external pressure vessel design

10/14/2015 ExternalPressure

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ExternalPressureFile:PVE3473,LastUpdated:July5,2012,By:LaurenceBrundrett

Externalpressure(vacuum)calculationsstartoffmorecomplexthaninternalpressurecalculationsandoncejacketsorothersourcesofpressureareaddedthedifficultyincreases.Theexternalpressureratingdependsuponmorevariablesandthefailuremechanismismoredifficulttounderstand.Thisarticleisonlyanintroduction,butitalsocoversmanyoftheareasofexternalpressurethatwerepeatedlyhavetoexplain.Commonmistakesmadewithexternalpressurecalculationsarelisted.

Samplevesselcalculationsareincludedthroughoutthisarticlebasedonavessel48"diameterx96"longwithaFlangedandDished(F&D)headatoneendandaSemiElliptical(SE)headattheother.Asthedesignconditionschange,therequiredshellthicknessisupdated.Internalpressuresarecalculatedat30psiforcomparison.Downloadthesamplecalculationsattheendofthisarticle.

1TheBasicsFailureMechanismsThemechanismofexternalpressurefailureisdifferentfrominternalpressurefailure.Differentmethodsarerequiredtodesignvesselstosafelyhandlethisdifferentfailuremechanism.Internalpressurefailurecanbeunderstoodasavesselfailingafterstressesinpartoralargeportionexceedsthematerialsstrength.Incontrast,duringexternalpressurefailurethevesselcannolongersupportitsshapeandsuddenly,irreversiblytakesonanewlowervolumeshape.Thefollowing3picturesshowvesselsofreducedvolumeafterexternalpressurefailure.Theforthpictureshowsaninternalpressurefailureforcontrast.

Astoragetanktestedcrushedafterhydrotestwhenaplasticsheet

blockedthetopventduringdraining

Vacuumfailureofabarometriccondenser(vacuumvessel)afterthe

internalsupportringsfailed



Astoragetanktestedtodestructionwithaninternalvacuum(external

pressure)

Unexpectedinternalpressurefailureduringhydrotest(causedbypressurestressandhelpedbyunacceptablematerialproperties)contrastthiswiththemechanismsshownduring

externalpressurefailure

Externalpressurecanbecreated3ways:1. Fromavacuuminsideavesselandatmosphericpressureoutside2. Fromapressureoutsideavesselgreaterthanatmospheric(typicallyfromsometypes

ofjacketorasurroundingvessel)3. Fromacombinationofthefirsttwovacuuminside+pressuregreaterthan

atmosphericoutside.Twosimpleandunexpectedsourcesofvacuumunloadingavesseloratankthatisnotadequatelyventedorcoolingdownavesselfilledwithsteamthatcondensestowater.Itisgoodpracticetodesignanyvesselexposedtosteamserviceforfullvacuum,thecooldownratecanbeveryfastoverloadingvacuumprotectionequipment.

Externalpressuregeneratedfromaninternalvacuum

Externalpressurefailurecanbeunderstoodasalossofstability.Thevesselnolongerhastheabilitytoholditsshapeandsuddenlycollapsestoashapewithlessinternalvolume.GoodvideoscanbefoundonYouTubeseethelinksatthebottomofthisarticle.

ASMEtypepressurevesselsusecoderulestocalculatethesafeexternalpressureload.Thestabilityofastraightshellunderexternalpressuredependsonfourvariables:

1. diameter(thelargerthediameter,thelessstable)2. length(thelongerthelessstable)3. thickness(thethinnerthelessstable)4. materialpropertiesaloweryieldpointislessstablefromplasticcollapseanda

lowermodulusofelasticityislessstablefromelasticcollapse.Elasticandplasticcollapsewillnotbediscussedfurtherhere.

Largevesselstypicallyhavelowerexternalthaninternalpressureratings.

ThesefourvariablesareusedinCodeequationswhichcanspecifythethicknessofasafestraightshell.Similarmethodsareusedtocalculateheads.Nozzlesarecalculatedusingthefamiliarareareplacementrules.Inadditionwecanuseburst(proof)testingorfiniteelementanalysistocalculatecomponentsnotcoveredbythecoderules.Thecoderulesareonaverageveryconservative,butgreatlysimplifywhatwouldotherwisebeverydifficultcalculationsthishasbeenagoodtradeoff.Thefiniteelementanalysisandbursttestingaredonetoausuallylessconservative3xfactorofsafety(SeeASMEVIII1UG101(p))whereexacttestingoranalysisinformationreplacesgeneralizedcoderules.

