Failure Analysis of Polypropylene Fiber Reinforced ... · Rajai Z. Al‐Rousan Failure Analysis of Polypropylene Fiber Reinforced Concrete Two‐Way Slabs Subjected to Static and

Original Article

LatinAmericanJournalofSolidsandStructures,2018,15 1 ,e05

FailureAnalysisofPolypropyleneFiberReinforcedConcreteTwo‐WaySlabsSubjectedtoStaticandImpactLoadInducedby

FreeFallingMass

AbstractTheimpactresistanceofconcreteisconsideredaspoorduetoarelativelyenergydissipatingcharacteristicsandtensilestrength.Therefore,thispaperinvestigatesthefeasibilityofusingpolypropylenefibers PF toenhancepunchingshearcapacityofreinforcedconcrete RC two‐wayslabssubjectedtodrop‐weightimpacts.Theevaluatedparametersincludedtwoslabthickness 70mmand90mm ,fivedifferentPFper‐centages 0%,0.3%,0.6%,0.9%,and1.2% ,andtwoimpactloadheight 1.2mand2.4m .Thetestedslabsdividedintothreegroups:notsubjectedtoimpactload,subjectedtoim‐pactloadataheightof1.2m,andsubjectedtoimpactloadataheightof2.4m,resultinginatotalof25slabs.Thebehaviorofeachtwo‐wayRCslabwasevaluatedintermsofthecrackpatterns,ultimatepunchingshearcapacity.Thepresentex‐perimental data can be used for further assessment of theperformance of PF reinforced concretes two‐way slabs aswellasprovidingawell‐documenteddatasetrelatedtotheimpact‐resistant applications which is presently limitedwithintheliterature.TheresultsshowedthataddingthePFatadosageof0.3to1.2%byvolumeofconcreteandincreas‐ingtheslabthicknessfrom70mmto90mmleadstoconsid‐erableenhancementintheoverallstructuralbehavioroftheslabsandtheirresistancetoimpactloading.Interestingly,thedegradation in the ultimate punching capacity of the slabssubjectedtoimpactloadataheightof1.2and2.4mis30.5%and34.6%,respectively.Finally,anempiricalmodelwaspro‐posedforpredictingthepunchingshearcapacityofRCtwo‐wayslabsbasedonreliableexperimentalresultsavailableinliterature

KeywordsPost Behavior; Impact Resistance; Polypropylene Fiber;ReinforcedConcrete;Two‐WaySlabs.

1INTRODUCTION

Theresponseofreinforcedconcrete RC elementssubjectedtoimpactloadisahottopicinthepreviouspublishedresearchworkandstillneedsmoreelaborationinordertounderstandtheircom‐plexbehavior.ThishottopicisveryimportantespeciallyintheareaofRCnuclearfacilitiesormilitary

RajaiZ.Al‐Rousana*

aDepartmentofCivilEngineering,JordanUni‐versityofScienceandTechnology,Irbid,Jordan,Email:[email protected]

*Corresponding author

http://dx.doi.org/10.1590/1679-78254895

Received:February04,2018InRevisedForm:February22,2018Accepted:February22,2018Availableonline:March19,2018

RajaiZ.Al‐RousanFailureAnalysisofPolypropyleneFiberReinforcedConcreteTwo‐WaySlabsSubjectedtoStaticandImpactLoadInducedbyFreeFallingMass

LatinAmericanJournalofSolidsandStructures,2018,15 1 ,e05 2/19

fortificationstructuresthatareusedinhigh‐hazardorhigh‐threatapplicationsaswellasinthestruc‐turesthataredesignedtoresisttheaccidentalimpactloadingduetofallingrockandshiporvehiclecollisionswithoffshorefacilities,bridges,andbuildings.Therefore,anextensiveworkshouldbeun‐dertakeninanattempttodevelopadesignprocedureforpostimpactresistantandtoimprovethebehaviorofRCelementssubjectedtoimpactloads.Uptonow,thedevelopingofempiricalprovisionsforestimatingthedamageandstructuralcapacityunderspecificimpactloadingisthemostfocusedtopicofthemajorityoftheimpactloadingrelatedresearch Kennedy 1976 ,Vimaletal. 2017 ,Weietal. 2013 ,ChenandMay 2009 .Furthermore,moreoftheresearchworkhasbeenexclusivelyfocusedonslabandwallmechanismoflocalizeddamagesuchasimpactorpenetration,concretescab‐bing,andimpactorperforation Chang‐Geunetal. 2015 ,Duc‐KienandSeung‐Eock 2014 ,Shujianetal. 2016 .Inaddition,littleeffortisfocusedontheenergydissipationduetodamagegrowthatlocalizedlocationandglobaldeformationsintermsofaxial,shearandbendingdeformationsofRCflatslabsunderimpactloading Duc‐KienandSeung‐Eock 2017 .Nowadaystwo‐wayRCflatslabscanbeconsiderasthesuperlativesolutionforresidential,commercial,andofficebuildingsbecauseoftheefficientandeconomicalissuessuchaseasyinstallationofelectricalandmechanicalinfrastructures,thegreatlysimplerandreducedformwork,andfastersiteoperationsaswellastheeasierandversa‐tilityspacepartitioning.Moreover,thepunchingfailurecanbeconsideredasacomplexbehaviorindesignoftheRCtwo‐wayflatslab.Inaddition,thepunchingfailureistypicallybrittleandconsideredasultimateloadcapacityoftwo‐wayRCslabsandcancauseasuddencollapsesoftheentirestructureLorenaetal. 2016 .Thebent‐upbars,closedstirrups,post‐installedshearreinforcementorshearstudstechniquesaswellashighstrengthconcreteareusedtoincreasethepunchingshearcapacityofRCtwo‐wayflatslabs Micaeletal. 2015 .

