土木工程专业英语.docx

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土木工程专业英语

土木工程专业英语

4.4ReinforcedConcreteColumn

4.4.1TypesofColumns

Columnsaredefinedasmembersthatcarryloadschieflyincompression.Usuallycolumnscarrybendingmomentaswell,aboutoneorbothaxesofthecross-section,andthebendingactionmayproducetensileforceoverapartofthecross-section.Eveninsuchcases,columnsaregenerallyreferredtoascompressionmembers,becausethecompressionforcesdominatetheirbehavior.Inadditiontothecommontypeofcompressionmembers,i.e.,verticalelementsinstructures,compressionmembersincludearchribs,inclinedrigidframemembers,compressionelementsintrussesorshell.

Columnsmaybeclassifiedbasedonthefollowingdifferentcategories:

（1）Basedonloading,columnsmaybeclassifiedasfollows:

a.Axiallyloadedcolumns,whereloadsareassumedactingatthecentroidofcolumnsection.

b.Eccentricallyloadedcolumns,wheretheloadsareactingatadistanceefromthecentroidofcolumnsection.Thedistanceecouldbealongthexoryaxis,causingmomentseitheraboutthexaxisandyaxis.

c.Biaxiallyloadedcolumns,wheretheloadsareappliedatanypointonthecolumnsection,causingmomentsaboutboththexaxisandyaxissimultaneously.

（2）Basedonlength,columnscanbeclassifiedasfollows:

a.Shortcolumns,wherethecolumn”sfailureisduetothecrushingofconcreteorduetotheyieldingofthesteelbarsunderthefullloadcapacityofthecolumn.

b.Longcolumns（slendercolumns）,wherethebucklingeffectandtheslendernessratiomustbetakeintoconsiderationinthedesign,thusreducingtheloadcapacityofthecolumnrelativetothatofashortcolumn.

（3）Basedonlateralreinforcement,columnscanbeclassifiedasfollows（Figure4.24）:

a.Columnsreinforcedwithlongitudinalbarsandlateralties.

b.Columnsreinforcedwithlongitudinalbarsandcontinuousspirals.

c.Compositecompressionmembersreinforcedlongitudinallywithstructuralsteelshapes,pipe,ortubing,withorwithoutadditionallongitudinalbars,andvarioustypesoflateralreinforcement.

Themainreinforcementincolumnsislongitudinal,paralleltothedirectionoftheload,andconsistsofbarsarrangedinasquare,rectangular,orcircularpattern.

Lateralreinforcement,intheformofindividualrelativelywidelyspacedtiesoracontinuouscloselyspacedspirals,servesseveralfunctions.Forone,suchreinforcemenisneededtoholdthelongitudinalbarsinpositionsintheformswhiletheconcreteisbeingplaced.Forthispurpose,longitudinalandtransversesteelarewiredtogethertoformcages,whicharethenmovedintotheformsandproperlypositionedbeforeplacingtheconcrete.Foranother,transversereinforcementisneededtopreventthehighlystressed,slenderlongitudinalbarsfrombucklingoutwardbyburstingthethinconcretecover.

Figure4.2

4.4.2ShortColumns

1BehaviororAxiallyLoadedShortColumn

Whenanaxialloadisappliedtoareinforcedconcreteshortcolumn,theconcretecanbeconsideredtobehaveelasticallyuptoalowstressofabout（1/3）f”c.Twodifferenttypesoffailureoccurincolumns,dependingonwhethertiesorspiralsareused.AtiedcolumnfailsattheloadNa（Figure4.25）.Atthisload,theconcretefailsbycrushingorshearingoutwardalonginclinedplanes,andthelongitudinalsteelbarsfailbybucklingoutwardbetweenties,asshowninFigure4.26a.Thecolumnfailureoccurssuddenly,muchlikethefailureofaconcretecylinder.

Inaspirallyreinforcedcolumn,whenthesameloadNaisreached,thelongitudinalsteelandtheconcretewithinthecorearepreventedfrommovingoutwardbythespiral.Theconcreteintheoutershell,however,notbeingsoconfined,doesfail;i.e.,theoutershellspallsoffwhenNaisreached,asshowninFigure4.26b.Itisatthisstagethattheconfiningactionofthespiralhasasignificanteffect,andifsizablespiralsteelisprovided,theloadwillultimatelyfailthecolumnbycausingthespiralsteeltoyield.Theaxialstrainwhenthecolumnfailscanbemuchlargerthanthatatwhichtheshellspallsoff.

Figure4.25Load-deformationoftiedandspirallyreinforcedconcretecolumn

Figure4.26Failureoftiedandspirallyreinforcedconcretecolumn

Iftheloadonthecolumnisincreasedtoreachitsultimatestrength,theconcretewillreachthemaximumstrengthandsteelwillreachitsyieldstrength,fy.SeeFigure4.27.theultimatebearingcapacityofashortcolumnreinforcedwithlongitudinalbarsandlateraltiescanbewrittenasfollows

Nu=f`yA`s+fcAc（4.4.1）

Where,

A`s=reinforcementarea

f`y=reinforcementyieldstrength

Ac=concretesectionarea

fc=concreteprismaticcompressivestrength

2.ShortColumnsunderCombinedAxialForceandMoment

WhenamemberissubjectedtocombinedaxialcompressionNandmomentM,suchasinFigure4.28a,itisusuallyconvenienttoreplacetheaxialloadandmomentwithanequalloadNappliedateccentricitye=M/N,asinFigure4.28b.Thetwoloadingsarestaticallyequivalent.Allcolumnsmaythenbeclassifiedintermsoftheequivalenteccentricity.

