_A706_5_01
M1_60_A706_5_02
M1_60_A706_5_03
43
4.3.1TypicalStressvs.RemainingBendAngleRelationsinBend/re-bendTests
Typicalbarstressversus remainingbendangle relationsareplotted inFigure23 forbars
that fractured prior to full straightening. Typical bar stress versus remaining bend angle
relationsareplottedinFigure24forbarsthatfracturedafterfullstraightening.Inthefigures,
90degreesdenotestheinitialbendangleand0degreesdenotesthatabar-bendhasbeenfully
straightened.TestshighlightedinFigure23andFigure24arethosehighlightedinFigure21and
Figure22,respectively.
44
Figure23:Typicalstressvs.remainingbendanglerelationsfornon-straightenedbars
Figure24:Typicalstressvs.remainingbendanglerelationsforstraightenedbars
0
0.2
0.4
0.6
0.8
1
1.2
020406080100
f ub/f "
Remainingbendangleduringre-bending,θb(degrees)
M1_60_A615_5_01
M1_60_A615_5_02
M1_60_A615_5_03
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
020406080100
f ub/f "
Remainingbendangleduringre-bending,θb(degrees)
M1_60_A706_5_01
M1_60_A706_5_02
M1_60_A706_5_03
45
4.3.2SummaryofResultsforBend/re-bendTests
Table 6 and Table 7 summarize values of the bend/re-bend test performancemeasures,
averagedoveratleastthreetestsperbartype.Table6containsresultsfrom#8and#11bars,
andTable7containsresultsfrom#5bars.
Thebend/re-bendtestssubjectedbarbendstoharsherstressandstrainhistoriesthanthey
typically encounter in concrete structures. As such, defining acceptance criteria values that
delineatedeficientin-situbendperformanceisnotstraightforward.However,selectingvalues
ofperformancemeasuresabovewhichbendperformancecanbedeemedadequateinconcrete
canbedoneconservatively.Inthisstudy,barswithvaluesofthenormalizedstressatfracture
(fub/fy) exceeding 1.0 are deemed to have adequate bend performance, as these bars have
reached their design strength prior to fracture. Likewise, barswith values of the normalized
fracture strain (!sb / !un)exceeding 0.2 are deemed to have adequate bend performance, as
thesebarstypicallystraightenfully,reachstressesinexcessofyield,andstraintoatleast20%
oftheiruniformelongationpriortofracture.
46
Table6:Bend/re-bendResultsfor#8and#11Bars
StraightRegions
45 90
A70660 M1_60_A706_11 64.3 93.2 12.5% 1.05 1.47 0 1/3 1/3 1/3 3/3A70680 M1_80_A706_11 81.7 111.2 10.3% 0.96 1.38 0 3/3 3/3MA100 M1_100_MA_11 110.4 139.6 8.8% 0.52 0.83 28 2/3 1/3 2/3A61560 M1_60_A615_11 63.2 104.0 11.2% 1.05 1.64 0 3/3 3/3A61580 M1_80_A615_11 80.5 121.1 9.1% 0.77 1.46 1 2/3 1/3 3/3
M2 A1035100 M2_100_A1035_11 125.0 162.1 4.9% 0.47 1.23 1 3/3 3/3M3 A70680 M3_80_A706_11 83.1 109.7 9.1% 0.86 1.32 0 3/3 3/3
A61560 M4_60_A615_11 63.6 90.7 12.1% 1.11 1.42 0 3/3 3/3A70660 M4_60_A706_11 67.5 95.8 11.5% 1.36 1.42 0 3/3 3/3
A70660 M1_60_A706_8 60.5 90.0 11.5% 1.01 1.50 0 3/3 3/3A70680 M1_80_A706_8 84.4 114.1 9.8% 0.92 1.35 0 3/3 3/3A706100 M1_100_MA_8 99.0 125.2 8.9% 1.11 1.28 0 3/3 3/3A61560 M1_60_A615_8 63.7 101.3 10.7% 1.12 1.61 0 3/3 3/3A61580 M1_80_A615_8 84.4 123.5 9.2% 0.73 1.45 0 3/3 3/3
M2 A1035100 M2_100_A1035_8 131.4 164.3 5.2% 0.43 1.17 1 3/3 3/3A70680 M3_80_A706_8 81.6 104.0 8.9% 0.99 1.28 0 3/3 3/3QT100 M3_100_QT_8 98.7 126.0 7.2% 0.38 1.16 1 1/3 2/3 3/3A61560 M4_60_A615_8 68.1 95.8 12.0% 1.06 1.41 0 2/3 1/3 3/3A70660 M4_60_A706_8 66.7 90.9 12.3% 1.18 1.36 0 1/3 2/3 3/3
YieldStressf y(ksi) θb<5degrees
TensileStressf t(ksi)
UniformStrainεun(%)
NormalizedStrainatFracture(εb/εun)
NormalizedStressatFracture(f ub/f y)
AngleatFracture
θb(degrees)
FractureLocationBarSize(Bend
Diameter)Manf. Grade
SpecimenName
M4
#11(8db)
#8(6db)
M3
M1
M1
M4
47
Table7:Bend/re-bendResultsfor#5Bars
48
4.3.3EffectsofBarYieldStrengthonRe-bendPerformance
AscanbeseeninFigure25to28theperformanceofbarbendsgenerallydecreasedasthe
measuredyieldstrengthofthebarsincreased.Thistrendholdsacrossallbarsizes.
A negative correlation can be observed between (fub/fy) during re-bending and the
measured bar yield strength (Figure 25). For #8 bar specimens with a target inside bend
diameter of 6db (or #8 (6db)) and for #11 (8db) specimens, test data exhibited relatively low
variability about the observed trends highlighted by the linear regression lines in Figure 25.
However, for #5 (4db) specimens, test data exhibited relatively large variability about the
observedtrend.The#8(6db)and#11(8db)specimensconsistentlyfailedatstresseswellabove
theyieldstrengthandclosertothetensilestrengthsofthebarsatallbarstrengthlevels;with
theexceptionoftheM1_Gr100_MA_11specimen.Todecouplethetrendof lowertensile-to-
yield-strength ratios with increasing yield strength from bend performance, the stresses at
fracturenormalizedbythetensilestrengthofthebars(fub/ft)areplottedversusthemeasured
yieldstrengthofthebarsinFigure26.Ascanbeseeninthefigure,thenegativecorrelationcan
beobservedfor#5barsasyieldstrengthincreases.#8and#11barsseemtoreachmorethan
95%offtwiththeexceptionofM3_Gr100_QT_8andM1_Gr100_MA_11.
