管道应力工程师应知问题大集锦

AUDITFORCHINESESTRESSENGINEER

A)UNDERSTANDINGCAESARII

1.WhatkindofcalculationandevaluationisnotcoveredbyC2inpipingsystem?

蠕变分析，管道或设备的局部应力分析，管道失稳等

HowtocheckifpipingsystemexposetobucklingproblembyusingC2?

负压、偶然荷载、集中荷载、埋地管的土壤约束等荷载都会引起管道的失稳；

但CAESARII并不能评定管道的失稳(需要借助压力容器设计软件进行管道的失稳设

计)；

CAESARIIaddressesnegativepressuresasfollows:theabsolutevalueofthelongitudinal

pressurestress(PD/4t)termisaddedtotheappropriatecodeequations;pressurethrustforces

appliedtoexpansionjointendswillbecompressive;andbucklingisnotaddressedin

CAESARII

临界失稳压力：匕=（土24E二/Ax—1

U"D：

E—弹性模量（MPa）；

I—截面惯性矩（mm4/mm）；

v—泊松比，0.35—0.45；

Dm—管道平均直径；

C—椭圆修正系数，（4/「丫，rl—椭圆管道的弯曲半径，圆形管道半径;

05

允许的管壁冲击荷载：N=（1/FS）D0\32RWBE（EI/£>,/）］

2.Global/localloadsinC2output,Thereasonwhyweneedthelocalelementsloads?

为了获得作用在设备管口上准确的外载，以进行局部应力分析；另外通过局部坐标推力

的分析，可以仔细察看管道单元内部的相互作用关系，协助发现问题，并尽快找到答案。

3.Oninputsheet,whatisdifferentforForce,Uniformload,Rigidelementwithweight,-the

temperaturebaseofElasticmodulusinput?

集中力（力或弯矩作用于管道上一点，一般模拟外载力的作用效果，对于一些额外重

量，如支架根部，最好不用力来输入，因为如果计算地震，这些质量都不存在。）、均

布载荷（荷载均布于管道所有点上，我们一般用它来模拟雪载）、带重量的刚性件（横

向刚度无穷大横向没有弯曲，刚性件只传导位移和力，我们一般用它来模拟阀门，管

道设备等，但要注意，刚性件有直径何壁厚，他们对他的横向变形会有影响软件

缺省的弹性模量是冷态的。但用户可以选择。

4.Whatisnon-linearsystem?Areathereanyspecialcautionsininput/outputfor

non-linearcase?

非线性系统就是：依据胡克定律F=K*X,我们认为k是变化的。管道在使用支架、吊

杆，支架加间隙，摩擦力的情况下，系统变成非线性的。管系从冷态一>热态或热态一〉

偶然工况过程中由于非线性约束的作用导致管系刚度发生改变；

如果你输入过多的非线性支架，可能导致软件计算不收敛。陷入时循环。我们一般先

判断，根据直观感觉决定一些点，加入非线性约束。其他处根据计算结果，在调整支

架。

5.Howtocheckthelift-offsupportpoint?WhatshouldEngineercheckforlift-offproblem?

Whatishotsustainedstress?

检查约束报告，垂直方向受力为0的点即支架托空点；

支架托空点应考虑采用弹性支吊；

Hotsustainstress—计算热态持续应力。依据B31.3AppendixP,用户可以校核热态持续

应力。主要是考虑支架脱空情况下持续应力。

GenerallyHotsustainedstressiscarriedoutbyremovingthesupportatthepointoflift

off,&checkforsustainedstresses.MyquestionisIsthereanyguidelinesoranyproper

basisavailablefbrneglectingsmallliftoffforhotsustainedstresscheck.Iassumethatthe

meaningofsmallliftoffmeansLiftoffbysmallpositivedisplacement..

Supposeu'rsystemhasthreecases

1operating

2design

3Upset

Andinthesystemu'rtwosupportaregoingtoliftoff(maybebysmalldisplacement)and

duetotheremovalofthesetwosupportu'rsystemgetfailedinsustainedcase...Whatucan

dohereisjustcheckwhetherthessetwosupportsareliftinginthesamecaseordifferent.,if

theyliftindifferentcasecheckforremovalofonesupportatonetime...inmyviewushould

notignoresmalldeflectionbecausetheywillactasconstantactingload....whichwillcause

failure

6.WhatisLiberalstressallowable?

