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高性能混凝土 High-Performance Concrete

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高性能混凝土 High-Performance Concrete高性能混凝土High-PerformanceConcreteCHAPTER17High-PerformanceConcrete•Highmodulusofelasticity•Highabrasionresistance•Highdurabilityandlonglifeinsevereenvironments•Lowpermeabilityanddiffusion•Resistancetochemicalattack•Highresistancetofrostanddeicerscalingdamage•Toug...

高性能混凝土 High-Performance Concrete
高性能混凝土High-PerformanceConcreteCHAPTER17High-PerformanceConcrete•Highmodulusofelasticity•Highabrasionresistance•Highdurabilityandlonglifeinsevereenvironments•Lowpermeabilityanddiffusion•Resistancetochemicalattack•Highresistancetofrostanddeicerscalingdamage•Toughnessandimpactresistance•Volumestability•Easeofplacement•Compactionwithoutsegregation•InhibitionofbacterialandmoldgrowthHigh-performanceconcretesaremadewithcarefullyselectedhigh-qualityingredientsandoptimizedmixturedesigns;thesearebatched,mixed,placed,compactedandcuredtothehighestindustrystandards.Typically,suchconcreteswillhavealowwater-cementingmaterialsratioof0.20to0.45.Plasticizersareusuallyusedtomaketheseconcretesfluidandworkable.High-performanceconcretealmostalwayshasahigherstrengththannormalconcrete.However,strengthisnotalwaystheprimaryre-quiredproperty.Forex-ample,anormalstrengthconcretewithveryhighdurabilityandverylowpermeabilityisconsid-eredtohavehigh-performanceproperties.BickleyandFung(2001)demonstratedthat40MPa(6,000psi)high-performanceconcreteforbridgescouldbeeco-nomicallymadewhileFig.17-1.High-performanceconcreteisoftenusedinbridges(left)andtallbuildings(right).(70017,70023)High-performanceconcrete(HPC)exceedsthepropertiesandconstructabilityofnormalconcrete.Normalandspe-cialmaterialsareusedtomakethesespeciallydesignedconcretesthatmustmeetacombinationofperformancerequirements.Specialmixing,placing,andcuringprac-ticesmaybeneededtoproduceandhandlehigh-perform-anceconcrete.Extensiveperformancetestsareusuallyrequiredtodemonstratecompliancewithspecificprojectneeds(ASCE1993,Russell1999,andBickleyandMitchell2001).High-performanceconcretehasbeenprimarilyusedintunnels,bridges,andtallbuildingsforitsstrength,dura-bility,andhighmodulusofelasticity(Fig.17-1).Ithasalsobeenusedinshotcreterepair,poles,parkinggarages,andagriculturalapplications.High-performanceconcretecharacteristicsaredevel-opedforparticularapplicationsandenvironments;someofthepropertiesthatmayberequiredinclude:•Highstrength•Highearlystrength299HOMEPAGEtemandresistancetochloridepenetration.Table17-1listsmaterialsoftenusedinhigh-performanceconcreteandwhytheyareselected.Table17-2listspropertiesthatcanbeselectedforhigh-performancecon-crete.Notallpropertiescanbeachievedatthesametime.High-performanceconcretespecificationsideallyshouldbeperform-anceoriented.Unfortunately,manyspeci-ficationsareacombinationofperformancerequirements(suchaspermeabilityorstrengthlimits)andprescriptiverequire-ments(suchasaircontentlimitsordosageofsupplementarycementingmaterial(FerrarisandLobo1998).Table17-3pro-videsexamplesofhigh-performancecon-cretemixturesusedinavarietyofstructures.Selectedhigh-performancecon-cretesarepresentedinthischapter.HIGH-EARLY-STRENGTHCONCRETEHigh-early-strengthconcrete,alsocalledfast-trackconcrete,achievesitsspecifiedstrengthatanearlieragethannormalconcrete.Thetimeperiodinwhichaspeci-fiedstrengthshouldbeachievedmayrangefromafewTable17-2.SelectedPropertiesofHigh-PerformanceConcretePropertyTestmethodCriteriathatmaybespecifiedHighstrengthASTMC39(AASHTOT22)70to140MPa(10,000to20,000psi)at28to91daysHigh-earlycompressivestrengthASTMC39(AASHTOT22)20to28MPa(3000to4000psi)at3to12hoursor1to3daysHigh-earlyflexuralstrengthASTMC78(AASHTOT97)2to4MPa(300to600psi)at3to12hoursor1to3daysAbrasionresistanceASTMC9440to1mmdepthofwearLowpermeabilityASTMC1202(AASHTOT277)500to2000coulombsChloridepenetrationAASHTOT259&T260Lessthan0.07%Clat6monthsHighresistivityASTMG59LowabsorptionASTMC6422%to5%LowdiffusioncoefficientWood,WilsonandLeek(1989)1000x10–13m/sTestunderdevelopmentbyASTMResistancetochemicalattackExposeconcretetosaturatedNodeteriorationafter1yearsolutioninwet/dryenvironmentSulfateattackASTMC10120.10%max.expansionat6monthsformoderatesulfateexposuresor0.5%max.expansionat6monthsforseveresulfateexposureHighmodulusofelasticityASTMC469Morethan40GPa(5.8millionpsi)(Aitcin1998)HighresistancetofreezingandASTMC666,ProcedureADurabilityfactorof95to100at300tothawingdamage1000cycles(max.masslossorexpansioncanalsobespecified)HighresistancetodeicerscalingASTMC672Scaleratingof0to1ormasslossof0to0.5kg/m3after50to300cyclesLowshrinkageASTMC157Lessthan400millionths(Aitcin1998)LowcreepASTMC512Lessthannormalconcretehours(orevenminutes)toseveraldays.High-early-strengthcanbeattainedbyusingtraditionalconcreteingredientsandconcretingpractices,althoughsometimesspecialmaterialsortechniquesareneeded.High-early-strengthcanbeobtainedbyusingoneoracombinationofthefollowing,dependingontheageatwhichthespecifiedstrengthmustbeachievedandonjobconditions:1.TypeIIIorHEhigh-early-strengthcement2.Highcementcontent(400to600kg/m3or675to1000lb/yd3)Table17-3(Metric).TypicalHigh-PerformanceConcretesUsedinStructuresMixturenumber123456Water,kg/m0Cement,kg/m3311398*500335*513315Flyash,kg/m33145———40Slag,kg/m347——125——Silicafume,kg/m31632*3040*4323Coarseaggregate,kg/m0801140Fineaggregate,kg/m0Waterreducer,L/m31.61.7—1.0—1.5Retarder,L/m3—1.8———Air,%7±1.55–8———5.5HRWRorplasticizer,L/m32.13146.515.75.0Watertocementingmaterialsratio0.370.300.270.290.250.34Comp.strengthat28days,MPa59—9399119—Comp.strengthat91days,MPa—60107104145—1.WackerDrivebi-levelroadway,Chicago,2001.2.ConfederationBridge,NorthumberlandStrait,PrinceEdwardIsland/NewBrunswick,1997.3.LaLaurentienneBuilding,Montreal,1984.4.BCEPlacePhase2,Toronto,1993.5.TwoUnionSquare,Seattle,1988.6.GreatBeltLink,EastBridge,Denmark,1996.*Originallyusedablendedcementcontainingsilicafume.Portlandcementandsilicafumequantitieshavebeenseparatedforcomparisonpurposes.Table17-3(Inch-PoundUnits).TypicalHigh-PerformanceConcretesUsedinStructuresMixturenumber123456Water,lb/yd9Cement,lb/yd3525671*843565*865531Flyash,lb/yd35376———67Slag,lb/yd379——211——Silicafume,lb/yd32754*5167*7239Coarseaggregate,lb/yd8201921Fineaggregate,lb/yd1551197Waterreducer,oz/yd34147—27—38Retarder,oz/yd3——48———Air,%7±1.55–8———5.5HRWRorplasticizer,oz/yd31Watertocementingmaterialsratio0.370.300.270.290.250.34Comp.strengthat28days,psi8,590—13,50014,36017,250—Comp.strengthat91days,psi—870015,30015,08021,000—1.WackerDrivebi-levelroadway,Chicago,2001.2.ConfederationBridge,NorthumberlandStrait,PrinceEdwardIsland/NewBrunswick,1997.3.LaLaurentienneBuilding,Montreal,1984.4.BCEPlacePhase2,Toronto,1993.5.TwoUnionSquare,Seattle,1988.6.GreatBeltLink,EastBridge,Denmark,1996.