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Chapter 6
Strength Design of Reinforced ConcreteStructures6.1 AnalysisandDesign- GeneralConsiderations
6.1.1 ConventionandNotationUnlessotherwiseexplicitlystated,thefollowingunitsshallbeimplicitforthecorresponding quantitiesin
thedesignandotherexpressionsprovidedinthischapter:
Lengths m m
Areas m m2
Secondmomentsofarea m m 4
Force(axial,shear) N
Moment,torsion N m m
Stress,strength MPa,N/mm2
6.1.1.1 Notation = Depthofequivalentrectangular stress blockasdefinedin6.3.2.7.1,mm, = Shearspan,equaltodistance from center ofconcentratedloadtoeither:(a)faceofsupportfor continuous or cantilevered members, or (b) center of support for simply supported
members,mm,Sec6.4,AppendixA = Area of an individual bar or wire, mm2,Sec6.3,Sec8.2
=Net
bearing
area
of
the
head
of
stud,
anchorbolt,
or
headed
deformed
bar,
mm
2
,
Sec8.2,
AppendixD = Crosssectionalarea of concrete section resisting sheartransfer,mm2,Sec6.4,Sec8.3 = Crosssectional area of a structural member measured to the outside edges of transversereinforcement,mm2,Sec6.3,Sec8.3 = Area enclosed by outside perimeter of concrete cross section, mm2, see 6.4.4.1, Sec 6.4,8.3.8.3 = Crosssectionalareaat one end of a strut inastrutandtiemodel,takenperpendiculartotheaxisofthestrut,mm2,AppendixA = Gross area of concrete section bounded by web thickness and length of section in thedirectionofshearforceconsidered,mm2,Sec8.3 = Area of concrete section of an individual pier, horizontal wall segment, or coupling beamresistingshear,mm2,Sec8.3
= Area of reinforcement in bracket or corbelresistingfactoredmoment,mm2,see6.4.7,Sec6.4 = Gross areaof concretesection,mm2 For ahollowsection, istheareaoftheconcreteonlyanddoesnotincludetheareaofthevoid(s), see 6.4.4.1, Secs6.2to6.4,6.6,6.7,6.10,8.3, = Total area of shear reinforcement parallel toprimary tension reinforcement ina corbelorbracket,mm2,see6.4.7,Sec6.4 = Effective crosssectional area within a oint in a plane parallel to plane of reinforcementgenerating shear in the joint, mm2, seeSec8.3 = Total area of longitudinal reinforcement toresisttorsion,mm2,Sec6.4,8.3, = Minimumareaoflongitudinalreinforcementtoresisttorsion,mm2,see6.4.4.5.3,Sec6.4
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= Area of reinforcement in bracket or corbelresisting tensile force, mm2, see 6.4.7,Sec6.4 = Areaofa faceofanodalzoneorasectionthroughanodalzone,mm2,AppendixA = Projected concrete failure area of a singleanchor or group of anchors, forcalculationofstrengthintension,mm2,seeD.5.2.1,AppendixD
= Projected concrete failure area of a singleanchor, for calculation of strength in tension if
not limited by edge distance or spacing,mm2,seeD.5.2.1,AppendixD = Gross area enclosed by shear flow path,mm2,Sec6.4 = Areaenclosedbycenterlineoftheoutermostclosedtransversetorsionalreinforcement,mm2,Sec6.4 = Areaofnonprestressed longitudinal tensionreinforcement,mm2,Sec6.3,6.4,6.6,6.8, = Areaof tensionreinforcementcorresponding tomomentofresistance,see6.3.15.1(b) = Areaofadditionaltensionsteel,see6.3.15.1(b) = Area of compression reinforcement, mm2,AppendixA = Areaofprimary tension reinforcement inacorbelorbracket,mm2,see6.4.7.3.5,Sec6.4, = Effective crosssectional area of anchor intension,mm2,AppendixD, = Effective crosssectional area of anchor inshear,mm2,AppendixD
= Area of reinforcement required to balance the longitudinal compressive force in the
overhangingportionoftheflangeofaTbeam,see6.3.15.2(b) = Totalcrosssectionalareaof transverse reinforcement(includingcrossties)withinspacingsandperpendicular to dimension,mm2,Sec8.3 = Total area of surface reinforcement atspacing si in the ith layer crossingastrut,withreinforcementatanangle totheaxisofthestrut,mm2,AppendixA, = Minimum area of flexural reinforcement,mm2,see6.3.5,Sec6.3 = Total area of nonprestressed longitudinal reinforcement (bars or steel shapes), mm2,Sec6.3,8.3 = Areaofstructuralsteelshape,pipe,ortubinginacompositesection,mm2,Sec6.3 = Areaofone legofaclosedstirrup resistingtorsionwithinspacings,mm2,Sec6.4 = Area of prestressing steel in a tie, mm2,AppendixA
=
Total
crosssectional
area
of
all transversereinforcement within spacing
sthat
crosses
the
potential plane of splitting through thereinforcement being developed,mm2,Sec8.2 = Area of nonprestressed reinforcement in atie,mm2,AppendixA = Areaofshearreinforcementspacings,mm2,Sec6.4,6.12 = Projected concrete failure area of a singleanchororgroupofanchors, forcalculationofstrengthinshear,mm2,seeD.6.2.1,AppendixD = Projected concrete failure area of a singleanchor, for calculation of strengthinshear,ifnotlimitedbycorner influences,spacing,ormemberthickness,mm2, seeD.6.2.1,AppendixD = Totalareaof reinforcement ineach group ofdiagonalbarsinadiagonallyreinforcedcouplingbeam,mm2,Sec8.3 = Area of shearfriction reinforcement, mm2,Sec6.4,8.3 = Area of shear reinforcement parallel to flexural tension reinforcement within spacing ,mm2,Sec6.4
, = Minimum area of shear reinforcement withinspacing s, mm2, see 6.4.3.5.1 and 6.4.3.5.3,Sec6.4 = Loadedarea,mm2,Sec6.3 = Areaof the lowerbaseof the largest frustumof a pyramid, cone, or tapered wedgecontainedwhollywithinthesupportandhavingforitsupperbasetheloadedarea,andhaving
sideslopesof1verticalto2horizontal,mm2,Sec6.3 = Widthof compression faceofmember, mm,Sec6.3 = Perimeterofcriticalsectionforshear in slabsand footings, mm, see 6.4.10.1.2,Sec6.4 = Widthofstrut,mm,AppendixA = Widthof thatpartof cross section containing theclosedstirrupsresisting torsion,mm,Sec
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6.4 = Width of cross section at contact surfacebeinginvestigatedforhorizontalshear,mm,Sec6.12 = Web width, or diameter of circular section,mm,Sec6.3,6.4,8.2,8.3 = Dimensionof thecritical section measuredinthedirectionofthespanforwhichmomentsaredetermined,mm,Sec6.5 = Dimensionofthecritical section measuredin the direction perpendicularto,mm,Sec6.5
= Distance fromextreme compression fiber toneutralaxis,mm,Sec6.2,6.3,6.6,8.3
= Critical edge distance required to develop the basic concrete breakout strength of a postinstalled anchor in uncracked concrete without supplementary reinforcement to controlsplitting,mm,seeD.8.6,AppendixD, = Maximumdistancefrom center of an anchorshaft to the edge of concrete,mm,Appendix D, = Minimumdistancefrom center of an anchorshaft to the edge of concrete,mm,Appendix D = Distance from the centerofananchor shafttotheedgeofconcreteinonedirection,mm.Ifshear isapplied toanchor, is taken in the direction of the applied shear. If tension isappliedtotheanchor, istheminimumedgedistance,appendixd = Distance from center of an anchor shaft to theedgeofconcrete in thedirectionperpendicularto,mm,AppendixD = Smallerof: (a) thedistance from center of abarorwiretonearestconcretesurface,and(b)onehalfthecentertocenterspacingofbarsorwiresbeingdeveloped,mm,Sec8.2
= Clear cover of reinforcement, mm, see6.3.6.4,Sec6.3
= Distancefromtheinterior face of the columnto the slab edge measuredparalleltoc1,butnotexceeding,mm,Sec8.3 = Dimension of rectangular or equivalent rectangular column, capital, or bracketmeasured in the direction of the span forwhichmomentsarebeingdetermined,mm,Sec
6.4,6.5,8.3 = Dimension of rectangular or equivalent rectangular column, capital, or bracketmeasured in the direction perpendicular to,mm,Sec6.5 = Crosssectional constant to define torsionalpropertiesofslabandbeam,see6.5.6.4.2,Sec6.5 = Factorrelatingactualmoment diagram to anequivalentuniformmomentdiagram,Sec6.3 = Distance fromextreme compression fiber tocentroidoflongitudinal tensionreinforcement,mm,Sec6.26.4,6.6,6.12,8.18.3,
= Distance from extreme compression fiber to centroid of longitudinal compressionreinforcement,mm,Sec6.2 = Outsidediameterofanchor or shaft diameterof headed stud, headedbolt,orhooked bolt,mm,seeD.8.4,AppendixD = Valuesubstitutedforwhenanoversizedanchorisused,mm,seeD.8.4,AppendixD = Nominal diameter of bar, wire, or prestressing strand, mm, Sec 8.1-8.3 = Distance from extreme compression fiber to centroid of prestressing steel, mm, Sec6.4 = Diameter of pile at footing base, mm, Sec 6.8 = Distance fromextreme compression fiber tocentroidofextremelayeroflongitudinaltensionsteel,mm,Sec6.2,6.3 = Deadloads,orrelated internal moments andforces,Sec6.1,6.2,6.11,8.3
= Distancefromtheinner surface of the shaft of aJorLbolttotheoutertipoftheJ orLbolt,mm,
AppendixD = Distance between resultant tension load on a group of anchors loaded in tension andtheCentroid of the group of anchors loaded in tension, mm; is always positive,appendix d = Distance between resultant shear load on a group of anchors loaded in shear in thesameDirection, and the centroid of the group of anchors loaded in shear in the samedirection, mm; is always positive, appendix d = Loadeffectsofearthquake,orrelatedinternalmomentsandforces,Sec6.2,8.3 = Modulusofelasticityofconcrete,mpa,see6.1.7.1,Sec6.16.3,6.6,6.9
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= Modulusofelasticityofbeamconcrete,mpa,Sec6.5 = Modulusofelasticityofslabconcrete,mpa,Sec6.5 = Flexuralstiffnessofcompressionmember,Nmm2,see6.3.10.6,Sec6.3 = Modulusofelasticityofprestressingsteel,mpa,see6.1.7.3,Sec6.1 = Modulusofelasticityofreinforcement andstructuralsteel,mpa,see6.1.7.2,Sec6.1,6.3,6.6 = Specifiedcompressivestrengthofconcrete,mpa,Sec6.16.4,6.6,6.9,8.2,8.3,AppendixesA,
D = Squarerootofspecifiedcompressivestrengthofconcrete,mpa,Sec6.1,6.2,6.4,6.9,8.2,8.3,AppendixD = Effective compressive strength of the concrete in a strut or a nodal zone, mpa, Sec 6.8,AppendixA = Averagesplittingtensilestrengthoflightweightconcrete,mpa,See6.1.8.1Sec6.1,6.4,8.2.3.4(d),Sec8.2 = Stressduetounfactoreddeadload,atextremefiberofsectionwheretensilestressiscausedbyexternallyappliedloads,mpa,Sec6.4 = Compressive stress in concrete (afterallowance forallprestress losses)at centroidof crosssectionresistingexternallyapplied loadsoratjunctionofwebandflangewhenthecentroid
lieswithintheflange,mpa.(Inacompositemember, istheresultantcompressivestressatcentroidofcompositesection,oratjunctionofwebandflangewhenthecentroidlieswithin
theflange,duetobothprestressandmomentsresistedbyprecastmemberactingalone),Sec
