输电铁塔节点滑移分析

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EngineeringStructures33(2011)1817–1827ContentslistsavailableatScienceDirectEngineeringStructuresjournalhomepage:www.elsevier.com/locate/engstructAccuratemodelingofjointeffectsinlatticetransmissiontowersW.Q.Jianga,Z.Q.Wanga,G.McClureb,∗,G.L.Wangc,J.D.GengdaEnergy&PowerEngineeringSchool,NorthChinaElectricPowerUniversity,BaoDing071003,ChinabDepartmentofCivilEngineeringandAppliedMechanics,McGillUniversity,Montreal,CanadaH3A2K6cGuizhouElectricPowerDesignResearchInstitute,Guizhou550002,ChinadChinaElectricPowerResearchInstitute,Beijing102401,ChinaarticleinfoabstractArticlehistory:LatticeTransmissiontowersarevitalcomponentsofoverheadtransmissionlineswhichplayanimportantReceived16September2010roleintheoperationofelectricalpowersystems.AccuratepredictionofthestructuralcapacityoflatticeReceivedinrevisedformtowersunderdifferentfailuremodesisveryimportantforaccurateassessmentofthereliabilityof19February2011transmissionlinesandpowergrids,andfordesignofefficientfailurecontainmentmeasures.Traditionally,Accepted21February2011latticetowersareanalyzedasidealtrussesorframe-trusssystemswithoutexplicitlyconsideringloadingAvailableonline23March2011eccentricitiesandslippageeffectsinboltedjoints.Sucheffectsarealwaysobservedinfull-scaletowertestsandintroducegreatdifferencesintheultimatebearingcapacityandfailuremodesobtainedfromKeywords:classicallinearanalysismodels.Inthispaperexperimentalresultsavailablefromfull-scaleprototypetestsLatticetransmissiontowerJointeccentricityofasingle-circuit110kVandasingle-circuit220kVlatticetransmissiontowerssubjectedtodifferentloadBoltedjointslippagecasesarepresentedandcomparedwiththoseobtainedfromfourseriesofnumericalmodelsthatincludeBearingcapacityjointeccentricityeffectsanddifferentjointslippagemodels.ThenumericalsimulationresultsconfirmPushoveranalysisthatjointslippagedramaticallyincreasesthedeformationofthelatticetowers,whileitsinfluenceonload-bearingcapacitywillvaryindifferentloadcasesaccordingtothemagnitudeofverticalloadingandthetowerfailuremode.Resultsfromthepushovernonlinearstaticanalysisofthetowersconsideringbothjointslippageandeccentricityarefoundinagreementwiththeexperimentalresults.Thistypeofanalysiscanbeusedtomodeljointeffectsinlatticetowers.©2011ElsevierLtd.Allrightsreserved.1.Introductioninservicearoundtheworldweredesignedusingtraditionalstresscalculationsobtainedfromlinearelasticidealtrussanalysis,Latticesteeltransmissiontowersarewidelyusedalloverwherebymemberswereassumedtobeconcentricallyloadedandtheworldasconductorsupportsinelectrictransmissiongrids.pin-connected.TowerdesignershavelongrecognizedthattheClassicallatticetowersareself-supportedandconstructedofresultsofthoseidealtrussanalysismodelscannotmatchfull-scaleanglesectionL-shapememberstypicallyconnectedwithboltedtestresultsverywell.Peterson[1]andMarjerrison[2]reportedjoints.Inmanyinstances,theseboltedconnectionsintroducethatduringfull-scaletransmissionlatticetowerteststheanalysiseccentricitiesbetweentheloadtransferredatthejointsandtheresultswouldgrosslyunderestimatethemeasureddeflections,longitudinalprincipalaxisofthemember.Eachtowercompriseswhichmightbeaslargeasthreetimesthetheoreticallinearelasticseveraljointconfigurationsintermsofgeometry,continuity,deflections.Thediscrepancybetweentheexperimentalresultsandpresenceofgussetplates,boltarrangementsandloadtransfertheanalyticalsolutionshastraditionallybeencompensatedbyeccentricity,whichmaketheselatticestructuresdifficulttosafetyfactorsinmemberandconnectiondesign.Howevermorebeanalyzedwithaccuracyusingclassicallinearmethodsevenanalysisaccuracyisnecessarytoassessrealisticfailuremodeswhenmaterialnonlinearitiesarenegligible.Whenloadsareandtowercapacityatultimateloads.Whenthetowermemberapproachingthetower’scapacity,however,bothgeometricanddeformationsremainintheirelasticrange,thediscrepancymaterialnonlinearitieshavecombinedeffectsthatcannotbebetweenlinearanalysismodelsandactualtowerresponsestemstracedwithlinearanalysis.Mostofthelatticedtowerspresentlyfromtwomainsources:(1)Second-ordereffectscausedbyjointeccentricity(asshownforexampleinFig.1whereey,ezaretherespectiveeccentricityaboutlocalprincipalaxesyandz),and∗(2)theoccurrenceofslippageeffectsinboltedjoints(seeFig.2),Correspondingaddress:DepartmentofCivilEngineeringandAppliedMechan-ics,McGillUniversity817SherbrookeStreetWestRoom475FMontreal,Quebec,whichleadstoadditionalsecond-ordereffects.CanadaH3A2K6.Tel.:+15143986677;fax:+15143987361.JointeffectsinlatticetransmissiontowershavebeenstudiedE-mailaddress:ghyslaine.mcclure@mcgill.ca(G.McClure).forseveraldecadesandarenowwell-understood.Knightand0141-0296/$–seefrontmatter©2011ElsevierLtd.Allrightsreserved.doi:10.1016/j.engstruct.2011.02.022 1818W.Q.Jiangetal./EngineeringStructures33(2011)1817–1827Santhakumar[3]conductedtestsonafull-scalequadrantofthelowestpanelofatransmissiontowerandcomparedthemeasuredresultswiththeclassicalanalysisresults.Theypointedoutthatthesecondarystressescausedbyboltedjointeffectscouldbesignificantenoughtocausefailureoflegmembersevenunderxnormalworking-loadconditions.Chanetal.[4–6]comparedeytheexperimentalfailureloadsofsingleanglestrutswiththosepredictedbydesigncodeequationsandnumericalanalysisresults,OyOandconcludedthatmorereasonableultimateloadpredictionscanbeobtainedbyconsideringboththeeffectsofjointfixity,whichezincreasemembercapacitycomparedtotheidealpinned-jointzconditions,andeccentricitywhichreducescapacitycomparedtoidealcentricloading.Inordertoobtainmoreaccuratepredictionsoflatticesteeltransmissiontowerresponseusingfiniteelementanalysis,LeeandMcClure[7]derivedanL-Sectionbeamfiniteelementwhichsuccessfullypredictstheresponseandultimatecapacityofanglemembersusedinlatticetowerswithconsiderationofloadingeccentricitiesandboundingconditionsaswellasmaterialandgeometricalnonlinearities[8].SimilaradvancedmodelingstudieswerecompletedbyAl-BermaniandKitipornchai[9,10].HoweverFig.1.Exampleofjointeccentricities.thetowerdeformationspredictedbythesenumericalmodelsstillPPPP(a)Beforeslippage.(b)Afterslippage.Fig.2.Boltedjointslippageeffects.Fig.3.110kVheight-adjustablesuspensiontower. W.Q.Jiangetal./EngineeringStructures33(2011)1817–18271819Fig.4.220kVanti-icingsuspensiontower.Fig.6.220kVtowerfailure(loadcase2—flexural).didnotagreewithtestresultsandthediscrepancywasattributedtojointslippageeffects.Kitipornchaietal.