2DesigningforExternalPressureTheeasiestwaytodesignforexternalpressureistomaketheshellthickenoughtomakethevesselstablewithanacceptablefactorofsafety(passcodecalculations).Thelengthofthevesselusedinthecalculationsincludessomeoftheheadateachend.ThecalculationsarefoundinASMEVIII1UG28.Theshellcalculationsareforacylinderwithsupportedends(theheadsateachend).Calculationsarealso



givenfortheheadswhicharetreatedasspheres.

Theeffectivelengthofavesselincludessomeofthelengthoftheheads.Theheadiscalculatedasasphere.

(Seethecompanioncalculationsetpart2startingonpage4.)Atypicalvessel48"diameterwithastraightshell96"longneedsashell0.056"thickforaninternalpressureof30psi,butneedstobe0.225"thickfora15psigexternalpressure(fullvacuum)perVIII1UG28.TheF&Dheadontheleftendneedstobe0.082"thickfortheinteriorpressurebut0.142"forthevacuum.ASEheadneedstobe0.046"thickfortheinteriorpressurebut0.127"forthevacuum.TheF&DandSEheadsarebothcalculatedasiftheyarepartofasphere,butthetwoheadsaregivendifferentequivalentradiusesresultingindifferentrequiredthicknesses.

4xfactorofsafetyinexternalpressurebucklinganalysis

4xfactorofsafetythedesignexceedsthecoderequired3xfactorof

safety

FEAresultsshowthattheshellwillcollapseat4.04xthe15psiappliedpressure.Thisisgreaterthanthe3xsafetyfactorexpectedinthecodeandshowsthecoderesultstobeacceptable.

3VacuumRingsInsteadofmakingtheshellthickenoughtohandletheexternalpressure,aneconomicalvesselcanoftenbedesignedbyreinforcingtheshell.WhenthereinforcementisasstrongasrequiredbyUG29,theeffectivelengthoftheshellisreducedandthinnershellscanbeused.Inthiscase,L1andL2arecalculatedseparately.Eachzoneindependentlypassesthecodecalculations.TheUG29reinforcingcalculationensuresthatthereinforcingisstrongenoughthatwhateverhappensononesideofithasnoimpactontheother.



Avesseldividedintozonesusingastiffeningring

(Seecompanioncalculationsstartingonpage9.)Thesamplevesselshellreducesinrequiredthicknessfrom0.225to0.168".Notbadfortheadditionofa0.25x2.5"barrolledthehardway.Moreringscouldbeaddedtolowertherequiredthicknessfurther.Therequiredheadthicknesscouldalsobereducedbyaddingsometypeofreinforcement.VIII1allowsforthis,butprovidesnoguidanceonthedesign.

8.1xfactorofsafetywithathinnershellandavacuumringadded.

Thecoderulesareexcessivelyconservativeinthiscase.

FEAresultsshowthattheshellwillcollapseat8.1xthe15psiappliedpressure.Thisismuchgreaterthanthe3xsafetyfactorexpectedinthecodeandisacceptable.Thevacuumringhassuccessfullyseparatedanyactionononesideoftheringfromaffectingtheotherside.(page13)

4ExternalPressurefromSimpleJacketsSimplejacketsmadefromrollingplateweldedtotheshellatbothendscreatezonesofexternalpressure.Ifthereisnointernalvacuumthenthelengthusedfortheexternalpressurecalculationisthelengthofthejacket.

ExternalpressureLexistsforthelengthofthejacket

(Seecompanioncalculationsstartingpage15.)Ifa24"longjacketat30psiisaddedtotheoutsideofthestraightshell,thentheexternalpressureof30psineedstobecalculatedforaneffectivelengthof24".Theshellneedstobe0.160"thickunderthejacketperUG28,butcouldbe0.063"elsewhereforthe30psi



internalpressure(minimumcodeallowedthickness=0.063").