6.4 = Compressivestress inconcretedue toeffectiveprestress forcesonly (afterallowance forallprestress losses) at extreme fiber of section where tensile stress is caused by externally
appliedloads,mpa,Sec6.4 = Stressinprestressingsteelatnominalflexuralstrength,mpa,Sec8.2 = Specifiedtensilestrengthofprestressingsteel,mpa,Sec6.4 = Modulusofruptureofconcrete,mpa,see6.2.5.2.3,Sec6.2,6.6 = Calculatedtensilestressinreinforcementatserviceloads,mpa,Sec6.3 = Stressincompressionreinforcementunderfactoredloads,mpa,AppendixA = Effective stress inprestressing steel (after allowance for allprestress losses),mpa, Sec8.2,AppendixA
=
Specifiedtensile
strength
ofanchor
steel,
mpa,
Appendix
D = Specifiedyieldstrengthofreinforcement, mpa,Sec6.26.4,6.6,6.9,6.12,8.18.3,AppendixA = Specifiedyieldstrengthofanchorsteel,mpa,AppendixD = Specifiedyieldstrengthoftransversereinforcement,mpa,Sec6.3,6.4,8.28.3 = Loads due to weight and pressures of fluids with welldefined densities and controllable
maximumheights,orrelatedinternalmomentsandforces,Sec6.2 = Nominalstrengthofastrut,tie,ornodalzone,N,AppendixA = Nominalstrengthatfaceofanodalzone,N,AppendixA = Nominalstrengthofastrut,N,AppendixA = Nominalstrengthofatie,N,AppendixA = Factored forceacting inastrut, tie,bearingarea,ornodalzone inastrutandtiemodel,N,AppendixA
= Overallthicknessorheightofmember,mm,Sec6.26.4,6.6,6.11,6.12,8.2,8.3,AppendixA
= Thicknessofmember inwhichananchor is located,measuredparallel toanchoraxis,mm,AppendixD = Crosssectional dimension of member core measured to the outside edges of the transversereinforcementcomposingarea,mm,Sec8.3 = Effectiveembedmentdepthofanchor,mm,seeD.8.5,AppendixD = ThicknessofoverhangingportionoftheflangeofaTbeam,see6.3.15.2(b) = Depthofshearheadcrosssection,mm,Sec6.4 = Heightofentirewallfrombasetotoporheightofthesegmentofwallconsidered,mm,Sec6.4,8.3 = Maximum centertocenter horizontal spacing of crossties or hoop legs on all faces of thecolumn,mm,Sec8.3
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= Loadsduetoweightandpressureofsoil,waterinsoil,orothermaterials,orrelatedinternalmomentsandforces,Sec6.2 = Momentofinertiaofsectionaboutcentroidalaxis,mm4,Sec6.3,6.4 = Momentofinertiaofgrosssectionofbeamaboutcentroidalaxis,mm4,see6.5.6.1.6,Sec6.5 = Momentofinertiaofcrackedsectiontransformedtoconcrete,mm4,Sec6.2 = Effectivemomentofinertiaforcomputationofdeflection,mm4,see6.2.5.2.3,Sec6.2 = Momentof inertiaofgrossconcretesectionaboutcentroidalaxis,neglectingreinforcement, mm
4
,Sec6.2,
6.3,
6.6
= Momentofinertiaofgrosssectionofslababoutcentroidalaxisdefinedforcalculatingand,mm4,Sec6.5 = Momentofinertiaofreinforcementaboutcentroidalaxisofmembercrosssection,mm4,Sec6.3 = Momentofinertiaofstructuralsteelshape,pipe,ortubingaboutcentroidalaxisofcompositemembercrosssection,mm
4,Sec6.3 = Effectivelengthfactorforcompressionmembers,Sec6.3,6.6 = Coefficientforbasicconcretebreakoutstrengthintension,AppendixD = Coefficientforpryoutstrength,AppendixD = Transversereinforcementindex,see8.2.3.3,Sec8.2
= Spanlengthofbeamoronewayslab;clearprojectionofcantilever,mm,Sec6.2
= Additionalembedmentlengthbeyondcenterlineofsupportorpointofinflection,mm,Sec8.2 = Length of compression member in a frame, measured centertocenter of thejoints in theframe,mm,Sec6.3,6.6 = Development length intensionofdeformedbar,deformedwire,plainanddeformedweldedwirereinforcement, orpretensionedstrand,mm,Sec6.9,8.18.3 = Developmentlengthincompressionofdeformedbarsanddeformedwire,mm,Sec8.2 = Development length in tension of deformed bar or deformed wire with a standard hook,measured fromcriticalsection tooutsideendofhook (straightembedment lengthbetween
criticalsectionand startofhook [pointof tangency]plus insideradiusofbendandonebar
diameter),mm,seeSec.8.2and8.3,Sec8.2,8.3 = Developmentlengthintensionofheadeddeformedbar,measuredfromthecriticalsectiontothebearingfaceofthehead,mm,Sec8.2
= Loadbearinglengthofanchorforshear,mm,seeD.6.2.2,AppendixD
= Lengthofclearspanmeasuredfacetofaceofsupports,mm,Sec6.16.5,6.10,8.2.9.3, Sec8.2,8.3 = Length, measured from joint face along axis of structural member, over which specialtransversereinforcementmustbeprovided,mm,Sec8.3 = Spanofmemberunder load test, takenas theshorterspan for twowayslab systems,mm.Span is the smaller of: (a) distance between centers of supports, and (b) clear distance
betweensupportsplusthicknessofmember.Span foracantilevershallbe takenas twicethedistancefromfaceofsupporttocantileverend,Sec6.11 = Unsupportedlengthofcompressionmember,mm,see6.3.10.1.1,Sec6.3 = Lengthofshearheadarmfromcentroidofconcentratedloadorreaction,mm,Sec6.4 = Lengthofentirewallorlengthofsegmentofwallconsideredindirectionofshearforce,mm,Sec6.4,6.6,8.3
= Lengthofspanindirectionthatmomentsarebeingdetermined,measuredcentertocenterofsupports,mm,Sec6.5 = Lengthofspan indirectionperpendicular to ,measuredcentertocenterofsupports,mm,see6.5.6.2.3and6.5.6.2.4,Sec6.5 = Liveloads,orrelatedinternalmomentsandforces,Sec6.1,6.2,6.11,8.3 = Roofliveload,orrelatedinternalmomentsandforces,Sec6.2 = Maximummoment inmemberdue to service loadsatstagedeflection is computed,Nmm,Sec6.2,6.6 = Factored moment amplified for the effects of member curvature used for design ofcompressionmember,Nmm,see6.3.10.6,Sec6.3 = Crackingmoment,Nmm,see6.2.5.2.3,Sec6.2,6.6
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= Momentcausingflexuralcrackingatsectiondue toexternallyappliedloads,Nmm,Sec6.4 = Factoredmomentmodified toaccount foreffectofaxialcompression,Nmm,see6.4.2.2.2,Sec6.4 = Maximumfactoredmomentatsectionduetoexternallyappliedloads,Nmm,Sec6.4 = Nominalflexuralstrengthatsection,Nmm,Sec6.4,6.6,8.2,8.3
= Nominalflexuralstrengthatsectionwithoutcompressionsteel,see6.3.15.1(b),andmoment
ofresistance developedbycompressionintheoverhangingportionoftheTflange,see6.3.15.2(b) = Additional nominal flexural strength at section due to added compression steel andadditionaltensionsteel,see6.3.15.1(b),andmomentofresistancedevelopedbythewebofaTbeam,see6.3.15.2(b) = Nominal flexural strength of column framing intojoint, calculated for factored axial force,consistentwiththedirectionoflateralforcesconsidered,resultinginlowestflexuralstrength,
Nmm,Sec8.3 = Totalfactoredstaticmoment,Nmm,Sec6.5 = Requiredplasticmomentstrengthofshearheadcrosssection,Nmm,Sec6.4 = Probable flexural strength of members, with or without axial load, determined using thepropertiesofthememberatthejointfacesassumingatensilestressinthelongitudinalbarsof
atleast
1.25andastrengthreductionfactor,
,of1.0,N
mm,Sec8.3
= Factoredmomentduetoloadscausingappreciablesway,Nmm,Sec6.3 = Portionofslabfactoredmomentbalancedbysupportmoment,Nmm,Sec8.3 = Factoredmomentatsection,Nmm,Sec6.36.6,8.3 = Momentatmidheightofwallduetofactoredlateralandeccentricverticalloads,notincludingeffects,Nmm,Sec6.6 = Momentresistancecontributedbyshearheadreinforcement,Nmm,Sec6.4 = Smallerfactoredendmomentonacompressionmember,tobetakenaspositiveifmemberisbentinsinglecurvature,andnegativeifbentindoublecurvature,Nmm,Sec6.3 = Factoredendmomentonacompressionmemberat theendatwhichM1acts,due to loadsthatcausenoappreciablesidesway,calculatedusingafirstorderelasticframeanalysis,Nmm,Sec6.3
, = Minimumvalueof
,N
mm,Sec6.3
=
Factoredend
moment
on
compression
member
atthe
end
atwhich
M2acts,
due
toloads
that
causenoappreciablesidesway,calculatedusingafirstorderelasticframeanalysis,Nmm,Sec6.3 = Factoredendmomentoncompressionmemberattheendatwhichacts,duetoloadsthatcauseappreciablesidesway,calculatedusingafirstorderelasticframeanalysis,Nmm,Sec6.3 = Numberofitems,suchasstrengthtests,bars,wires,monostrandanchoragedevices,anchors,orshearheadarms,Sec6.4,8.2,AppendixD = Basic concrete breakout strength in tension of a single anchor in cracked concrete, N, seeD.5.2.2,AppendixD = Nominalconcretebreakoutstrengthintensionofasingleanchor,N,seeD.5.2.1,AppendixD = Nominalconcretebreakoutstrengthintensionofagroupofanchors,N,seeD.5.2.1,AppendixD
= Nominalstrengthintension,N,AppendixD
= Pulloutstrength intensionofasingleanchorincrackedconcrete,N,seeD.5.3.4andD.5.3.5,AppendixD = Nominalpulloutstrengthintensionofasingleanchor,N,seeD.5.3.1,AppendixD = Nominalstrengthofasingleanchororgroupofanchors intensionasgovernedbythesteelstrength,N,seeD.5.1.1andD.5.1.2,AppendixD = Sidefaceblowoutstrengthofasingleanchor,N,AppendixD = Sidefaceblowoutstrengthofagroupofanchors,N,AppendixD = Factoredaxialforcenormaltocrosssectionoccurringsimultaneouslywith or ;tobetakenaspositiveforcompressionandnegativefortension,N,Sec6.4 = Factoredtensileforceappliedtoanchororgroupofanchors,N,AppendixD = Factoredhorizontaltensileforceappliedattopofbracketorcorbelactingsimultaneously with
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Vu,tobetakenaspositivefortension,N,Sec6.4 = Outsideperimeterofconcretecrosssection,mm,see6.4.4.1,Sec6.4 = Perimeterofcenterlineofoutermostclosedtransversetorsionalreinforcement, mm,Sec6.4 = Nominalaxialstrengthatbalancedstrainconditions,N,see6.3.3.2,Sec6.2,6.3 = Criticalbucklingload,N,see6.3.10.6,Sec6.3 = Nominalaxialstrengthofcrosssection,N,Sec6.2,6.3,6.6, = Maximumallowablevalueof,N,see6.3.3.6,Sec6.3
= Nominalaxialstrengthatzeroeccentricity,N,Sec6.3
= Unfactoredaxial loadatthedesign(midheight)section includingeffectsofselfweight,N,Sec6.6 = Factoredaxialforce;tobetakenaspositiveforcompressionandnegativefortension,N,Sec6.3,6.6,8.3 = Factoreddeadloadperunitarea,Sec6.5 = Factoredliveloadperunitarea,Sec6.5 = Factoredloadperunitarea,Sec6.5 = Stabilityindexforastory,see6.3.10.5.2,Sec6.3 = Radiusofgyrationofcrosssectionofacompressionmember,mm,Sec6.3 = Rainload,orrelatedinternalmomentsandforces,Sec6.2 = Centertocenter spacing of items, such as longitudinal reinforcement, transversereinforcement, prestressingtendons,wires,oranchors,mm,Sec6.3,6.4,6.9,6.11,6.12,8.2,
8.3,AppendixD
= Centertocenter spacing of reinforcement in the ith layer adjacent to the surface of themember,mm,AppendixA = Centertocenterspacingoftransversereinforcementwithinthelength,mm,Sec8.3 = Samplestandarddeviation,mpa,AppendixD = Centertocenterspacingoflongitudinalshearortorsionreinforcement, mm,Sec6.4 = Snowload,orrelatedinternalmomentsandforces,Sec6.2,8.3 = Moment, shear, or axial force at connection corresponding to development of probablestrengthat intended yield locations,based on the governingmechanism of inelastic lateral