*Originallyusedablendedcementcontainingsilicafume.Portlandcementandsilicafumequantitieshavebeenseparatedforcomparisonpurposes.3.Lowwater-cementingmaterialsratio(0.20to0.45bymass)4.Higherfreshlymixedconcretetemperature5.Highercuringtemperature6.Chemicaladmixtures7.Silicafume(orothersupplementarycementingmate-rials)8.Steamorautoclavecuring9.Insulationtoretainheatofhydration10.Specialrapidhardeningcements.High-early-strengthconcreteisusedforprestressedconcretetoallowforearlystressing;precastconcreteforrapidproductionofelements;high-speedcast-in-placeconstruction;rapidformreuse;cold-weatherconstruction;rapidrepairofpavementstoreducetrafficdowntime;fast-trackpaving;andseveralotheruses.Infast-trackpaving,useofhigh-early-strengthmix-turesallowstraffictoopenwithinafewhoursaftercon-creteisplaced.Anexampleofafast-trackconcretemixtureusedforabondedconcretehighwayoverlaycon-sistedof380kg(640lb)ofTypeIIIcement,42kg(70lb)ofTypeCflyash,61⁄2%air,awaterreducer,andawater-to-cementingmaterialsratioof0.4.Strengthdataforthis40-mm(11⁄2-in.)slumpconcretearegiveninTable17-4.Figs.17-2and17-3illustrateearlystrengthdevelopmentofcon-cretesdesignedtoopentotrafficwithin4hoursafterplacement.Fig.17-4illustratesthebenefitsofblanketcuringtodevelopearlystrengthforpatchingorfast-trackapplications.Whendesigningearly-strengthmixtures,strengthdevelopmentisnottheonlycriteriathatshouldbeevalu-ated;durability,earlystiffening,autogenousshrinkage,dryingshrinkage,temperaturerise,andotherpropertiesalsoshouldbeevaluatedforcompatibilitywiththeproject.Specialcuringprocedures,suchasfogging,maybeneededtocontrolplasticshrinkagecracking.Table17-4.StrengthDataforFast-TrackBondedOverlayCompressivestrength,Flexuralstrength,Bondstrength,AgeMPa(psi)MPa(psi)MPa(psi)4hours1.7(252)0.9(126)0.9(120)6hours7.0(1020)2.0(287)1.1(160)8hours13.0(1883)2.7(393)1.4(200)12hours17.6(2546)3.4(494)1.6(225)18hours20.1(2920)4.0(574)1.7(250)24hours23.9(3467)4.2(604)2.1(302)7days34.2(4960)5.0(722)2.1(309)14days36.5(5295)5.7(825)2.3(328)28days40.7(5900)5.7(830)2.5(359)AdaptedfromKnutsonandRiley1987concretemixtureusing390kg/m3(657lb/yd3)ofrapidhardeningcement,676kg/m3(1140lb/yd3)ofsand,1115kg/m3(1879lb/yd3)of25mm(1in.)nominalmax.sizecoarseaggregate,awatertocementratioof0.46,aslumpof100to200mm(4to8in.),andaplasticizerandretarder.Initialsetwasatonehour(Pyle2001).concretemixturesmadewith504to528kg/m3(850to890lb/yd3)ofTypeIIIorTypeII/IIIcement,anominalmaximumsizecoarseaggregateof25mm(1in.),awatertocementratioof0.30,aplasticizer,ahydrationcontroladmixture,andanaccelerator.Initialsetwasatonehour(Pyle2001).HIGH-STRENGTHCONCRETEThedefinitionofhighstrengthchangesovertheyearsasconcretestrengthusedinthefieldincreases.Thispublica-tionconsidershigh-strengthconcrete(HSC)tohaveastrengthsignificantlybeyondwhatisusedinnormalprac-tice.Forexample,todayabout90%ofreadymixedcon-cretehasa28-dayspecifiedcompressivestrengthrangingfrom20MPa(3000psi)to40MPa(6000psi),withmostofitbetween28MPa(4000psi)and35MPa(5000psi).Therefore,HSCconsideredherehasadesignstrengthofatleast70MPa(10,000psi).Mosthigh-strengthconcreteapplicationsaredesignedforcompressivestrengthsof70MPa(10,000psi)orgreaterasshowninTables17-3and17-5.Forstrengthsof70MPa(10,000psi)andhigher,stringentapplicationofthebestpracticesisrequired.CompliancewiththeguidelinesandTheconcretehadaTypeIcementcontentof421kg/m3(710lb/yd3)andawatertocementratioof0.30(Grove1989).MixnumberUnitsperm3123456Cement,TypeI,kgSilicafume,kg—2447897427Flyash,kg—59——10487CoarseaggregateSSD(12.5mmcrushedlimestone),kg106810681068106810681121FineaggregateSSD,kgHRWRTypeF,liters11.611