Recently,utilizationoffiberreinforcedconcrete FRC hasemergedasapracticalapproachforenhancingtheperformanceofRCelementsunderimpactloading.NumerousstudieshaveshownFRCelementscontainingconventionalsteelreinforcingbarsdemonstratesuperiorresistances toglobalimpactbehaviorthanlocaldamagemechanismdevelopmentand,asaresult,acquireenhancedenergyabsorptioncapabilitiesunderimpactloadingwithrespecttoRCelements Ongetal. 1997 ,Kurihashietal. 2006 ,Zhangetal. 2007 .Inaddition,FRCisusedtoincreasethepunchingshearcapacityandthedeformationcapacityofRCflatslabsduetothecapabilityoffibersinthebridgingafterthecreationofthecracks ChengandParra‐Montesinos 2010 ,Mayaetal. 2012 .

Currentdesigncodeprovisions ACI318‐14 2014 ,FédérationInternationaleduBéton‐Vol.12010a , Fédération InternationaleduBéton‐Vol. 2 2010b , JSCE 2007 forpunching shearhadbeenproposedfornormalweightconcretestructuresandtheirappliancetoforFRCflatslabisnotconstantlystraightforwardespeciallyforempiricaldesignformula.Overthelastdecades,severalstip‐ulatedempiricalmodelsforpunchingshearofFRCflatslabhavebeenproposedbytakingintoaccountthecontributionoftensileandcompressivestrengthatthecriticalsectionofthepunchingshearaswellasthepulloutstrengthandquantityoffibers Choietal. 2007 ,Higashiyamaetal. 2011 ,ASTM2004 .Base donthepreviousliteraturereview,thepunchingshearstrengthoftheRCtwo‐wayflatslabsafter impact loadisomitted.Therefore, thispaperpresentsthemethodologyandconclusionsfromanexperimentalprogramundertakentostudytheeffectofimpactloadonthepunchingshearbehaviorofRCandpolypropylenefiberreinforced PFR concretetwo‐wayslabs.Highlightingwasplacedonassessingtheeffectofslabthicknesses,fibervolumefractions,andfreelydroppedweightheightson theRC two‐way flat slabbehavior in termsofultimate load capacity,deflectionprofile,toughnessorenergyabsorptionaswellasmodeoffailure.InanefforttofullydetainthepostimpactbehaviorsofthetestedRCslabs,thetestdatacollectedwereusedtoproposeananalyticalformulathatcanestimatethepreimpactandpost impactpunchingshearcapacityofRCflattwo‐wayslabswithandwithoutPFR.



2DESCRIPTIONOFEXPERIMENTALPROGRAM

2.1Testspecimens

Theexperimentalprogramincludedtestingtwentyeighttwo‐wayreinforcedconcreteslabsassimplysupportedsystemwithequalclearlengthandwidthof1.0masshowninFigure1.Theinves‐tigatedparametersincludetheslabthicknesses,hs 7cmand9cm ,fibervolumefractions,Vf 0%,0.3%,0.6%,0.9%,and1.2% ,andfreelydropweight 10cmindiameterandweighs7kg heights,hI1.2mand2.4m .Theslabswerereinforcedwithsevensteelbarswithadiameterof5mmineachdirectionwhichisequivalenttosteelreinforcementratiosof0.0018and0.0025forthe9cmand8cmslabsaccordingtotheACI318‐14Code 2014 .Adroppedmassheightof1.2mand2.4mproducesimpactvelocityof4.85m/sand6.86m/s,respectively,aswellaskineticenergyof82.32Jand164.64J,respectively.

Figure1:Testedslabslayoutandsetupdetails alldimensionsinmm .

2.2ConcreteMixture

ThemixtureingredientsincludeTypeIordinarycement 375kg/m3 ,localcoarseaggregate 916kg/m3 , local fineaggregate 700kg/m3 ,andsilicasand 64kg/m3 .Thespecificgravities for thecoarseandfineaggregateswere2.5and2.6,respectively.Polypropylenefiberswithamonofilamentconfigurationwereusedwithalengthof19mm,tensilestrengthof165MPa,specificgravityof0.91,



excellentalkaliresistance,abilityindecreasingdryingandplasticshrinkage,abilityinincreasingim‐pactresistanceofyoungconcrete,ability toreinforcedconcretebyactingmechanicallywithmulti‐dimensionalfibernetworkcoatedwithmortar.AlltheingredientsweremixedconsistentlyandthenthefiberswerefeedingmanuallytoensuretheuniformdistributionoffibersintheconcretemixtureasshowninFigure2.Thentheconcreteisplacedinthewoodenmolds,vibratingthem,straighteningthetopoftheconcretespecimen,de‐moldingthespecimensfor24hoursaftercasting,andplacingthespecimensinlime‐saturatedwaterfor28daysforcuring.