deformation, consideringbothgravityandearthquakeloadeffects,Sec8.3 = Nominalflexural,shear,oraxialstrengthofconnection,Sec8.3 = Yieldstrengthofconnection,basedon,formoment,shear,oraxialforce,Sec8.3
= Wallthicknessofhollowsection,mm,Sec6.4
= Cumulative effect of temperature, creep, shrinkage, differential settlement, and shrinkagecompensatingconcrete,Sec6.2 = Nominaltorsionalmomentstrength,Nmm,Sec6.4 = Factoredtorsionalmomentatsection,Nmm,Sec6.4 = Requiredstrengthtoresistfactoredloadsorrelatedinternalmomentsandforces,Sec6.2 = Nominalshearstress,mpa,see6.4.10.6.2,Sec6.4,8.3 = Basicconcretebreakoutstrengthinshearofasingleanchorincrackedconcrete,N,seeD.6.2.2andD.6.2.3,AppendixD = Nominalshearstrengthprovidedbyconcrete,N,Sec6.1,6.4,6.5,8.3 = Nominalconcretebreakoutstrengthinshearofasingleanchor,N,seeD.6.2.1,AppendixD = Nominalconcretebreakoutstrengthinshearofagroupofanchors,N,seeD.6.2.1,AppendixD = Nominalshearstrengthprovidedbyconcretewhendiagonalcrackingresultsfromcombinedshearandmoment,N,Sec6.4
= Nominalconcretepryoutstrengthofasingleanchor,N,seeD.6.3.1,AppendixD = Nominalconcretepryoutstrengthofagroupofanchors,N,seeD.6.3.1,AppendixD = Nominal shear strength provided by concrete when diagonal cracking results from highprincipaltensilestressinweb,N,Sec6.4 = Shearforceatsectionduetounfactoreddeadload,N,Sec6.4 = Designshearforcecorrespondingtothedevelopmentoftheprobablemomentstrengthofthemember,N,Sec8.3 = Factoredshearforceatsectionduetoexternallyappliedloadsoccurringsimultaneously with,N,Sec8.3 = Nominalshearstrength,N,Sec6.1,6.3,6.4,8.3,AppendixD = Nominalhorizontalshearstrength,N,Sec6.12
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= Verticalcomponentofeffectiveprestressforceatsection,N,Sec6.4 = Nominalshearstrengthprovidedbyshearreinforcement,N,Sec6.4 = Nominal strength in shearofa singleanchoror groupofanchorsas governedby the steelstrength,N,seeD.6.1.1andD.6.1.2,AppendixD = Factoredshearforceatsection, N,Sec6.4,6.5,6.12,8.2,8.3
= Factoredshearforceappliedtoasingleanchororgroupofanchors,N,AppendixD
= Factoredshearforceontheslabcriticalsectionfortwowayactionduetogravityloads,N,seeSec.8.3 = Factoredhorizontalshearinastory,N,Sec6.3 = Density(unitweight)ofnormalweightconcreteorequilibriumdensityoflightweightconcrete,kg/m3,Sec6.1,6.2 = Factoredloadperunitlengthofbeamoronewayslab,Sec6.1 = Windload,orrelatedinternalmomentsandforces,Sec6.2 = Shorteroveralldimensionofrectangularpartofcrosssection,mm,Sec6.5 = Longeroveralldimensionofrectangularpartofcrosssection,mm,Sec6.5 = Distancefromcentroidalaxisofgrosssection,neglectingreinforcement, totensionface,mm,Sec6.2,6.4
= Angledefiningtheorientationofreinforcement, Sec6.4,8.3,AppendixA
= Coefficient defining the relative contribution of concrete strength to nominal wall shear
strength,Sec8.3 = Ratio of flexural stiffness of beam section to flexural stiffness of a width of slab boundedlaterallybycenterlinesofadjacentpanels(ifany)oneachsideofthebeam,see6.5.6.1.6,Sec
6.2,6.5 = Averagevalueofforallbeamsonedgesofapanel,Sec6.2 = indirectionofl1,Sec6.5 = indirectionof,Sec6.5 = Anglebetweentheaxisofastrutandthebarsintheithlayerofreinforcementcrossingthatstrut,AppendixA = Constantusedtocompute inslabsandfootings,Sec6.4 = Ratioofflexuralstiffnessofshearheadarmtothatofthesurroundingcompositeslabsection,see6.4.10.4.5,Sec6.4
= Ratiooflongtoshortdimensions:clearspansfortwowayslabs,see6.2.5.3.3;sidesofcolumn,concentratedloadorreactionarea,see6.4.10.2.1;orsidesofafooting,see6.8.4.4.2,Sec6.2,6.4,6.8 = Ratioofareaofreinforcementcutofftototalareaoftensionreinforcement atsection,Sec8.2 = Ratioused toaccount forreductionofstiffnessofcolumnsdue tosustainedaxial loads,see6.3.10.6.2,Sec6.3 = Ratiousedtoaccountforreductionofstiffnessofcolumnsduetosustainedlateralloads,see6.3.10.4.2,Sec6.3 = Factortoaccountfortheeffectoftheanchorageoftiesontheeffectivecompressivestrengthofanodalzone,AppendixA = Factorusedtocompute inprestressedslabs,Sec6.4 = Factor to account for the effect of cracking and confining reinforcement on the effectivecompressivestrengthoftheconcreteinastrut,AppendixA
= Ratiooftorsionalstiffnessofedgebeamsectiontoflexuralstiffnessofawidthofslabequaltospanlengthofbeam,centertocenterofsupports,see6.5.6.4.2,Sec6.5 = Factorrelatingdepthofequivalentrectangularcompressivestressblocktoneutralaxisdepth,see6.3.2.7.3,Sec6.3 = Factor used to determine the unbalanced moment transferred by flexure at slabcolumnconnections,see6.5.5.3.2,Sec6.4,6.5,8.3 = Factorusedtodeterminetheportionofreinforcement located incenterbandoffooting,see6.8.4.4.2,Sec6.8 = Factorusedtodeterminetheunbalancedmomenttransferredbyeccentricityofshearatslabcolumnconnections, see6.4.10.7.1,Sec6.4
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= Moment magnification factor to reflect effects of member curvature between ends ofcompressionmember,Sec6.3 = Momentmagnification factor for framesnotbracedagainstsidesway, to reflect lateraldriftresultingfromlateralandgravityloads,Sec6.3 = Designdisplacement,mm,Sec8.3 = Computed, outofplane deflection at midheight of wall corresponding to crackingmoment,,mm,Sec6.6
= Increaseinstressinprestressingsteelduetofactoredloads,mpa,AppendixA
= Computed, outofplane deflection at midheight of wall corresponding to nominal flexuralstrength,,mm,Sec6.6 = Relative lateral deflection between the top and bottom of a story due to lateral forcescomputedusinga firstorderelastic frameanalysisandstiffnessvalues satisfying6.3.10.5.2,
mm,Sec6.3 = Differencebetweeninitialandfinal(afterloadremoval)deflectionsforloadtestorrepeatloadtest,mm,Sec6.11 = Computed,outofplanedeflectionatmidheightofwallduetoserviceloads,mm,Sec6.6 = Computeddeflectionatmidheightofwallduetofactoredloads,mm,Sec6.6 = Measuredmaximumdeflectionduringfirstloadtest,mm,see6.11.5.2,Sec6.11 = Maximumdeflectionmeasuredduringsecondloadtestrelativetothepositionofthestructureatthebeginningofsecondloadtest,mm,see6.11.5.2,Sec6.11
= Nettensilestraininextremelayeroflongitudinaltensionsteelatnominalstrength,excluding
strainsduetoeffectiveprestress,creep,shrinkage,andtemperature,Sec6.16.3 = Anglebetweenaxisofstrut,compressiondiagonal,orcompressionfieldandthetensionchordofthemember,Sec6.4,AppendixA = Modification factor reflecting the reducedmechanicalpropertiesof lightweightconcrete,allrelative tonormalweight concrete of the same compressive strength, see6.1.8.1,6.4.5.4.3,
8.2.3.4(d),8.2.6.2,8.2.10.2(b),Sec6.2,6.4,6.9,8.2,8.3andAppendixesA,D = Multiplierforadditionaldeflectionduetolongtermeffects,see6.2.5.2.5,Sec6.2 = Coefficientoffriction,see6.4.5.4.3,Sec6.4,8.3 = Timedependentfactorforsustainedload,see6.2.5.2.5,Sec6.2 = Ratioof to,Sec6.4,6.5,8.3
= Ratioof
to
,see6.3.15.1(b), Sec6.2
= Ratioof toproducingbalancedstrainconditions,see6.3.3.2,Sec6.3,6.5,6.6 = Ratioofto,see6.3.15.2(b) = Ratioofareaofdistributedlongitudinal reinforcementtogrossconcreteareaperpendicular tothatreinforcement, Sec6.4,6.6,8.3 = Maximum reinforcement ratio allowed for beams corresponding to 0.004 , see6.3.15.1(a) = Ratio of volume of spiral reinforcement to total volume of core confined by the spiral(measuredouttooutofspirals),Sec6.3,8.3 = Ratio of area distributed transverse reinforcement to gross concrete area perpendicular tothatreinforcement, Sec6.4,6.6,8.3 = Ratiooftiereinforcementareatoareaofcontactsurface,see6.12.5.3.3,Sec6.12 = Ratioof to,see6.3.15.2(b),Sec6.4
= Strengthreductionfactor,see6.2.3,Sec6.16.6,6.9,6.11,6.12,8.3,AppendixesA&D
, = Factorusedtomodifytensilestrengthofanchorsbasedonpresenceorabsenceofcracks inconcrete,seeD.5.2.6,AppendixD, = Factorusedtomodifypulloutstrengthofanchorsbasedonpresenceorabsenceofcracksinconcrete,seeD.5.3.6,AppendixD, = Factorused tomodifyshearstrengthofanchorsbasedonpresenceorabsenceofcracks inconcreteandpresenceorabsenceofsupplementaryreinforcement, seeD.6.2.7foranchorsin
shear,AppendixD, = Factorusedtomodifytensilestrengthofpostinstalledanchors intendedforuse inuncrackedconcretewithoutsupplementaryreinforcement, seeD.5.2.7,AppendixD = Factorusedtomodifydevelopmentlengthbasedonreinforcementcoating,Sec8.2, = Factorusedtomodifytensilestrengthofanchorsbasedoneccentricity ofapplied loads,see
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D.5.2.4,AppendixD, = Factorused tomodifyshearstrengthofanchorsbasedoneccentricityofapplied loads,seeD.6.2.5,AppendixD, = Factorused tomodify tensile strengthofanchorsbasedon proximity toedgesof concretemember,seeD.5.2.5,AppendixD
, = Factor used to modify shear strength of anchors based on proximity to edges of concrete
member,seeD.6.2.6,AppendixD, = Factor used to modify shear strength of anchors located in concrete members with 1.5,seeD.6.2.8,AppendixD = Factorusedtomodifydevelopmentlengthbasedonreinforcementsize,Sec8.2 = Factorusedtomodifydevelopmentlengthbasedonreinforcementlocation,Sec8.2 = Factor used to modify development length for welded deformed wire reinforcement intension,Sec8.2 = Effectivetensionareaofconcretesurroundingtheflexuraltensionreinforcement andhavingthe same centroid as that of the reinforcement, divided by the number of bars. When the
flexural reinforcement consists ofdifferent bar sizes the numberof bars or wires shallbe
computedasthetotalareaofreinforcement dividedbytheareaofthelargestbarused = Areaofskinreinforcementperunitheightinasideface = Factorrelatingshearandtorsionalstressproperties= = Thicknessof concrete cover measured fromextreme tension fibre to centreof bar or wire
locatedclosestthereto = Momentofresistanceofasectionwithoutcompressionsteel = Additionalmomentof resistancedue toadded compressionsteel andadditional tensionsteelas2 = Spacingofshearortorsionreinforcementindirectionparalleltolongitudinal reinforcement = Torsionalmomentstrengthprovidedbyconcrete = Torsionalmomentstrengthprovidedbytorsionreinforcement = Shortercentretocentredimensionofclosedrectangularstirrup = Longercentretocentredimensionofclosedrectangularstirrup
= Quantitylimitingdistributionofflexuralreinforcement,seeEq(6.2.35)
= Coefficientequalto2 3 butnotmorethan1.51 = Factordefinedin6.2.3.7 = Timedependentfactorforsustainedload = Minimumratiooftensionreinforcement
6.1.2 General6.1.2.1 Membersshallbedesignedforadequatestrength inaccordancewiththeprovisions
ofthischapter,usingloadfactorsspecifiedin2.6.5.1andstrengthreductionfactors in6.2.3.1.