.611.2220.1116.446.3HRWRTypeG,liters—————3.24Retarder,TypeD,liters1.121.050.971.461.5—Watertocementingmaterialsratio0.280.290.290.220.230.32FreshconcretepropertiesSlump,mmDensity,kg/m4592454Aircontent,%1.60.71.31.11.41.2Concretetemp.,°C242418171723Compressivestrength,100x200-mmmoist-curedcylinders3days,MPa5754557253437days,MPa677days,MPa6days,MPa849495122116—91days,MPadays,MPa9710597128120—426days,MPa—1085days,MPa—Modulusofelasticityincompression,100x200-mmmoist-curedcylinders91days,GPa50.649.950.156.553.447.9Dryingshrinkage,75by75x285-mmprisms7days,millionths19312310087137—28days,millionths—90days,millionths—369days,millionths—1075days,millionths—Table17-5(Metric).MixtureProportionsandPropertiesofCommerciallyAvailableHigh-StrengthConcrete(BurgandOst1994)cementingmaterialsareusuallyincorporatedintothecon-cretemixture.Thisproducesadditionalbenefitsintheformofreducedheatgenerationduringhydration.Withuseoflow-slumporno-slumpmixes,high-compressive-strengthconcreteisproducedroutinelyundercarefulcontrolinprecastandprestressedconcreteplants.Thesestiffmixesareplacedinruggedly-builtformsandconsolidatedbyprolongedvibrationorshockmethods.However,cast-in-placeconcreteusesmorefragileformsthatdonotpermitthesamecompactionprocedures,hencemoreworkableconcretesarenecessarytoachievetherequiredcompactionandtoavoidsegrega-recommendationsforpreconstructionlaboratoryandfield-testingproceduresdescribedinACI363.2areessen-tial.Concretewithadesignstrengthof131MPa(19,000psi)hasbeenusedinbuildings(Fig.17-5).Traditionally,thespecifiedstrengthofconcretehasbeenbasedon28-daytestresults.However,inhigh-riseconcretestructures,theprocessofconstructionissuchthatthestructuralelementsinlowerfloorsarenotfullyloadedforperiodsofayearormore.Forthisreason,compressivestrengthsbasedon56-or91-daytestresultsarecommonlyspecifiedinordertoachievesignificanteconomyinmate-rialcosts.Whenlateragesarespecified,supplementary304MixnumberUnitsperyd3123456Cement,TypeI,lbSilicafume,lb—408015012545Flyash,lb—100——175147CoarseaggregateSSD(1⁄2in.crushedlimestone),lb0180018001890FineaggregateSSD,lb001251HRWRTypeF,flozHRWRTypeG,floz—————84Retarder,TypeD,floz2927253839—Watertocementingmaterialsratio0.280.290.290.220.230.32FreshconcretepropertiesSlump,in.73⁄493⁄481⁄21091⁄48Density,lb/ft3153.0153.1151.9155.2153.5153.2Aircontent,%1.60.71.31.11.41.2Concretetemp.,°F757565636274Compressivestrength,4x8-in.moist-curedcylinders3days,psi8,2207,9007,97010,4307,6306,1707days,psi9,66010,23010,36013,28011,1509,17028days,psi11,46013,30013,07017,00014,53012,27056days,psi12,23013,66013,84017,63016,760—91days,psi12,80015,17013,95018,03017,35013,310182days,psi14,11015,16014,14018,59017,400—426days,psi14,91017,10014,56019,23017,290—1085days,psi16,72017,73016,65021,75019,190—Modulusofelasticityincompression,4x8-in.moist-curedcylinders91days,millionpsi7.347.247.278.207.756.95Dryingshrinkage,3x3by11.5-in.prisms7days,millionths19312310087137—28days,millionths—90days,millionths—369days,millionths—1075days,millionths753677603527523—Table17-5(Inch-PoundUnits).MixtureProportionsandPropertiesofCommerciallyAvailableHigh-StrengthConcrete(BurgandOst1994)tionandhoneycomb.SuperplasticizingadmixturesareinvariablyaddedtoHPCmixturestoproduceworkableandoftenflowablemixtures.Productionofhigh-strengthconcretemayormaynotrequirethepurchaseofspecialmaterials.Theproducermustknowthefactorsaffectingcompressivestrengthandknowhowtovarythosefactorsforbestresults.Eachvariableshouldbeanalyzedseparatelyindevelopingamixdesign.Whenanoptimumornearoptimumisestab-lishedforeachvariable,itshouldbeincorporatedastheremainingvariablesarestudied.Anoptimummixdesignisthendevelopedkeepinginmindtheeconomicadvan-tagesofusinglocallyavailablematerials.Manyoftheitemsdiscussedbelowalsoapplytomosthigh-perform-anceconcretes.CementSelectionofcementforhigh-strengthconcreteshouldnotbebasedonlyonmortar-cubetestsbutshouldalsoincludetestsofcomparativestrengthsofconcreteat28,56,and91days.Acementthatyieldsthehighestconcretecompressivestrengthatextendedages(91days)isprefer-able.Forhigh-strengthconcrete,acementshouldproduceaminimum7-daymortar-cubestrengthofapproximately30MPa(4350psi).Trialmixtureswithcementcontentsbetween400and550kg/m3(675to930lb/yd3)shouldbemadeforeachcementbeingconsideredfortheproject.Amountswillvarydependingontargetstrengths.Otherthandecreasesinsandcontentascementcontentincreases,thetrialmixturesshouldbeasnearlyidenticalaspossible.SupplementaryCementingMaterialsFlyash,silicafume,orslagareoftenmandatoryinthepro-ductionofhigh-strengthconcrete;thestrengthgainobtainedwiththesesupplementarycementingmaterialscannotbeattainedbyusingadditionalcementalone.Thesesupplementarycementingmaterialsareusuallyaddedatdosageratesof5%to20%orhigherbymassofcementingmaterial.Somespecificationsonlypermituseofupto10%silicafume,unlessevidenceisavailableindicatingthatconcreteproducedwithalargerdosageratewillhavesat-isfactorystrength,durability,andvolumestability.Thewater-to-cementingmaterialsratioshouldbeadjustedsothatequalworkabilitybecomesthebasisofcomparisonbetweentrialmixtures.Foreachsetofmaterials,therewillbeanoptimumcement-plus-supplementarycementingmaterialscontentatwhichstrengthdoesnotcontinuetoincreasewithgreateramountsandthemixturebecomestoostickytohandleproperly.Blendedcementscontainingflyash,silicafume,slag,orcalcinedclaycanbeusedtomakehigh-strengthconcretewithorwithouttheadditionofsupplementarycementingmaterials.AggregatesInhigh-strengthconcrete,carefulattentionmustbegiventoaggregatesize,shape,surfacetexture,mineralogy,andcleanness.Foreachsourceofaggregateandconcretestrengthlevelthereisanoptimum-sizeaggregatethatwillyieldthemostcompressivestrengthperunitofcement.Tofindtheoptimumsize,trialbatchesshouldbemadewith19mm(3⁄4in.)andsmallercoarseaggregatesandvaryingcementcontents.Manystudieshavefoundthat9.5mmto12.5mm(3⁄8in.to1⁄2in.)nominalmaximum-sizeaggregatesgiveoptimumstrength.Inhigh-strengthconcretes,thestrengthoftheaggre-gateitselfandthebondoradhesionbetweenthepasteandaggregatebecomeimportantfactors.Testshaveshownthatcrushed-stoneaggregatesproducehighercompressivestrengthinconcretethangravelaggregateusingthesamesizeaggregateandthesamecementingmaterialscontent;thisisprobablyduetoasuperioraggregate-to-pastebondwhenusingrough,angular,crushedmaterial.Forspecifiedconcretestrengthsof70MPa(10,000psi)orhigher,thepotentialoftheaggregatestomeetdesignrequirementsmustbeestablishedpriortouse.Coarseaggregatesusedinhigh-strengthconcreteshouldbeclean,thatis,freefromdetrimentalcoatingsofdustandclay.Removingdustisimportantsinceitmayaffectthequantityoffinesandconsequentlythewaterdemandofaconcretemix.Claymayaffecttheaggregate-305Fig.17-5.TheTwoUnionSquarebuildinginSeattleusedconcretewithadesignedcompressivestrengthof131MPa(19,000psi)initssteeltubeandconcretecompositecolumns.High-strengthconcretewasusedtomeetadesigncriteriaof41GPa(6millionpsi)modulusofelasticity.