[11]developedgenericinstantaneousandcontinuousbolt-slippagemodelsfortypicallatticetowerjoints.Theirmodelingworkindicatedthatalthoughjointslippagesignificantlyaffectsthepredictedtowerdeformation,ithaslittleinfluenceonthestressanalysisresultsandalmostnoeffectonthepredictedultimatecapacityoflatticetowers.Ungkurapinan[12]andhiscollaborators[13]carriedoutanexperimentalstudytoderivemoreaccuratejoint-slippagemodels.Theyconductedexperimentsonangleshapesconnectedbytypicalsingle-legandlap-spliceboltedjointsanddevelopedempiricalmathematicalexpressionstodescribeslipandload–deformationbehavior;theseFig.5.220kVtowerduringfull-scaletesting.joint-slipmodelshavebeenusedinthepresentstudy(seeFig.10). 1820W.Q.Jiangetal./EngineeringStructures33(2011)1817–1827fromstaticprototypetestsconductedin2007and2009attheChinaElectricPowerResearchInstituteinBeijing.Itshouldbeemphasizedherethatfulldetailsofthetestedprototypescannotbepublishedsincetheyareproprietary.2.Full-scaletowertesting2.1.110kVheight-adjustablesuspensiontoweryThefirstseriesoffull-scaletestresultsusedinthestudywereobtainedfromstatictestsona25-mtall110kVheight-adjustablextransmissiontowerusedinsubsidence-proneareaduetocoalmining.ThetowerheightcanbeadjustedbyusingdifferentbodyOextensionlengths.TheoutlineofthetowergeometryisshowninFig.3(a)andtheloadingcaseappliedduringthetestsislistedzinTable1(loadingpointsareidentifiedonFig.3(b)),andthecorrespondingdeflectionsofpointsA,B,C,D,E,FandG(identifiedFig.7.Localcoordinatesystemfordiagonalmembers.onFig.3(a))wererecorded(showninFig.11)aftereachloadlevel.ThisloadcasetestistoverifythetowercapacityfollowingMorerecentlyastudybyAhmedetal.[14]concludedthatjointaconductorbreakage.TheloadingdirectionsinFig.3refertoslippagehasasignificantinfluenceontowerbehaviorbyeitherlongitudinal(L),transverse(T),andvertical(V).Itisseeninreducingitsload-carryingcapacityorincreasingdeflectionsunderTable1thatonlythelongitudinalunbalancedloadresultingfromworkingloads.However,itshouldbenotedthatmembershapeconductorbreakageatLoadingPoint5isappliedprogressively,andjointeccentricityeffectswerenotincludedintheirmodelsandfrom50%to95%ofthedesignload,whilethegravityloadsattowerfailureanalysisresultswerenotverifiedbyexperimentaltheintactcablesuspensionpoints(LoadingPoints1–4)areonlyresults.appliedinthefinalloadingstage.ThemaximumexperimentalAsindicatedabove,anumberofresearchershavestudiedload,whichisusedasthereferencevalueincomparisonswithjointeffectsonlatticetransmissiontowerresponse,buttodatenumericalpredictions,reached95%ofthedesignloadinthisnopublishedresearchhasreportedacompletestudycombiningcase.Notethatthetowerdidnotcollapseduringthetest,sothelatticetoweranalysisincludingbothjointeccentricityandslippagemaximumexperimentalloadisnotthecollapseload.effects,andverificationbyfull-scaletowertestresults.Inthispaperallthesejointeffectsaresuccessfullyaccountedforinstaticpushoverfailureanalysisoftwolatticesteeltransmission2.2.220kVanti-icingsuspensiontowertowersusingUSFOS(UltimateStrengthforOffshoreStructures)commercialsoftware[15],andthenumericalresultsarecomparedThesecondfull-scaletestresultsusedinthestudywerewithfull-scaleexperimentalmeasurementsandobservationsobtainedfromstatictestsona36-mtall220kVanti-icingL-SectionBeamL-SectionBeamL-SectionBeamNonlinearSpringSpringNonlinearSpringL-SectionBeam(a)Lap-spliceBoltedJoint(b)Single-legBoltedJoint(c)CrossedDiagonalMemberFig.8.Typicalbolted-jointconnections.PPPP(a)Bearing.