Figure2:Mixingprocedureofthetestedtwowayslab

2.3TestSetupandInstrumentation

TheRCtwo‐wayslabsweretestedfirstlyunderimpactload Asteelballof7kgmasswithadjust‐ableheightsof1.2mto2.4misallowedtofallfreelythrough150mmindiameterhollowtubememberplacedverticallytostickthetopsurfaceofthetestedtwowayslabsatthecenter byusingaspecialdesignsetupconsistsofsteelmemberswithI‐sectionjoinedtogethertoprovideahorizontalplatformtogivesimplysupportedconditionforthetwowayslabasshowninFigure1 Stage1 .Then,allslabswereloadeduptofailureusingahydraulicjackcentrallypositionedatthetopoftheslabasshowninFigure1 Stage2 .Thereferenceslabsthathavenotsubjectedtoimpactloadwerejustloadeduptofailure Stage2 .Asquaresteelplatewithathicknessof50mmandasidelengthof200mmwasusedtosimulatetheacolumnwith200mmsidesasshowninFigure1.Theappliedloadwasmeasuredbyusingloadcellandthreelinearvariabledifferentialtransformers LVDT wereplacedatspecificloca‐tiontomeasurethedeflectionprofileofthetestedslabsasshowninFigure1.

3RESULTSANDDISCUSSION

3.1ConcreteStrengthResults

Figure3showsthestress‐straindiagramsfortheconcretewithdifferentfibervolumefractionsaswellasthecompressivestrength,splittingtensilestrength,andmodulusofelasticity.Inspectionof



Figure3revealsthattheslopeofthestress‐straincurveislinearup young’smodulesofelasticity toabout30–40%oftheultimatecompressivestrength,afterthatthecurvesbecomenon‐linearduetotheinitiationofthemicrocracksatthepaste‐aggregateinterface.Theultimatestressoccurredaftertheformulationofthelargecrackwithintheconcrete.Also,Figure3showsthatthemaximumcom‐pressivestrength f’c ,splittingtensilestrength fr ,andyoung’smodulesofelasticity Ec increasedwiththeincreaseoftheincreasingofpolypropylenecontentaccordingtoASTM‐C39,ASTMC496,andASTM‐C469 ASTM 2004 , respectively.The results also show that thepolypropylene fibershadhighereffectonthetensilestrengthanddynamicmodulesofelasticitythanthecompressivestrength.

Strain,

0 2000 4000 6000 8000

Stre

ss, M

Pa

0

10

20

30

40

50Fiber density,0.9%

Fiber density,1.2%

Fiber density,0.6%

Fiber density,0.3%

Fiber density,0%

Fiber density,%0

0.30.60.91.2

f /c,MPa38.940.842.444.347.1

fr,MPa2.923.133.323.463.77

Ec,MPa1662617934190242048121617

Figure3:Stress‐straindiagramsandmechanicalpropertiesofconcrete/

cf :compressivestrength, rf :

splittingtensilestrength,and cE :young’smodulesofelasticity

3.2AnalysisofFailureModeandUltimateLoadCapacity

Basedontheexperimentalresults,alltestedslabswerefailedinthepunchingshearmodeandflexuralcracksstarted fromthe loadingsteelplateandextendeduntil theedgesof the testedslab.Punchingshearmodeorfailurewasbrittlefailurewhichoccurredneartheloadingsteelplate com‐pressionfaceortopsurface attheultimatefailureload,followedbythedevelopmentofapunchingshearfailureconeatthetensileface Bottomsurface .Figures4‐6showthetypicalpunchingshearfailureonthecompressionfaceandtensileface.InspectionofFigure4revealsthatthe90mmslabthicknesshadaremarkableimpactontheflexuralcracksandpunchingshearconethan70mmslabthicknessbydecreasing thenumberof the flexural cracks Tensile face andsmallpunchingshearcone.Also,Figure5showsthatslabssubjectedtoimpacthadmoreflexuralcracksandlargepunchingshearconethanslabsnotsubjectedtoimpact.Inaddition,Figure6showstheincreasingoffibervol‐umedecreasedthenumberofflexuralcrackandthesizeofpunchingshearconebecausethefiberscontributionintheresistingoftheappliedforcesuntilthefiberswerepulledoutfromtheconcrete.Additionally,theoccupationoffibersinstretchingthefailedbottomsurface tensionface oftheslabawayfromtheloadingsteelplatethusincreasedtheirpunchingshearcapacity.



Figure4:Effectofslabthicknessoncrackpatterns

Figure5:Effectofimpactloadoncrackpatterns

Figure6:Effectoffibervolumeoncrackpatterns



Table1:Specimens’DetailsandTestResults

SlabPercentoffibersbyvolume Vf

Slabthickness hs ,m

Heightofthefallingmass hI ,m

Ultimate punchingshearload VR ,kN

Toughness,kN.mm

Sf0.0t0.07h0 0

0.07

None

88.9 1588

Sf0.3t0.07h0 0.30% 93.4 1852

Sf0.6t0.07h0 0.60% 96.1 2094

Sf0.9t0.07h0 0.90% 100.7 2470

Sf1.2t0.07h0 1.2% 108.4 2859

Sf0.0t0.09h0 0

0.09

120.1 2169

Sf0.3t0.09h0 0.30% 126.1 2519

Sf0.6t0.09h0 0.60% 128.8 2671

Sf0.9t0.09h0 0.9% 135.3 3076

Sf1.2t0.09h0 1.20% 144.8 3410

Sf0.0t0.07h1.2 0

0.07 1.2

61.8 1432

Sf0.3t0.07h1.2 0.30% 67.8 1768

Sf0.6t0.07h1.2 0.60% 74.9 2028

Sf0.9t0.07h1.2 0.90% 83.0 2335

Sf1.2t0.07h1.2 1.2% 91.0 2616

Sf0.0t0.07h2.4 0

0.07

2.4

58.1 1339

Sf0.3t0.07h2.4 0.30% 63.9 1658

Sf0.6t0.07h2.4 0.60% 70.4 1982

Sf0.9t0.07h2.4 0.90% 77.9 2285

Sf1.2t0.07h2.4 1.2% 85.5 2528

Sf0.0t0.09h2.4 0

0.09

80.7 1813

Sf0.3t0.09h2.4 0.30% 88.9 2203

Sf0.6t0.09h2.4 0.60% 94.0 2526

Sf0.9t0.09h2.4 0.90% 105.2 2932

Sf1.2t0.09h2.4 1.2% 116.6 3367

Note:Toughnessisdefinedastheareaundertheloadversusdeflectioncurve

Figure7:Effectoffibervolumepercentageandimpactloadonpunchingshearload



Table1andFigure7showthesummarizedresultsandtheeffectoffibervolumepercentageandimpactloadonpunchingshearloadofthetestedslabs.InspectionofFigure7revealsthattheultimatepunchingshearcapacityofcontrolslab slabsnotsubjectedtoimpact generally increasesandthedegradationinslabstrengthduetoimpactloaddecreaseswiththeincreasingfibervolumepercentage.AddingPFRin0.3to1.2%byvolumefractionincreasedtheultimatepunchingcapacitywithrespecttoslabwithoutPFRbyabout5to22%,respectively.While, theslabthickness hs 90mm hasastrongimpactontheultimatepunchingshearcapacitywithanenhancementof35%withrespecttoslabwithathicknessof70mm.Inaddition,theimpact loadataheightof1.2mand2.4mcreateddegradationintheultimatepunchingshearcapacityof30.5%and34.6%,respectively,aswellastheefficiencyof fiber inabsorbingof impact loadordecreasingtheultimate loadcapacitydegradation30.5%to16.1% isincreasedwiththeincreasingofPFRpercentage.

Figure8:Typicalloadversusdisplacementcurves

3.3LoadDeflectionBehavior

Figure8 a‐c showstheeffectoftheimpactload,slabthickness,andfibervolumeontheloaddisplacementbehavior,stiffness,andtoughness.Thestiffnessisdefinedastheslopeofthepartbe‐tweentheinitiationofthefirstcrack reachingthetensilestrengthoftheconcrete andtheloadat



whichthedisplacementequalto3mmandthetoughnessisdefinedastheareaundertheloaddis‐placementbehavior.Theloaddisplacementbehaviorcanbedividedintotwostagesbasedonthecrackgrowthandtheshapeoftheload‐displacementbehaviorasshowninFigure8 d .Inthefirststagezeroloadingtoloadatwhichthedisplacementequalto3mm ,thebehaviorisapproximatelyelasticlinerbeforetheinitiationofthefirstcrack whichislocatedatthecenterofslabandclosetotheload‐ingsteelplate whichiscausedareductioninthestiffnessofthecurve.Then,inthesecondstage,thestiffnesswasreducedsuddenly,followedbythedevelopmentofthepunchingshearcone.InspectionofFigure8 a revealsthattheimpactloadataheightof1.2mand2.4mcausedareductionof3.8%and4.2%,respectively,instiffnessand5.5%and7.5%,respectively,intoughnesswithrespecttocon‐trolslab noimpactload .While,theslabthickness hs 90mm hasahelpfulstrongimpactonthestiffnessandtoughnesswithanenhancementof151%and127%,respectively,withrespecttoslabwithathicknessof70mmasshowninFigure8 b .Inaddition,Figure8 c showsthatthestiffnessandtoughnessgenerallyincrease 30%to128% and 22%to86% ,respectively,withtheincreasingfibervolumepercentage 0.3%to1.2% becauseaddingPFRassisttodelayandresisttheformulationandexpandingofcracks,thusslabstiffnessandtoughnessareenhanced.