Anegativecorrelationbetweentheyieldstrengthandthenormalizedstrainatfracturecan
also be observed in Figure 27. Most #8 bars (6db) and #11 (8db) bars, regardless of yield
strength, straightenedalmost fullyduring re-bending (Figure28). For#5 (4db)bars,however,
there is a clear increase in the remaining bend angle at fracture as the bar yield strength
increased.
49
Figure25:Normalizedre-bendstressatfracturevsmeasuredbaryieldstrength
50
Figure26:Normalizedre-bendstressatfracturevsmeasuredbaryieldstrength
51
Figure27:Normalizedre-bendstrainatfracturevsmeasuredbaryieldstrength
52
Figure28:Remainingbendangleatfracturevsmeasuredbaryieldstrength
53
4.3.4EffectsofBarSizeonRe-bendPerformance
Therelationshipbetween(fub/fy)andbaryieldstrengthiscomparedfordifferentbarsizes
in Figure 29. As can be seen in the figure, #11 (8db) and #8 (6db) bars reached significantly
largerstressesat fracturethan#5(4db)bars. In fact,exceptforonebartype,all#11and#8
barsreachedstressesinexcessoftheiryieldstrengthduringre-bending.However,asthebend
diameterof#5barswasincreasedfrom4db,thebendperformanceof#5barsimprovedand
becamecomparabletothatofthe largerbarswhenthetarget insidebenddimeterofthe#5
barswas6db(sameasthatof#8bars).Testdatathereforesuggesta limited influenceofbar
sizeonthebarstressat fractureduringre-bending,butasignificant influenceofbend inside
diameter on stress at fracture. Similar trends can be observed between bar size and the
normalizedstrainatfractureFigure30.
54
Figure29:Comparisonofnormalizedstressatfracturevsmeasuredyieldstrengthforvariousbarsizes
55
Figure30:Comparisonofnormalizedstrainatfracturevsmeasuredyieldstrengthforvariousbarsizes
56
Giventherelativelylargescatterintheperformanceof#5barscomparedwiththatofthe
largerbars,thepossibleeffectsofthemanufacturingprocessesontheperformanceof#5bars
areexploredinFigure31.The#5barsfromManufacturer1bentat4db,withtheexceptionof
M1_Gr60_A706bars,fracturedatstressesbelowthelinearregressiontrendlineforall#5(4db)
bars.However,thefracturesstressesofbarsfromManufacturer1bentat5dbweredistributed
aboveandbelowthetrendline,butexhibitedhighvariability.BarsproducedbyManufacturer
3showedthehighvariabilityaswell,withsomebarsfailingatsignificantlyhigherstressesthan
thetrendlinesandothersatsignificantlylowerstresses.BarsfromManufacturers2and4were
consistentlyabovethetrendlines.
57
4db
5db
6db
Figure31:Re-bendstressatfracturenormalizedbytensilestrengthvsmeasuredyieldstrengthfor#5bars
58
4.3.6EffectsofBendDiameteronRe-bendPerformance
The #11 (8db) and #8 (6db) bar specimens performed reasonably well across all grades.
However,the#5(4db)barsdidnot.Forthisreason,additional#5barswerebentatinsidebend
diametersof5dband6db.
Theeffectsofincreasingbenddiameterson(fub/fy)canbeseeninFigure32.Inthefigure,
lineswith short dashesdenotebarswith yield strengths around60 ksi (grade60), lineswith
longerdashesdenotebarswithyieldstrengthsaround80ksi(grade80),andsolidlinesdenote
barswithyieldstrengthsaroundorexceeding100ksi(grade100).Ascanbeseenin
Figure 32, the stress at fracture of grade 60 bars is not affected significantly when
increasingbenddiametersfrom4dbto5db;withtheexceptionofM1_60_A615specimens.This
is because these bars are failing at stresses close to their tensile strength at both bend
diameters(Figure31).Ontheotherhand,thehighergrades80and100,fracturedatstresses
significantlybelowtheirtensilestrengthatabenddiameterof4db.Thismaybethereasonwhy
bars of these grades experienced significantly higher stresses at fracture with larger bend
diameters.
Whilemostgrade60barsfracturedatstressesaboveyieldwithbenddiametersof4db,the
majorityofgrade80and100barsdidnot.Evenwithabenddiameterof5db,themajorityof
grade 80 and 100 bars still did not reach their yield strengths prior to fracture during re-
bending.Itisonlywhenthebenddiameterisincreasedto6dbthatthemajorityofgrade80and
100barsreachedtheiryieldstrengthsatfracture.
Consideringthestrainperformancemeasure(!b/!un),allgradessawincreasesinstrainsatfracturewith increasing bend diameters,with only a few reaching their uniform elongations
duringre-bending(Figure33). Interestingly,eventhoughgrade60barsdidnotseesignificant
increasesintheirstressesatfracture,theydidseemarkedincreasesintheirstrainatfracture
duringre-bendingwithincreasingbenddiameters.
Considering the remaining bend angle at fracture (Figure 34), all grade 60 and 80
specimens bent at 5db essentially straightened during re-bending andmost did so with 4db
59
bends.Mostgrade100bars,ontheotherhand,fullystraightenedonlywhentheywerebentat
6dbandmostdidnotstraightenwhenbenttotighterdiameters.
Figure32:NormalizedRe-bendFractureStressvsTargetBendDiameter
TargetInsideBendDiameter(db)
60
Figure33:NormalizedRe-bendFractureStrainvsTargetBendDiameter
TargetInsideBendDiameter(db)
61
Figure34:NormalizedRe-bendFractureAnglevsTargetBendDiameter
Insummaryforallperformancemeasuresconsidered,increasingthebenddiameterfrom
4db to 6db was found to generally have a positive effect. Overall, #5 bars of all grades saw
increasedductilityatthebendswithincreasingbenddiameters.Grade80and100#5barssaw
increases instressatfractureduringre-bendingwith increasingbenddiameters.Grade60#5
bars,howeverdidnotastheyreachedstressesclosetotheirtensilestrengthevenwithabend
diameterof4db.