(b)Normal.PP(c)Maximum.Fig.9.Differentbolt/holeconstructionclearanceconfigurations. W.Q.Jiangetal./EngineeringStructures33(2011)1817–18271821CBLOAD(kN)APQRDEFORMATION(mm)SLOPE(a)Single-legboltedjoint.LOAD(kN)(b)Lap-spliceboltedjoint.Fig.10.Ungkurapinanjointslippagemodel[12,13].suspensiontowerforuseinareasexposedtoatmosphericicing.loadwasgraduallyincreaseduntiltowercollapse.Fig.5showstheTheoutlineofthetowergeometryisshowninFig.4(a).For220kVtowerduringtestingandFig.6showsthecollapsedtowerthistower,twoloadcasesareusedwhicharelistedinTables2attheendofthistest.Thefailuremodewastheinelasticbucklingand3(theloadingpointsareidentifiedonFig.4(b))wheretheofthetowermainlegsandtheensuinggloballossofstabilityandmaximumexperimentalloadappliedis100%ofthedesignload.overturningofthesuperstructure.ThecorrespondingdeflectionsofpointsA,B,C,D,E,F,GandH3.Numericalsimulationoftowertests(identifiedonFig.4(a))wererecorded(showninFigs.12and13)aftereachloadlevel.Thetestsusingthesetwoloadcasesareto3.1.TowermodelingverifythetorsionalandbendingcapacityofthetowerwhenthelineissubjectedtounbalancedconductorloadswithglazeiceInthenumericalmodel,theindividualmembersarerepre-accretionequivalentto30-mmradialthickness.sentedbyangleshapeswithproperspatialorientationwithre-Forloadcase2(Table3)thetowerismainlybentaboutthespecttotheirlocalprincipaldirections(seeFig.7),andthetransversedirectionduetolongitudinalloadimbalance,andthemembereccentricitieseyandezarespecifiedinaccordancewith 1822W.Q.Jiangetal./EngineeringStructures33(2011)1817–1827(a)50%load.(b)75%load.(c)90%Load.(d)95%Load.Fig.11.110kVtowerlongitudinaldisplacement.Table1Table2Experimentalconductorbreakageloadingforthe110kVtower.Experimentalloadingforthe220kVtower(loadcase1—torsional).PointDirectionLoad(kN)PointDirectionLoad(kN)Transverse0.000Transverse6.0001Longitudinal0.0001Longitudinal31.298Vertical1.820Vertical31.468GroundwireGroundwireTransverse0.000Transverse6.8322Longitudinal0.0002Longitudinal−33.015Vertical1.820Vertical22.243Transverse0.000Transverse9.2203Longitudinal0.0003Longitudinal46.380Vertical5.000Vertical75.930Transverse0.000Transverse9.220ConductorConductor4Longitudinal0.0004Longitudinal46.380Vertical5.000Vertical75.930Transverse0.000Transverse8.4475Longitudinal15.7505Longitudinal−48.494Vertical5.000Vertical75.930WT1Transverse4.800theprototypedesigndetaileddrawings.Thefree(unconnected)WT2Transverse4.400WT3Transverse0.800legofalldiagonalmemberswasassignedalongthelocaly-axisasWindloadWT4Transverse1.200showninFig.7.EachmemberismeshedwithasinglemateriallyWT5Transverse2.400nonlinearbeamelementavailableinUSFOS[15],basedonplasticWT6Transverse1.600hingetheory.Inthisformulation,plastichingesmaybeintroducedWT7Transverse3.200atbothendsandmidspanofeachmember.Whentheanalysisindi-catestheonsetofyieldinginamember,aplastichingeisinsertedat235MPaforallmembersexceptthemainlegsofthe220kVtower,thecorrespondingelementnode.Ifyieldingistakingplaceatmid-whicharemadeofastrongersteelgradewithayieldstressofspanoftheelement,thememberisautomaticallysplitintotwo345MPa.Thetowermodelsareassumedtobefixedonarigidbase.newsub-elementsconnectedbyaplastichingeandthestiffnessFig.8showsthethreetypicalboltedjointconfigurationsmatrixforthetwosub-elementsisassembled.Thesteelmaterialusedinthelatticetowersandtheirrespectivemechanicalmodelpropertiesspecifiedinthenumericalmodelarethenominalvaluesimplementedintheanalysis.Takingforexamplethediagonalusedindesign:aYoung’smodulusof200GPaandayieldstressofmemberwithasingle-legboltedjointtothetowermainleg(see W.Q.Jiangetal./EngineeringStructures33(2011)1817–18271823(a)50%load.(b)75%load.(c)90%load.(d)100%load.Fig.12.220kVtowerlongitudinaldisplacement(loadcase1—torsional).Table3Table4Experimentalloadingforthe220kVtower(loadcase2—flexural).Jointstiffnessmodels.PointDirectionLoad(kN)StiffnessSingle-legjointLap-splicejointTransverse6.000SingleboltTwoandmorebolts1Longitudinal31.298KxSemi-rigidSemi-rigidSemi-rigidGroundwireVertical31.468KyRigidRigidRigidTransverse6.000KzRigidRigidRigid2Longitudinal31.298KrotxRigidRigidRigidVertical31.468KrotyPinnedRigidRigidKrotzRigidRigidRigidTransverse9.2203Longitudinal46.380Vertical75.930jointtype,numberofboltsandassumedboltpositionintheTransverse9.220holebeforeloading.AsshowninFig.9,threemodelsofinitialConductor4Longitudinal46.380bolt/holeclearancearestudied:(a)thefullbearingcondition,Vertical75.930(b)thenormalconditionoftheboltcenteredinthehole,and(c)theTransverse9.220maximumclearanceallowingmaximumslippage.Ofcourse,these5Longitudinal46.380threeclearancescenariosdonotrepresenttheactualvariabilityVertical75.930ofclearanceslikelytobepresentintheprototypessinceallthreeWT1Transverse4.800conditionsmayexistinanyonestructure,asfurtherdiscussedWT2Transverse4.400in[11];theyshouldbeconsideredasthreeidealscenariosforWT3Transverse0.800WindloadWT4Transverse1.200thepurposeofcomparisons.Fig.10illustratesthedifferentWT5Transverse2.400load–displacementmodelsusedtodefineKxfor(a)diagonalandWT6Transverse1.600horizontalmemberswithsingle-legboltedjointsand(b)mainWT7Transverse3.200legmemberswithlapsplices.Forthelap-spliceboltedjoint,thevaluesofK1,K2,K3,andK4showninFig.10(b)areprescribedFig.8(b)),sixnonlinearspringsaredefinedateachendnodeofaccordingtothenumberofboltsinarowanddefinedaccordingthememberwithtranslationalstiffnessalongx,y,zandrotationaltoUngkurapinan’sphysicaltestspecimens[13].stiffnessaboutx,y,z.Thesameprocessisappliedfortowerleglap-Basedontheaboveassumptionsandconsiderations,fourspliceboltedjoints(Fig.8(a))andback-to-backcrosseddiagonalnumericalmodelsarebuiltforeachtowerinUSFOSasshownmembers(Fig.8(c)).inTable5.NominaljointeccentricitiesandbothgeometricandAslistedinTable4,jointslippageeffectsareconsideredbymaterialnonlinearitiesareintroducedinallmodelssothestudyprescribingtheaxialstiffnessKxwhichvariesdependingonthecanfocusonjointslippageeffects.FormodelInojointslippage 1824W.Q.Jiangetal./EngineeringStructures33(2011)1817–1827(a)50%load.(b)90%load.(c)120%load.