Reinforced Concrete(专业外语).ppt

REINFORCEDCONCRETE,byVincentMcKinnone-mail:vincentmckinnon,SYLLABUS,1MaterialsConcrete&Reinforcement2Beams3Slabs4Columns5Walls6Bases&Foundations,TypesofCement,OPCthemostcommonRapidhardeningPortlandCementLowheatPortlandCementSulphateresistingPortlandCement,Aggregates,CourseaggregateFineaggregate,Water,Water/cementratioMinimumis0.23weightofwaterNormally,rangesfrom0.450.6,Admixtures,Hardening/settingacceleratorsorretardersWaterreducingtoimproveworkabilityAir-entrainingimprovedamageresistanceSuperplasticisersforcomplicatedsections,REINFORCEDCONCRETEDESIGN,Reinforcedconcreteisacompositematerialofsteelbarsembeddedinahardenedconcretemix.Concrete,assistedbythesteelcarriesthecompressiveforceswhilstthesteelresiststhetensileforces.,CONCRETE&REINFORCEMENT,Concreteitselfisacompositematerial.Thedrymixconsistsofcementtogetherwithcourseandfineaggregates.Waterisaddedandthisreactswiththecementwhichhardensandbindstheaggregateintotheconcretematrixwhichsticksorbondsontothereinforcingbars.,CONCRETE&REINFORCEMENT,Knowledgeofthepropertiesandanunderstandingofthebehaviorofconcreteisanimportantfactorinthedesignprocess.,Cement,OrdinaryPortlandcementisthecommonesttypeinuse.rawmaterialsofOPC:lime,silica,aluminaandironoxide.Theseconstituentsarecrushedandblendedinthecorrectproportionsandthenburntinarotarykiln.Theclinkeristhencooled,mixedwithgypsumandgroundtoafinepowdertoproducecement.Themainchemicalcompoundsincementarecalciumsilicatesandaluminates.,Aggregates,Aggregatesareclassedintothefollowingtwosizes:courseaggregategravelorcrushedrockgreaterthan5mminsizefineaggregatesand,lessthan5mminsize,Aggregates,Aggregatesshouldbechemicallyinert,clean,hardanddurable.alkali-silicareaction:Someaggregatescontainingsilicamayreactwithalkalisinthecementcausingtheconcretetodisintegrate.thepresenceofchloridesintheaggregateegsaltinmarinesandswillcausecorrosionofthesteelreinforcement.Excessiveamountsofsulphatewillalsocausetheconcretetodisintegrate.,Water,Thewatertocementratio:mostimportantfactorinaffectingconcretestrength.Forfullhydration,cementabsorbs0.23ofitsweightofwater.Butthisamountofwaterwouldproduceaverydrymixandsoextrawateristhereforerequiredtoimproveworkability.Theactualwater/cementratiousedisgenerallyfrom0.450.6.,Admixtures,Admixturesaresubstancesaddedtoconcretemixesinverysmallamountsinordertoimprovecertainpropertiesbytheirchemicalorphysicaleffects.,Typesofadmixture,hardeningorsettingacceleratorsorretarderswater-reducingwhichgivesanincreaseinworkabilitywithalowerwater/cementratioair-entrainingwhichincreasesresistancetodamagefromfreezingorthawingsuperplasticiserswhichareusedincomplicatedsections,ConcreteMixDesign,twotypesofmixesareused:DesignMix.StrengthformsanessentialpartoftherequirementforcompliancePrescribedMix.Here,proportionsoftheconstituentsneededtogivetherequiredstrengthandworkabilityarespecified.Strengthtestingisnotrequired.,CONCRETEPROPERTIES,TheCOMPRESSIVEstrengthisthemostimportantpropertyofconcrete.Thecharacteristicstrengthismeasuredbythe28daycubestrength.standardcubesof100mmor150mmarecrushedtodeterminethestrength.Typicalstrengthvaluesare30N/mm2or40N/mm2.Thesearethe28daycubestrength.,CONCRETEPROPERTIES,TENSILEstrengthThisisnormallyassumedtobearound10%oftheconcretescompressivestrength.So,foragrade30concreteieonewhoscompressivestrengthis30N/mm2,thetensilestrengthwouldbeassumedtobe3N/mm2andforagrade40concrete,itwouldbeassumedtobe4N/mm2.Thetensilestrengthismeasuredbyloadingaconcretecylinderacrossadiameterasshowninthediagram(seeDia1).,SHEAR,Averticalshearforceinabeamcausescomplimentaryshearstressesanddiagonaltensileandcompressiveforcesofthesamemagnitudetooccur.Thisisshowninthenextdiagram(seeDia2)wherethestressesareshowninasmallelementneartheneutralaxis.Themaximumshearstressattheneutralaxisofthesectionisvmax=1.5*V/(b*h)Youwillnoteanimportantpointabouttheshearstrengthofasection.Itdependsupontheamountofreinforcementpresent,onthegradeofconcreteanduponthesectionsdepth.,MODULUSOFELASTICITY,Theshorttermstress-straincurveforconcreteincompressionisalsoshowninDia1.ThisisknownastheshorttermvalueofYoungsModulus.(SeealsoDia3).,CREEP,Thisisthegradualincreaseinstrainwithtimeinamembersubjectedtoprolongedstress.Whenloaded,itisobservedthatthecreepstrainismuchlargerthantheelasticstrain.Ifthespecimenisunloaded,thereisanimmediateelasticrecoveryandaslowerrecoveryinthestrainduetocreep.Bothamountsofrecoveryaremuchlessthantheoriginalstrainsunderload.,CREEP,Themainfactorsaffectingcreepstrainare,theconcretemixandstrength,thetypeofaggregate,thecuring,theambientrelativehumidityandthemagnitudeanddurationofthesustainedloading.,SHRINKAGE,Shrinkage,ordryingshrinkageisthecontractionwhichoccursinconcretewhenitdriesandhardens.Theaggregatetypeandcontentarethemostimportantfactorsaffectingshrinkage.Thelargerthesizeofaggregate,theloweristheshrinkage.Atthesametime,thelowertheworkabilityandwater/cementratiotheloweristheshrinkage.,REINFORCEMENT,Reinforcingbarsareproducedintwogradeshotrolledmildsteelbarshaveayieldstrengthoffy=250N/mm2.Hotrolledorcoldworkedbarshaveayieldstrengthoffy=460N/mm2.Steelfabricismadefromcolddrawnsteelwirestoformamesh.Ithasayieldstrengthoffy=460N/mm2.,REINFORCEMENT,Thestress-straincurveforsteelisshowninDia3.TheYoungsModulusortheModulusofElasticityforsteelis200kN/mm2.Thebehaviourintensionandcompressionisassumedtobethesame.Mildsteelbarsareproducedasroundbars.Buthighyieldsteelbarsareproducedasdeformedbarswithtransverseribs.,COVER,Thecover(includinglinks)toareinforcingbarwilldependupontheexposureconditions.TheseareasshowninthetableofDia4.Noticealsotheexposureconditionswhich,asyouwillnote,rangefrommildtoextreme.Forsevereexposuresinamarineenvironment,75mmisconsideredappropriate,2LIMITSTATEDESIGNANDSTRUCTURALANALYSIS,TheBritishcode(BS8110)forreinforcedconcretedesignstatesthattheaimofthedesignistheachievementofanacceptableprobabilitythatthestructurewillperformsatisfactorilythroughoutitslifetime.Itmustcarrytheappliedloadssafely,itmustnotdeformexcessivelyanditmusthaveadequateresistancetoeffectsofmisuseandfire,2LIMITSTATEDESIGNANDSTRUCTURALANALYSIS,Thecriterionforasafedesignisthatthestructureshouldnotbecomeunfitforuseiethatitshouldnotreachalimitstateduringitsdesignlife.Thisisachievedinparticularbydesigningthestructuretoensurethatitdoesnotreach:-,2LIMITSTATEDESIGNANDSTRUCTURALANALYSIS,theultimatelimitstatewherethewholestructureoritselementsshouldnotcollapse,overturnorbucklewhensubjectedtodesignloadstheserviceabilitylimitstatewherethestructureshouldnotbecomeunfitforuseduetoexcessivecracking,deflectionorvibration.,2LIMITSTATEDESIGNANDSTRUCTURALANALYSIS,Thestructuremustalsobedurableieitmustnotdeteriorateorbedamagedexcessivelybytheactionofsubstancescomingintocontactwithit.Forreinforcedconcretestructuresthenormalpracticeistodesignfortheultimatelimitstateandthentocheckforserviceabilityandtotakeallnecessaryprecautionstoensuredurability.,2LIMITSTATEDESIGNANDSTRUCTURALANALYSIS,UltimateLimitStateThestructuremustbedesignedtocarrythemostseverecombinationofloadstowhichitissubjected.Thesectionsoftheelementmustbecapableofresistingtheaxialloads,theshearsandmomentsderivedfromtheanalysis.Thedesignismadeforultimateloadsanddesignstrengthsofmaterialswithpartialfactorsappliedtotheloadsandmaterialstrengths.,2LIMITSTATEDESIGNANDSTRUCTURALANALYSIS,StabilityThecodeofpracticealsostatesthatthelayoutshouldbesuchastogiveastableandrobuststructure.Itstressesthattheengineerresponsiblefortheoverallstabilityshouldensurecompatibilityofdesignanddetailsofpartsandcomponents.,2LIMITSTATEDESIGNANDSTRUCTURALANALYSIS,Overallstabilityofastructureisprovidedbyshearwalls,liftshafts,staircasesandrigidframeactionoracombinationofthesemeans.Thestructureshouldbesuchastotransmitallloads,dead,imposedandwindsafelytothefoundations.,2LIMITSTATEDESIGNANDSTRUCTURALANALYSIS,RobustnessThecodestatesthattheplanninganddesignofthestructureshouldbesuchthatdamagetoasmallareaorfailureofasingleelementshouldnotcausethecollapseofamajorpartofthestructure.Thismeansthatthedesignshouldberesistanttoprogressivecollapse.,2LIMITSTATEDESIGNANDSTRUCTURALANALYSIS,ServiceabilityLimitStateThemainserviceabilitylimitstateprovisionsrelateto:-DeflectionThedeformationofthestructureshouldnotadverselyaffectitsappearanceorefficiency.Deflectionscanbecalculated,butinnormalcases,span-to-effectivedepthratioscanbeusedtocheckcompliancewithrequirementsCrackingCrackwidthscanbecalculated,butinnormalcasescrackingcanbecontrolledbyadheringtodetailingruleswithregardtobarspacinginzoneswheretheconcreteisintension.,3.0CHARACTERISTICANDDESIGNLOADS,DesignLoadsThecharacteristicorserviceloadsaretheactualloadsthestructureisdeignedtocarry.Theyarenormallythoughtofasthemaximumloadswhichwillnotbeexceededduringthelifeofthestructure.Instatisticaltermsthecharacteristicloadshavea95%probabilityofnotbeingexceeded.,3.0CHARACTERISTICANDDESIGNLOADS,Therearefourcharacteristicloadswhichwearemostlyconcernedwith:-ThecharacteristicdeadloadGkThisistheselfweightofthestructuretogetherwiththeweightoffinishes,ceilings,servicesandpartitions.ThecharacteristicimposedloadQkThisiscausedbypeople,furnitureandequipmentonfloorsandsnowonroofs.ThecharacteristicwindloadWkThisdependsuponthelocation,theshapeandthedimensionsofthebuilding.,3.0CHARACTERISTICANDDESIGNLOADS,Thecharacteristicearthload-EnThecodesaysthatearthloadsaretobeobtainedinaccordancewithnormalpractice.Thedesignloadsarethenobtainedfromthefollowingequation:-DesignLoad=Fk*fWhereFk=characteristicloadandf=partialsafetyfactorforloads.,3.0CHARACTERISTICANDDESIGNLOADS,Thepartialsafetyfactortakesaccountof:-PossibleincreasesinloadsInaccurateassessmentsoftheeffectsofloadsUnforeseenstressdistributionsinmembersTheimportanceofthelimitstatebeingconsidered(SeeDia.5),3.0CHARACTERISTICANDDESIGNLOADS,MaterialFactorsThecharacteristicstrengthsorgradesofmaterialsareasfollows:-Concrete,fcuisthe28daystrengthinNewtonspersquaremillimetreReinforcement,fyistheyieldorproofstressinNewtonspersquaremillimetre,3.0CHARACTERISTICANDDESIGNLOADS,Gradesforconcreteare:-Fcu=30,35,40,45and50.Gradesforsteelare:-Hotrolledmildsteel,fy=250N/mm2.Highyieldsteel,hotrolledorcoldworked,fy=460N/mm2.,3.0CHARACTERISTICANDDESIGNLOADS,Theresistanceofsectionstoappliedstressesisbaseduponthedesignstrengthwhichisdefinedas:-Characteristicstrength/partialfactorofsafetyformaterials=fk/m,Minimumrebar-tension,MildsteelbarsTypeR,Eg2-R10Fortensionreinforcementinabeam,theminimumamountofmildsteelis0.24%ie100*As/Ac=0.24HighyieldsteelbarsTypeT,Eg2-T25Fortensionreinforcement,theminimumamountofHYSis0.13%ie100*As/Ac=0.13,Minimumrebar-compression,Incompression,theminimumamountofreinforcementtobeprovidedforbothmildaswellashighyieldsteelis0.2%.Thus100*Asc/Ac=0.2Intheabbreviations,Ac=totalconcreteareaandAsc=Areaofsteelincompression.As=areaofsteelintension,Maximumareaofreinforcement,Themaximumareaofreinforcementinbothtensionaswellascompressionshouldnotexceed4%ofthegrosscrosssectionalareaofthebeam.,Reinforcementspacing,Firstofall,rememberthecoverrequirementsInthehorizontaldirection,theminimumspacingbetweenbarsshouldnotbelessthanthemaximumaggregatesizeplus5mm.Rememberalsotoleaveroomforthevibrator.,Reinforcementspacing,Wherethereare2ormorerows,thebarsshouldbeverticallyinlineandtheverticaldistancebetweenbarsshouldnotbelessthan2/3timesthemaximumaggregatesize.Notethatbundlesofbarsaretreatedasasinglebarofequivalentarea.Thisspacingshouldensurethattheconcretecanbeproperlycompactedaroundthereinforcement.,Loadfactors,Loadfactors,ThedesignloadisthecharacteristicloadmultipliedbytheloadfactorieDL=Fk*partialsafetyfactorforloads,Materialsfactor,Resistanceofsection,Theresistanceofsectionstoappliedstressesisbaseduponthedesignstrengthwhichisdefinedas:-Thecharacteristicstrengthdividedbythepartialsafetyfactorformaterials,Singlyreinforcedrectangularbeams,DesignAssumptions:-Planesectionsremainplane-iethestrainsintheconcreteandinthereinforcementarederivedassumingthattheplanesectionsremainplane.Thestressesintheconcreteincompressionarederivedusingthesimplifiedstressblockwherethedepthofthestressblockis0.9timesthedepthtotheneutralaxis.,Singlyreinforcedrectangularbeams,Thestrainintheconcreteatfailureis0.0035Thetensilestrengthoftheconcreteisignored,Singlyreinforcedrectangularbeams,Singlyreinforcedrectangularbeams,Singlyreinforcedconcretebeams,Thestressintheconcreteis:-0.67*fcu/gm0.67*fcu/1.50.45*fcu,Singlyreinforcedconcretebeams,Thestressinthesteelis:-fy/1.15=0.87*fyHowever,forinternalcompatibility,C=T,Singlyreinforcedconcretebeams,Henceequatingforces,Forceinconcrete0.67*fcu*b*0.9*x/1.5=0.4*fcu*b*xNotethefactor0.67.Thisisrelationshipbetweenthebendingandthecubestrengthofconcrete,Singlyreinforcedconcretebeams,Similarlytheforceinthesteelfy*As/gm=0.87*fy*AsNowweintroduceanewfactorcalledtheleverarm.ItssymboliszTheleverarmisthedistancebetweenthecentroidoftheconcreteincompressionandthecentroidofthesteelincompression,Singlyreinforcedconcretebeams,z=d0.45*xSo,byequatingC=Twecaneliminatexandfindanexpressionforz,suchthatz=d(0.87*fy*As/b*fcu),Singlyreinforcedconcretebeams,Then,bytakingmomentsforthetensileforceaboutthecentreofcompression,M=0.87*fy*As*zThen,byeliminatingAswecanarriveattheimportantequationforcalculatingz,Singlyreinforcedconcretebeams,z=d*(0.5+sqrt(0.25K/0.9)Where,K=M/b*d2*fcuHavingcalculatedz,wecanfindthereinforcementneededfromAs=M/0.87*fy*z,Singlyreinforcedconcretebeams,Example:Supposeourspanis10.0m.Ourbeamissay,600mmdeepand400mmwide.Assumealsothatadditionaldeadloadis10kN/mandthattheliveorimposedloadis15kN/m.Assumegrade30concrete.,Singlyreinforcedconcretebeams,Thentheweightofthebeamis:-24.0*0.6*0.4=5.76kN/mSo,thetotaldeadload=5.76+10.0=15.76kN/mThedeadloadfactor=1.4,Singlyreinforcedconcretebeams,Sothetotaldesigndeadload=1.4*15.76=22.06kN/mThetotaldesignimposedload=1.6*15.0=24.0kN/m,Singlyreinforcedconcretebeams,NowwecombinethedeadplusimposedloadsThetotaldesignload=22.06+24.0=46.06kN/m,Singlyreinforcedconcretebeams,Ourspan,ifyourememberwas10.0mSothemidspanbendingmomentM=46.06*10.0*10.0/8.0=575.75kNmHence,K=575.75*106/400.0*600.02*30.0K=0.133,Singlyreinforcedconcretebeams,NowweknowK,sowecancalculatezWefirsthavetodetermined.So,letsassume20mmbarswillbeusedwith12mmlinksand35mmcover.d=600.0035.012.00.5*20.0d=543.0mm,Singlyreinforcedconcretebeams,z=d*(0.5+sqrt(0.25K/0.9)z=543.0*(0.5+sqrt(0.250.133/0.9)z=480.2mmIfweusehighyieldsteel,thenAs=M/0.87*fy*z,Singlyreinforcedconcretebeams,As=575.75*106/0.87*460.0*480.2As=2995.95mm2Use4-T32(As=3216mm2)forcompressionreinforcement.,Singlyreinforcedconcretebeams,Weknowthat:-z=d0.45*xand,M=0.87*fy*As*zand,C=THence,0.402*fcu*b*x=0.87*fy*Asor,x=0.87*fy*As/(0.402*fcu*b),Singlyreinforcedconcretebeams,Thus,substitutinginthefirstequation,z=d0.45*0.87*fy*As/(0.402*fcu*b)And,sinceAs=M/(0.87*fy*z)z=d0.45*0.87*fy*M/(0.87*fy*z*0.402*fcu*b),Singlyreinforcedconcretebeams,Hence,z=d0.45*M/(0.402*z*fcu*b)LettingK=M/(b*d2*fcu)z=d1.11*K*d2/zorz2z*d+1.11*K*d2=0,Singlyreinforcedconcretebeams,Hence,z=(d+(d2-4.0*1.11*K*d2)/2.0z=d*(0.5+(0.25K/0.9)Oncezisknownthentheareaofsteelreinforcementcanbecalculated.,Singlyreinforcedconcretebeams,Letusnowlookatanotherexample.Supposeasimplysupportedbeamwithaspanof8.0mcarriesauniformlydistributeddeadloadwhichincludesanallowanceforselfweightof7.0kN/m(ietotaldeadweight)andanimposedloadof5.0kN/m.Thewidthofthebeamis250mmanditsdepth450mm.Findthereinforcementareaandthemaximumdeflection.Usegrade30concreteandHYS.AssumeE=26.4*106kN/m2.Assumec=30.0mm,links=12.0mmdiaandT20used,Singlyreinforcedconcretebeams,Thedesignload=1.4*7.0+1.6*5.0=17.8kN/mHence,M=17.8*8.02/8.0=142.4kNmLetd=450.030.012.00.5*20.0d=398.0mmK=M/(b*d2*fcu)=142.4*106/(250.0*398.02*30.0)=0.12,Singlyreinforcedconcretebeams,Hence,z=398.0*(0.5+(0.250.12/0.9)z=335.0mmThus,As=M/(0.87*fy*z)As=142.4*106/(0.87*460.0*335.0)As=1062.2mm2,Singlyreinforcedconcretebeams,Use3T25(As=1472.0mm2)Fortheserviceabilityconditions,Thedesignload=1.0*7.0+1.0*5.0=12.0kN/mThesecondmomentofarea=b*h3/12.0=0.25*0.453/12.0=0.0019,Singlyreinforcedconcretebeams,So,themaximumdeflection,=5.0*12.0*8.04/(384.0*26.4*106*0.0019)=12.8mm=span/625sodeflectionisacceptable.,Singlyreinforcedconcretebeams,Now,letuslookatshear.Wehaveseenhowtoreinforceasimplysupportedbeamwhichissinglyreinforcedieonlycarriestensionsteel.Inabeam,supposethemaximumshearforceisVThen,theshearstress,v=V/(b*d),Singlyreinforcedconcretebeams,InBS8110,thedesignshearisgivenbytheequation:-vc=(0.79*(100*As/(b*d)1/3*(400/d)1/4/mWhere,forshear,m=1.25Notethat400/dshouldnotbelessthan1Notealsothattheaboveequationisforgrade25concrete,forhighergrades,vcobtainedfromtheaboveequationshouldbemultipliedby(fcu/25.0)1/3Notethatthepercentagereinforcement(ie100*As/(b*d)shouldnotexceed3.,Singlyreinforcedconcretebeams,Thus,fortheexamplejustconsidered,v=0.5*8.0*17.8*103/(250.0*398.0)v=0.72N/mm2.And,sincevc=(0.79*(100.0*1472.0/(250.0*398.0)1/3*(400.0/398.0)1/4)/1.25=0.72N/mm2.,Singlyreinforcedconcretebeams,But,sincegrade30concreteisused,Thenvcisincreasedby(30.0/25.0)1/3orby1.06Ievc=1.06*0.72=0.77N/mm2.,Singlyreinforcedconcretebeams,Thecodesaysthattheminimumshearshouldnotexceed(0.8*fcu0.5)or5.0N/mm2.0.8*30.00.5=4.38N/mm2So,weareokthere.Thecodealsosaysthatlinksshouldprovideaminimumshearresistanceof0.4N/mm2.,Singlyreinforcedconcretebeams,Theshearforcetakenbythelinksisequaltothestrengthofthelinks.So,whilst(vvc)isnormallypositiveievisgreaterthanvcthisfactorismultipliedbytheconcreteareatogivetherequiredshearforce.(vvc)*b*d=0.87*fyv*Asv*d/sv,Singlyreinforcedconcretebeams,Here,Asvisequaltotheareaofbothlegsofthelink,fyvisequaltothedesignsteelstrengthandsvisequaltothelinkspacing.Thecodealsoassumesthatshearcrackswouldoccurat45degreestothehorizontal.Furthermorethespacingshouldnotexceed0.75*d,Singlyreinforcedconcretebeams,Theaboveequationcanberearangedsoastogivetheshearareaneeded:-Asv=b*sv*(vvc)/(0.87*fyv)And,sincewemustdesignforaminimumshearstressof0.4N/mm2,thenAsv=0.4*b*sv/(0.87*460.0),Singlyreinforcedconcretebeams,Thecoderequiresthatallbeamsofstructuralimportanceshouldbeprovidedwithminimumlinksthroughouttheirlength.Insomeminorbeamssuchaslintelslinksmaybeomittedprovidedvislessthan0.5*vc.Additionally,wherecompressionreinforcem