6.1.2.2 Design of reinforced concrete members using Working Stress Design method
(AppendixB)isalsopermitted.
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6.1.2.3 Structuresand structuralmembers shallbedesigned tohavedesignstrengthatall
sectionsatleastequaltotherequired strength(U)calculatedforthefactoredloads
and forces insuchcombinations asarestipulated inChapter2,Loads.Thenominal
strengthprovidedforthesectionmultipliedbythestrengthreductionfactorshallbeequaltoorgreaterthanthecalculatedrequiredstrengthU.
6.1.2.4 MembersshallalsomeetalltheotherrequirementsofthisCodetoensureadequate
performanceatserviceloads.
6.1.2.5 Design strength of reinforcement represented by the values of and used indesign calculationsshallnotexceed550MPa,except forprestressingsteeland for
transversereinforcement in6.3.9.3andSec.8.3. or mayexceed420MPa,onlyif theratiooftheactualtensilestrengthtotheactualyieldstrengthisnotlessthan
1.20,andtheelongationpercentageisnotlessthan16.
6.1.2.6 Forstructuralconcrete, shallnotbe less than17MPa.NomaximumvalueofshallapplyunlessrestrictedbyaspecificCodeprovision.
6.1.3 Loading
6.1.3.1 Loadsandtheircombinationsshallbeinaccordancewiththerequirementsspecified
inChapter2,Loads.
6.1.3.2 Structuresshallbedesignedtoresistallapplicableloads.
6.1.3.3 Effects of forces due to prestressing, crane loads, vibration, impact, shrinkage,
temperature changes, creep, expansion of shrinkagecompensating concrete, and
unequalsettlementofsupportsshallbedulyconsidered.
6.1.4 Methodsofanalysis6.1.4.1 Members of frames or continuous construction (beams or oneway slabs) shall be
designedforthemaximumeffectsoffactored loadsasdeterminedbythetheoryof
elastic analysis, except as modified for redistribution of moments in continuous
flexuralmembersaccordingto6.1.5.Designispermittedtobesimplifiedbyusingthe
assumptionsspecifiedin6.1.6&6.1.9through6.1.12.
6.1.4.2 Frame analysis by approximate methods shall be permitted for buildings of usual
typesofconstruction, spans,andstoryheights.
6.1.4.3 Provided (a)through (e)belowaresatisfied, theapproximatemomentsandshears
given here shall be permitted for design of continuous beams and oneway slabs
(slabs reinforced toresist flexuralstresses inonlyonedirection),asanalternate to
frameanalysis:
a) Therearetwoormorespans;
b) Spansareapproximately equal,withthelargeroftwoadjacentspansnotgreaterthan
theshorterbymorethan20percent;
c) Loadsareuniformlydistributed;
d) Unfactoredliveload,,doesnotexceedthreetimesunfactoreddeadload,;ande) Membersareprismatic.
Forcalculatingnegativemoments,istakenastheaverageoftheadjacentclearspanlengths.Positivemoment
Endspans
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Discontinuous endunrestrained 11 Discontinuousendintegralwithsupport 14 Interiorspans
16
Negativemomentsatexteriorfaceoffirstinteriorsupport
Twospans 9 Morethantwospans 10 Negativemomentatotherfacesofinterior
Supports 11
Negativemomentatfaceofallsupportsfor
Slabswithspansnotexceeding3.048m;
andbeamswhereratioofsumofcolumnstiffnessestobeamstiffnessexceeds8ateachendofthespan 12
Negativemomentatinteriorfaceofexteriorsupportformembersbuiltintegrallywith
supportsWheresupportisspandrelbeam 24 Wheresupportisacolumn
16
Shearinendmembersatfaceoffirst
interiorsupport1.152
Shearatfaceofallothersupports 2 6.1.4.4 Strutandtiemodels,providedinAppendixA,shallbepermittedtobeusedinthedesignof
structuralconcrete.
6.1.5 Redistributionofmomentsincontinuousflexuralmembers6.1.5.1 Itshallbepermittedtodecreasefactoredmomentscalculatedbyelastictheoryatsectionsof
maximumnegativeormaximumpositivemomentinanyspanofcontinuousflexuralmembers
foranyassumedloadingarrangementbynotmorethan1000percent,withamaximumof20percent,exceptwhereapproximatevaluesformomentsareused.
6.1.5.2 Redistribution ofmomentsshallbemadeonlywhenisequaltoorgreaterthan0.0075atthesectionatwhichmomentisreduced.
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6.1.5.3 Atallothersectionswithinthespans,thereducedmomentshallbeusedforcalculating
redistributedmoments.Staticequilibriumshallhavetobemaintainedafterredistribution of
momentsforeachloadingarrangement.
6.1.6 Spanlength6.1.6.1 Thespanlengthofasimplysupportedbeamshall betakenasthesmallerofthedistance
betweenthecentresofbearings,orthecleardistancebetweensupportsplustheeffective
depth.
6.1.6.2 Fordetermination ofmomentsinanalysisofframesorcontinuousconstruction, spanlength
shallbetakenasthedistancecentertocenterofsupports.
6.1.6.3 Designonthebasisofmomentsatfacesofsupportshallbepermittedforbeamsbuilt
integrallywithsupports.
6.1.6.4 Itshallbepermittedtoanalyzesolidorribbedslabsbuiltintegrallywithsupports,withclear
spansnotmorethan3m,ascontinuousslabsonknifeedgesupportswithspansequaltothe
clearspansoftheslabandwidthofbeamsotherwiseneglected.
6.1.7 Modulusof
elasticity
6.1.7.1 Modulusofelasticity,,forconcreteshallbepermittedtobetakenas .0.043 (inMPa)forvaluesofbetween1440and2560kg/m3.Fornormalweightconcrete,shallbepermittedtobetakenas4700.
6.1.7.2 Modulusofelasticity,,forreinforcement shallbepermittedtobetakenas200,000MPa.
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6.1.8 Lightweightconcrete6.1.8.1 Toaccountfortheuseoflightweightconcrete,unlessspecificallynotedotherwise,a
modificationfactorappearsasamultiplierofinallapplicableequationsandsectionsofthisCode,where 0.85forsandlightweightconcreteand0.75foralllightweightconcrete.Linearinterpolationbetween0.75and0.85shallbepermitted,onthebasisof
volumetricfractions,whenaportionofthelightweightfineaggregateisreplacedwith
normalweightfineaggregate.Linearinterpolation between0.85and1.0shallbepermitted,
onthebasisofvolumetricfractions,forconcretecontainingnormalweightfineaggregateand
ablendoflightweightandnormalweightcoarseaggregates.Fornormalweightconcrete, 1.0.Ifaveragesplittingtensilestrengthoflightweightconcrete,,isspecified, /0.56 1.0.6.1.9 Stiffness6.1.9.1 Forcomputingrelativeflexuralandtorsionalstiffnessesofcolumns,walls,floors,androof
systems,useofanysetofreasonableassumptionsshallbepermitted.Theassumptions
adoptedshallbeconsistentthroughoutanalysis.
6.1.9.2 Bothindeterminingmomentsandindesignofmembers,effectofhaunchesshallbe
considered.
6.1.10 Effectivestiffnessfordetermininglateraldeflections6.1.10.1 Lateraldeflectionsresultingfromservicelateralloadsforreinforcedconcretebuildingsystems
shallbecomputedbyeitheralinearanalysiswithmemberstiffnessdeterminedusing1.4
timestheflexuralstiffnessdefinedin6.1.10.2and6.1.10.3orbyamoredetailedanalysis.
Memberpropertiesshallnotbetakengreaterthanthegrosssectionproperties.
6.1.10.2 Lateraldeflectionsresultingfromfactoredlateralloadsforreinforcedconcretebuilding
systemsshallbecomputedeitherbylinearanalysiswithmemberstiffnessdefinedby(a)or
(b),orbyamoredetailedanalysisconsideringthereducedstiffnessofallmembersunderthe
loadingconditions:
a) Bysectionpropertiesdefinedin6.3.10.4.1(a)through(c);or
b) 50percentofstiffnessvaluesbasedongrosssectionproperties.
6.1.10.3 Lateraldeflectionsresultingfromfactoredlateralloadsshallbepermittedtobecomputedby
usinglinearanalysis,wheretwowayslabswithoutbeamsaredesignatedaspartofthe
seismicforceresistingsystem.Thestiffnessofslabmembersshallbedefinedbyamodelthat
isinsubstantialagreementwithresultsofcomprehensivetestsandanalysisandthestiffness
ofotherframemembersshallbeasdefinedin6.1.10.2.
6.1.11 ConsiderationsforColumns6.1.11.1 Columnsshallbedesignedtoresisttheaxialforcesfromfactoredloadsonallfloorsorroof
andthemaximummomentfromfactoredloadsonasingleadjacentspanofthefloororroof
underconsideration. Loadingconditionresultingthemaximumratioofmomenttoaxialload
shallalsobeconsidered.
6.1.11.2 Inframesorcontinuousconstruction,considerationshallbegiventotheeffectofunbalanced
floororroofloadsonbothexteriorandinteriorcolumnsandofeccentricloadingduetoother
causes.
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6.1.11.3 Itshallbepermittedtoassumefarendsofcolumnsbuiltintegrallywiththestructuretobe
fixed,whilecomputinggravityloadmomentsincolumns.
6.1.11.4 Resistancetomomentsatanyfloororrooflevelshallbeprovidedbydistributing themoment
betweencolumnsimmediatelyaboveandbelowthegivenfloorinproportiontotherelative
columnstiffnessesandconditionsofrestraint.
6.1.12 Liveloadarrangement
6.1.12.1 Thefollowingshallbepermittedtoassume:
a) Theliveloadisappliedonlytothefloororroofunderconsideration;and
b) Thefarendsofcolumnsbuiltintegrallywiththestructureareconsideredtobefixed.
6.1.12.2 Arrangementofliveloadshallbepermittedtobeassumedtobelimitedtocombinations of:
a) Factoreddeadloadonallspanswithfullfactoredliveloadontwoadjacentspans;and
b) Factoreddeadloadonallspanswithfullfactoredliveloadonalternatespans.
6.1.13 ConstructionofT-beam6.1.13.1 IntheconstructionofTbeam,theflangeandwebshallbebuiltintegrallyorotherwise
effectivelybondedtogether.
6.1.13.2 WidthofslabeffectiveasaTbeamflangeshallnotexceedonequarterofthespanlengthof
thebeam,andtheeffectiveoverhangingflangewidthoneachsideofthewebshallnot
exceed:
a) Eighttimestheslabthickness;and
b) Onehalfthecleardistancetothenextweb.
6.1.13.3 Theeffectiveoverhangingflangewidthforbeamswithaslabononesideonlyshallnot
exceed:
a) Onetwelfththespanlengthofthebeam;
b) Sixtimestheslabthickness;and
c) Onehalfthecleardistancetothenextweb.