Figure9:Typicaldisplacementshapes



3.4DeflectionProfile

Assessmentofthedisplacementprofileofthetestedslabsprovidesfurtherinformation quanti‐tativemeasure onthetopicoftheeffectoftestedparameters Figure9 ontheglobalstructuralbe‐haviorthatisnotdirectlyobviousfromstudyingoftheload‐displacementbehaviorandultimatemid‐pointdisplacement.Figure9 a‐c showstheeffectoftheimpactload,slabthickness,andfibervolumeonthedisplacementprofile.WhileFigure9 d showsthedisplacementprofileatdifferentloadvalueA:pointbetweenzeroloadandtheloadatwhichthedisplacementequalto3mm;B:pointatdis‐placementequalto3mm;C:pointbetweentheBandfailurepoint;andD:pointatfailureatultimatepunchingloadcapacity.InspectionofFigure9 a revealsthattheimpactloadataheightof2.4mhadthehighestdisplacementprofilespecificallyatthemid‐pointcomparingwithimpactloadataheightof1.2m.Thisconclusionisobservedthesameinthemodeoffailurewherethatslabssubjectedtoimpactataheightof2.4hadmoreflexuralcracksandlargepunchingshearconethanslabssubjectedtoimpactataheightof1.2m.Whilethedisplacementatthequarter‐pointisalmostequalforbothimpactheights.Inadditiontheslabthicknesshadthesameeffectonthedisplacementprofile mid‐pointandquarter‐point astheimpactloadanddecreasedwiththeincreasingoftheslabthicknessasshowninFigure9 b .IncomparingallofthedisplacementprofileshowedinFigure9 c ,itcanbeseenthatthePFRweresuccessfulinjustifyingthegrowthoflocalizedfailuresintermsofnumberofflexuralcrackandthesizeofthepunchingshearcone,thePFRslabsexhibiteddisplacementprofileinwhichdisplacementweremoreconsistentlydistributedand,asaresult,wereabletoachievelargerdisplace‐mentprofileatfailure.

4EMPIRICALMODEL

4.1PunchingShearModelforTwo‐WayRCSlabsSubjectedtoImpactLoad

PredictionofpunchingshearstrengthinRCtwo‐wayslabswithdifferentslabthicknesses,fibervolumefractions,andfreelydropweightheights Impact load is fundamental inordertoproposestructuraldesignproceduresforstructuressubjectedtoimpactload.Thus,anempiricalmodelwasproposedtopredictthepunchingshearstrengthoftwo‐wayRCslabssubjectedtoimpactloadasafunctionoftestedparameters.Mostmodelsfoundedintheliteratureanddesigncodesbasetheirver‐ificationsonacriticalsectiontofindthepunchingshearstrengthofnon‐impactedRCslabswithoutshear reinforcement Lorena et al. 2016 ,Micael et al. 2015 ,Ong et al. 1997 , Kurihashi et al.2006 ,Zhangetal. 2007 ,ChengandParra‐Montesinos 2010 ,Mayaetal. 2012 ,ACICommittee318 2014 ,FédérationInternationaleduBéton FIB‐Vol.1 2010a ,FédérationInternationaleduBéton FIB‐Vol.2 2010b ,JSCE 2007 ,Choietal. 2007 ,Higashiyamaetal. 2011 ,ASTM 2004 ,SelcukandFrank 2009 .Eq. 1 showstheACI318‐14 2014 expressionforcircularorsquarecol‐umnsoftwowayslabmoderaterelativetotheconcretecompressivestrengthandthicknessoftheslab

/33.0 coR fdbV 1

whereVRisthepunchingshearcapacityoftwo‐wayslabsatcriticalsectionlocatedatd/2fromthefaceofthesquareorcircularcolumn.distheeffectivedepthoftheslab,f′cistheconcretecompressivestrengthat28days,andboistheperimeterofthecriticalsection.Basedontheaboveequation,Eq. 2 canbeusedtodescribethepunchingshearcapacityofRCtwo‐wayslabssubjectedto impactwithsomemodificationsasfollowing:

/coR fdbV 2



whereαandβisafactoraccountingforfibervolumefractionandimpactloadeffects,respectively.BasedontheregressionanalysisoftheRCtwo‐wayslabsnotsubjectedtoimpactload β 1 Figure10 ,Eq. 3 presentstherelationshipbetweenthefibervolumefractionandαfactor.

fVe 1523.0321.0 3

whereVfisthefibervolumefractionpercentage.BasedontheregressionanalysisoftheRCtwo‐wayslabssubjectedtoimpactloadataheightof1.2and2.4mwhichisequivalenttoakineticenergy KE of82.32Jand164.64J,respectively, Figure11 ,Eq. 4 and 5 presentstherelationshipbetweenthefibervolumefractionandβfactor,respectively.

J 82.32 KEfor 0.700 172.0 fVe 4

J 164.64 KEfor 0.664 16.0 fVe 5

Vf , %

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40.25

0.30

0.35

0.40

0.45

Test Results

R2 = 0.9602

RC two-way slabs not subjected impact load ( = 1)