TargetInsideBendDiameter(db)
62
4.3.7TheoreticalStraininBentSpecimens
TheimpactofthelowerductilityofHSRBonbendperformanceisinvestigatedby
comparingthestrainsinducedbybendingwiththestraincapacityofbars,namelytheiruniform
elongation(!un).Uniformelongatingisusedhereasitislessdependentonbarsizeand
measurementgaugelengththanfractureelongation.Sincebendingstrainsaredifficultto
measure,themaximumtheoreticaltensionstrainattheoutersurfaceofthebarswas
estimatedasfollows,assumingzeroelongationattheneutralaxis(!!!!"#!$%&'().
Figure35:MaxTheoreticalStrainDerivation
!!!!"#!$%&'( = !!!!"
(Equation4.3.1)
!! = 2 ∗ ! ∗ ! ∗ !! + !! ∗ !!"# (Equation4.3.2)
!!" = 2 ∗ ! ∗ ! ∗ !! + !!!! ∗ !
!"# (Equation4.3.3)
!!!!"#!$%&'( = !∗!!!!!!∗!!!!!!!− 1 = !!!
!!!!− 1 (Equation4.3.4)
As canbe seen inEquation4.3.4, the theoretical strain is independentofbar sizeand is
onlyafunctionofβ,theratioofbendinsidediametertobardiameter.
! d!
63
UsingEquation4.3.4,themaximumtheoreticalstrain,εmt,experiencedattheedgeofthe
specimensusing the targetedACI318-14minimumbenddiameterswas calculated. Similarly,
themaximumtheoreticalbendstaincorrespondingtotheactualpinsizesusedduringbending,
εma,wascalculatedusingEquation4.3.4.Thestrainsbasedonpindiameterratherthanthose
based on the final bend diameter after spring back (Table 1) were considered as theywere
deemedtobemore representativeof themaximumstrainsexperiencedduringbending.The
calculatedstrainvaluesarepresentedinTable8.
Table8:TheoreticalStrainsatBends
BarSpecimens
#5(4db) #5(5db) #5(6db) #8(6db) #11(8db)
PinDiametersUsed(in.) 2.0 2.5 3.0 5.0 10.0
βACI=TargetBendDiameter/db 4 5 6 6 8
βPin=PinDiameter/db 3.20 4.00 4.80 5.00 7.27
TargetMaximumTheoreticalStrain,εmt
0.110 0.091 0.077 0.077 0.059
MaxTheoreticalStrainBasedonPinSize,εma
0.135 0.111 0.094 0.091 0.064
Figure 36 compares the maximum theoretical strains associated with the bending pin
diameters(εma)withtheuniformstrainvaluesofthebarstested.Apointbelowthetheoretical
strain linesuggeststhatthebarspecimenwasbentpast itsuniformstrain.Ascanbeseen in
the figure, all but one of the #11 bars were bent to a maximum estimated strain that is
considerablylowerthantheuniformstrainsofthebars.Thisisowingtothelargeratioofbend
tobardiameterusedfor#11bars(βPin).Most#8barswerealsostrainedsignificantlylessthan
uniform strains (Figure 36). All #5 bars, including grade 60 bars, were strained past their
uniform strain with βPin = 3.2 (for a 4db target bend diameter). In addition, most #5 bars,
especiallyhighergradebars,werestrainedpast theiruniformstrainwithβPin=4.0 (fora5db
targetbenddiameter). It isonlywhen#5barsarebendtoaβPin=4.8 (fora6db targetbend
diameter), that grade 60 and 80 bars experience an estimatedbend strain at or below their
64
uniformstrains.Grade100#5bars,however,stillappearedtohavebeenstrainedhigherthan
theiruniformstrainvaluesatβPin=4.8.
65
Figure36:Baruniformstrainvsmeasuredyieldstrengthoverlaidwiththeestimatedmaximumbendstrains(εma)
66
These observed trends between strains experienced and bar uniform strains may help
explain the poorer performance of #5 bars compared with the larger bars, and the poorer
performance of higher grade bars that typically have lower uniform elongations than their
lower grade counterparts. To explore these relations further, (εma/εun) values were plotted
versus(fub/fy)forallbarsinFigure37,versus(fub/ft)inFigure38andversus(εb/εun)inFigure39.
These figures indicateaclearnegativecorrelationbetweenthe ratioof theoreticalmaximum
strainsincurredduringbendingandbaruniformstrains(εma/εun)forallperformancemeasures
considered.Thefiguresthereforecorroboratethehypothesisthatbendsin#5andhighergrade
bars showed poorer performance because they were strained higher with respect to their
uniformelongations.
Relations can be drawn between performance measures and the demand parameter
(εma/εun)asseeninFigure37toFigure39.Givenatargetperformancemeasure,thesefigures
allow the selection of the maximum permissible bending strain to uniform strain (εma/εun)
allowable in bending. For a performance objective defined as fub/fy ≥ 1.0 during re-bending,
Figure 37 indicates that εma/εun should not exceed about 1.2 during bending. With the
exception of an outlying #11 data point and one #5 bar data point, we can see that all bar
specimenswithεma/εun≤1.2wereabletodeveloptheiryieldstrengthduringre-bending(Figure
37).Moreover,withtheexceptionofa limitednumberofspecimens, thosewithanεma/εun≤
1.2 were also able to achieve stresses during re-bending that exceed 80% of their tensile
strength(Figure38),andstrainsthatexceed50%oftheiruniformstraincapacities(Figure39).
Accordingtoanεma/εun≤1.2criteria,thebendpindiametersusedfor#11(8db),#8(6db)
and#5(6db)bars(Table8)resultinadequatebendperformanceforallbarsandgradestested
inthisstudy(Figure36).Atighterpindiameteroffourtimesthebardiameter,βPin=4.0,used
for #5 (5db) specimens, can be permitted for grade 60 and 80 bars but not grade 100 bars.
FinallyaβPin=3.2valueshouldonlybeusedforgrade60bars.
Otherlimitsonεma/εuncanalsobeselectedbasedonotherperformanceobjectivesusingFigure37toFigure39.