6.1.13.4 Isolatedbeams,inwhichtheTshapeisusedtoprovideaflangeforadditionalcompression
area,shallhaveaflangethicknessnotlessthanonehalfthewidthofwebandaneffective
flangewidthnotmorethanfourtimesthewidthofweb.
6.1.13.5 WhenprimaryflexuralreinforcementinaslabthatisconsideredasaTbeamflange
(excludingjoistconstruction)isparalleltothebeam,reinforcementshallbeprovidedinthe
topoftheslabinthedirectionperpendicular tothebeamandinaccordancewiththe
following:
6.1.13.5.1 Transversereinforcementshallbedesignedtocarrythefactoredloadontheoverhanging
slabwidthassumedtoactasacantilever.Forisolatedbeams,thefullwidthofoverhangingflangeshallbeconsidered.ForotherTbeams,onlytheeffectiveoverhangingslabwidthneed
beconsidered.
6.1.13.5.2 Spacing of transverse reinforcement shall be not farther apart than five times the slab
thickness,norfartherapartthan450mm.
6.1.14 Constructionofjoist6.1.14.1 Constructionofjoistconsistsofamonolithiccombinationofregularlyspacedribsandatop
slabarrangedtospaninonedirectionortwoorthogonaldirections.
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6.1.14.2 Widthofribsshallnotbelessthan100mm,andtheribsshallhaveadepthofnotmorethan
31/2timestheminimumwidthofrib.
6.1.14.3 Clearspacingbetweenribsshallnotexceed750mm.
6.1.14.4 Joistconstruction notmeetingthelimitationsof6.1.14.1through6.1.14.3shallbedesignedas
slabsandbeams.
6.1.14.5 Whenpermanentburnedclayorconcretetilefillersofmaterialhavingaunitcompressive
strengthatleastequaltointhejoistsareused:6.1.14.5.1 Forshearandnegativemomentstrengthcomputations, theverticalshellsoffillersincontact
withtheribsshallbepermittedtoinclude.Otherportionsoffillersshallnotbeincludedin
strengthcomputations.
6.1.14.5.2 Slabthicknessoverpermanentfillersshallbenotlessthanonetwelfththecleardistance
betweenribs,norlessthan40mm.
6.1.14.5.3 Reinforcement normaltotheribsshallbeprovidedintheslabinonewayjoists,asrequiredby8.1.11
6.1.14.6 Whenremovableformsorfillersareused,whichdonotcomplywith6.1.14.5,then:
6.1.14.6.1 Slabthicknessshallbenotlessthanonetwelfththecleardistancebetweenribs,norlessthan
50mm.
6.1.14.6.2 Reinforcementnormaltotheribsshallbeprovidedintheslabasrequiredforflexure,
consideringloadconcentrations,ifany,butnotlessthanrequiredby8.1.11
6.1.14.7 Whereconduitsorpipesaspermittedbyrelevantprovisionsofembedmentsinconcreteare
embeddedwithintheslab,slabthicknessshallbeatleast25mmgreaterthanthetotaloverall
depthoftheconduitsorpipesatanypoint.Conduitsorpipesshallnotimpairsignificantlythe
strengthoftheconstruction.
6.1.14.8 Forjoistconstruction, shallbepermittedtobe10percentmorethanthatspecifiedinSec6.4.
6.1.15 Separatefloorfinish6.1.15.1 Unlessplacedmonolithicallywiththefloorslabordesignedinaccordancewithrequirements
ofSec.6.12,floorfinishshallnotbeincludedaspartofastructuralmember.
6.1.15.2 Allconcretefloorfinishesshallbepermittedtobeconsideredaspartofrequiredcoveror
totalthicknessfornonstructuralconsiderations.
6.2 STRENGTHANDSERVICEABILITYREQUIREMENTS
6.2.1 General6.2.1.1 Structuresandstructuralmembersshallbedesignedtohavedesignstrengthsatallsections
atleastequaltotherequiredstrengthscalculatedforthefactoredloadsandforcesinsuch
combinations asarestipulatedinthisCode.
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6.2.1.2 MembersalsoshallmeetallotherrequirementsofthisCodetoensureadequateperformance
atserviceloadlevels.
6.2.2 Requiredstrength6.2.2.1 Requiredstrengthshallbeatleastequaltotheeffectsoffactoredloadsinsuch
combinationsasarestipulatedinChapter2,Loads.
6.2.2.2 Ifresistancetoimpacteffectsistakenintoaccountindesign,sucheffectsshallbeincludedwith.
6.2.2.3 Estimationsofdifferentialsettlement,creep,shrinkage,expansionofshrinkagecompensating
concrete,ortemperaturechangeshallbebasedonarealisticassessmentofsucheffects
occurringinservice.
6.2.3 DesignStrength6.2.3.1 Designstrengthprovidedbyamember,anditsconnectionstoothermembers,intermsof
flexure,axialload,shear,andtorsion,shallbetakenasthenominalstrengthcalculatedin
accordancewiththerequirementsandassumptionsofthischapter,multipliedbyastrength
reductionfactorsasstipulatedin6.2.3.2,6.2.3.3,and6.2.3.4.6.2.3.2 Strengthreductionfactorshallbeasgivenin6.2.3.2.1through6.2.3.2.6:6.2.3.2.1 Tensioncontrolledsectionsasdefinedin6.3.3.4............................................... 0.90
6.2.3.2.2 Compressioncontrolledsections,asdefinedin6.3.3.3:
Memberswithspiralreinforcement conformingto6.3.9.3........................ 0.75
Otherreinforcedmembers.......................................................................... 0.65
Forsectionsinwhichthenettensilestrainintheextremetensionsteelatnominalstrength,,isbetweenthelimitsfor compressioncontrolledandtensioncontrolledsections,shallbepermittedtobelinearlyincreased from that for compressioncontrolled sections to0.90as
increases from the compression
controlledstrainlimitto0.005(AlsoseeFig. 6.2.3.1).While interpolating, it shallbepermittedtoroundtoseconddigitafterdecimal.
Fig.6.2.3.1Variationof withnettensilestrain inextremetensionsteel,and forGrade420reinforcementandforprestressingsteel(seesec.6.2.3.2.2)
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6.2.3.2.3 Itshallbepermittedforcompressioncontrolledsections,asdefinedin6.3.3.3,thefollowing
optional, more conservative alternative values of strength reduction factor, where lesscontrolled construction environment justifies such selection according to engineering
judgmentofthedesigner:
Memberswithspiralreinforcementconformingto6.3.9.3 0.70
Otherreinforcedmembers 0.60
Forsectionsinwhichthenettensilestrainintheextremetensionsteelatnominalstrength,,isbetweenthelimitsforcompressioncontrolledandtensioncontrolledsections,shallbepermittedtobelinearlyincreased from that for compressioncontrolled sections to 0.90 as increases from the compressioncontrolledstrainlimitto0.005(AlsoseeFig. 6.2.3.2).While interpolating, it shallbepermittedtoroundtoseconddigitafterdecimal.
Fig. 6.2.3.2Variation of with net tensile strain in extreme tension steel,
and
for Grade 420
reinforcementand
for
prestressing
steel
with
reduced
values
of
(0.6
and
0.7)
for
compression
controlled sections (see sec.6.2.3.2.3, Optional application in case of less controlled
environmentasperengineeringjudgment)
6.2.3.2.4 Shearandtorsion 0.75
6.2.3.2.5 Bearingonconcrete(exceptforposttensionedanchoragezonesandstrutandtiemodels:
0.65
6.2.3.2.6 Strutandtiemodels(AppendixA),andstruts,ties,nodalzones,andbearingareasinsuch
models:0.75
6.2.3.2.7CalculationofdevelopmentlengthspecifiedinSec8.2doesnotrequirea strengthreduction
factor.
6.2.3.3 ForstructuresrelyingonintermediateprecaststructuralwallsinSeismicDesignCategoryD,
specialmomentframes,orspecialstructuralwallstoresistearthquakeeffects,,shallbemodifiedasgivenin(a)through(c):
a) Foranystructuralmemberthatisdesignedtoresist,ifthenominalshearstrengthofthememberislessthantheshearcorrespondingtothedevelopmentofthenominal
flexuralstrengthofthemember,forshearshallbe0.60.Thenominalflexuralstrengthshallbedeterminedconsideringthemostcriticalfactoredaxialloadsandincluding;
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b) Fordiaphragms,forshearshallnotexceedtheminimumforshearusedfortheverticalcomponentsoftheprimaryseismicforceresistingsystem;
c) Forjointsanddiagonallyreinforcedcouplingbeams,forshearshallbe0.85.6.2.3.4 Strengthreductionfactor shallbe0.60forflexure,compression, shear,andbearingof
structuralplainconcrete.
6.2.4 Designstrengthforreinforcement
The values of and used in design calculations shall not exceed 550 MPa, except for transversereinforcement in6.3.9.3andSec.8.3.6.2.5 Controlofdeflections6.2.5.1 Reinforcedconcretememberssubjectedtoflexureshallbedesignedtohaveadequate
stiffnesstolimitdeflectionsoranydeformationsthatmayadverselyaffectstrengthor
serviceabilityofastructure.
6.2.5.2 Onewayconstruction(nonprestressed)
6.2.5.2.1 MinimumthicknessstipulatedinTable6.2.5.1shallapplyforonewayconstruction not
supportingorattachedtopartitionsorotherconstruction likelytobedamagedbylarge
deflections, unlesscomputationofdeflectionindicatesalesserthicknesscanbeusedwithout
adverseeffects.
6.2.5.2.2 Wheredeflectionsaretobecomputed,deflectionsthatoccur immediatelyonapplicationof
load shall be computed by usual methods or formulas for elastic deflections, considering
effectsofcrackingandreinforcement onmemberstiffness.
TABLE 6.2.5.1 MINIMUM THICKNESS OF NONPRESTRESSED BEAMS OR ONEWAY SLABS UNLESS
DEFLECTIONSARECALCULATED
Minimumthickness,Simplysupported Oneend
continuous
Bothendscontinuous
Cantilever
MemberMembersnotsupportingorattachedtopartitionsorotherconstructionlikelytobe
damagedbylargedeflections
Solidone way
slabs
/20 /24 /28 /10
Beamsorribbedone wayslabs /16 /18.5 /21 /8
Notes:
Values given shall be used directly for members with normalweight concrete and Grade 420
reinforcement.Forotherconditions,thevaluesshallbemodifiedasfollows:
a) For lightweight concrete having equilibrium density, , in the range of1440 to1840kg/m3
, thevaluesshallbemultipliedby1.65 0 .0003 butnot lessthan1.09.b)For otherthan420MPa,thevaluesshallbemultipliedby0.4/700.6.2.5.2.3 Ifnotstiffnessvaluesareobtainedbyamorecomprehensiveanalysis,immediatedeflection
shallbecomputedwiththemodulusofelasticityforconcrete,,asspecifiedin6.1.7.1(normalweightorlightweightconcrete)andwiththeeffectivemomentofinertia,,asfollows,butnotgreaterthan 1 6.2.1
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where
6.2.2and
0.62
6.2.36.2.5.2.4 shallbepermittedtobetakenforcontinuousmembersastheaverageofvaluesobtainedfromEq.(6.2.1)forthecriticalpositiveandnegativemomentsections.Forprismaticmembers,shallbepermittedtobetakenasthevalueobtainedfromEq.(6.2.1)atmidspanforsimpleandcontinuousspans,andatsupportforcantilevers.
6.2.5.2.5 Ifthevaluesarenotobtainedbyamorecomprehensiveanalysis,additionallongterm
deflectionresultingfromcreepandshrinkageofflexuralmembers(normalweightor
lightweightconcrete)shallbedeterminedbymultiplyingtheimmediatedeflectioncausedby
thesustainedloadconsidered,bythefactor 6.2.4 whereshallbethevalueatmidspanforsimpleandcontinuousspans,andatsupportforcantilevers. Itshallbepermittedtoassume,thetimedependentfactorforsustainedloads,tobeequalto:
5yearsormore 2.0
12months 1.4
6months 1.2
3months 1.0
6.2.5.2.6 Thevalueofdeflectioncomputedinaccordancewith6.2.5.2.2through6.2.5.2.5shallnot
exceedlimitsstipulatedinTable6.2.5.2.