(d)135%load.Fig.13.220kVtowerlongitudinaldisplacement(loadcase2—flexural).Table5Fig.11alsoshowsthatbyconsideringthejointslippageJoint-slippagefeaturesofnumericalmodels.effects,thetowerdeformationsincreaseddramaticallyandareModelJointslippagemodelclosertomeasureddisplacements.TakingpointAagain,modelIIModelINo(jointslippagewithnormalconstructionclearance),themeasuredModelIINormal(Fig.9(b))displacementis0.64timesthepredictedvalueat50%load,0.89ModelIIIBearing(Fig.9(a))timesat75%load,1.12timesat90%loadand1.16timesatModelIVMaximum(Fig.9(c))95%load.ItisclearthatmodelsconsideringjointslippageareinbetteragreementwiththeexperimentalresultsthanmodelIisconsidered,whichisequivalenttotakingKxasrigid.Forespeciallywhentheloadlevelisrelativelylarge.TheevolutionofmodelIIIslippageeffectsareintroducedwiththeassumptionthatthediscrepanciesbetweenthenumericalandexperimentalresultsbolt/holeclearancesarelimitedwiththebearingconditionshownsuggestthatslippageeffectsstartdevelopingonlyaftersignificantonFig.9(a).FormodelsIIandIVjointslippageisconsideredwithloadisappliedandthemaximumslippagemodel(modelIV)normal(Fig.9(b))andmaximum(Fig.9(c))bolt/holeconstructionprovidesthebestpredictionofthefinaltestresults(95%load)atclearances,respectively.pointsA,BandCinthetowertopsections.Forthe220kVanti-icingtower,similarlongitudinaldisplace-3.2.ResultsanddiscussionmentresultsareplottedinFigs.12and13,fortorsional(loadcase1)andflexural(loadCase2)loadings,respectively.ThefollowingdiscussionisbasedonthelongitudinaltowerInFig.12forloadcase1,thetowerdeformationsaresmalldisplacementsreportedinFigs.11–13;thetransverseandverticalbelowpointD(towerwaist,identifiedonFig.4(a))asexpecteddisplacementsarenotpresentedastheyaremuchsmallerthanthesincethemaintowershaftcontributeshighertorsionalstiffnesslongitudinaltowerdeformation.thanthetowertopportion.Onceagain,modelIisfoundtoForthe110kVheight-adjustabletower,Fig.11(a)showsthatbegrosslyinadequatetopredictthetowerdeflections:thewhentheloadisrelativelysmall(50%load)modelIwithnoboltexperimentalresultatpointAis4.51timesmodelIresultatslippageagreeswiththeexperimentalresults.However,asthe50%load,4.25timesat75%load,4.19timesat90%and4.09atloadisincreasedthisagreementisprogressivelylostasshowninFig.11(b)–(d).Forhighloadlevels(at90%and95%),thebest100%load.However,modelIIinwhichthejointslippagemodelnumericalpredictionsarethosefrommodelIVwithmaximumwithnormalconstructionclearancewasusedyieldsveryaccuratebolt/holeclearanceslippage.TakingpointAforexample(identifiedresults:theexperimentalvalueis1.09timesthenumericalonFig.3(a)atthegroundwirepeak),theexperimentalresultispredictionat50%load,whilethetwovaluesarepracticallyequal0.83timesthemodelIresultat50%load,1.32timesat75%load,atallthreehigherloadlevelsconsidered(75%,90%and100%).1.74timesat90%loadand1.83timesat95%load.ThisshowsTheinaccuracyofmodelIisconfirmedagainfortheflexuraltheinabilityofmodelIwithnoconsiderationofjointslippagetoloadcaseinFig.13:theexperimentalresultatpointAis3.30timespredictaccuratetowerdeflections.thepredictionat50%load,2.83timesat90%load,2.50timesat