Thejacketringsarenotfunctioningasvacuumsupportrings(actionononesideoftheringisnotisolatedfrom

theotherside)butthefactorofsafetyisacceptableat4.3x.

Thejacketclosureisnotstiffenoughtofunctionasavacuumringthejacketseffectsextendbeyondthe

effectivelengthofthejacketbutthedesignisacceptable.

Finiteelementanalysisresultsshowthattheeffectoftheexternalpressureisnotconfinedtothelengthofthejacket.ThejacketclosureperApp95isnotasstrongasrequiredbyUG29buttheouterjacketshelladdstothestiffnessoftheshell.TheFEAshowsthefactorofsafetyisadequateat4.3xandexperienceindicatesthatthistypeofdesignissafe.

Strongerendringsonthejacketcanisolatetheactioninsidethejacketareafromtherestoftheshell.ThisgoesaboveandbeyondtheVIII1coderequirementwhichdoesnotrequireUG29onjackets.

ThejacketclosureringisstrongeritnowmeetsUG29requirements.

Theeffectofthepressureisnowconfinedtothespanofthejacket.

Thefactorofsafetyis5.8x(Acceptable).

(Seecompanioncalculationsstartingpage17.)Thejacketclosureisnow1"x1.5"andpassesUG29rulesforavacuumring.Actionofthejackethasbeenisolatedwithinthespanofthejacket.Thefactorofsafetyis5.8x.Thislevelofsafetygoesbeyondwhatthecodeandpracticalexperienceindicatesisnecessary.

Thesimplejacketsinthepicturebelowdonotconnecttwoseparatezonesofexternalpressurearecalculated.Asthezonesgetshorter,therequiredthicknesstopassexternalpressurecalculationsisreduced.SeeFigUG28foradefinitionofLthatshowsthetreatmentofthezonesasseparatelengths.



Acommonmistakeistoassumethattheexternalpressurehastoapplytothefullvessellengthorthattheseparatesectionsneedtobetreatedascommon.SeeUG28.

Twounconnectedjackets(perFigUG28)

5HalfPipeJacketsMultipleunconnectedjacketsleadtothecaseofhalfpipejackets.Thelengthoftheexternalpressurehasbeenreducedenoughthatitoftenhasnoimpactonthedesign(butitstillneedstobecalculated).ThecodecalculationcouldbebasedonthedimensionLandtheregularcodecalculationsappliedforthestraightshell,buttherearenocoderulesavailableforthehalfpipeonthehead.AppendixEEcontainsruleEE2(1)whichprovidesameansofcalculatingtherequiredshellthicknesstohandlethejacketpressure.Thisprovidesthesamerequiredthicknessfortheshellunderthejacketregardlessofthelocalshapeofthevesselitisthesamefortheheadandthestraightshell.

HalfpipejacketsperVIII1AppendixEE

(Seecompanioncalculationsstartingpage22.)IftheshelliscalculatedusingUG28,thenathicknessofonly0.095"isrequired,howevertheseresultscannotbeappliedtothehead.TheappendixEEhalfpipecalculationrequiresawallthicknessof0.188"(thelowestvalueprovidedforonthecharts)fora3"halfpipejacketpressurizedupto243psionshellorhead.

Acommonmistakewithhalfpipejacketsistoassumethatthevesselhastobedesignedforexternalpressurethisisonlytrueifthereisanothersourceforexternalpressureotherthanthepressureinthehalfpipejacket.TheacceptedmethodofcalculatingtherequiredshellthicknessistousetherulesofappendixEE2.EE2isnotmandatorysoothermethodssuchasUG28,bursttestandfiniteelementanalysisarealsoavailabletothedesigner.

Acommonmistakewithhalfpipejacketsistoassumethatthefullheadofavesselunderthejacketneedstobecalculatedforexternalpressure.TheEE2methodisveryusefulbecausenocoderulesexistforaheadthatisonlypartlyexposedtoexternalpressure.

AcommonmistakewithhalfpipejacketsisnottocalculatetherequiredvesselthicknessunderthejackettoEE2(1)orothermethods.