6.2.5.3 Twowayconstruction(nonprestressed)
6.2.5.3.1 Theminimumthicknessofslabsorothertwowayconstruction designedinaccordancewith
theprovisionsofSec.6.5andconformingwiththerequirementsof6.5.6.1.2shallbegoverned
bySection6.2.5.3.Thethicknessofslabswithoutinteriorbeamsspanningbetweenthe
supportsonallsidesshallsatisfytherequirementsof6.2.5.3.2or6.2.5.3.4.Thethicknessof
slabswithbeamsspanningbetweenthesupportsonallsidesshallsatisfyrequirementsof
6.2.5.3.3or6.2.5.3.4.
6.2.5.3.2 Ifslabsarewithoutinteriorbeamsspanningbetweenthesupportsandhavearatiooflongto
shortspannotgreaterthan2,theminimumthicknessshallbeinaccordancewiththe
provisionsofTable6.2.5.3andshallnotbelessthanthefollowingvalues:
Slabswithoutdroppanelsasdefinedin6.5.2.5 125mm;
Slabswithdroppanelsasdefinedin6.5.2.5 100mm.
TABLE6.2.5.2MAXIMUMALLOWABLECOMPUTEDDEFLECTIONS
Typeofmember Deflectiontobeconsidered Deflection
Flatroofsnotsupportingorattachedto
nonstructuralelementslikelytobedamaged
bylargedeflections
Immediatedeflectionduetoliveload /180
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Floorsnotsupportingorattachedto
nonstructuralelementslikelytobedamaged
bylargedeflections
Immediatedeflectionduetoliveload /360
Rooforfloorconstructionsupportingor
attachedtononstructuralelementslikelyto
bedamagedbylargedeflections
Thatpartofthetotaldeflection
occurringafterattachmentof
nonstructuralelements(sumofthe
longtermdeflectionduetoallsustainedloadsandtheimmediate
deflectionduetoanyadditionallive
load)
/480
Rooforfloorconstructionsupportingor
attachedtononstructuralelementsnotlikely
tobedamagedbylargedeflections
l/240
*Limitnotintendedtosafeguardagainstponding.Pondingshouldbecheckedbysuitablecalculations
ofdeflection,includingaddeddeflectionsduetopondedwater,andconsideringlongtermeffectsofall
sustainedloads,camber,constructiontolerances,andreliabilityofprovisionsfordrainage.
Longtermdeflectionshallbedeterminedinaccordancewith6.2.5.2.5,butmaybereducedbyamount
ofdeflectioncalculatedtooccurbeforeattachmentofnonstructuralelements.Thisamountshallbe
determinedon
basis
ofaccepted
engineering
data
relating
totime
deflection
characteristics
of
memberssimilartothosebeingconsidered.
Limitmaybeexceededifadequatemeasuresaretakentopreventdamagetosupportedorattached
elements.
Limitshallnotbegreaterthantoleranceprovidedfornonstructuralelements.Limitmaybeexceeded
TABLE6.2.5.3MINIMUM THICKNESSOFSLABSWITHOUTINTERIORBEAMS*
, MPaWithout drop panels With drop panels
Exteriorpanels Interior Exteriorpanels Interior
Without
edgebeams
Withedge
beams
Without
edgebeams
Withedge
beams
280 /33 /36 /36 /36 /40 /40420 /30 /33 /33 /33 /36 /36520 /28 /31 /31 /31 /34 /34
*For twoway construction, is the length of clear span in the long direction,measuredfacetofaceofsupportsinslabswithoutbeamsandfacetofaceofbeamsor
othersupportsinothercases.
For between the values given in the table, minimum thickness shall bedeterminedbylinearinterpolation.
Droppanelsasdefinedin6.5.2.5.
Slabswithbeamsbetweencolumnsalongexterioredges.Thevalueof fortheedgebeamshallnotbelessthan0.8.6.2.5.3.3 Theminimumthickness,forslabswithbeamsspanningbetweenthesupportsonallsides,
shallbeasfollows:
a) Forequaltoorlessthan0.2,theprovisionsof6.2.5.3.2shallapply;b) Forgreaterthan0.2butnotgreaterthan2.0,shallnotbelessthan . . (6.2.5)
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andnotlessthan125mm;
c) For greaterthan2.0,shallnotbelessthan . 6.2.6andnotlessthan90mm;
d) An edge beam with a stiffness ratio not less than 0.80 shall be provided atdiscontinuousedges,ortheminimumthicknessrequiredbyEq.(6.2.5)or(6.2.6)shallbeincreasedbyatleast10percentinthepanelwithadiscontinuousedge.
Termin(b)and(c)islengthofclearspaninlongdirectionmeasuredfacetofaceofbeams.Term in(b)and(c)isratioofclearspansinlongtoshortdirectionofslab.
6.2.5.3.4 WhencomputeddeflectionsdonotexceedthelimitsofTable6.2.5.2,slabthicknesslessthan
the minimum required by6.2.5.3.1, 6.2.5.3.2, and 6.2.5.3.3 shall be permitted.Deflections
shallbecomputedtakingintoaccountsizeandshapeofthepanel,conditionsofsupport,and
natureofrestraintsatthepaneledges.Themodulusofelasticityofconcrete,,shallbeasspecified in6.1.7.1.Theeffectivemomentof inertia, , shallbe thatgivenbyEq. (6.2.1);othervaluesshallbepermittedtobeusediftheyresultincomputeddeflectionsinreasonable
agreement with results of comprehensive tests. Additional longterm deflection shall be
computedinaccordancewith6.2.5.2.5.
6.2.5.4 Compositeconstruction
6.2.5.4.1 Shoredconstruction
Where composite flexural members are supported during construction so that, after removal of
temporarysupports,deadloadisresistedbythefullcompositesection,itshallbepermittedtoconsider
the compositememberequivalent toa monolithically castmember for computationofdeflection. For
nonprestressedmembers,theportionofthemember incompressionshalldeterminewhethervalues in
Table6.2.5.1fornormalweightorlightweightconcreteshallapply.Ifdeflectioniscomputed,accountshall
betakenofcurvaturesresultingfromdifferentialshrinkageofprecastandcastinplacecomponents,and
ofaxialcreepeffectsinaprestressedconcretemember.
6.2.5.4.2 Unshoredconstruction
When the thickness of a nonprestressed precast flexural member meets the requirements of Table
6.2.5.1,deflectionneednotbecomputed.Ifthethicknessofanonprestressedcompositemembermeets
the requirementsofTable6.2.5.1, it isnotrequired tocomputedeflectionoccurringafter themember
becomes composite, but the longterm deflection of the precast member shall be investigated for
magnitudeanddurationofloadpriortobeginningofeffectivecompositeaction.
6.2.5.4.3 The computed deflection in accordance with 6.2.5.4.1 or 6.2.5.4.2 shall not exceed limits
stipulatedinTable6.2.5.2.
6.3 AXIALLOADSANDFLEXURE
6.3.1 ScopeTheprovisionsofSec.6.3shallbeapplicabletothedesignofmemberssubjecttoflexureoraxialloadsor
acombinationthereof.
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6.3.2 Designassumptions6.3.2.1 Theassumptionsgiven in6.3.2.2through6.3.2.7,andsatisfactionofapplicableconditionsof
equilibriumandcompatibilityofstrainsshallformthebasisofstrengthdesignofmembersfor
flexureandaxialloads.
6.3.2.2 Itshallbeassumed thatstrain inreinforcementandconcrete isdirectlyproportional tothe
distancefromtheneutralaxis,exceptthat,fordeepbeamsasdefinedin6.3.7.1,ananalysis
that considers a nonlinear distribution of strain shall be used. Alternatively, it shall be
permittedtouseastrutandtiemodel.See6.3.7,6.4.6,andAppendixA.
6.3.2.3 Itshallbeassumedthatthemaximumusablestrainatextremeconcretecompressionfiberis
equalto0.003.
6.3.2.4 For stress in reinforcementbelow, it shallbe takenas times steel strain.For strainsgreater than that corresponding to , stress in reinforcement shall be consideredindependentofstrainandequalto.
6.3.2.5 Inaxialandflexuralcalculations ofreinforcedconcrete,thetensilestrengthofconcreteshall
beneglected.
6.3.2.6 Therelationshipbetweenconcretecompressivestressdistributionandconcretestrainshall
be assumed to be rectangular, trapezoidal, parabolic, or any other shape that results in
predictionofstrengthinsubstantialagreementwithresultsofcomprehensive tests.
6.3.2.7 Anequivalentrectangularconcretestressdistributiondefinedby6.3.2.7.1through6.3.2.7.3
belowshallsatisfytherequirementsof6.3.2.6.
6.3.2.7.1 Concrete stress of 0.85shall be assumed uniformly distributed over an equivalentcompressionzoneboundedbyedgesofthecrosssectionandastraightlinelocatedparallelto
theneutralaxisatadistance fromthefiberofmaximumcompressivestrain.6.3.2.7.2 Distance from the fiber of maximum strain to the neutral axis, , shall be measured in adirectionperpendicular totheneutralaxis.6.3.2.7.3 Forbetween17and28MPa,shallbetakenas0.85.Forabove28MPa,shallbe
reducedlinearlyatarateof0.05foreach7MPaofstrengthinexcessof28MPa,butshallnotbetaken lessthan0.65.Forbetween28and56MPa,maybecalculatedfromEq.(6.3.1). 0.85 0.007143 28 0.65 0.85 6.3.1
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6.3.3 Generalprinciplesandrequirements6.3.3.1 Stressandstraincompatibilityusingassumptionsin6.3.2shallbethebasisfordesignofcross
sectionssubjecttoflexureoraxialloads,oracombinationthereof.
6.3.3.2 A cross section shall be considered to be in balanced strain conditions when the tension
reinforcement reachesthestraincorrespondingto justasconcreteincompressionreachesitsassumedultimatestrainof0.003.6.3.3.3 Sectionsarecompressioncontrolledifthenettensilestrainintheextremetensionsteel,,is
equal to or less than the compressioncontrolled strain limit when the concrete in
compression reaches its assumed strain limit of 0.003 (Fig.6.3.3.1). The compression
controlled strain limit is the net tensile strain in the reinforcement at balanced strain
conditions. For Grade 420 reinforcement, it shall be permitted to set the compression
controlled strain limit equal to 0.002. For other grades compressioncontrolled strain limit
maybedeterminedbydividingtheyieldstrengthbymodulusofelasticityEandthenrounding
the value obtained to four significantdigits after the decimal. For example, for Grade500
reinforcement,the
compression
controlled
strain
limit
shall
equal
to0.0025.
Fig.6.3.3.1Straindistributionandnettensilestrain
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6.3.3.4 Sections are tensioncontrolled if the net tensile strain in the extreme tension steel, , isequaltoorgreaterthan0.005whentheconcreteincompressionreachesitsassumedstrain
limit of 0.003. Sections with between the compressioncontrolled strain limit and 0.005constitute a transition region between compressioncontrolled and tensioncontrolled
sections.
6.3.3.5 Nettensilestrain intheextremetensionsteelatnominalstrength,
shallnotbe lessthan
0.004fornonprestressedflexuralmembersandnonprestressedmemberswithfactoredaxialcompressiveloadlessthan0.10
6.3.3.5.1 Useofcompressionreinforcement shallbepermitted inconjunctionwithadditionaltension
reinforcementtoincreasethestrengthofflexuralmembers.
6.3.3.6 Forcompressionmembers,designaxialstrengthshallnotbetakengreaterthan,,computedbyEq.(6.3.2)or(6.3.3).
6.3.3.6.1 FornonprestressedmemberswithspiralreinforcementconformingtoSec.8.1orcomposite
membersconformingto6.3.13:
, 0.850.85
(6.3.2)
6.3.3.6.2 Fornonprestressed memberswithtiereinforcementconformingtoSec.8.1:, 0.800.85 (6.3.3)6.3.3.7 Memberssubjecttocompressiveaxialloadshallbedesignedforthemaximummomentthat
canaccompanytheaxialload.Thefactoredaxialforceatgiveneccentricityshallnotexceedthatgiven in6.3.3.6.Themaximumfactoredmomentshallbemagnifiedforslendernesseffectsinaccordancewith6.3.10.