67
Figure37:Normalizedfracturestressvsnormalizedtheoreticalbendstrain
68
Figure38:Normalizedfracturestress(fub/ft)vsnormalizedtheoreticalbendstrain
69
Figure39:Normalizedfracturestrainvsnormalizedtheoreticalbendstrain
70
CHAPTER5:RecommendationsforMinimumBendDiameters
In this chapter, recommendations forminimum inside bend diameters for reinforcing
barsaregivenforvariousbarsizesandASTMsteelgrades.Therecommendationsaregivenasa
function of the minimum required fracture elongation of the bars, as given in the ASTM
standards A615, A706, and A1035. Minimum bend diameter recommendations are also
provided as a function of the historic elongation data obtained from the CRSIMill Database
(CRSI).Theminimumbenddiametersprovidedareintendedtodeliverbendsthatarecapable,
at aminimum, of sustaining their yield strength prior to fracture in a re-bend test. Fracture
elongation,!f,isusedhereasitisthestraingiveninASTMstandardsforreinforcingbarsandin
the CRSI Mill Database; even though this measure is dependent on the ratio between the
standard8”measurementgaugelengthandbardiameter.
71
5.1PerformanceObjective
AsdemonstratedinChapter4,theratiooftheoreticalmaximumtensilestrainatabend
basedonpindiameters(εma)tobaruniformelongation(εun)governsbendperformanceunder
load.Asimilarrelationcanbeobservedwithrespecttothefractureelongationofbars(εf)
(Figure40).AscanbeseeninFigure40,allbarsbenttopindiametersthatdidnotgeneratea
theoreticalpeakstrainexceeding0.8εf(εma≤0.8εf)wereabletoreachtheyieldperformance
objective;exceptforoneoutlying#11bartest.Forathresholdstrainratioαf=εma/εfbetween
0.8and1.0,8bartypesexceedtheyieldstressperformanceobjectivewhile5donot(Figure
40).Forαf=εma/εf>1.0,allbutonebartypesfailtheperformanceobjective.Barbendsthat
donotexceedthethresholdvalueofεma=0.8εfarethereforedeemedtosatisfytheminimum
performanceobjectiveandshouldhaveadequateperformanceunderloading.
Figure40:Normalizedfracturestressvsnormalizedtheoreticalbendstrain
72
5.2RelationbetweenInsideBendDiameterandThresholdStrainRatio(αf)
RecallEquation4.3.4relatingthetheoreticalpeaktensilestrain inabend(!!!!"#!$%&'()tothebenddiameterratio(! = !"#$ !"#$%&' !!).
!!!!"#!$%&'( =! + 1! + 1/2− 1
Substituting !!!!"#!$%&'( with !!!!, the threshold peak strain, we get the theoreticalminimumbenddiameterratiotobe:
!!" =!!!
!!!!!
!!!! (Equation5.1.1)
Figure41illustratesthegeometricrelationshipbetweenβTHandabar’sfracturestrain
(εf) for various threshold strain ratios (αf) based on Equation 5.1.1. This graph indicates the
minimumbendpindiametertousetogenerateapeakbendstrainwithinaprescribedfraction
(αf)ofthebarfractureelongation.Forexample,forabarwithafractureelongationεf=0.1,a
pindiameterβTH=5.75shouldbeusedtoachieveatheoreticalpeakstrainof80%ofεf(orαf=
0.8).
73
Figure41:RelationbetweenβTHandbarfracturestrain(εf)forvariousthresholdstrainratios(αf)
0123456789
10
0 0.05 0.1 0.15 0.2
β TH
εf
α=0.6
α=0.8
α=1.0
f
f
f
74
5.3MinimumBendDiametersbasedonMinimumASTMElongations
Theminimum bend pin diameter (βASTM) based on ASTMminimum elongation values
thatachievesthedesiredyieldstrengthperformanceobjectivecanbeobtainedbysettingthe
bar fractureelongationεf,ASTM=minimumASTMspecified fractureelongation,andαf=0.8 in
Equation5.1.1.Thisestimateofthepindiameterisconservativebecauseallbarswithanαf=
0.8 are expected to achieve the performance objective while all bars satisfying the ASTM
specificationhavefractureelongationsexceedingεf,ASTM(Table9,
75
Table 10,andTable11).Alessconservativeestimateonpindiametercanbeobtained
byusingεf,ASTMbutαf=1.0.Table12presentsthebendpindiameters(βASTM)basedonASTM
elongations forvarioussteel specifications,grades,andαfvalues.Aspring-back resulting ina
15%increaseinbenddiameterfromthepindiametertothefinalat-restinsidebenddiameter
canbeconservativelyassumedbasedonmeasuredspring-backvalues in thisstudy (Table1).
Thisassumptionresults in theadjustedvaluesβASTM,ADI =βASTM*1.15 thatcanbecompared
with current ACI 318-14 minimum inside bend diameters (βACI). Figure 42 illustrates this
comparison forA615,#5barsofvarioussteelgrades. InTable12,boldedratiosofβASTM,ADJ /
βACIindicatethatACIbenddiametersachievethedesiredperformanceobjective.
Table9:ASTMA615FractureElongationRequirements
ASTMA615FractureElongationRequirementsεf,ASTM=Min.elongationin8in.%
BarDesignationNo. Grade40 Grade60 Grade80 Grade100
3 11 9 7 7
4,5 12 9 7 7
6 12 9 7 7
7,8 … 8 7 7
9,10,11 … 7 6 6
14,18,20 … 7 6 6
76
Table10:ASTMA706FractureElongationRequirements
ASTMA706FractureElongationRequirementsεf,ASTM=Min.elongationin8in.%
BarDesignationNo. Grade60 Grade80
3,4,5,6 14 12
7,8,9,10,11 12 12
14,18 10 10
Table11:ASTMA1035FractureElongationRequirements
ASTMA1035FractureElongationRequirementsεf,ASTM=Min.elongationin8in.%
BarDesignationNo. Grade100 Grade120
3,4,5,6,7,8,9,10,11 7 7
14,8 6 6
77
Table12:Comparisonbetweenminimumbenddiameterstoachievetheyieldstrength
performanceobjectiveandACI318-14minimumbenddiameters(assumingthesameACI
318-14benddiametersapplytohigh-strengthbars)
βASTM,ADJ βASTM,ADJ/βACI βASTM,ADJ βASTM,ADJ/βACI40 4.0 5.4 1.35 4.3 1.0660 4.0 7.4 1.84 5.9 1.4780 4.0 9.7 2.42 7.6 1.90100 4.0 9.7 2.42 7.6 1.9040 6.0 5.4 0.90 4.3 0.7160 6.0 7.4 1.23 5.9 0.9880 6.0 9.7 1.61 7.6 1.27100 6.0 9.7 1.61 7.6 1.2760 6.0 8.4 1.40 6.7 1.1180 6.0 9.7 1.61 7.6 1.27100 6.0 9.7 1.61 7.6 1.2760 8.0 9.7 1.21 7.6 0.9580 8.0 11.4 1.42 9.0 1.12100 8.0 11.4 1.42 9.0 1.12
ASTMA615 Grade βACIαf=0.8 αf=1.0
#5
transverse
#5
longitu
dinal
#8
#11
βASTM,ADJ βASTM,ADJ/βACI βASTM,ADJ βASTM,ADJ/βACI60 4.0 4.6 1.15 3.6 0.8980 4.0 5.4 1.35 4.3 1.0660 6.0 4.6 0.77 3.6 0.5980 6.0 5.4 0.90 4.3 0.7160 6.0 5.4 0.90 4.3 0.7180 6.0 5.4 0.90 4.3 0.7160 8.0 5.4 0.68 4.3 0.5380 8.0 5.4 0.68 4.3 0.53
αf=1.0
#5
tran.