/co

R

fdb

V

fVe

1523.0321.0

Figure10:Relationshipsbetweenfibervolumefractionpercentage Vf andαfactorforRCtwowayslabs

notsubjectedimpcatload

/co

R

fdb

V

Vf , %

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.40.5

0.6

0.7

0.8

0.9

1.0

Test ResultsR2 = 0.978

RC two-way slabs not subjected impact load

164.64 KEfor 0.66416.0 fV

e

82.32 KEfor 0.700 172.0 fV

e

R2 = 0.982

Figure11:Relationshipsbetweenfibervolumefractionpercentage Vf andβfactorforRCtwowayslabs

subjectedimpcatload



ThusthepunchingshearstrengthoftheRCtwo‐wayslabssubjectedtoimpactcanbedefinedbythefollowingequations

impact) (No 0 KEfor 321.0 /1523.0 coV

R fdbeV f 6

J 32.28 KEfor 213.0 /3123.0 coV

R fdbeV f 7

J 64.164 KEfor 225.0 /324.0 coV

R fdbeV f 8

Table2:ExistingPunchingShearStrengthModels

Authors PunchingShearStrengthModel

NarayananandDarwish 1987

sf

fffs

f

ffbspR he

d

laVh

d

lafV 3455.01002.06.141.01624.0

fibers duoformfor 0.1

fibers crimpedfor 75.0

fibers roundfor 5.0

fa

ShaabanandGesund 1994 /4567.027.325.06.0 cfR fddeVV

Harajlietal.1995 /4075.033.0 cfR fddeVV

Higashiyamaetal. 2011

dd

laVde

d

laVfV

f

fff

f

fffbpcdrpdR

32.0141.0

MPaff cpcd 2.12.0 / , 5.11000

4 dd , 5.11003 p

der /25.01

11

PresentStudy /1523.0 4321.0 cV

R fddeeV f

Note:wherefspistheindirectcylindertensilestrengthoffiberreinforcedconcrete,τb 4.15MPaistheaveragefiber‐matrixinterfacialbondstress,αfisafactordependingofthefibergeometry,lfisthelengthofthefiber,dfisthediameterofthefiber,Vfisthevolumeofthefiber,distheeffectivedepthoftheslab,eisthecolumnsidelength,ρisthesteelreinforcementratio,andf’cistheconcretecompressivestrengthat28days

Table3:Predictedtotestpunchingshearstrength

Slab

VR,kN

TestedNarayananand

Darwish1987

ShaabanandGesund 1994

Harajlietal. 1995


PresentStudy

Sf0.0t0.07h0 88.9 96.8 93.4 90.6 113.5 88.1

Sf0.3t0.07h0 93.4 100.2 97.4 96.8 123.5 92.2

Sf0.6t0.07h0 96.1 103.6 101.5 102.9 132.9 96.5

Sf0.9t0.07h0 100.7 106.8 105.5 109.1 141.7 101.1



Sf1.2t0.07h0 108.4 109.9 109.5 115.3 149.9 105.8

Sf0.0t0.09h0 120.1 144.8 127.4 123.5 162.0 120.2

Sf0.3t0.09h0 126.1 150.0 132.9 132.0 176.3 125.8

Sf0.6t0.09h0 128.8 155.0 138.4 140.4 189.8 131.7

Sf0.9t0.09h0 135.3 159.8 143.9 148.8 202.3 137.8

Sf1.2t0.09h0 144.8 164.4 149.4 157.2 214.0 144.3

Predicted/Test 1.123 1.049 1.063 1.397 0.999

Coefficientofvariation 0.061 0.017 0.027 0.051 0.014

CorrelationCoefficient 0.978 0.995 0.993 0.991 0.997

Figure12:Testedpunchingshearstrengthversuspredictedofexistingmodels Model1:Narayananand

Darwish 1987 ;Model2:ShaabanandGesund 1994 ;Model3:Harajlietal. 1995 ;Model4:Hi‐gashiyamaetal. 2011 ;Model5:PresentStudy



4.2PredictabilityofVariousTheoreticalModels

TofindthepredictabilityandtheaccuracyoftheproposedmodelinEq. 6 ,itwascomparedwiththepunchingshearmodelswhicharethemostvalidandaccuratemodelforproposedmodel Nara‐yanan andDarwish 1987 ; Shaaban andGesund 1994 ;Harajli et al. 1995 ;Higashiyama et al.2011 asshowninTable2.Theaveragevalue predicted/tested ,coefficientofvariationandcorre‐lationcoefficientforpunchingshearcapacitypredictedbyusingvarioustheoreticalmodelsareshowninTable3.InspectionofTable3revealsthatthepredictedvalueShaabanandGesund 1994 andHa‐rajlietal. 1995 isclosedtothetestedvaluewithanaveragevalue predicted/tested of1.049and1.063,respectively,aswellasthecorrelationcoefficientsaremorethan0.95whichreflectsthatthebehaviorofthetestdataarewelldescribedbythesemodels.Also,NarayananandDarwish 1987 haveanacceptable predicted/tested of1.123.While,Higashiyamaetal. 2011 isoverestimatedthepunchingshearcapacitywithanaveragevalueof1.397.Figure12showsthetestedpunchingshearstrengthversuspredictedofexistingmodels.InspectionofFigure12 a‐d revealsthatthetheoreticalmodelsareoverestimatedthepunchingshearstrengthofthetestedslabswithhigherR2morethan90%.Inaddition,Figure12 f showsthattheproposedmodelprovidesthehighestnumberofpredic‐tionsof predicted/tested intheintervals 0.98‐1.02 andtheHigashiyamaetal. 2011 havethelow‐estnumberofpredictionsof predicted/tested intheintervals 1.28‐1.49 .