6StayedSurfacesforExternalPressureStayedsurfacesprovidefreedomtothedesignerusingjackets.Nolongerdowecareabouttheshapeoftheobjectunderthejacket,ortheshapeofthejacketitself.Wedonotcarewhethertheshapehaspressureonaninternal(concave)orexternal(convex)shape.Wedonotcareifthefailuremechanismisthecrushingtypeofcollapse(external)ortearing(internal).Whatwecareaboutisthedistancebetweenstayrodsarethestayrodsstrongenough,attachedwellenough,andaretheshellandjacketsurfaces



thickenoughtosupportthespanbetweenstays.

HalfpipejacketsperVIII1AppendixEE

TherulesforstayeddesignarefoundinVIII1UG47andworkthesamewayasthedesignofflatheadsfoundinUG34butnowwelookatthedistancebetweenstaysinsteadofthediameterofthehead.Becausetherulesaredesignedforflatsurfaces(theweakestshapefoundinpressurevessels)theywillworkforanyshapeofvesselorjacket.Thedistinctionbetweenwhatisthevesselandwhatisthejacketisoftennotimportant.

Thecomplexshapeofthislocomotivefireboxcanbecalculatedasifitisasimpleflatplatewithcorrectly

spacedstaysupports

Adimplejacketisaformofstayedsurface

(Seecompanioncalculationsstartingpage25.)Ifourvesselhasajacketsupportedbystaysona6"spacing,thentherequiredheadorcylindricalshellthicknessis0.164".Thestayshavetobe0.4"dia

TherulesforthedimplejacketarefoundinAppendix17.Theinternal(pressurevesselwall)thicknessiscalculatedper175(b)(1)or(2)modifiedflatplatecalculationsthatcanbeusedforanyshapeofvessel.Thejacketportionistestedbybursttestandcanbeusedforanyshapeofvessel.Notethatlaserweldedandinflatedjacketshavespecialrestrictionsregardingthebursttest(lastportionofsection175(a)(2).

Samplelaserweldeddimplejacketpriortoinflation



Thislaserweldeddimplejacketwillbeinflatedonceitisrolledintotheshapeofashellandweldedtotherestofthevessel.Theinflationpressurecanbeashighas800psi.Thisinflationpressureishigherthantherequiredburstpressureandisfarinexcessofanyallowedexternalpressureforthevessel.Thisonlyworksbecausethepressureinsideadimplejacketisnotanexternalpressure.Thedimplejacketisaformofstayedjacketthatcanbeanyshape.

Ifourvesselhasadimplejacketwitha6"spacingthentherequiredheadorcylindricalshellthicknessis0.140inch.(Equation175(2),notincludedinthecalculationset.)

Acommonmistakewithdimplejacketsistoassumethatthevesselhastobedesignedforexternalpressurethisisonlytrueifthereisanothersourceforexternalpressureotherthanthepressureinthejacket.Theacceptedmethodtocalculatetherequiredshellthicknessistousetherulesof175.

Acommonmistakewithdimplejacketsistonotcalculatetherequiredthicknessoftheheadorshellbutassumingthatitwillbeadequatebecauseitisthickerthanthedimplejacket.Ashellofinadequatethicknesscanleadtoyieldingunderhydrotestshowingthelocationofthedimpleweldsfrominsidethevessel(theinsidesurfaceisnolongersmooth).Thedimplejackethassomestrengthfromitsshapethattheshelldoesnothave.

7MorethanOneSourceofExternalPressureExternalpressurecalculationsaremoredifficultwithmorethanonesourceofexternalpressureatypicalexampleisavesselwithaninternalvacuumandpressureinajacket.Thecaseswiththestayrods,halfpipejacketsanddimplejacketsarethesimplestfirstcalculatethecompletevesselforthevacuumconditionasifthejacketdoesnotexist(seethefirstcasesabove).Nextcalculatetheshellforthelocalloadsunderthedimple/pipe/stayusingthecombinedP+Vacuum.FinallydesignthejacketforthepressureP.

Vacuum+externalpressureonhalfpipe,dimpleandstayedsurfaces

Step1:theexternalpressureisnow15+30=45psi(vacuum+30psijacketpressure).Therequiredthicknessunderthedimplejacketrisesto0.172"(FormulaApp175(2)).Theminimumstayedthicknessisnow0.200"(Page29).Thethicknessunderthehalfpipejacketremainsat0.188",theminimumthicknessprovidedforintheappendixEEcharts(Page30).