#5
long.
#8
#11
ASTMA706 Grade βACIαf=0.8
βASTM,ADJ βASTM,ADJ/βACI βASTM,ADJ βASTM,ADJ/βACI100 4.0 9.7 2.42 7.6 1.90120 4.0 9.7 2.42 7.6 1.90100 6.0 9.7 1.61 7.6 1.27120 6.0 9.7 1.61 7.6 1.27100 6.0 9.7 1.61 7.6 1.27120 6.0 9.7 1.61 7.6 1.27100 8.0 9.7 1.21 7.6 0.95120 8.0 9.7 1.21 7.6 0.95
#5
tran.
#5
long.
#8
#11
ASTMA1035 Grade βACIαf=0.8 αf=1.0
78
Figure42:βASTM,ADJandbarfracturestrain(εf)forvariousthresholdstrainratios(αf)forASTMA615#5bars
Ascanbe seen inTable12,allASTMA615bar types,exceptone,bent toACI318-14
diametersaredeemednot toachievetheyieldstrengthperformanceobjectivewithαf=0.8,
withonlyafewmoreachievingitwithanαfof1.0.Ontheotherhand,Table12indicatesthat
all longitudinal bars satisfying the ASTM A706 specifications can achieve the desired
performance with an αf of 0.8. Transverse bars satisfying ASTM A706 specifications having
tighterACI318benddiametersthanlongitudinalbarsdonotmeetthisobjectivebutonlybya
smallmargin.SimilarlytoA615bars,allA1035barsbenttoACI318-14diametersaredeemed
nottoachievetheyieldstrengthperformanceobjectivewithαf=0.8,withonlythe#11bars
achievingitwithanαfof1.0.
TheseresultsthereforeindicatethatmostA615andA1035barbendssatisfyingACI318-14
shouldexhibitpoorperformancewhileA706barsbendsshouldexhibitadequateperformance.
012345678910
0 0.05 0.1 0.15 0.2
β ASTM,ADJ
εf
ASTMA615#5
Grade40Grade60Grade80&100
α=0.8α=1.0
βACIforlong.reinf.
βACIfortrans.reinf.
79
However,thatisnotthecaseinconcretestructureswhereA615grade60barsandA1035bars
have been shown to have adequate performance. The disconnectmay be attributed to the
conservative nature of the acceptance criteria selected. Of particular concern is the overly
conservative use of the minimum specified ASTM values for fracture strains (εf,ASTM) in the
evaluation.Thefollowingsectioninvestigatesthispointfurther.
80
5.4MinimumBendDiametersbasedonCRSIMillDatabaseElongations
Because the ASTM values for εf are minimum values and are typically exceeded by a
significantmargininproduction(especiallyforthelowergradebars),itisusefultocomparethe
βTHobtainedbyusingthestatisticalvaluesoffractureelongations(εf)andthecurrentACI318-
14benddiameterratios(βACI).
Thiscomparisonisfirstmadeusingstatisticalelongationsforgrade60barsobtainedfrom
the Concrete Reinforcing Institute’s (CRSI) Mill Database (CRSI, 2015), presented in Section
5.4.1.Theprobabilitiesoffailingtheyieldstressperformanceobjectiveforgrade60barsbent
to ACI 318-14 diameters were evaluated using statistical elongation data, and used to
demonstratethattheyieldstressobjectiveisinlinewithactualbendperformanceinconcrete
structures(Section5.4.2).
InSection5.4.3,thetargetbenddiameterratiosrequiredtoachieveagivenprobabilityof
failingtheyieldperformanceobjective(βPf)areevaluatedforallbartypesandgrades,forwhich
sufficient elongation data was available in the CRSI database. Particularly, the fracture
elongationvalues forASTMA615grade60,80and100andA706grade60and80barswere
used.Benddiameterrecommendationsaregivenforthosebartypesandgradesbasedonthis
analysis.
5.4.1CRSIMillDatabase
TheCRSIMillDatabase (2015) summarizes thevariousmonotonic-testpropertiesofbars
produced in the United-States in 2015. The mean (μ) and standard deviation values (σ) for
fractureelongationsobtainedfromthedatabasearesummarizedforgrade60barsinTable13
toTable15forthevariousbarsizesusedinthisstudy.
81
Table13:SummaryoffractureelongationvaluesfromCRSIMillDatabaseforASTMA615
bars
Table14:SummaryoffractureelongationvaluesfromCRSIMillDatabaseforASTMA706
bars
Table15:SummaryoffractureelongationvaluesfromCRSIMillDatabasefordualgrade
ASTMA615/A706bars
Themean(μ)andstandarddeviationvalues(σ)forfractureelongationsobtainedfrom
thedatabasearesummarizedforgrade80and100barsinTable13toTable15forthevarious
barsizesusedinthisstudy.
