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Sagandtensionclaculation22,498views

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PublishedonFeb06,2013

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1.14SagandTensionofConductor14.1CatenaryCables...............................................................142LevelSpans.ConductorLength.ConductorSlack.InclinedSpans.IceandWindConductorLoads.ConductorTensionLimits14.2ApproximateSagTensionCalculations.........................149SagChangewithThermalElongation.SagChangeDuetoCombinedThermalandElasticEffects.SagChangeDuetoIceLoading14.3

NumericalSagTensionCalculations...........................1414StressStrainCurves.SagTensionTables14.4RulingSpanConcept....................................................1422TensionDifferencesforAdjacentDeadEndSpans.TensionEqualizationbySuspensionInsulators.RulingSpanCalculation.StringingSagTables14.5LineDesignSagTensionParameters...........................1425CatenaryConstants.WindSpan.WeightSpan.UpliftatSuspensionStructures.TowerSpottingD.A.DouglassPowerDeliveryConsultants,Inc.14.6ConductorInstallation..................................................1428ConductorStringingMethods.TensionRidleyThrashStringingEquipmentandSetup.SaggingProcedureSouthwireCompany14.7DeningTerms..............................................................1439Theenergizedconductorsoftransmissionanddistributionlinesmustbeplacedtototallyeliminatethepossibilityofinjurytopeople.Overheadconductors,however,elongatewithtime,temperature,andtension,therebychangingtheiroriginalpositionsafterinstallation.Despitetheeffectsofweatherandloadingonaline,theconductorsmustremainatsafedistancesfrombuildings,objects,andpeopleorvehiclespassingbeneaththelineatalltimes.Toensurethissafety,theshapeoftheterrainalongtherightofway,theheightandlateralpositionoftheconductorsupportpoints,andthepositionoftheconductorbetweensupportpointsunderallwind,ice,andtemperatureconditionsmustbeknown.Bareoverheadtransmissionordistributionconductorsaretypicallyquiteexibleanduniforminweightalongtheirlength.Becauseofthesecharacteristics,theytaketheformofacatenary(Ehrenberg,1935Winkelmann,1959)betweensupportpoints.Theshapeofthecatenarychangeswithconductortemperature,iceandwindloading,andtime.Toensureadequateverticalandhorizontalclearanceunderallweatherandelectricalloadings,andtoensurethatthebreakingstrengthoftheconductorisnotexceeded,thebehavioroftheconductorcatenaryunderallconditionsmustbeknownbeforethelineisdesigned.Thefuturebehavioroftheconductorisdeterminedthroughcalculationscommonlyreferredtoassagtensioncalculations.Sagtensioncalculationspredictthebehaviorofconductorsbasedonrecommendedtensionlimitsundervaryingloadingconditions.Thesetensionlimitsspecifycertainpercentagesoftheconductors2006byTaylor&FrancisGroup,LLC.2.ratedbreakingstrengththatarenottobeexceededuponinstallationorduringthelifeoftheline.Theseconditions,alongwiththeelasticandpermanentelongationpropertiesoftheconductor,providethebasisfordeterminatingtheamountofresultingsagduringinstallationandlongtermoperationoftheline.Accuratelydeterminedinitialsaglimitsareessentialinthelinedesignprocess.Finalsagsandtensionsdependoninitialinstalledsagsandtensionsandonproperhandlingduringinstallation.Thenalsagshapeofconductorsisusedtoselectsupportpointheightsandspanlengthssothattheminimumclearanceswillbemaintainedoverthelifeoftheline.Iftheconductorisdamagedortheinitialsagsareincorrect,thelineclearancesmaybeviolatedortheconductormaybreakduringheavyiceorwindloadings.14.1CatenaryCablesAbarestrandedoverheadconductorisnormallyheldclearofobjects,people,andotherconductorsbyperiodicattachmenttoinsulators.Theelevationdifferencesbetweenthesupportingstructuresaffecttheshapeoftheconductorcatenary.Thecatenarysshapehasadistincteffectonthesagandtensionoftheconductor,andtherefore,mustbedeterminedusingwelldenedmathematicalequations.14.1.1LevelSpansTheshapeofacatenaryisafunctionoftheconductorweightperunitlength,w,thehorizontalcomponentoftension,H,spanlength,S,andthemaximumsagoftheconductor,D.ConductorsagandspanlengthareillustratedinFig.14.1foralevelspan.Theexactcatenaryequationuseshyperbolicfunctions.RelativetothelowpointofthecatenarycurveshowninFig.14.1,theheightoftheconductor,y(x),abovethislowpointisgivenbythefollowingequation:Hww(x2)y(x)coshx1(14:1)wH2HYaxisTSLD2y(x)xHa=H/wXaxisFIGURE14.1Thecatenarycurveforlevelspans.2006byTaylorFrancisGroup,LLC.3.Notethatxispositiveineitherdirectionfromthelowpointofthecatenary.TheexpressiontotherightisanapproximateparabolicequationbaseduponaMacLaurinexpansionofthehyperboliccosine.Foralevelspan,thelowpointisinthecenter,andthesag,D,isfoundbysubstitutingxS=2intheprecedingequations.Theexactandapproximateparabolicequationsforsagbecomethefollowing:HwSw(S2)Dcosh1(14:2)w2H8HTheratio,H=w,whichappearsinalloftheprecedingequations,iscommonlyreferredtoasthecatenaryconstant.Anincreaseinthecatenaryconstant,havingtheunitsoflength,causesthecatenarycurvetobecomeshallowerandthesagtodecrease.Althoughitvarieswithconductortemperature,iceandwindloading,andtime,thecatenaryconstanttypicallyhasavalueintherangeofseveralthousandfeetformosttransmissionlinecatenaries.Theapproximateorparabolicexpressionissufcientlyaccurateaslongasthesagislessthan5%ofthespanlength.Asanexample,considera1000ftspanofDrakeconductor(w1.096lb=ft)installedatatensionof4500lb.Thecatenaryconstantequals4106ft.Thecalculatedsagis30.48ftand30.44ftusingthehyperbolicandapproximateequations,respectively.Bothestimatesindicateasagto