Figure4.27Stressandforceatultimatestrengthofaxialloadedcolumn

Figure4.28Equivalenteccentricityofcolumnload

（1）Failremodesofcolumns

Underthecombinedactionsofaxialforceandmoment,therearetwotypesoffailuremodesofcolumn（a）balancedfailure,（b）compressionfailure,whentheneutralaxisisoutsidethesection,causingcompressionthroughoutthesection,and（c）tensionfailure,whentheneutralaxisiswithinthesection,developingtensilestrainontheleftoftheneutralaxis.

Balancedfailure

Underthismodeoffailure,yieldingofthetensilesteelonthefarsideofthecolumnoccurssimultaneouslywiththeattainmentoflimitcompressivestrainof0.0033inconcrete.

Compressionfailure

Compressionfailureofthecolumnoccurswhen（a）therelativeeccentricityeo/hoissmall,or（b）althoughtherelativeeccentricityeo/holarge,thetensionreinforcementratioislarge.Columnshavingsmallrelativeeccentricityaregenerallycharacterizedbycompressionovertheentireconcretesection,butcolumnswithlargeeccentricityaresubjectedtotensionovertensionoveratleastapartofthesection.Columnsofthistypefailbycrushingoftheconcreteandcompressiveyieldingofthesteelonthesideneartheload,whilethereinforcementonthesidefarthestfromtheloaddoesnotyield.SeeFigure4.29b.

Figure4.29Failuremodesofcolumns

Tensionfailure

Tensionfailureoccurswhen（a）therelativeeccentricitye0/h0islarge,and（b）thetensionreinforcementratioismoderate.Thelongitudinalsteelonthesidefarthestfromtheloadyieldsfirst.Gradually,withtheincreaseoftensilestrain,thecompressivestrainreaches0.0033atthecompressiveedgeandcompressionreinforcementyields.

（2）Capacityofshortcolumnsundercombinedaxialforceandmoment

Underthecombinedactionsofaxialforceandmoment,astrengthinteractiondiagram（seeFigure4.30）generallydescribesthecapacityenvelopeofacolumn.Thestrengthinteractiondiagramdefinesthefailureloadandfailuremomentforagivencolumnforthefullrangesofeccentricityfromzerotoinfinity.Foranyeccentricity,thereisauniquepairofvalueof（Mu,Nu）thatwillproducetheincipientfailure.ThatpairsofvaluescanbeplottedasapointonagraphrelatingNuandMu.Anyradicallinerepresentsaparticulareccentricityeo=M/N.Loaddemandpoints（M,N）fromallloadcombinationsmustfallinsidethe（M0,N0）capacityenvelope;otherwise,thecolumnisconsideredinadequateandshouldberedesigned.

Figure4.30Strengthinteractiondiagram

Theupperpointofaninteractioncurveisthecaseofpureaxialcompression.Wheretheinteractioncurveintersectswiththemomentaxis,thecolumnisunderpurebending,inwhichcasethecolumnbehaves^likeabeam.Thepointofmaximummomentontheinteractiondiagramcoincideswiththebalancedcondition.Theextremeconcretefiberstrainreachesultimatestrain（0.0033）simultaneouslywithyieldingoftheextremelayerofsteelontheoppositeside（fy/Es=0.002）.

TheinteractiondiagramfurtherrevealsthatastheaxialforceNubecomeslargerthesectioncancarrysmallerMubeforefailinginthecompressionzone.Thereverseisthecaseinthetensionzone,wherethemomentcarryingcapacityMuincreaseswiththeincreaseofaxialloadN„.Inthecompressionfailurezone,thefailureoccursduetooverstrainingofconcrete.Thelargeaxialforceproduceshighcompressivestrainofconcretekeepingsmallermarginavailableforadditionalcompressivestrainduetobending.Ontheotherhand,inthetensionfailurezone,yieldingofsteelinitiatesfailure.Thistensilesteelstressreduceswiththeadditionalcompressivestressduetoadditionalaxialload.Asaresult,furthermomentcanbeapplieduntilthecombinedstressofsteelduetoaxialforceandincreasedmomentreachestheyieldstrength.

Figure4.31showsamemberloadedparalleltoitsaxisbyacompressiveforceNataneccentricitye0measuredfromthecenterline.TheactualgeometricalshapeoftheconcretestressesdistributionisshowninFigure4.31a.Justasforsimplebending,theactualconcretecompressivestressdistributionisreplacedbyanequivalentrectangulardistributionhavingdepth.r.Equilibriumbetweenexternalandinternalaxialforcesrequiresthat

Figure4.31Actualandequivalentrectangularstressdistributionofeccentricallyloadedcolumnatultimatestrength

Inaddition,sumofthemomentsoftheconcretecompressivestress,reinforcementforceandtheexternalforceNaboutthecenterlineoftheresultantforceinthetensionreinforcementmustequaltozero

where.

e