4.3PredictabilityoftheProposedModel

Theproposedmodelischeckedagainstpublishedexperimentalresultsbypredictingthepunch‐ingshearstrengthasshowninTable4.Inaddition,theaveragevalue predicted/tested ,coefficientofvariationandcorrelationcoefficientfortheexperimentalresultspresentedbyTheodorakopoulosandSwamy 1993 ,AlexanderandSimmonds 1992 ,SwamyandAli 1982 ,Harajlietal. 1995 ,NarayananandDarwish 1987 ,andHigashiyamaetal. 2011 aresummarizedinTable4.InspectionofTable4revealsthattheaveragepredictionerrorrangedfrom2%forTheodorakopoulosandSwamy1993 to37%forNarayananandDarwish 1987 ,wheretheaveragevalueandtheCorrelationCoef‐ficient forall theexperimentalresultswasapproximatelyequal87%and94%,respectively,whichshowsthattheproposedmodelhasagoodprospectivetopredictpunchingshearstrength

5CONCLUSIONS

Basedontheresultsandobservations,thefollowingconclusionsaredrawn:1.Theincreasinginslabthicknesshadanotableeffectontheflexuralcracksandpunchingshear

conebydecreasingthenumberoftheflexuralcracks Tensileface andthesizeofpunchingshearconewhiletheincreasinginimpactloadandthefibervolumeareincreasedthenumberofthenumberofflexuralcracksandthesizeofpunchingshearcone.

2.Theincreasinginslabthicknessof28%hadanenhancementoftheultimatepunchingshearcapacityof35%andtheaddingPFRin0.3to1.2%byvolumefractionenhancedtheultimatepunchingcapacitywith5to22%whiletheimpactloadataheightof1.2mand2.4mcreateddegradationintheultimatepunchingshearcapacityof30.5%and34.6%.

3.Theimpactloadcausedareductionoflessthan10%instiffnessandtoughnessofthetestedslabsbuttheslabthicknessenhancedthestiffnessandtoughnesswithanenhancementof151%and127%,respectively,aswellasthestiffnessandtoughnessincreased 30%to128% and22%to86% ,respectively,withtheincreasingfibervolumepercentageof0.3%to1.2%.

4.ThePFRslabsexhibiteddisplacementprofileinwhichdisplacementweremoreconsistentlydistributedand,asaresult,wereabletoachievelargerdisplacementprofileatfailure.

5.Theproposedempiricalmodelwasingoodagreementwiththeoreticalmodelsexperimentalresultsavailableinliteratureinpredictingtheultimatepunchingshearcapacityoftwowayslabsnotsubjectedtoimpact.



Table4:LiteratureExperimentaldataandpunchingshearstrengthprediction

Specimen h,mm d,mm e,mm/

cf ,

MPaρ,% Vf,%

Vexp,kN

VPre‐dicted,kN

(Tested)