μ σ μ-2×σ
#5 0.132 0.018 0.096
#8 0.137 0.021 0.095
#11 0.131 0.026 0.079
A615GR60εf
μ σ μ-2×σ
#5 0.16 0.017 0.126
#8 0.162 0.026 0.110
#11 0.149 0.027 0.095
A706GR60εf
μ σ μ-2×σ
#5 0.154 0.017 0.120
#8 0.165 0.017 0.131
#11 0.172 0.021 0.130
DUALA615/A706εf
82
5.4.1ProbabilitiesofFailureofBendsBasedonGrade60ProductionDataInthissection,thepercentagesofgrade60barsinproductionthatwouldfailtheyield
strengthperformanceobjectiveifbenttoACI318-14minimumbenddiametersareevaluated
basedonbarpropertiessummarizedinTable13-Table15.
To achieve this, the following probabilities of failing the yield strength performance
objectiveareassumedbasedontestdataillustratedinFigure40:
Pf1=P[fub/fy≤1.0|αf≤0.8]=0.0 Equation5.4.1
Pf2=P[fub/fy≤1.0|0.8<αf≤1.0]=0.5 Equation5.4.2
Pf3=P[fub/fy≤1.0|1.0<αf]=1.0 Equation5.4.3
Then the probability of failure of bends for a given bar type, size, and target bend
diameterratio(βACI)canbeestimatedas:
PfTotal=P[εf<εf,1.0]*Pf3+P[εf,1.0<εf≤εf,0.8]*Pf2+P[εf≥εf,0.8]*Pf1 Equation5.4.4
With:
P[εf<εf,1.0],P[εf,1.0<εf≤εf,0.8],andP[εf≥εf,0.8]beingtheprobabilitiesthatbarsinabar
typehaveameasuredfractureelongationwithintherangesspecifiedbytheminimumrequired
fracturestrainsforbarsbenttocurrentACI318-14benddiametersandforagivenαf.Inthese
calculations,thefractureelongation(εf)isassumedtofollowanormaldistributionwithmean
(μ)andstandarddeviationvalues(σ)giveninTables13to15.
!!,!.! =!!"#/!.!"!!!!"#/!.!"!!/!
!!!.! Equation5.4.5
83
!!,!.! =!!"#/!.!"!!!!"#/!.!"!!/!
!!!.! Equation5.4.6
Table16summarizestheminimumrequiredfracturestrainsforbarsbenttocurrentACI318-14
benddiametersbasedonEqs.5.4.5and5.4.6.
Table16:MinimumrequiredfracturestrainsforbarsbenttocurrentACI318-14bend
diameters
Table17summarizestheprobabilitiesoffailingtheperformanceobjectiveofbendsfor
ASTMA615andA706grade60barsproducedin2015intheU.S.Ascanbeseeninthetable,all
barsbenttoachieveafinalbenddiameterratioof6.0ormore,regardlessofsize,haveverylow
probabilitiesoffailureandshouldexhibitadequateperformanceunderload.Atatargetbend
diameterratioof5.0,grade60A706anddualgradebarsstillhaverelativelylowprobabilitiesof
failure. However, at a target ratio of 4.0, Table 17 indicates that A615 bars have a 64%
probability of not reaching the performance objective, while those probabilities remain
relativelyhighbutdropto23%and31%forA706anddualgradebars,respectively.
Given that this failure analysis,whichutilizes actual productiondata, determines that
the vast majority of bars bent to ACI 318-14 specifications achieve the yield strength
performanceobjective,which in linewithobservedbendperformance in concrete structure,
this performance objective is deemed to be a reasonable measure of performance for bar
bendsinconcretestructures.
βACI εf,0.8 εf,1.04.0 0.157 0.126
5.0 0.129 0.103
6.0 0.109 0.087
8.0 0.084 0.067
84
Based on these findings and results in Table 17, it may therefore be warranted to
increase theminimumbenddiameter requirement inACI318-14 form4db to5db for#5and
smallergrade60transversebars.
Table17:Probabilitiesoffailingtheperformanceobjectiveforbarsinproductiontoday
benttoACI318-14insidediameters
BarSize TargetBendDiameterRatio Pf,Totalβtarget=4db 64.1%
βtarget=5db 24.3%
βtarget=6db 5.5%
#8 βtarget=6db 5.1%
#11 βtarget=8db 2.1%
#5
A615Grade60
BarSize TargetBendDiameterRatio Pf,Totalβtarget=4db 22.7%
βtarget=5db 1.7%
βtarget=6db 0.1%
#8 βtarget=6db 1.2%
#11 βtarget=8db 0.0%
A706Grade60
#5
BarSize TargetBendDiameterRatio Pf,Totalβtarget=4db 31.0%
βtarget=5db 3.6%
βtarget=6db 0.2%
#8 βtarget=6db 0.0%
#11 βtarget=8db 0.0%
DUALA615/A706Grade60
#5
85
5.4.2RequiredBendDiameterstoAchieveTargetProbabilitiesofFailureBasedonProductionData
The target bend diameter ratios required to achieve a given probability of failing the
yield performance objective (βPf) are presented in Table 18 for all bar types and grades, for
whichsufficientelongationdatawasavailableintheCRSIdatabase.Theratioswerecalculated
fortheprobabilitiesoffailureof2%,5%,10%,and20%.
AscanbeseeninTable17abenddiameterratioof4.0,whichisspecifiedinACI318-14
for#5andsmaller transversebars, shouldnotbeused foranyof thegradesandtypesof#5
barsconsidered,evenifprobabilitiesoffailureof20%areaccepted.However,grade60ASTM
A706anddualgrade#5barsdocomeclosetobeingabletobebenttoaratioof4.0.
Table19presentsrecommendedtargetbarbendinsidediametersthroughbendratiosthat
achieveprobabilitiesoffailurewithin5%formostbartypesandgrades.Incaseswhereresults
support reducing the bend diameters prescribed in ACI 318-14, the recommended bend
diameterswerenotreducedasthatmayhaveunintendedconsequencesontheperformance
of concrete around thebends.Departures fromcurrentlyprescribedbenddiameter ratios in
ACI318-14arehighlightedinthetable.Notably,A615andA706#5andsmallertransversebars
arerecommendedtobebenttoatleastabenddiameterratioof5.0forgrade60and80and
6.0forgrade100.Grade100A615longitudinalbarsarerecommendedtobebenttoaratioof
9.0for#9to#11barsand8.0for#6to#8bars.Itisnoteworthythelatterrecommendationfor
#6to#8grade100barsismadewithoutthesupportofelongationdata.