一次应力的余量可以添加到二次应力的许用应力上来，我们将这个余量称为Liberalstress

allowableo

Perhapsitwouldbeofsomebenefittoreviewthemeaningoftheterm?liberalallowable

stressrange?.Firstofall,thisisnotatermthatisusedbytheASMEB31PressurePipingCodes.

CaesarII(C2)usesthetermasasortof?short-hand?forreferringtotheincreaseinthermal

(displacement)allowablestressrangethatisallowedinB31.1(paragraph102.3.2(D))andB31.3

(paragraph302.3.5(d).Intheseparagraphs,theB31Codesallowthepositivedifferencebetween

thecalculatedcombinedlongitudinalstresses(duetoweight(bending)andlongitudinalpressure)

andthemaximumallowablestress,Sh,tobeaddedtotheterm?0.25Sh?(thesecondterm)inthe

equationforcalculatingthemaximumallowablestressrange,SA.TheB31Codessaythat

it?MAY?beaddedintothe?0.25Sh?term,therebymakingitoptional.Iftheanalystelectsto

ignoretheadditionalallowablestressrangethedecision(allotherthingsbeingequal)wouldbe

judgedconservative.Iftheanalystelecttoemploythisadditionalallowablestressrange,the

resultingallowablestressrangeissometimestermed?liberal?.Itis,ofcourse,allsemantics.The

Codeallowstheadditionalallowablestressrangeforaverygoodreason.

TheconceptunderlyingthisruleisverywelldescribedinthefamousbookbyS.W.Spielvogle

(PipingStressCalculationsSimplified,FifthEdition,1955).SpielvogleexplainsthattheB31rules

intendfortheanalysttobeabletousetheentirerangeofstressfromthematerialyieldpointatthe

operating(hot)temperaturetothematerialyieldpointattheambient(cold)temperature(lessa

factorofsafety).SinceSh(neglectingthepossibilityofcreep)issetat2/3Syforboththehotand

coldconditions,wecancalculatethehotyieldstressasSh*1.5andwecancalculatethecoldyield

stressasSc*1.5.Takentogetherthetotalallowablestressrangeforthecombinedloadingsof

weight(bending),longitudinalpressure(tension)andthermalexpansion(displacement)wouldbe

(1.5*Sc)+(1.5*Sh),or1.5(Sc+Sh).Thisrangeofallowablestresshasbeenreducedslightlyto

allowforthevagariesofmaterialandforother?realworld?inaccuracies.TheCodephilosophy

wouldthenpermitthetotalallowablestressrange(afterthefactorofsafetyisapplied)forallthe

combinedloadingdescribedabovetobe1.25(Sc+Sh)(if,inthisdiscussion,weneglectthestress

rangereductionfactorforsimplicity).ButtheCodeusesl.OShforthesustainedloadingsof

weightandlongitudinalpressureandthisleaves1.25*Sc+0.25*Shfortheallowablethermal

expansion(displacement)stressrange(betyouwonderedwherethatcamefrom).Becausethe

Codeintendsfortheentirestrengthofthematerial(fromhotyieldtocoldyield)tobeused

(exceptforthe?adjustment?madeforvagaries),itfollowsthattheruleintheparagraphscited

aboveallowstheanalysttoputtheunused(differencebetweencalculatedsustainedlongitudinal

stressesandtheallowable1.0*Sh)portiontouseinincreasingtheallowablethermalexpansion

(displacement)stressrange.Youwillrecognizethatthe?excess?sustainedcaseallowablestress

willvaryacrossthesystembeinganalyzedandthatthevariationwilldirectlyreflecthowwell

supportedthesystemis(bendingstresseswillhavethegreatereffect).Thisvariationin?excess?

sustainedcaseallowablestressfromnodetonodeinthemodelwill(whenthe?liberal?optionis

used)resultintheallowablestressrange,Sa,beingdifferentateverynodewhentheCode

compliancereportisviewed.

