外文翻译钢结构青岛理工大学.docx

外文翻译钢结构青岛理工大学.docx

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外文翻译钢结构青岛理工大学

4-6InadequateLateralSupport

Asthedistancebetweenpointsoflateralsupportonthecompressionflange（l）becomeslarger,thereisatendencyforthecompressionflangetobucklelaterally.Thereisnoupperlimitforl.Toguardagainstthebucklingtendencyaslbecomeslarger,however,theASDSprovidesthatbereduced.This,ineffect,reservessomeofthebeamstrengthtoresistthelateralbuckling.Figure4-10bshowsabeamthathasdeflectedverticallywithacompressionflangethathasbuckledlaterally.Theresultisatwistingofthemember.Thisiscalledlateral-torsionalbuckling.Forsimplicitywerefertothisbucklingmodeofthebeamaslateralbuckling.Twogeneralresistancesareavailabletocounteractlateralbuckling:

torsionalresistanceofthecrosssectionandlateralbendingresistanceofthecompressionflange.Thetotalresistancetolateralbucklingisthesumofthetwo.TheASDSconservativelyconsidersonlythelargerofthetwointhedeterminationofareduced

.

TheASDS,SectionF1.3,establishesempiricalexpressionsfor

fortheinadequatelateralsupportsituation.Tensionandcompressionallowablebendingstressesaretreatedseparately.Thetension

isalways0.60

.Onlythecompression

isreduced.Fortypicalrolledshapes,thisisofnoconsequencebecausetheshapesaresymmetricalandthelower

ofthetwovalueswillcontrol.Notethattheprovisionsofthissectionpertaintomembershavinganaxisofsymmetryin,andloadedin,theplaneoftheirweb.Theyalsoapplytocompressiononextremefibersofchannelsbentabouttheirmayjoraxis.

TheASDSprovidesthreeempiricalequationsforthereducedcompression

.Themathematicalexpressionsthatgiveanexactpredictionofthebucklingstrengthofbeamsaretoocomplexforgeneraluse.Therefore,theASDSequationsonlyapproximatethisstrengthforpurposesofdeterminingareasonable

.The

thatisfinallyusedisthelargerofthevaluesdeterminedfromtheapplicableequations.Thefirsttwo,ASDSEquations（F1-6）and（F1-7）,givethe

valuewhenthelateralbendingresistanceofthecompressionflangeprovidesthelateralbucklingresistance.Thethird,ASDSEquation（F1-8）,gives

whenthetorsionalresiastanceofthebeamsectionprovidestheprimaryresistancetolateralbuckling.Innocaseshould

begreaterthan0.6

forbeamsthathaveinadequatelateralsupport.Theequationsthatwillbeapplicablewilldependonthevalueoftheratiol/

where

l=distancebetweenpointsoflateralsupportforthecompressionflange（in.）

=radiusofgyrationofasectioncomprisingthecompressionflangeplusone-thirdofthecompressionwebareatakenaboutanaxisinthepaneoftheweb（in.）,asshowninFigure4-11

Here

isatabulatedquantityforrolledshapes（seetheASDM,Part1）,and

maybeconsideredaslendernessratioofthecompressionportionofthebeamwithrespecttothey-yaxis.Theequationsforareasfollows:

Where

=aliberalizingmodifyingfactorwhosevalueisbetween1.0and2.3thataccountsforamomentgradientoverthespanandadecreaseinthelateralbucklingtendency;

maybeconservativelytakenas1.0;seeASDS,SectionF1.3,fordetails

d=depthofcrosssection（in.）

=areaofcompressionflange（

）

Figure4-12depictsthedecision-makingprocessforthecalculationof

.NotethatonewilluseASDSEquations（F1-6）and（F1-8）orASDSEquations（F1-7）and（F1-8）.Thelargerresulting

isused.NotethatTable5oftheNumericalValuessectionoftheASDSprovidesthefollowingnumericalequivalentsforA36steel（

=36ksi）:

4-7DesignofBeamsforMoment

Thebasisformomentdesignistoprovideabeamthathasamomentcapacity（

）equaltoorgreaterthantheanticipatedmaximumappliedmomentM.TheflexureformulaisusedtodeterminearequiredsectionmodulusS:

Thesectionmodulusonwhichtheselectionwillbebasedisassumedtobethestrong-axissectionmodulus

.TheAllowableStressDesignSelectionTable（

Table）intheASDM,Part2,canbeusedtomakethisselection.Itlistscommonbeamshapesinorderofdecreasingsectionmodulus.Thistablealsoliststheresistingmoment

ofeachsection.Thevalueof

iscalculatedusinganallowablebendingstress

of23.8ksi（or23.76ksi）ratherthantheroundedvalueof24.0ksi.Thismaycausesomesmallinconsistenciesincalculationsandresults.

4-8:

BeamDesignforMoment

Basedontheforegoingexamples,ageneralproceduremaybeestablishedforthedesignofbeamsformoment.

1.Establishtheconditionofload,span,andlateralsupport.Thisisbestdonewithasketch.Establishthesteeltype.

2.Determinethedesignmoment.Ifnecessary,completeshearandmomentdiagramsshouldbedrawn.Anestimatedbeamweightmaybeincludedintheappliedload.