86
Table18:Targetbenddiameterratiosrequiredtoachieveagivenprobabilityoffailing
theyieldperformanceobjective
μ σ
5 0.132 0.018 6.6 6.1 5.6 5.28 0.137 0.021 6.6 6.0 5.5 5.011 0.131 0.026 8.0 7.0 6.2 5.55 0.123 0.016 7.0 6.5 6.0 5.58 0.132 0.013 6.0 5.7 5.4 5.011 0.123 0.02 7.7 6.9 6.3 5.75 N/A N/A N/A N/A N/A N/A8 N/A N/A N/A N/A N/A N/A11 0.096 0.017 10.4 9.3 8.4 7.5
5 0.16 0.017 4.9 4.6 4.4 4.18 0.162 0.026 5.6 5.1 4.6 4.211 0.149 0.027 6.6 5.8 5.3 4.75 0.129 0.011 6.0 5.7 5.4 5.18 0.134 0.014 6.0 5.6 5.3 5.011 0.139 0.018 6.1 5.6 5.3 4.8
5 0.154 0.017 5.2 4.9 4.6 4.38 0.165 0.017 4.7 4.4 4.2 3.911 0.172 0.021 4.7 4.4 4.1 3.85 N/A N/A N/A N/A N/A N/A8 N/A N/A N/A N/A N/A N/A11 N/A N/A N/A N/A N/A N/A
βPf=2% βPf=5% βPf=10%
DUALASTM
A615/A7
06 Grade
60
Grade
80
βPf=20%Grade
60
Grade
80
ASTMA615
ASTMA706
BarSizeεf
Grade
80
Grade
100
Grade
60
87
Table19:Recommendedtargetbarbenddiameterratios
BarSize βACI βRecom
ASTMA61
5
Grade
60
3to5Transverse 4.0 5.0*
3to5Longitudinal 6.0 6.0
6to8 6.0 6.0
11 8.0 8.0Grade
80
3to5Transverse 4.0 5.0*
3to5Longitudinal 6.0 6.0
6to8 6.0 6.0
11 8.0 8.0
Grade
100
3to5Transverse
NotSpecified 6.0
3to5Longitudinal
NotSpecified 6.0
6to8Not
Specified 8.0
9to11Not
Specified 9.0
ASTMA70
6 Grade
60
3to5Transverse 4.0 5.0
3to5Longitudinal 6.0 6.0
6to8 6.0 6.0
9to11 8.0 8.0
Grade
80
3to5Transverse 4.0 5.0
3to5Longitudinal 6.0 6.0
6to8 6.0 6.0
9to11 8.0 8.0
*thesebendratiosresultinhigherthan5%probabilitiesoffailure,whichisdeemedacceptablesincetheA615barsareusedinnon-seismicapplications
88
Chapter6:SummaryandConclusions
Summary
Bend/re-bendtestswereconductedonreinforcingbarswithyieldstrengthsrangingfrom
60ksitoapproximately120ksi.Strainagingtestswerealsoconductedonthebarstoensure
that the bar bends were re-bent after most of the strain aging embrittlement effects had
occurred. The bend/re-bend test variables were: bar grade, bar manufacturing process, bar
diameter (db),andbend insidediameter.High-strengthreinforcingbars (grade80andabove)
producedusingthemostprevalentmethods intheU.S.wereobtainedfromfourofthemain
manufacturersintheU.S.Barsizeswere#5,#8,and#11andthebarswerebenttomeetthe
minimumspecifiedACI318-14benddiameters foreachof the sizes. #5barswerebentwith
inside bend diameters of 4 bar diameters (transverse steel requirement) to 6 bar diameters
(longitudinal steel requirements). Thebar specimenswerebent into aV-shapeandpulled in
tensionuntilfracture.Allbarswerebentandtestedatatemperatureofabout20°C.Anoptical
measurementsystemwasusedtorecordbarsstrainsandchangesinthebendangleduringre-
bending.Performancemeasuresusedtoquantifytheperformanceofbendsincluded:
a) Theremainingbendangleatfractureduringre-bending(θb)
b) Theaxialstrainatfracturenormalizedbythebaruniformelongationstrain(!b/!un)c) Theaxialstressatfracturenormalizedbythebaryieldstrength(fub/fy)
d) Theaxialstressinbaratfracturenormalizedbythebartensilestrength(fub/ft)
89
Conclusions
Thechemistryofthebarswasfoundtoaffecttheextentofstrainagingsignificantly.The
highertheconcentrationofVanadiuminthesteel,whichwasusedbysomemanufacturersto
increase strength, the lower the embrittlement due to strain aging was found. Overall,
however, strain aging embrittlement never resulted in more than a 20% reduction in bar
fracturestrains.
Overall,forallbarsizesandtypes,asbarstrength(orgrade)increased,bendperformance
decreased as demonstrated by lower stresses, strains, and changes in the bend angle at
fractureduringre-bending.Moreover,forallbartypes,asthebendinsidediameterincreased,
bendperformancewasseentoimprove.
Overall, bends in #8 and#11barswere found toperformadequately at the currentACI
318-14minimumbenddiametersforallgrades.Most#8and#11barbendsstrengthenedfully,
priortofracturingatstressesaboveyieldandatrelativelylargeinelasticstrains.
Bends in #5 bars showed significantly varied performance. Grade 60 #5 bars, bent to
achieve a target inside diameter of 4db, were able to reach stresses close to yield prior to
fractureduringre-bending.Bendsingrade80and100bars,however,onlyreachedfractionsof
their yield strength during re-bending when bent to achieve a 4db inside diameter. The
performanceofbendsinhighergrade#5barsreachedlargerstressesandstrainsasthebend
diameterwasincreased,withgrade80barsreachingstressesclosetotheiryieldwith5dbbends
andgrade100barsreachingyieldstrengthswithbenddiametersof6db.