)(Predicted

R

R

V

V

TheodorakopoulosandSwamy 1993

FS‐1 125 100 150 35.4 0.56 0.00 173.5 191 1.10

FS‐2 125 100 150 34.0 0.56 0.50 225 202 0.90

FS‐3 125 100 150 35.6 0.56 1.00 247.4 223 0.90

FS‐4 125 100 150 35.7 0.56 1.00 224.4 223.3 1.00

FS‐5 125 100 150 38.0 0.37 1.00 198.1 230.4 1.16

FS‐6 125 100 150 35.7 0.37 1.00 174.5 223.3 1.28

FS‐7 125 100 150 36.6 0.37 1.00 192.4 226.1 1.18

FS‐19 125 100 150 34.5 0.37 0.00 136.5 188.5 1.38

FS‐20 125 100 150 37.0 0.37 1.00 211 227.4 1.08

FS‐8 125 100 100 36.7 0.56 0.00 150.3 155.6 1.04

FS‐9 125 100 100 35.6 0.56 1.00 216.6 178.4 0.82

FS‐10 125 100 200 36.4 0.56 0.00 191.4 232.4 1.21

FS‐11 125 100 200 34.2 0.56 1.00 259.8 262.3 1.01

FS‐12 125 100 150 36.1 0.56 1.00 217.5 224.6 1.03

FS‐13 125 100 150 33.5 0.56 1.00 235.5 216.4 0.92

FS‐14 125 100 150 35.0 0.56 1.00 239.5 221.1 0.92

FS‐15 125 100 150 31.2 0.56 1.00 238 208.8 0.88

FS‐16 125 100 150 27.9 0.56 1.00 227.8 197.4 0.87

FS‐17 125 100 150 46.8 0.56 1.00 268.4 255.7 0.95

FS‐18 125 100 150 14.2 0.56 1.00 166 140.9 0.85

AlexanderandSimmonds 1992

P11F0 155 132.7 200 33.2 0.5 0.00 257.0 326.6 1.27

P11F31 155 132.7 200 35.8 0.5 0.39 324.0 359.9 1.11

P11F66 155 132.7 200 35.0 0.5 0.84 345.0 381.1 1.10

P38F0 155 105.7 200 38.1 0.63 0.00 264.0 256.1 0.97

P38F34 155 105.7 200 38.4 0.63 0.43 308.0 274.5 0.89

P38F69 155 105.7 200 38.5 0.63 0.88 330.0 294.4 0.89

SwamyandAli 1982

S‐1 125 100 150 37.80 0.56 0.00 197.7 197.4 1.00

S‐2 125 100 150 39.00 0.56 0.60 243.6 219.6 0.9

S‐3 125 100 150 37.80 0.56 0.90 262.9 226.3 0.86

S‐4 125 100 150 36.90 0.56 1.20 281.0 234.1 0.83

S‐5 125 100 150 37.80 0.56 0.90 267.2 226.3 0.85

S‐6 125 100 150 38.00 0.56 0.90 239.0 226.9 0.95

S‐7 125 100 150 38.90 0.74 0.00 221.7 200.2 0.90

S‐13 125 100 150 39.30 0.74 0.90 236.7 230.8 0.98



S‐12 125 100 150 36.80 0.74 0.90 249.0 223.3 0.90

S‐11 125 100 150 37.10 0.74 0.90 262.0 224.2 0.86

S‐8 125 100 150 41.10 0.74 0.90 255.7 236.0 0.92

S‐16 125 100 150 38.90 0.56 0.90 213.0 229.6 1.08

S‐10 125 100 150 38.90 0.46 0.90 203.0 229.6 1.13

S‐9 125 100 150 38.90 0.37 0.90 179.3 229.6 1.28

S‐19 125 100 150 38.90 0.37 0.00 130.7 200.2 1.53

Harajlietal. 1995

A1 55 39 100 29.60 1.12 0.00 58.8 37.9 0.64

A2 55 39 100 30.00 1.12 0.45 63.6 40.8 0.64

A3 55 39 100 31.40 1.12 0.80 73.1 44.1 0.60

A4 55 39 100 24.60 1.12 1.00 64.7 40.2 0.62

A5 55 39 100 20.00 1.12 2.00 58.3 42.2 0.72

B1 75 55 100 31.40 1.12 0.00 91.8 61.3 0.67

B2 75 55 100 31.40 1.12 0.45 105.9 65.7 0.62

B3 75 55 100 31.80 1.12 0.80 108.4 69.7 0.64

B4 75 55 100 29.10 1.12 1.00 108.8 68.8 0.63

B5 75 55 100 29.20 1.12 2.00 134.5 80.2 0.60

NarayananandDarwish 1987

S1 60 45 100 43.3 1.84 0.00 86.50 55.1 0.64

S2 60 45 100 52.1 1.84 0.25 93.40 62.8 0.67

S3 60 45 100 44.7 1.84 0.50 102.00 60.4 0.59

S4 60 45 100 46.0 1.84 0.75 107.50 63.7 0.59

S5 60 45 100 53.0 1.84 1.00 113.60 71.0 0.63

S6 60 45 100 53.0 1.84 1.25 122.20 73.8 0.60

S7 60 45 100 47.0 1.6 1.00 92.60 66.9 0.72

S8 60 45 100 45.3 2.08 1.00 111.10 65.7 0.59

S9 60 45 100 43.5 2.3 1.00 111.30 64.3 0.58

S10 60 45 100 47.6 2.53 1.00 111.30 67.3 0.60

S11 60 45 100 29.8 1.84 1.00 82.10 53.3 0.65

S12 60 45 100 32.4 1.84 1.00 84.90 55.5 0.65


t100‐0.67 100 70 100 24.6 0.85 0.67 137.50 83.9 0.61

t140‐0.67 140 110 100 24.6 0.54 0.67 210.20 162.9 0.78

t180‐0.67 180 150 100 24.6 0.4 0.67 297.60 264.5 0.89

t100‐0.72 100 65 100 42.4 0.91 0.72 140.80 100.1 0.71

t140‐0.72 140 105 100 42.4 0.57 0.72 213.20 200.8 0.94

t180‐0.72 180 145 100 42.4 0.41 0.72 290.70 331.4 1.14

t100‐0.91 100 65 100 21.6 0.91 0.91 120.80 73.5 0.61

t140‐0.91 140 105 100 21.6 0.57 0.91 183.10 147.5 0.81

t180‐0.91 180 145 100 21.6 0.41 0.91 231.20 243.5 1.05



t100‐0.63 100 70 100 27.8 0.85 0.63 152.30 88.7 0.58

t100‐0.94 100 70 100 31.1 0.85 0.94 147.90 98.3 0.66

t100‐1.03 100 70 100 30.4 0.85 1.03 158.90 98.6 0.62

Summary

Authors Predicted/Test Coefficientofvariation CorrelationCoefficient

TheodorakopoulosandSwamy1993

1.02 0.15 0.64

AlexanderandSimmonds1992 1.04 0.14 0.53

SwamyandAli 1982 1.00 0.19 0.55

Harajlietal. 1995 0.64 0.06 0.99

NarayananandDarwish1987 0.63 0.07 0.87

Higashiyamaetal. 2011 0.78 0.24 0.97

All 0.87 0.26 0.94

Acknowledgement

TheauthorsacknowledgethetechnicalsupportprovidedbytheJordanUniversityofScienceandTechnology JUST .

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