Step2:thewholevesselhastobecalculatedunderthe15psiexternalpressure.Thiswascalculatedbackatpages5,6and7inthecalculationset:TheF&Dhead0.142"thick,theSEhead0.127"thick,thestraightshell0.225"thick.

Step3:themaximumthicknessfromstep1and2aboveisused.Thestraightshellislimitedbythe15psiexternalpressureitneedstobe0.225"thick.TheF&DandSEheadsarelimitedbythehalfpipejacketsfoundonthemandneedtobe0.188"thick.

AcommonmistakeistoattempttocalculatetheentirevesselforanexternalpressureofP+V.



Vacuum+externalpressureonhalfpipe,dimpleandstayedsurfacesVesselstraightshellissupportedbyaUG29stylevacuumring

Therequiredthicknessofthestraightshellfromthevacuumonlyloadcanbereducedbyaddingthevacuumstiffeneraspreviouslycalculated.Morestiffenerscanbeaddeduntiltheshellsrequiredthicknessfromvacuumpressureisequaltothatrequiredbythedimple/pipe/staycalculations.

Thestraightshellexternalpressurecalculationwithvacuumringwascalculatedonpage10.Therequiredthickness=0.169"lessthanrequiredunderthedimples,staysorhalfpipejackets.Thoserequiredthicknessesnowgovernandtheshellthicknesscannotbefurtherreducedbyaddingmorevacuumrings.

Halfpipejacket Thehalfpipejacketincreasesthestiffnessoftheshell

Therequiredshellthicknesshasbeencalculatedfortwocases:1)fortheP+Vcaseunderthestays/dimples/halfpipesand2)thewholevesselundertheexternalpressurefromthevacuumonly.However,thevesselisnotthesameastheoriginalvessel.Theexternaljacketsandstaysincreasethestiffnessofthevesselitsstrengthagainstexternalpressurecollapsehasincreasedbutcoderulesarenotprovidedtodeterminehowmuchstrongeritnowis.RefertointerpretationVIII8147July1,1981fileBC80326:

Question:Whensingleembossed,jacketedassemblies,suchasdescribedinAppendix14,areusedasshellssubjectedtoexternalpressureloadingontheembossedside,maypropertiesoftheembossedassemblybeconsideredwhendeterminingtherequiredthicknessoftheflatplatefortheexternalpressure?Reply:Yes.ThegeometrycoveredbyyourinquiryisnotspecificallycoveredbyanyoftherulesofDivision1.However,therulesofU2(g)shallapply.

Externalpressurebursttestingorfiniteelementanalysiscouldbeusedtodetermineathinnersafevesselthicknessthanpossibleusingstandardcodecalculations.ThebursttestorFEAwouldincludethestiffeningeffectofthejacket.

8Cones,LinesofSupportandJunctions



Inadditiontojacketsandvacuumrings,conicaltransitionscanalsoreducetheeffectivelengthofavessel.Aconicalsectionmustbecalculatedwitheachendofthesectionasalineofsupportinorderfortheeffectivelengthtobereduced.Alineofsupportisdescribeas:

1. 1/3thedepthofaformedhead,excludingconicalheads(FigUG28.1)2. avacuumringmeetingUG293. ajacketclosuremeetingAppendix954. aconetocylinderjunctionorheadjunctionthatmeetstherequirementsofAppendix

18Thegoalofalineofsupportistoeffectivelysegmentthevesselintosectionsthatcanbearthepressureloadindependentofadjacentcomponents.Whathappensononesideofthelineofsupportdoesnotaffecttheotherside.ThiscanbeseenintheUG29vacuumringexamplebackatthebeginningofthisarticle.OneconeactsastwolinesofsupportifeachconeshelljunctionpassestheareareplacementorspecialanalysisrulesofApp18.Theareareplacementrulesworkforconeswithanangleupto30degrees.Specialanalysisisrequiredover30degrees.

Effectivelengthisnotchangedbytheadditionofaconicalsection

IfaconeisnotcheckedagainstAppendix18theeffectivelengthwillcontinuestraightthroughtheconicalsection.Eachadjacentcylinderwillbecalculatedusingthefulleffectivelength,Le(seeillustration).