So,onemightask,whywouldananalystopttonotusethe?liberal?allowablestressrangefor

comparisontocalculatedexpansion(displacement)stressrange?Thisisanengineeringjudgement.

Forexample,ifthesustainedstresseswerecalculatedas80or90percentofShandthesystem

wereoperatedinthematerialscreeprange,thedesignermightwanttotaketheconservative

decisiontonotusethe?liberal?allowablestressrangewhenevaluatingthermal(displacement)

stressranges.Anotherexamplemightbeofferedasacasewhenthesystemisinseverecyclic

service(seeB31.3paragraph300.2forthedefinition)andthedesignerislookingforalonger

fatiguelife.Goingthe?conservative?routemightalsoappealtothedesigner(orowner)ifthe

systemwouldbeoperatingwithinthepressure/temperaturevariationsdescribedinparagraph

302.2.4inB31.3orparagraph102.2.4inB31.1.Ifwehavesomedegreeofuncertainty,we

employanadditionalmeasureofconservatism.Asthesayinggoes,?whenindoubt,builditstout?.

Thankyouforbringingupthetopicfordiscussion.Goodluckwithyourprojects.

Ofcourse,alltheaboveisjustmyopinionanddoesnotreflecttheopinionofASMEoranyCode

Committee.John.

AconservativeformulationoftheallowableexpansionstressrangefarmanycodesinCAESARU

iscalculatedfrom:f(1.25Sc+.25Sh)Whentheuserrequeststhatthe"LiberalAllowableube

used,thedifferencebetweenShandSI,providedSh>SI,willbeaddedtotheterminsidethe

parenthesis,i.e.SA(Liberal)=f[J.25Sc+.25Sh+(Sh-SI)]Theliberalexpressionwillonlyhe

employedwhenthereisatleastonesustainedstresscaseintheloadset.Ifthereismorethan

onesustainedstresscaseinasingleproblem,thenthelargestofSI,ideringallofthe

sustainedcases,foranysingleelementendwillbechosentosubtractfromSh.Becausethe

sustainedstressvariesfromonepipetoanother,theallowableexpansionstresswillalsovary.

7HowtoincorporatetheinstallationtemperatureinC2?

可在Cll环境变量中更改环境温度；环境温度在管道应力分析中是个很重要的设计条

件，我们一般会去年平均的温度来进行考虑。真正的环境温度是指管道安装最后焊缝施工时

的环境温度，这样就可以决定安装的初态。

8.Whatisthermalbowingeffect?

管道暴露在阳光下，管道上部的温度和下部的温度会不同，管道会在这个温度作用下出

现热拱效果。

9.WhatkindofpipingsystemshouldtheBourdoneffectbeconsideredto?

包尔登效应，盘管在压力作用下有伸直的效果。一般是指弯头在压力作用下，有要伸直

的效果。

Thereisapressure-sensingdevicecalledabourdontubewhichisacoiledflexibletube

withfluidpressureontheinside.Aspressureincreases,thecoiltendstowanttostraighten

outagainstspringpressure(sincethereisabiggersurfaceareaaroundtheoutsidecurveofthe

coilthantheinsidecurveofthecoil...withsamepressureappliedonboth).

Iwouldassumethatapipingelbowwantstostraightenoutforthesamereason.The

higherthepressure,thehighertheforce...alsoprobablydependsonthegeometryofthe

elbow.

thebourdoneffectisthedifferencebetweenthepressureinsidethetubeorpipein

relationtothepressureoutsidethetubeorpipe.Iftheinsidepresurerisgreaterthanthe

outsidepresurethetubeorpipewillexpand.Andifthetubeorpipeisbentinacircularform,

theexpansionisnoticableandcanbeconvertedtoacalibratedreadingasinapressure

gauge.

Electricpeteiscorrect.Internalpressurecanaffectthepipebendorelbowin2ways.