(59577)thesetrialbatches,itwillbepossibletodeterminetheworkability,settingtime,andamountofwaterreductionforgivenadmixturedosageratesandtimesofaddition.Theuseofair-entrainingadmixturesisnotnecessaryordesirableinhigh-strengthconcretethatisprotectedfromtheweather,suchasinteriorcolumnsandshearwallsofhigh-risebuildings.However,forbridges,concretepiles,piers,orparkingstructures,wheredurabilityinafreeze-thawenvironmentisrequired,entrainedairismandatory.Becauseairentrainmentdecreasesconcretestrengthofrichmixtures,testingtoestablishoptimumaircontentsandspacingfactorsmayberequired.Certainhigh-strengthconcretesmaynotneedasmuchairasnormal-strengthconcretetobefrostresistant.PintoandHover(2001)foundthatnon-air-entrained,high-strengthconcreteshadgoodfrostanddeicer-scalingresistanceatawatertoportlandcementratioof0.25.BurgandOst(1994)foundgoodfrostresistancewithnon-air-entrainedconcretecontainingsilicafumeatawatertocementingmaterialsratioof0.22(MixNo.4inTable17-5);however,thiswasnotthecasewithothermixtures,includingaportland-onlymixturewithawatertocementratioof0.28.ProportioningThetrialmixtureapproachisbestforselectingpropor-tionsforhigh-strengthconcrete.Toobtainhighstrength,itisnecessarytousealowwatertocementingmaterialsratioandahighportlandcementcontent.Theunitstrengthobtainedforeachunitofcementusedinacubicmeter(yard)ofconcretecanbeplottedasstrengtheffi-ciencytoassistwithmixdesigns.Thewaterrequirementofconcreteincreasesasthefineaggregatecontentisincreasedforanygivensizeofcoarseaggregate.Becauseofthehighcementingmaterialscontentoftheseconcretes,thefineaggregatecontentcanbekeptlow.However,evenwithwell-gradedaggregates,alowwater-cementingmaterialsratiomayresultincon-cretethatisnotsufficientlyworkableforthejob.Ifasuperplasticizerisnotalreadybeingused,thismaybethetimetoconsiderone.Aslumpofaround200mm(8in.)willprovideadequateworkabilityformostappli-cations.ACICommittee211(1998),FarnyandPanarese(1994),andNawy(2001)provideadditionalguidanceonproportioning.MixingHigh-strengthconcretehasbeensuccessfullymixedintransitmixersandcentralmixers;however,manyoftheseconcretestendtobestickyandcausebuild-upinthesemixers.Wheredry,uncompactedsilicafumehasbeenbatchedintoamix,“balling”ofthemixhasoccurredandmixinghasbeenlessthancomplete.Insuchinstancesithasbeenfoundnecessarytoexperimentwiththesequenceinwhichsolidsandliquidsareadded,andthepastebond.Washingofcoarseaggregatesmaybeneces-sary.Combiningsinglesizesofaggregatetoproducetherequiredgradingisrecommendedforclosecontrolandreducedvariabilityintheconcrete.Thequantityofcoarseaggregateinhigh-strengthconcreteshouldbethemaximumconsistentwithrequiredworkability.Becauseofthehighpercentageofcementitiousmaterialinhigh-strengthconcrete,anin-creaseincoarse-aggregatecontentbeyondvaluesrecom-mendedinstandardsfornormal-strengthmixturesisnecessaryandallowable.Inhigh-risebuildingsandinbridges,thestiffnessofthestructureisofinteresttostructuraldesigners.Oncer-tainprojectsaminimumstaticmodulusofelasticityhasbeenspecifiedasameansofincreasingthestiffnessofastructure(Fig.17-5).Themodulusofelasticityisnotneces-sarilyproportionaltothecompressivestrengthofacon-crete.Therearecodeformulasfornormal-strengthconcreteandsuggestedformulasforhigh-strengthcon-crete.Themodulusachievableisaffectedsignificantlybythepropertiesoftheaggregateandalsobythemixtureproportions(Baalbakiandothers1991).Ifanaggregatehastheabilitytoproduceahighmodulus,thentheo
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