A relationship was derived between the bend inside diameter and the theoretical peak
tensile strain at the bend. This relationship indicates that the ratio of bend diameter to bar
diameter(β)governsthelevelofstrainappliedduringbending;i.e.,giventhesamebendratio,
thetheoreticalpeakstrainsincurredatbarbendswillbethesameregardlessofbarsize.The
relation derived assumes zero net strain at the bar centerline and therefore only applies to
bendingprocesseswherebarsarefreetomovelongitudinallyduringbending.Therelationdoes
not apply to simultaneous double bending applications that can introduce additional tensile
strains due to longitudinal restraint during bending. Strain parameters were obtained by
90
normalizingthetheoreticalpeakstrainsincurredduringbendingbythebaruniformorfracture
straincapacities(εma/εunorεma/εf).Theparameterswerefoundtobenegativelycorrelatedwith
all performance measures. As bending strains increased with respect strain capacities, bent
specimens were found to sustain lower stress and strain at fracture during re-bending. To
achieve specimens that reached at least their yield stress at fracture, it was found that the
εma/εun should not exceed 1.2, or εma/εf should not exceed 0.8, which corresponds
approximatelytotargetinsidebenddiametersofnolessthan4dbforthegrade60,5dbforthe
grade80,and6dbforthegrade100barstestedinthisstudy.
To generalize recommendations for bar bend diameters, relations between ASTM
minimumfractureelongationvaluesaswellasactualproductionelongationvaluesobtainfrom
theCRSIMillDatabasewerestudied.Inthisstudy,barbendsthatareabletosustaintheiryield
strengthduringre-bendingweredeemedtohaveacceptableperformance.
When setting bar fracture elongations equal to theminimum ASTM fracture elongation
limits, most bar bends of grade 60 and 80 ASTM A706 were found to have acceptable
performance.On the other hand, the vastmajority of grade 60 A615 andA1035 bar bends,
regardless of grade, were found to have unacceptable performance, which is contrary to
observed bend performance in concretemembers. Thiswas attributed to the fact that bars
generallyexceedtheminimumASTMspecifiedelongationbyasubstantialmargin.
Astatisticalanalysiswasconductedtodeterminetheprobabilityoffailure,ornotachieving
the performance objective, for bar bends using the statistical distribution of fracture
elongationsobtainedfromtheCRSIMillDatabasefor2015.Theanalysisshowedthatgrade60
bars in production today should have acceptable performance based on their measured
fractureelongationdowntoabenddiameterof5db.Thisfindingcorroboratedthattheselected
performance objective is a reasonable measure of performance for bar bends in concrete
structures.Atabenddiameterof4db,however,alargeportionofgrade60barsdidnotachieve
acceptable performance. Increasing theminimumbenddiameter for 4 db to 5db for # 5 and
smallerbarsisthereforerecommendedforgrade60bars.
91
The statistical analysiswas extended using elongation values for grade 80 and 100 bars
obtained from theCRSIMillDatabase.Recommendations forbarbenddiameters for various
A615andA706gradesandbarsizeswereprovidedtoachieveaprobabilityoffailingtheyield
stressperformanceobjectivearound5%,formostcases.Departuresfromcurrentlyprescribed
benddiameterrationinACI318-14werehighlighted.Notably,A615andA706#5andsmaller
transverse bars were recommended to be bent to a bend diameter ratio of at least 5.0 for
grade60and80and6.0forgrade100.Grade100A615longitudinalbarsarerecommendedto
bebenttoaratioofatleast9.0for#9to#11barsand8.0for#6to#8bars.
Since the performance evaluations of bends based on ASTM minimum elongations
estimate poor bend performance for a majority of bar types while those based on actual
elongationvaluesdidnot, results imply that theACI318-14benddiameter specificationsare
relyingontheinherentadditionalstraincapacityofbarsbeyondtheASTMminimumvaluesto
achieveacceptablebendperformance.Thesameistruefortherecommendedbenddiameters.
Currently, ACI 318-14 provides minimum bar-bend diameters as a function of bar size
mainlyandbarapplication(transverseor longitudinalbars).However,asproductionmethods
evolveorhigherandlessductilegradesofbarsareintroduced,itmaybecomenecessarytoset
minimumbend diameters as a function of uniformor fracture elongations and possibly as a
function of loading (i.e., seismic or non-seismic), such that bends achieve performance
objectivesthatmaybedifferent.
Therecommendationsforminimumbarbenddiametersprovided inthisstudyarebased
oncurrentproductionelongationstatistics.Theserecommendationswillneedtobeadjustedif
actual bar elongation values change significantly over time.Moreover, since all bending and
testing was conducted at relatively warm ambient temperatures, cold weather bend
performancemayresult indifferentbendperformanceattherecommendedbenddiameters.
Lowtemperaturebendperformanceshouldbeassessedforcoldweatherregions.
92
References
[1]AS/NZS4671:2001(2001)."SteelReinforcingMaterials."StandardsAustralia/StandardsNewZealand,Wellington,NewZealand.
[2]ASTMStandardA615/A615M-13(2013)."StandardSpecificationforDeformedandPlainCarbon-SteelBarsforConcreteReinforcement."ASTMInternational,WestConshohocken,PA.
[3]ASTMStandardA706/A706M-13(2013)."StandardSpecificationforLow-AlloySteelDeformedandPlainBarsforConcreteReinforcement."ASTMInternational,WestConshohocken,PA.
[4]ASTMStandardA1035/A1035M-11(2011)."StandardSpecificationforDeformedandPlain,Low-carbon,Chromium,SteelBarsforConcreteReinforcement."ASTMInternational,WestConshohocken,PA.
[5]ASTMStandardE8/E8M-15a(2015)."StandardTestMethodsforTensionTestingofMetallicMaterials."ASTMInternational,WestConshohocken,PA.
[6]CRSIMaterialPropertiesandBarProducersCommitteeandMillDatabaseSub-Committee(2015)CRSIMillDatabase.Schaumburg,IL. [7]BS4449:2005+A2:2009(2005)."Steelforthereinforcementofconcrete.Weldablereinforcingsteel.Bar,coilanddecoiledproduct.Specification",BSI.ISBN:9780580645853
[8]G.T.VanRooyen(1986)."Theembrittlementofhardened,temperedlow-alloysteelbystrainaging."JournaloftheSouthAfricanInstituteofMininingMetallurgy,vol.86,no.2.(1986):67-72
[9]Hopkins,D.,andPoole,R.(2008)."Grade500EReinforcingSteel:TestsonMicro-alloyandQuenchedandTemperedsamplesavailableinNewZealand."DepartmentofBuildingandHousing,Wellington,NewZealand,11.
[10]RashidM.S.(1976)."StrainAgingKinteticsofVanadiumorTitaniumStrengthenedHigh-StrengthLow-AlloySteels."MetallurgicalTransactionsA,vol.7A,(1976):497-503.