TheBourdoneffectdescribesthetendencyforthepipebendto"open"underinternalpressure

and"close"underexternalpressure.ThereasonisasdescribedbyElectricpete.Theother

effectisthe''stiffening"ofpipebendsandelbowsasinternalpressureisincreased.The

stiffeningresultsfromtheinternalpressureresistingthe"ovalization"ofthecrosssectionthat

normallyoccurswhenabendingmomentisappliedtothebend.Oneorbothoftheseeffects

canoccurinlargediameterpipewithlargeD/tratios.ReferenceB31.3,AppendixD,Table

D300andnote(7).Ifyouhavepipingsystemsofmoderatediameterbutaredesigningto

B31.3,ChapterIX(highpressure-Class2500orhigher)youwillwanttoconsidertheseeffects.

Goodpipestresscomputerprograms(e.g.,CaesarII)willgiveyoutheoptionof"toggling"

theseeffectsofforon.

CommentsonPressureExpansion

InCAEPIPEVersion5.IE(Mar14,2002)achangetotheprogramstates:

Presentlypressureexpansion(Bourdoneffect)istreatedasthermalexpansionandappliedto

expansion(T)andoperating(W+P+T)loadcases.IfanenvironmentvariableBOURDONPisset

(i.e.setBOURDONP=y),pressureexpansionisnottreatedasthermalexpansion(i.e.pressure

expansionistreatedaspressureexpansionandappliedtosustained(W+P)andoperating(W+P+T)

loadcases).

Treatingapressurecausedstressasathermalexpansion-likestressmayseemincorrecttosome

analysts,buttreatingpressureexpansionasaloadsimilartothermalexpansionisthecorrect

interpretationofthetypeofloadandthefailuremoderelatedtothattypeofload.Pressure

expansioncausesdisplacement(secondary)stressesandleadstoafatiguefailure.Hooppressure

(PD/2t)andlongitudinalpressure(PD/4t)typestressesaresustained(primary)stresses,but

pressureexpansion,ifthepipingisunrestrainedwouldnotcauseanydisplacement(secondary)

stresses.Restrainingthepipe,asinintroducingmorethanoneanchororanintermediatesupport

opposedtothedirectionofpressureexpansion,causesstressesfromtheintroductionofthat

restraint.Asimpleillustrationisshownbelow:

Shownaretwoweightlesspipinglayouts.Notethelayoutonthelefthasasingleanchorandwhen

pressurizedwillexpandasshowntothedashedlineconfiguration.Sustainedloadstressesduetohoop

andlongitudinalpressureexist,butnoadditionalstressesduetopressureexpansionexist.However,

notewhathappenswhenanadditionalanchorisintroduced,restrainingthepipingpressureexpansion

intherighthandlayout.Thedeformedshapeisindicativethatstressesexistduetothe"restraintof

freeenddisplacement"inadditiontothehoopandlongitudinalpressurestresses.Thesepressure

expansionstressesaredisplacement(secondary)stressesandshouldbetreatedinasimilarmannerto

thermalexpansionstresses.

Notealso,theBourdoneffect,whichtriesopenelbowsorcurvedmemberswhensucharepressurized,

isapressureexpansioneffectandshouldbetreatedthesamewaythatsimplepressureexpansionas

discussedaboveis,i.e.,theBourdoneffectcausesdisplacement(secondary)stresses.

FurthernotethatPressureexpansionwasusuallyignoredpriortotheuseofcomputeraidedanalysis

techniquesbecausemostpipinganalyzedwasmetallic,typicallysteel,piping.Itwasignoredbecause

theamountofpressureexpansionwasnormallysmallcomparedtothermalexpansion,i.e.,typically

lessthan10percent.However,withlowmodulusmaterials,suchasnonmetallics(plastics),theamount

ofpressureexpansioncanbesignificantandmayneedtobeconsideredintheanalysisofpiping

systemsmadefromsuchmaterials.

Editor'sNote:Sinceversion3.32(4/22/1992)CAEPIPEhasbeentreatingpressureexpansionasa

secondaryload(similartothermalexpansion)andapplyingittothermalandoperatingloadcases.This

isthedefaultbehaviorofCAEPIPE(evennow).

However,afewuserswanttotreatpressureexpansionasaprimaryloadandapplyittothesustained

andoperatingloadcasesbecausefiniteelementprogramsandotherpipingprogramsdoitthisway.