6.3.4 Spacingoflateralsupportsforflexuralmembers6.3.4.1 Distancebetweenlateralsupportsforabeamshallnotexceed50times
,theleastwidthof
compressionflangeorface.
6.3.4.2 Effects of lateral eccentricityof load shallbe taken intoaccount in determining spacing of
lateralsupports.
6.3.5 Minimumreinforcementformembersinflexure6.3.5.1 Atevery sectionofa flexuralmemberwhere tensile reinforcement is requiredbyanalysis,
except as provided in 6.3.5.2, 6.3.5.3, and 6.3.5.4, provided shall not be less than thatgivenby
,.
6.3.4andnotlessthan1.4/.
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6.3.5.2 Forstaticallydeterminatememberswithaflangeintension,,shallnotbelessthanthevaluegivenbyEq.(6.3.4),exceptthatisreplacedbyeither2orthewidthoftheflange,whicheverissmaller.
6.3.5.3 If,ateverysection,providedisatleastonethirdgreaterthanthatrequiredbyanalysis,therequirementsof6.3.5.1and6.3.5.2neednotbeapplied.
6.3.5.4 Forstructuralslabsandfootingsofuniformthickness,,inthedirectionofthespanshallbe the same as that required by 8.1.11. Maximum spacing of this reinforcement shall not
exceedthreetimesthethickness,nor450mm.
6.3.6 Distributionofflexuralreinforcementinone-wayslabsandbeams6.3.6.1 Rules fordistributionof flexural reinforcement to control flexural cracking inbeamsand in
onewayslabs(slabsreinforcedtoresistflexuralstressesinonlyonedirection)areprescribed
inthissection.
6.3.6.2 Distribution offlexuralreinforcementintwowayslabsshallbeasrequiredby6.5.3.
6.3.6.3 As prescribed in 6.3.6.4, flexural tension reinforcement shall be well distributed within
maximumflexuraltensionzonesofamembercrosssection.
6.3.6.4 Thespacingofreinforcementclosesttothetensionface,,shallbelessthanthatgivenby 380 2.5 (6.3.5)but shall not exceed 300280/, where is the least distance from surface ofreinforcement to the tension face. If there isonly onebar orwire nearest to the extreme
tensionface,usedinEq.(6.3.5)isthewidthoftheextremetensionface.Calculated stress in reinforcement closest to the tension face at service load shall becomputedbasedontheunfactoredmoment.Itshallbepermittedtotake
as
2/3.
6.3.6.5 Forstructuressubjecttoveryaggressiveexposureordesignedtobewatertight,provisionsof
6.3.6.4 are not sufficient. For such structures, special investigations and precautions are
required.
6.3.6.6 When flanges of Tbeam construction are in tension, part of the flexural tension
reinforcement shallbedistributedoveraneffective flangewidthasdefined in6.1.13,ora
widthequaltoonetenththespan,whicheverissmaller.Iftheeffectiveflangewidthexceeds
onetenththespan,some longitudinalreinforcement shallbeprovided intheouterportions
oftheflange.
6.3.6.7 Longitudinal skin reinforcement shall be uniformly distributed along both side faces of a
member(Fig.6.3.6.1),whereofabeamorjoistexceeds900mm.Skinreinforcementshallextendforadistance 2 fromthetensionface.Thespacingshallbeasprovidedin6.3.6.4,where isthe leastdistancefromthesurfaceoftheskinreinforcementtothesideface.Itshall be permitted to include such reinforcement in strength computations if a strain
compatibility analysisismadetodeterminestressintheindividualbarsorwires.
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Fig.6.3.6.1Skinreinforcementforbeamsandjoistswithh >900mm.
6.3.7 Deepbeams6.3.7.1 Deepbeamsaremembers loadedonone faceand supportedon theopposite face so that
compressionstrutscandevelopbetweentheloadsandthesupports,andhaveeither:
a) clearspans,,equaltoorlessthanfourtimestheoverallmemberdepth;orb) regions with concentrated loadswithin twice thememberdepth from the face of the
support.
Deepbeamsshallbedesignedeithertakingintoaccountnonlineardistributionofstrain,orby
AppendixA.(Seealso6.4.6.1and8.2.7.6)Lateralbucklingshallbeconsidered.
6.3.7.2 ofdeepbeamsshallbeinaccordancewith6.4.6.6.3.7.3 Minimumareaofflexuraltensionreinforcement,,,shallconformto6.3.5.6.3.7.4 Minimumhorizontalandverticalreinforcementinthesidefacesofdeepbeamsshallsatisfy
eitherA.3.3or6.4.6.4and6.4.6.5.
6.3.8 Designdimensionsforcompressionmembers6.3.8.1 Isolatedcompressionmemberwithmultiplespirals
Outerlimitsoftheeffectivecrosssectionofacompressionmemberwithtwoormoreinterlockingspirals
shallbetakenatadistanceoutsidetheextremelimitsofthespiralsequaltotheminimumconcretecover
requiredby8.1.7.
6.3.8.2 Monolithicallybuiltcompressionmemberwithwall
Outerlimitsoftheeffectivecrosssectionofaspirallyreinforcedortiedreinforcedcompressionmember
builtmonolithicallywithaconcretewallorpiershallbetakennotgreaterthan40mmoutsidethespiral
ortiereinforcement.
6.3.8.3 Equivalentcircularcompressionmemberreplacingothershapes
Inlieuofusingthefullgrossareafordesignofacompressionmemberwithasquare,octagonal,orother
shaped cross section, it shallbepermitted tousea circular sectionwithadiameterequal to the least
lateraldimensionoftheactualshape.Grossareaconsidered,requiredpercentageofreinforcement,and
designstrengthshallbebasedonthatcircularsection.
6.3.8.4 Limitsofsection
Foracompressionmemberwithacrosssectionlargerthanrequiredbyconsiderations ofloading,itshall
bepermittedtobasetheminimumreinforcementandstrengthonareducedeffectiveareanot less
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thanonehalfthetotalarea.Thisprovisionshallnotapplytospecialmomentframesorspecialstructural
wallsdesignedinaccordancewithSec.8.3.
6.3.9 Limitsofreinforcementforcompressionmembers6.3.9.1 Fornoncompositecompressionmembers,theareaoflongitudinalreinforcement,
,shallbe
not less than 0.01
or more than 0.06. To avoid practical difficulties in placing andcompactingofconcreteaswellastodeliverductilitytononcompositecompressionmembers,areaoflongitudinal reinforcement, ,ispreferrednottoexceed0.04 unlessabsolutelyessential.
6.3.9.2 Minimumnumber of longitudinal bars in compressionmembers shallbe4 for bars within
rectangularorcircularties,3forbarswithintriangularties,and6forbarsenclosedbyspirals
conformingto6.3.9.3.
6.3.9.3 Volumetricspiralreinforcementratio,,shallbenotlessthanthevaluegivenby
0.45
1
6.3.6wherethevalueofusedinEq.(6.3.6)shallnotexceed700MPa.Forgreaterthan420MPa,lapsplicesaccordingto8.1.9.3(e)shallnotbeused.6.3.10 Slendernesseffectsincompressionmembers
6.3.10.1 Slendernesseffectsshallbepermittedtobeneglectedinthefollowingcases:
a) forcompressionmembersnotbracedagainstsideswaywhen: 22 6.3.7b) forcompressionmembersbracedagainstsideswaywhen: 34 12 40 6.3.8
where
ispositiveifthecolumnisbentinsinglecurvature,andnegativeifthemember isbentin
doublecurvature.
Compressionmembersmaybeconsideredtobebracedagainstsideswaywhenbracingelementshavea
total stiffness, resisting lateral movement of that story, of at least 12 times the gross stiffness of the
columnswithinthestory.
TheJacksonandMorelandAlignmentCharts(Fig.6.3.10.1),whichallowagraphicaldeterminationofforacolumnofconstantcrosssectioninamultibayframemaybeusedastheprimarydesignaidtoestimate
theeffectivelengthfactor.
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6.3.10.1.1 Theunsupported lengthofa compressionmember, , shallbe takenas the cleardistancebetween floor slabs,beams, orother members capable of providing lateral support in the
direction being considered. Where column capitals or haunches are present, shall bemeasuredtothelowerextremityofthecapitalorhaunchintheplaneconsidered.
6.3.10.1.2 It shall be permitted to take the radius of gyration, , equal to 0.30 times the overalldimensioninthedirectionstabilityisbeingconsideredforrectangularcompressionmembers
and0.25timesthediameterforcircularcompressionmembers.Forothershapes, itshallbepermittedtocomputeforthegrossconcretesection.
Fig.6.3.10.1Effectivelengthfactorsk.
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6.3.10.2 When slenderness effects are not neglected as permitted by 6.3.10.1, the design of
compressionmembers,restrainingbeams,andothersupportingmembersshallbebasedon
thefactoredforcesandmomentsfromasecondorderanalysissatisfying6.3.10.3,6.3.10.4,or
6.3.10.5.Thesemembersshallalsosatisfy6.3.10.2.1and6.3.10.2.2.Thedimensionsofeach
membercrosssectionusedintheanalysisshallbewithin10percentofthedimensionsofthe
membersshown
on
the
design
drawings
orthe
analysis
shall
be
repeated.
6.3.10.2.1 Totalmomentincludingsecondordereffectsincompressionmembers,restrainingbeams,or
otherstructuralmembersshallnotexceed1.4timesthemomentduetofirstordereffects.
6.3.10.2.2 Secondordereffectsshallbeconsideredalongthe lengthofcompressionmembers.Itshall
bepermittedtoaccountfortheseeffectsusingthemomentmagnificationprocedureoutlined
in6.3.10.6.
6.3.10.3 Nonlinearsecondorderanalysis
Secondorderanalysisshallconsidermaterialnonlinearity,membercurvatureandlateraldrift,durationof
loads,shrinkageandcreep,and interactionwiththesupportingfoundation.Theanalysisprocedureshall
have
been
shown
to
result
in
prediction
of
strength
in
substantial
agreement
with
results
of
comprehensivetestsofcolumnsinstaticallyindeterminatereinforcedconcretestructures.
6.3.10.4 Elasticsecondorderanalysis
Elastic secondorder analysis shall consider section properties determined taking into account the
influenceofaxialloads,thepresenceofcrackedregionsalongthelengthofthemember,andtheeffects
ofloadduration.
6.3.10.4.1 Itshallbepermittedtousethefollowingpropertiesforthemembersinthestructure:
a) Modulusofelasticity...................... from6.1.7.1b) Momentsofinertia,Compressionmembers:
Columns 0.70Walls Uncracked 0.70Cracked 0.35
Flexuralmembers:
Beams 0.35Flatplatesandflatslabs 0.25c) Area 1.0Alternatively, the moments of inertia of compression and flexural members, , shall bepermittedtobecomputedasfollows:
Compressionmembers: 0.80 25 1 0.5 0.875 (6.3.9)where and shall be determined from the particular load combination underconsideration, orthecombinationofanddeterminedinthesmallestvalueof.neednotbetakenlessthan0.35.Flexuralmembers: 0.10 25 1.20.2 0.5 (6.3.10)
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Forcontinuous flexuralmembers,shallbepermitted tobetakenas theaverageofvaluesobtainedfromEq.(6.3.10)forthecriticalpositiveandnegativemomentsections.neednotbetakenlessthan0.25.Thecrosssectionaldimensionsandreinforcementratiousedintheaboveformulasshallbewithin10percentofthedimensionsandreinforcement ratioshown
onthedesigndrawingsorthestiffnessevaluationshallberepeated.
6.3.10.4.2 When sustained lateral loads are present, for compression members shall be divided by1
.The term
shallbe takenas the ratioofmaximum factoredsustainedshear
withina story to themaximum factored shear in that storyassociatedwith the same load
combination,butshallnotbetakengreaterthan1.0.
