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Inconstructionofbuildings,concreteisplacedinthebeamsandslabinamonolithicpour.Thismeansthattheslabservesasthetopflangeofthebeams.

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Ifwearetodesignforpositivemomentanddoublereinforcementlater,wewouldstumbleatdefiningwhatshouldbethewidthlengthtouse.Toidentifythewidthlength,wemaybeconsideringtwopossiblecases.CaseA,wehaverectangularcompressionzone(FigB),andCaseB,theNAshiftsdownthedepthgivingusaTShapedcompressionzone(FigD).Soreally,theproblemcomesindefiningthewidthofthecompressionzone,

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Girdersareclassifiedasmainbeams.Soyouhavetheslab,supportedbybeams,andthenbeamsaresupportedbygirders.Thesupportedloadoftheslabinthisexampleistransferredtobeaminonedirection(onewayslab,alongtheshortestroute)thentobeams,togirders,andthentocolumns.Thereisalsothethirdtypeofbeam,calledtheedgeorspandrelbeam.

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Compressivestressesinflangedecreasesasitmovesawayfromthewebduetoshearlag.Itisunderstandablesincethewebsectionisstifferthantheflangesection,thereforethereisstressconcentrationatthejunctionanditreducesasyoumovefarawayfromthatjunctionshearlageffect.

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Insteadofconsideringavaryingstressdistributionacrossthefullwidthoftheflange,theACICode(8.12.2)callsforasmallerwidthwithanassumeduniformstressdistributionfordesignpurposes.Thegoalistorepresentthesamecompressionforcedevelopedinthefullwidthofthecompressionzoneusingonlytheeffectivewidth,(effectiveflangewidth)

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Thelastequationcanalsoberewrittenas:

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Thefirststepactuallygivesyoualreadyanestimateofthevalueoftheeffectivedepth,Notethatthesizeofthebeamstemischosensothat 0.005atthepointofmaximumnegativemomentadcorrespondstosteelreinforcementsattheflangeandattheweb,respectively.1. Solveforusing 2. Computethedesignstrengthdueto(i.e.)3. Calculatetheremainingdesignstrengthneededtoberesistedbytheweb,

4. Calculate(note:,,andareallprovidedatthispoint)5. Finally,

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ANS:24kNm

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Case2:a>hfAsf=1,724.637mm2Asw=1,640.5mm2ANS:3,365.136mm2

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Additionofcompressionreinforcement,reducesthecompressivestressintheconcretecompressivesection(i.e. ).Ineffect,thedepthofthecompressivestressblockisreduced(fromto)Thisscenariowouldthenallowmoretensionreinforcementtobeusedwhilekeepingthebeamundertensioncontrolledregion,againduetothereducedcompressivestressinconcrete.Therefore,increasestheductilityofthebeam.(Onepracticalimplicationisthatbeamsectioncanbereducedwhilemaintainingtensioncontrolledlimit)

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Notehowever,thatcompressionreinforcementdoesnotincreasethestrengthofthebeamsignificantly.Iftheleverarmiscomparedfromthepreviousslide,thereisindeedlittledifferencebetweenand

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Thecompressionsteelpreventscreepoftheconcretereducingthedeflection

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The"compressionzone"failsintensionbeforecompression.Comparethegraphfrom 0to Crosssectionaldimensionsinsomeapplicationsmaybelimitedbyarchitecturalandfunctionalrequirements.

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Forceequilibrium 0;

0.85 0.85

Strainrelationships

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, 0.005 Momentequilibrium

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If3aisfalse:compressivereinforcementisnotworkingIf3bisfalse:solvebysubstitutingstrainrelationshipequationtoforceequilibriumequationfor .Thiswillyieldtoquadraticequation.If3cisfalse:substitutestrainrelationshipequationtoforceequilibriumequationfor.

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ANS:270.87kNm

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Notethatincreasingthetensileareainspecifyingactualrebarsizeswouldresultto 0.004(seestraindistributiondiagram).Consequently,thedesignstrengthofthesectionwouldbereducedduetoreduced.Thiscanberesolvedbyincreasingthecalculatedcompressionsteelareawiththesame(ormore)increasedintensileareaused.

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ANS:As=near1200mm2,As=near400mm2

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