Startingv5.1E,theseusers(withsomeeffortbysettinganenvironmentvariable)canalterCAEPIPE's

behavior(i.e.,treatpressureexpansionasaprimaryload)tosuittheirneeds.Pleaseseethesecond

para,aboveinthisarticleforhowtosetthevariable.

Author:Mr.RonHaupt,P.E.,ofPressurePipingEngineering(www.DDeacet)isamemberofseveral

pipingcodecommittees(B31fB31.1,B31.3,BPTCS,andothers).Heconsultsv/ithusinthecapacityof

NuclearQAManager.

NoteonBranchConnectionPressureDesign

RecentlytherewassomediscussionregardingthebranchconnectionpressuredesignrulesinB31.3,

Para.304.3.3.Somedifferenceswerenotedbetweentherules(alsoreferredtoasthearea

replacementrules)asmanifestedinthecurrentequationsinB31.3-2002andPara.104.3.1of

B31.1-2001includingthe2002Addenda.Thediscussionendedwiththeconclusionthatthereshouldbe

nodifferencebetweentheB31.1andB31.3equationsexceptintheuniquenomenclatureusedbyeach.

B31.1hasrecentlyspentaconsiderableefforttotrytomakeitsareareplacementequationscorrect,

andtheycanbeassumedtobecorrect(unlesstheASMEeditorshavemessedthemup--asituation

possibletoencounter).

Awaytocheckbranchconnectionpressuredesignrulesistoreviewtheequationssoastoassurethe

designerthatthereisanadequatewallthicknessattheendofplantlife,i.e.,fromtherunandbranch

pipingremovethemanufacturer'sunderthicknesstolerance,removethecorrosionallowance(onthe

inside)andtheremainingmetalmustsatisfytheareareplacementrules.Thatis,theamountof

remainingmetalremovedthatisrequiredforpressuredesignmustbeatleastreplacedwithinthe

reinforcementzone.Ifonefollowsthisconceptthedesignercanalwaysbeassuredofmeetingthe

B31.1orB31.3requirements.

Inaddition,thereshouldbenodifferencebetweentherulesorequationsforbranchconnection

pressuredesigninanyB31book(orfornozzlesinanyASMEboilerandpressurevesselcode),withthe

exceptionthatsomeB31booksconsidereithermanufacturer'sunderthicknesstolerancesorcorrosion

allowancesorbothasnegligible,eg,B31.4andB31.8.

Author:Mr.RonHaupt,P.E.,ofPressurePipingEngineering/www.DD)isamemberofseveral

pipingcodecommittees(B31,B31.1,B31.3,BPTCS,andothers).Heconsultswithusinthecapacityof

NuclearQAManager.

TipfortheMonth(Aug2004)

ToIncludeorNottoIncludeHangerStiffnesses?

Inthe1970s,performingpipestressanalysisonmainframecomputerswasexpensive(about$1000/run).

So,pipestressanalystswouldrunaThermal(T1)casealonefirst.Then,theywouldrunadeadweight

(DW)casewithrigidsupportsatchosenhangerlocations.Usingthesupportloadsandthehangertravel,

analystswouldselectappropriatevariablespringhangersfromhangermanufacturercatalogs.Tosave

oncomputingcosts,theywouldnotupdatetheglobalstiffnessmatrix[K]withthehangerstiffnesses

fromthenewlyselectedhangersbecausetheywouldhavetoreanalyzethemodelwhichwouldcost

moremoney.Manyindustrialplantsbuilt30or40yearsagointheUSAandpresumablyinother

countrieshavepipestressanalysesdoneinthismanner.Theseplantshavearchivedsuchanalysis

reportsthatdonotincludehangerstiffnesses(aspartoftheglobalstiffnessmatrix[K]).

Inlateryears,asandwhentheanalystsintheseplantsneededtoreanalyzethosepipingsystems,they

hadtousemodernprogramslikeCAEPIPE.But,beforetheyacceptedthenewresults,theysometimes

likedtoverifythatthenewresults(fromCAEPIPE)matchedtheresultsfromtheoldreportsgenerated

bythemainframepipestressanalysisprograms.ThisisthereasonwhyCAEPIPEprovidestheoption"Do

notinclude(orinclude)hangerstiffnesses."IthelpstheengineerscompareresultsfromCAEPIPEwith

theoldarchivedreports.