3.Thebeamcurvesshouldbeusedtoselectanappropriatesectionwhenpossible.Asanalternative,

mustbeestimatedandtherequiredsectionmodulusdetermined.

4.Afterthesectionhasbeenselected,recomputethedesignmoment,includingtheeffectoftheweightofthesection.Checktoensurethatthesectionselectedisstilladequate.

5.Checkanyassumptionthatmayhavebeenmadeconcerning

or

.

6.Besurethatthesolutiontothedesignproblemisplainlystated.

4-9:

ShearinBeams

Exceptunderveryspecialloadingconditions,allbeamsaresubjectedtoshearaswellasmoment.Inthenormalprocessofdesign,beamsareselectedonthebasicofthemomenttoberesistedandthencheckedforshear.Shearrarelycontrolsadesignunlessloadsareveryheavy（and,possibly,closetothesupports）and/orspansareveryshort.Fromstrengthofmaterial,theshearstressthatexistswithinabeammaybedeterminedfromthegeneralshearformula

Where

shearstressonahorizontalplanelocatedwithreferencetotheneutralaxis（ksi）

V=verticalshearforceatthatparticularsection（kips）

Q=staticalmomentofareabetweentheplaneunderconsiderationandtheoutsideofthesection,abouttheneutralaxis（

）

I=momentofinertiaofthesectionabouttheneutralaxis（

）

b=thicknessofthesectionattheplanebeingconsidered（in.）

Thisformulafurnishesuswiththehorizontalshearstressatapoint,which,asshowninanystrengthofmaterialtext,isequalinintensitytotheverticalshearstressatthesamepointinabeam.

Deflection

Whenabeamissubjectedtoaloadthatcreatesbending,thebeammustsagordeflect,asshowninFigure4-22.Althoughabeamissafeformomentandshear,itmaybeunsatisfactorybecauseitistooflexible.Therefore,theconsiderationofthedeflectionofbeamsisanotherpartofthebeamdesignprocess.

Excessivedeflectionsaretobeavoidedformanyreasons.Amongthesearetheeffectsonattachednonstructuralelementssuchaswindowsandpartitions,undesirablevibrations,andtheproperfunctioningofroofdrainagesystems.Naturally,avisiblysaggingbeamtendstolessonone’sconfidenceinboththestrengthofthestructureandtheskillofthedesigner.

Tocounteractthesaginabeam,anupwardbendorcambermaybegiventothebeam.Thisiscommonlydoneforlongerbeamstocanceloutthedeadloaddeflectionand,sometimes,partoftheliveloaddeflection.Oneproductionmethodinvolvescoldbendingofthebeambyapplyingapointloadwithahydraulicpressortam.Forshorterbeam,whicharenotintentionallycambered,thefabricatorwillprocessthebeamsothatanynaturalsweepwithinacceptedtoleranceswillbeplacedsoastocounteractexpecteddeflection.

Normally,deflectioncriteriaarebasedonsomemaximumlimittowhichthedeflectionofthebeammustbeheld.Thisisgenerallyintermsofsomefractionofthespanlength.Forthedesignerthisinvolvesacalculationoftheexpecteddeflectionforthebeaminquestion,adeterminationoftheappropriatelimitofdeflection,andacomparisonofthetwo.

Thecalculationofdeflectionsisbasedonprinciplestreatedinmoststrength-of-materialstexts.Variousmethodsareavailable.Forcommonbeamsandloadings,theASDM,part2,BeamDiagramsandFormulas,containsdeflectionformulas,Theuseofsomeofthesewillbeillustratedinsubsequentexamples.

Thedeflectionlimitationsofspecificationsandcodesareusuallyintheformofsuggestedguidelinesbecausethestrengthadequacyofthebeamisnotatstake.Traditionally,beamsthathavesupportedplasteredceilingshavebeenlimitedtomaximumliveloaddeflectionsofspan/360.ThisisarequirementoftheASDS,SectionL3.1.Thespan/360deflectionlimitisoftenusedforliveloaddeflectionsinothersituation.Itiscommonpractice,andinaccordancewithsomecodes,tolimitmaximumtotaldeflection（duetoliveloadanddeadload）tospan/240forroofsandfloorsthatsupportotherthanplasteredceilings.

TheASDSCommentary,SectionL3.1,containguidelineofanothernature.Itsuggests:

1.Thedepthoffullystressedbeamsandgirdersinfloorsshould,ifpracticable,benotlessthan

timesthespan.

2.Thedepthoffullystressedroofpurlinsshould,ifpracticable,benotlessthan

timesthespan,exceptinthecaseofflatroofs.

Further,itrecommendsthatwherehumancomfortisthecriterionforlimitingmotion,asinthecaseofvibrations,thedepthofasteelbeamsupportinglarge,openfloorareasfreeofpartitionsorothersourcesofdampingshouldbenotlessthan1/20ofthespan.

Sincethemomentofinertiaincreaseswiththesquareofthedepth,theguidelinesforminimumbeamdepthlimitdeflectionsinageneralway.TheASDSCommentary,SectionK2,alsocontainsamethodforcheckingtheflexibilityofroofsystemswhenponding,theretentionofwateronflatroofs,isaconsideration.

HolesinBeams

Beamsarenormallyfoundaselementsofatotalstructuralsystemratherthanasindividual,isolatedentities.Theyare