Morecommonly,eachendoftheconeiscalculatedasalineofsupport.App18providestherulesforareareplacement.Specialanalysisisrequiredforconeangles>30degrees.Theconeandshellthicknessbothaffectifthejuncturepasses.Alternately,stiffeningringslikevacuumringscanincreasethestiffnessofthejunctiontomeetcoderules.

Effectivelengthissegmentedattheconejunctions

(Seepage31ofthecompanioncalcs.)Thelefthead,andstraightshellsectionsarecalculatedthesamewayasbefore.Theconeiscalculatedtopassexternalpressureonitsown(page34),andagainasajuncturewiththeshells(page36).Becausetheangleoftheconeis45degrees,aspecialanalysisbasedonBoardman'smethodsaspresentedbyBednarin"PressureVesselDesignHandbook"isused.ThismeetstherequirementsofASME18andtheconeprovidestwolinesofsupport.FEAanalysisverifiesthatthemethodisacceptable(seepage40).

9UnderstandingStabilityAtthebeginningofthisarticle,thefailuremechanismforexternalpressurewasgiven,butnotanexplanationofhowthefailuremechanismworks.Astablesystemisonethatisstrongerthanrequired.Whenthevesselispushedon,itpushesbackandreturnstoitsoriginalshape.Asexternalpressureis



addedtothesystem,thevesselhaslessreservestrengthlefttopushback.Eventuallythevesselreachesapointwhereithasverylittlereservestrength.Youpushonthewallofthevesselanditcannotpushback.Atthispointthevesselcanchangeshapetoasmallervolumeconfiguration.ThechangeissuddenandirreversibleandifyouwatchtheYouTubevideos,veryscary.

Alternately,onecanvisualizealongpolemountedintheground.Whenthepoleispushedonfromtheside,itbends.Oncetheloadisremoved,itbendsback.Asmallweightcanbeplacedontopofthepole.Thepolestayscentereduntilitispushed,andreturnsbacktocenteroncethesidewaysforceisremoved.However,astheweightonthetopofthepoleisincreased,thepolelosesitsabilitytopushbackagainstthesidewaysforce.Atacriticalweight,thepolehasnoadditionalstrength,andaflylandingontopcausesittotopplewithoutanysidewaysforce.Thefailureisirreversibleandsudden.Theweightontopofthepoleissimilartotheexternalpressureontheoutsideofapressurevessel.

Becausetheexactcalculationofthecriticalexternalpressureonavesselisdifficult,weseta3xfactorofsafety,higherthanmanyothersafetyfactorsinpressurevessels.Thecodeaimsfora3xfactorofsafety,sometimescalculatinghigh,sometimeslow.Lessconservativeapproacheswouldrequiremoreexactcalculations,suchasprovidedbyFEA,butatthecostofextraengineeringeffort.

YouTubevideos:

CollapseofacylinderAcylinderimplodingunderinternalvacuum,equivalent

toexternalpressure.

BucklingofasubmarineThisverybriefvideoshowstheFEA

animatedcollapseofasubmarinehull

CollapseofarailtankThisiconicvideoshowsvacuumcollapseofarailway

transporttanker.

55gallondrumHowtocollapseastoragedrumwiththehelpof

condensingsteam.

CollapsingCokeCanCondensingsteamagainusedtocreateavacuum.

CollapsedWagonAlookatavacuumcollapsedhoneywagon.

OtherWebsites:

ShellBucklingAnextensivephotographiclibraryofshellbucklingfailuresandmechanismsalongwithexplanationsofthefailuremechanism.

RiceUniversityJ.EdAkinatRiceUniversity,Houston,TexashaswrittenaveryreadablebookonusingSolidWorkstodoFiniteElementAnalysis(FEA).Chapter12coversbucklinganalysiswithoutgettinglostinmath.Theapproachusedwouldbeofinteresteventopeoplenot

doingFEA.ThislinkdownloadsapdfversionofthebookfromRiceUniversity,itisalsoavailableatAmazon.

CompanionCalculationSet(pdfformat):CalculationSet

2015PressureVesselEngineeringLtd.

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