Today,withcheapPCcomputingpower,thereisnoreasonwhyhangerstiffnessesshouldbeexcluded

fromanalysis.Infact,includinghangerstiffnessesprovidesamoreaccuratepictureofsystembehavior.

Assuch,werecommendthatyou"includehangerstiffnesses"ineveryanalysis.Duetothelimited

utilityofthisoption,weplantoremovethe"Donotincludehangerstiffnesses"optionfromCAEPIPEin

thenearfuture,andincludehangerstiffnessesforeveryanalysis.

TipfortheMonth(Sep2004)

BourdonEffect—StraightPipe

Incontinuationtoourtiponpressureexpansion,wehaveincludedhereatechnicalverificationofthis

feature.Asthepreviousarticlesays,theexpansionduetointernalpressurewasusuallyignoredin

metallicpipespreviously,butifyouareusingnon-metallicpipesorhaveahighpressuresystem,the

effectcanbesignificant.So,itisrecommendedthatyoualwaysincludethisoptionduringmodel

analysis.

Determinantsofsubjectivecontour:Bourdonillusionsand"unbending"

effects.

WenderothP,CrissG,vaederZwanR.

DepartmentofPsychology,UniversityofSydney,NewSouthWales,

Australia.

Wenderothand0,Connor(1987b)reportedthat,althoughmatchestothe

straightedgeoftwotrianglesplacedapextoapexrevealedanapparent

bendinginthedirectionofthechevronformedbythehypotenusepair(the

Bourdoneffect),noperceptualunbendingofthebentchevronoccurred.

Usingsubjectivecontourfigures,WalkerandShank(1988b)foundlarge

andapproximatelyequalbendingandunbendingeffects,consistentwith

twotheoriesthattheyproposed.InExperiment1,usingadjustablechevron

matchingandsubjectivecontours,wefoundthatBourdoneffects,

equivalentinmagnitudetothosereportedbyWalkerandShank,were4-5

timeslargerthanunbendingeffects.InExperiment2,weusedavariation

ofWalkerandShank5smeasurementtechnique,inwhichsubjectsselected

amatchinganglefromagradedseries.WeobtainedBourdoneffectssimilar

tothoseinExperiment1,butmuchlargerunbendingeffects.Nevertheless,

Bourdoneffectsweresignificantlylargerthanunbendingeffectsinone

setofdata;andinanother,Bourdontestmeanswerelargerthanunbending

testmeans.Inbothdatasets,therewasalargeandsignificantpretest

bendingeffect,whichenhancedthemagnitudeofunbendingtestminus

pretestscores.Theseresultswereconsistentwithourtheorybutnotthe

theoriesofWalkerandShank.Thevarianceofunbendingtestmatches,3-4

timesthatofBourdontestmatches,reflectedthetaskdifficulty.We

proposethatsubjectiveobtuseanglecontractionthatexceedsrealobtuse

anglecontractionexplainsthefactthatunbendingeffectsarelargerin

subjectivethaninrealcontours.

10.WhataredifferentforHotloadsettingandColdloadsetting?

答：热态荷载设置和冷态荷载设置的区别：

冷态荷载：W、P

热态荷载：W、T、P

SUS=W+P;OPE=W+P+T

11,Arethereanyspecialcautionforloadcombinationmethodtogetvalidstressand

supportload?Ifsystemincludethenon-linearcase,howtoprepareloadcombination

foreachstress(SUSOCC,EXP)?

答：

SELECTCOMBINATIONMETHODFORCOMBINATIONCASESONLY

Summaryofmostcommonlyusedcombinationtypes:

ALG-signedalgebraiccombinationdisp./forcelevel

Scalar-signedcombinationdisp./force/stresslevel

ABS-unsignedcombinationdisp./force/stresslevel

DetailedDescriptionofallcombinationtypes:

ALG-Combinethedisplacementvectorsandtheforcevectors

ALGebraicallyandcalculatethestressesfromthecombined

forces.