W.Q.Jiangetal./EngineeringStructures33(2011)1817–18271825FailurePositionFailurePosition(a)Loadcase1—torsional(load(b)Loadcase2—flexural(loadfactor=1.92).factor=1.53).Fig.14.220kVtowerfailuremodes(ModelII).120%loadand2.38timesat135%load(onsetofcollapse).TheTable6goodperformanceofmodelIIisalsoconfirmed,especiallynearthe220kVtowerultimateloadfactor.ultimateload:theexperimentalresultamountsto1.35timestheModelUltimateloadfactornumericalpredictionat50%load,1.11timesat90%load,1.03atLoadcase1—torsionalLoadcase2—flexural120%loadand0.95at135%load.Experimental–1.40ThoseresultsclearlyindicatetheinabilityofthemodelwithoutModelI2.011.79jointslippage(modelI)topredicttowerdeflectionsandthegoodModelII1.921.53ModelIII1.971.57agreementofnumericalpredictionsaccountingforjoint-slippageModelIV1.871.47effectswiththemeasuredtowerdeformation,especiallyathigherloadlevelsandevenintheinelasticrangeofresponseofthe220kVslippagedisplacementsaremoredifficulttoseparateandidentifytowerinloadcase2.individually.TherelativeimportanceofjointslippageeffectsontheFig.14showscolorplotsgeneratedbyUSFOSmodelsofthedisplacementresponseoftowerswasfoundtovarywiththe220kVtowertoillustratethestressstateinmembersatfailure:loadingtypeaswellasthemagnitudeoftheloadsandthemembersshowninredhavedevelopedplastichingeswhiletowersize.Fig.11(a)showsthatthereisalmostnojointslippagemembersinbluehaveverylowstresslevels.Notethattheseinvolvedinthedeformationofthe110kVtowerat50%loadascolorplotsaresuperimposedtotheinitialundeformedtowerthenumericalresultswithoutconsideringjointslippage(modelconfiguration.InFig.14(a)thefailureinitiatesinthetowerheadI)agreewiththeexperimentalresults:Thisisaspecialconditionundertorsionalloading.Forflexuralloading,Fig.14(b)showsthatwhereconnectionslippageduetoself-weightwouldhavealreadythefailuredevelopsfromthetowerbasetotheheadalongthetakenplacewhiletheappliedloadisonlylongitudinal.However,mainlegs;asobservedduringthetest(seeFig.6)globalcollapseofjointslippageeffectsarealreadysignificantat50%loadinthethetowerwascausedbytheinelasticbucklingfailureofthetower220kVtower,asshowninFigs.12(a)and13(a),consideringthatmainlegs.significantverticalloadsareappliedgraduallywiththetransverseFig.15showstheloadfactorvs.longitudinaldisplacementandlongitudinalloads.Typically,themainconnectionslippagecurvesforthe220kVtowerandtheultimateloadfactorsareeffectsresultingfromhorizontalloads(andtorsionaleffectsincalculatedandlistedinTable6.Theloadfactorsarecalculatedparticular)involvediagonalmembersconnectedwithoneortwowithreferencetothetestloadsdefinedinTables2and3.Forboltsonly,especiallyinthesmaller110kVtower:thisisobservedthetwoloadcases,itisseenthatthenumericalmodelincludingbothinthetestresultsandinthenumericalmodels.Globaljointjointslippageeffectswithnormalbolt/holeclearance(modelII)slippageeffectsinvolvingthelegmembersareeasiertoidentify,yieldsthemostaccuratepredictionsoftheglobaltowerresponseespeciallyintallerandstrongertowersbuiltfromlargermembers,representedbytheexperimentalload–displacementresults.becausetheboltedjointsarerelativelymoreflexiblethantheAsindicatedinFig.15(a)and(b),thefournumericalmodelsconnectedmembers.Withlightertowers,thelegmemberandjointyieldalmostthesameultimateloadfactor,whichmeansthatjoint 1826W.Q.Jiangetal./EngineeringStructures33(2011)1817–1827(a)Loadcase1—pointB.(b)Loadcase1—pointC.(c)Loadcase2—pointA.