6.3.10.5 Procedureformomentmagnification
Columnsandstoriesinstructuresshallbedesignatedasnonswayorswaycolumnsorstories.Thedesign
ofcolumnsinnonswayframesorstoriesshallbebasedon6.3.10.6.Thedesignofcolumnsinswayframes
orstoriesshallbebasedon6.3.10.7.
6.3.10.5.1 A column in a structure shall be permitted to be assumed as nonsway if the increase in
column end moments due to secondordereffects does not exceed 5 percent of the first
orderendmoments.
6.3.10.5.2 Astorywithinastructureispermittedtobeassumedasnonswayif: 0.05 (6.3.11)whereandarethetotalfactoredverticalloadandthehorizontalstoryshear,respectively,inthestorybeingevaluated,andisthefirstorderrelativelateraldeflectionbetweenthetopandthebottomofthatstorydueto.6.3.10.6 ProcedureformomentmagnificationNonsway
Compressionmembersshallbedesignedforfactoredaxial forceandthefactoredmomentamplifiedfortheeffectsofmembercurvaturewhere (6.3.12)
where
. 1.0 (6.3.13)and
6.3.146.3.10.6.1 shallbetakenas
. (6.3.15)or
.
(6.3.16)
Asanalternative,shallbepermittedtobecomputedusingthevalueoffromEq.(6.3.9)dividedby1 .
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6.3.10.6.2 Thetermshallbetakenastheratioofmaximumfactoredaxialsustainedloadtomaximumfactoredaxialloadassociatedwiththesameloadcombination, butshallnotbe
takengreaterthan1.0.
6.3.10.6.3 Theeffectivelengthfactor,,shallbepermittedtobetakenas1.0.6.3.10.6.4 Formemberswithnotransverseloadbetweensupports,shallbetakenas 0.6 0.4 (6.3.17)where ispositiveifthecolumnisbentinsinglecurvature,andnegativeifthememberisbentindoublecurvature.Formemberswithtransverseloadsbetweensupports,shallbetakenas1.0.6.3.10.6.5 Factoredmoment,,inEq.(6.3.12)shallnotbetakenlessthan, 15 0.03 (6.3.18)abouteachaxisseparately,where0.6andare inmm.Formembers inwhich,exceeds,thevalue of in Eq. (6.3.17) shall either be taken equal to 1.0, or shall be based on the ratio of thecomputedendmoments, .6.3.10.7 Procedure
for
moment
magnification
Sway
Momentsandattheendsofanindividualcompressionmembershallbetakenas (6.3.19) (6.3.20)whereiscomputedaccordingto6.3.10.7.3or6.3.10.7.4.6.3.10.7.1 Flexuralmembersshallbedesignedforthetotalmagnifiedendmomentsofthecompression
membersatthejoint.
6.3.10.7.2 Thevaluesofand given in6.3.10.4shallbeused fordetermining theeffective lengthfactoranditshallnotbelessthan1.0.
6.3.10.7.3 Themomentmagnifiershallbecalculatedas 1 (6.3.21)IfcalculatedbyEq. (6.3.21)exceeds1.5,shallbecalculatedusingsecondorderelasticanalysisor6.3.10.7.4.
6.3.10.7.4 Alternatively,itshallbepermittedtocalculateas . 1 (6.3.22)whereisthesummationforallthefactoredverticalloadsinastoryandisthesummationforallswayresistingcolumnsinastory.iscalculatedusingEq.(6.3.14)with determinedfrom6.3.10.7.2andfrom6.3.10.6.1.
6.3.11 AxiallyloadedmemberssupportingslabsystemAxiallyloadedmemberssupportingaslabsystemincludedwithinthescopeof6.5.1shallbedesignedas
providedinSec.6.3andinaccordancewiththeadditionalrequirementsofSec.6.5.
6.3.12 ColumnloadtransmissionthroughfloorsystemIfofacolumnisgreaterthan1.4timesthatofthefloorsystem,transmissionofloadthroughthefloorsystemshallbeprovidedby6.3.12.1,6.3.12.2,or6.3.12.3.
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6.3.12.1 Concrete of strength specified for the column shall be placed in the floor at the column
location. Top surface of the column concrete shall extend 2 ft into the slab from face of
column.Columnconcreteshallbewell integratedwithfloorconcrete,andshallbeplaced in
accordancewithrelevantprovisionsforconstructionjointsofcolumns,wallsetc.withbeams,
slabsetc.Toavoidaccidentalplacingoflowerstrengthconcreteinthecolumns,thestructural
designershall indicateon thedrawingwherethehighand lowstrengthconcretesare tobe
placed.
6.3.12.2 Strengthofacolumn througha floorsystemshallbebasedon the lowervalueofconcrete
strengthwithverticaldowelsandspiralsasrequired.
6.3.12.3 Forcolumns laterallysupportedonfoursidesbybeamsofapproximatelyequaldepthorby
slabs,itshallbepermittedtobasestrengthofthecolumnonanassumedconcretestrengthin
the columnjointequal to75percentof column concrete strengthplus35percentof floor
concretestrength.Intheapplicationof6.3.12.3,theratioofcolumnconcretestrengthtoslab
concretestrengthshallnotbetakengreaterthan2.5fordesign.
6.3.13 Compositecompressionmembers6.3.13.1 All
members
reinforced
longitudinally
with
structural
steel
shapes,
pipe,
or
tubing
with
or
withoutlongitudinalbarsshallbeincludedincompositecompressionmembers.
6.3.13.2 Acompositememberstrengthshallbecomputedforthesamelimitingconditionsapplicable
toordinaryreinforcedconcretemembers.
6.3.13.3 Anyaxial loadstrengthassigned toconcreteofacompositemembershallbe transferredto
theconcretebymembersorbracketsindirectbearingonthecompositememberconcrete.
6.3.13.4 Allaxialloadstrengthnotassignedtoconcreteofacompositemembershallbedevelopedby
directconnectiontothestructuralsteelshape,pipe,ortube.
6.3.13.5 Forevaluationofslendernesseffects,radiusofgyration,
,ofacompositesectionshallbenot
greaterthanthevaluegivenby
/ (6.3.23)and,asanalternativetoamoreaccuratecalculation,inEq.(6.3.14)shallbetakeneitherasEq.(6.3.15)or
/ (6.3.24)6.3.13.6 Concretecoreencasedbystructuralsteel
6.3.13.6.1 Whenacompositemember isastructuralsteelencasedconcretecore,thethicknessof the
steelencasementshallbenotlessthan foreachfaceofwidthnor forcircularsectionsofdiameter6.3.13.6.2 Whencomputingand,longitudinalbarslocatedwithintheencasedconcretecoreshall
bepermittedtobeused.
6.3.13.7 Spiralreinforcementaroundstructuralsteelcore
A composite member with spirally reinforced concrete around a structural steel core shall conform to
6.3.13.7.1through6.3.13.7.4.
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6.3.13.7.1 Designyieldstrengthofstructuralsteelcoreshallbethespecifiedminimumyieldstrengthfor
thegradeofstructuralsteelusedbutnottoexceed350MPa.
6.3.13.7.2 Spiralreinforcementshallconformto6.3.9.3.
6.3.13.7.3 Longitudinalbarslocatedwithinthespiralshallbenotlessthan0.01normorethan0.06times
netareaofconcretesection.
6.3.13.7.4 Longitudinalbarslocatedwithinthespiralshallbepermittedtobeusedincomputingand.6.3.13.8 Tiereinforcementaroundstructuralsteelcore
Laterally tied concrete around a structural steel core forming a composite member shall conform to
6.3.13.8.1through6.3.13.8.7.
6.3.13.8.1 Designyieldstrengthofstructuralsteelcoreshallbethespecifiedminimumyieldstrengthfor
thegradeofstructuralsteelusedbutnottoexceed350MPa.
6.3.13.8.2 Lateralties
shall
extend
completely
around
the
structural
steel
core.
6.3.13.8.3 Lateral ties shall have a diameter not less than 0.02 times the greatest side dimension of
compositemember,exceptthattiesshallnotbesmallerthan10mmandarenotrequired
tobelargerthan16mm.Weldedwirereinforcementofequivalentareashallbepermitted.
6.3.13.8.4 Vertical spacing of lateral ties shall not exceed 16 longitudinal bar diameters, 48 tie bar
diameters,or0.5timestheleastsidedimensionofthecompositemember.
6.3.13.8.5 Longitudinalbarslocatedwithinthetiesshallbenotlessthan0.01normorethan0.06times
netareaofconcretesection.
6.3.13.8.6 A longitudinal barshallbe locatedateverycornerofarectangularcrosssection,withother
longitudinal bars spaced not farther apart than onehalf the least side dimension of the
compositemember.
6.3.13.8.7 Longitudinalbarslocatedwithinthetiesshallbepermittedtobeusedincomputingand.6.3.14 Bearingstrength6.3.14.1 Design bearing strength of concrete shall not exceed 0.85, except when the
supportingsurfaceiswideronallsidesthantheloadedarea,thenthedesignbearingstrength
of the loadedareashallbepermittedtobemultipliedby butbynotmore than2(Fig.6.3.14.1).
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Fig.6.3.14.1 DeterminationorareaA2insteppedorslopedsupportsusingfrustum(6.3.14.1).
6.3.15 DesignforFlexure6.3.15.1 DesignofRectangularBeams
a) Formula for singly reinforced beams : The following equations which are based on the
simplifiedstressblockof 6.3.2.7,are applicabletosinglyreinforcedrectangular beamsalongwithTbeamswheretheneutralaxislieswithintheflange.
/ (6.3.25)where
. (6.3.26)
Loaded area
Loaded area
A 1
A 1
A 2
45 deg
45 deg
Plan
Load
is measured on this plane
Elevation
2
1
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Byestimatinganinitialvalueofa,Eq(6.3.25)canbeusedtodetermineanapproximate
valueof.ThatvaluecanbesubstitutedinEq(6.3.26)togetabetterestimateofandhenceanew /2 canbedeterminedforsubstitutioninEq(6.3.25).InEq(6.3.25),nominalflexuralstrengthofsection,
maybetakenasfactoredmoment
atsection,dividedbystrengthreduction factor, 0.9asapreliminaryvalue.determined fromEq (6.3.25) shallhave togivea reinforcement ratio, notexceeding,where 0.85 1 0.004 (6.3.27)Above, 0.003 Additionally,determined fromEq (6.3.25) shallhave to satisfy the requirementsofminimumreinforcementformembersinflexureasper6.3.5.
Revisedshallbedeterminedfrom6.2.3.2basedoneither 1 or,whereisthenettensilestraininthereinforcementfurthestfromthecompressionfaceofthe
concrete at the depth. Strain, may be calculated from Eq. (6.3.27) by replacing0.004by andby.b) Design formulae fordoublyreinforcedbeams:Adoublyreinforcedbeamshallbedesigned
onlywhenthere isarestrictionondepthofbeamandmaximumtensilereinforcementallowed
cannotproducetherequiredmoment.Toestablishifdoublyreinforcedbeamisrequiredthefollowingapproachcanbefollowed:
Determine,
0.005 0.85 1
0.005 (6.3.28)
0.005 . (6.3.29)If is less thanrequiredmomentwith 0.9 ,adoubly reinforcedbeam isneededandthentakingvaluesofandfromabove,put and Then,thefollowingvaluesaretobeevaluated,
(6.3.30)
Assumingcompressionsteelyields(needstobecheckedlater), Check forcompressionsteelyielding,where
0.85 (6.3.31)If (i.e.compressionsteelyields),
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find . andfind,andconfirm 0.9 intheaboveequations.Valueof shallbe determined from 6.2.3.2 based on either or , as stated above forrectangularbeams.
If compression steel does not yield, is to be found from concrete section force equilibriumcondition,C=Twhichwillresultinaquadraticequationof.needstobecalculatedfromstraindiagramand revised.
shallbecalculatedfromforfinding.6.3.15.2 DesignofTBeams
a) General:
For effective widths and other parameters for T, L or isolated beams, 6.1.13.2 to
6.1.13.4shallapply.
b) FormulaeforTbeams:ATbeamshallbetreatedasarectangularbeamif
where
isobtainedfrom Eq(6.3.26).InusingEq(6.3.