Displacementsarethealgebraiccombinationofthe

displacementvectors.

Forcesarethealgebraiccombinationoftheforcevectors.

Stressesarenotcombined;stressesarecalculatedfrom

thealgebraicallycombinedforces.

ALGwouldtypicallybeusedtocalculateEXPcodestresses.

Scalar-Combinethedisplacementvectors,theforcevectors,

andthestressscalars.

Displacementsarethealgebraiccombinationofthe

displacementvectors.

Forcesarethealgebraiccombinationoftheforcevectors.

Stressesarethescalarcombinationofthestressscalars.

TheDisplacementsandForcesofanALGcaseandScalarcase

areequivalent.Theremaybevariationatthestresslevel,

sinceinanALGcombinationthestressesarecalculatedand

inaScalarcombinationthearecombined.Forexample:

LoadCase1:Bendingstress=100psi,duetoX-moment

LoadCase2:Bendingstress=100psi,duetoZ-moment

Algebraic(vectorial)sum=sqrt(100*100+100*100)=144psi

Scalarsum=100+100=200psi

Scalarwouldtypicallybeusedtosum(SUS+OCC)code

stresses.

SRSS-Combinesquarerootofthesumofthesquares(SRSS)ofthe

displacements,squarerootofthesumofthesquares(SRSS)

oftheforces,andsquarerootofthesumofthesquares

(SRSS)ofthestresses.

Displacementsarethethesquarerootofthesumofthe

squaresofthedisplacementsofallcasesincludedinthe

combination.

Forcesarethethesquarerootofthesumofthesquares

oftheforcesofallcasesincludedinthecombination.

Stressesarethethesquarerootofthesumofthesquares

ofthestressesofallcasesincludedinthecombination.

SRSSwouldtypicallybeusedtocombineseismicdirectional

components.

ABS-CombinetheABSolutevalueofthedisplacements,the

ABSolutevalueoftheforces,andtheABSolutevalue

ofthestresses.

Displacementsarethesumoftheabsolutevalueofthe

displacementsofallcasesincludedinthecombination.

Forcesarethesumoftheabsolutevalueofthe

forcesofallcasesincludedinthecombination.

Stressesarethesumoftheabsolutevalueofthe

stressesofallcasesincludedinthecombination.

MAX-ComparetheABSOLUTEvaluesofthedisplacements,forces,and

stressesandreporttheMAXimumdisplacement,theMAXimum

force,andtheMAXimumstressvalueofthecasescombined

(retainingtheoriginalsign).

Displacementsarethedisplacementshavingthemaximum

ABSOLUTEvaluesofalltheloadcasesincludedinthe

combination.

ForcesaretheforceshavingthemaximumABSOLUTE

valuesofalltheloadcasesincludedinthecombination.

StressesarethestresseshavingthemaximumABSOLUTE

valuesofalltheloadcasesincludedinthecombination.

MAXwouldtypicallybeusedtoreportthegreatestrestraint

loadsfromamongaselectedsetofloadcases.

MIN-ComparetheABSOLUTEvaluesofthedisplacements,forces,and

stressesandreporttheMINimumdisplacement,theMINimum

force,andtheMINimumstressvalueofthecasescombined

(retainingtheoriginalsign).

Displacementsarethedisplacementshavingtheminimum

ABSOLUTEvaluesofalltheloadcasesincludedinthe

combination.

ForcesaretheforceshavingtheminimumABSOLUTE

valuesofalltheloadcasesincludedinthecombination.

StressesarethestresseshavingtheminimumABSOLUTE

valuesofalltheloadcasesincludedinthecombination.

SIGNMAX-Comparethedisplacements,forces,andstressesandusethe

theMAXimumdisplacement,theMAXimumforce,andthe

MAXimumstressvalueofthecasescombined(i.e.,signis

consideredinthecomparison).

DisplacementsarethemaximumSIGNEDvaluesofallthe

displacementsfromeachcaseincludedinthecombination.

ForcesarethemaximumSIGNEDvaluesofalltheforces

fromeachcaseincludedinthecombination.

Stressesarethemaxi