(d)Loadcase2—pointC.Fig.15.220kVtowerload–displacementcurve.slippageisnotsignificantlyinfluencingthebearingcapacityofThemainconclusionsofthestudyareasfollows:towerforthetorsionalloading(loadcase1).However,forload(1)Numericalresultswithoutconsideringjointslippageeffectscase2(seeFig.15(c)and(d))modelIisunsafeasitoverestimatesareinadequatetopredicttowerswaydisplacements.How-theultimatecapacitybynearly28%comparedwithexperimentalever,numericalmodelsthatincorporatejointslippageeffectsresults,whiletheothermodelswithjointslippageoverestimatebothonthediagonalmembersandthemainlegsplicecon-thecapacityby5%–12%.Inthiscase,thetowerbendingcapacitynectionscanpredictthetowerdisplacementswithreasonableisinfluencedbyjointslippageeffectswhichreducedtheultimateengineeringaccuracy.loadbyabout15%comparedwithmodelIwithoutjoint(2)Consideringjointslippagewilldramaticallyincreasetheslippage.predictedtowerdeformationbutwillnotaffectitsfailureAsobservedabovewhendiscussingtowerdeformationresults,modesandsequence.jointslippagehasdifferentinfluenceontowercapacityfor(3)Theinfluenceofjointslippageontheultimateload-bearingdifferentloadcases.Forloadcase2(flexural)thefailurestartscapacityofthetowerswillbedeterminedbythemagnitudeofinthecompressedtowerlegsnearthebase(seeFig.14(b))andlargeverticalloadsareappliedonthetowerhead.Thereforelargetheappliedverticalloadandbytheloadpathsandassociateddeflectionsoftheloadingpointswillcauseimportantsecondtowerfailuremode.ordereffects(globalP-Deltaeffects)thatcausefurtherbendinginthelegsthusreducingtheultimateload-bearingcapacityofAcknowledgementstower.However,forloadcase1(torsional)thefailureoccursinthetowerheadsection(seeFig.14(a))wherethesecondorderTheauthorsacknowledgethefinancialsupportprovidedbytheeffectscausedbythelongitudinaldeflectionsdonotsignificantlyFundamentalResearchFundsfortheCentralUniversitiesofChinaaffectthecriticalmembers.Consequentlytherelativeinfluenceundertheproject‘‘Jointeffectsontheultimatebehavioroflatticeofjointslippageeffectsonthebearingcapacityoftowerswillbetransmissiontower(10QX39)’’.FundingfromtheNaturalSciencesdeterminedbythemagnitudeoftheappliedverticalloadandtheandEngineeringCouncilofCanadaisalsoacknowledgedbytheassociatedtowerfailuremode.thirdauthor.4.ConclusionReferencesAccuratepredictionoftheultimateloadcapacityoftrans-[1]PetersonWO.DesignofEHVsteeltowertransmissionlines.JStructDiv,Procmissiontowersisimportantfordesigndecision-making.TheAmerSocCivEng1962;88(PO1):39–65.[2]MarjerrisonMM.Electrictransmissiontowerdesign.JStructDiv,ProcAmertraditionalstructuralanalysismodelswhichignorejointeccentric-SocCivEng1968;94(PO1):1–23.itiesandslippageeffectsarenon-conservativeinpredictingthe[3]KnightGMS,SanthakumarAR.Jointeffectsonbehavioroftransmissionglobalresponseoflatticetowersmeasuredinfull-scaletests.Intowers.JStructDiv,ASCE1993;119(3):689–712.[4]ChanSL,ChoSH.Second-orderanalysisanddesignofangletrussespartI:thispaperseveralmodelstorepresentjointeffectsweredescribedelasticanalysisanddesign.EngStruct2008;30(3):616–25.andthenumericalpredictionswerecomparedwithexperimental[5]ChanSL,ChoSH.Second-orderanalysisanddesignofangletrussespartII:results.plasticanalysisanddesign.EngStruct2008;30(3):626–31. 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