spanratioof3.4%andasagdifferenceofonly0.5in.Thehorizontalcomponentoftension,H,isequaltotheconductortensionatthepointinthecatenarywheretheconductorslopeishorizontal.Foralevelspan,thisisthemidpointofthespanlength.Attheendsofthelevelspan,theconductortension,T,isequaltothehorizontalcomponentplustheconductorweightperunitlength,w,multipliedbythesag,D,asshowninthefollowing:THwD(14:3)Giventheconditionsintheprecedingexamplecalculationfora1000ftlevelspanofDrakeACSR,thetensionattheattachmentpointsexceedsthehorizontalcomponentoftensionby33lb.Itiscommontoperformsagtensioncalculationsusingthehorizontaltensioncomponent,buttheaverageofthehorizontalandsupportpointtensionisusuallylistedintheoutput.14.1.2ConductorLengthApplicationofcalculustothecatenaryequationallowsthecalculationoftheconductorlength,L(x),measuredalongtheconductorfromthelowpointofthecatenaryineitherdirection.Theresultingequationbecomes:wxHx2w2L(x)SINHx1(14:4)wH6H2Foralevelspan,theconductorlengthcorrespondingtoxS=2ishalfofthetotalconductorlengthandthetotallength,L,is:2HSwS2w2LSINHS1(14:5)w2H24H2Theparabolicequationforconductorlengthcanalsobeexpressedasafunctionofsag,D,bysubstitutionofthesagparabolicequation,giving:8D2LS(14:6)3S2006byTaylorFrancisGroup,LLC.4.14.1.3ConductorSlackThedifferencebetweentheconductorlength,L,andthespanlength,S,iscalledslack.Theparabolicequationsforslackmaybefoundbycombiningtheprecedingparabolicequationsforconductorlength,L,andsag,D:2w8LSS3D2(14:7)24H23SWhileslackhasunitsoflength,itisoftenexpressedasthepercentageofslackrelativetothespanlength.NotethatslackisrelatedtothecubeofspanlengthforagivenH=wratioandtothesquareofsagforagivenspan.ForaseriesofspanshavingthesameH=wratio,thetotalslackislargelydeterminedbythelongestspans.Itisforthisreasonthattherulingspanisnearlyequaltothelongestspanratherthantheaveragespaninaseriesofsuspensionspans.Equation(14.7)canbeinvertedtoobtainamoreinterestingrelationshipshowingthedependenceofsag,D,uponslack,LS:r3S(LS)D(14:8)8Ascanbeseenfromtheprecedingequation,smallchangesinslacktypicallyyieldlargechangesinconductorsag.14.1.4InclinedSpansInclinedspansmaybeanalyzedusingessentiallythesameequationsthatwereusedforlevelspans.Thecatenaryequationfortheconductorheightabovethelowpointinthespanisthesame.However,thespanisconsideredtoconsistoftwoseparatesections,onetotherightofthelowpointandtheothertotheleftasshowninFig.14.2(Winkelmann,1959).Theshapeofthecatenaryrelativetothelowpointisunaffectedbythedifferenceinsuspensionpointelevation(spaninclination).Ineachdirectionfromthelowpoint,theconductorelevation,y(x),relativetothelowpointisgivenby:Hwwx2y(x)coshx1(14:9)wH2HTLSS1hDLTRDDRXLXRFIGURE14.2Inclinedcatenaryspan.2006byTaylorFrancisGroup,LLC.5.Notethatxisconsideredpositiveineitherdirectionfromthelowpoint.Thehorizontaldistance,xL,fromtheleftsupportpointtothelowpointinthecatenaryis:ShxL1(14:10)24DThehorizontaldistance,xR,fromtherightsupportpointtothelowpointofthecatenaryis:ShxR1(14:11)24DwhereShorizontaldistancebetweensupportpoints.hverticaldistancebetweensupportpoints.Slstraightlinedistancebetweensupportpoints.Dsagmeasuredverticallyfromalinethroughthepointsofconductorsupporttoalinetangenttotheconductor.Themidpointsag,D,isapproximatelyequaltothesaginahorizontalspanequalinlengthtotheinclinedspan,Sl.Knowingthehorizonaldistancefromthelowpointtothesupportpointineachdirection,theprecedingequationsfory(x),L,D,andTcanbeappliedtoeachsideoftheinclinedspan.Thetotalconductorlength,L,intheinclinedspanisequaltothesumofthelengthsinthexRandxLsubspansections:33w2LSxRxL(14:12)6H2Ineachsubspan,thesagisrelativetothecorrespondingsupportpointelevation:22wxRwxLDRDL(14:13)2H2Horintermsofsag,D,andtheverticaldistancebetweensupportpoints:h2h2DRD1DLD1(14:14)4D4Dandthemaximumtensionis:TRHwDRTLHwDL(14:15)orintermsofupperandlowersupportpoints:TuTlwh(14:16)whereDRsaginrightsubspansectionDLsaginleftsubspansectionTRtensioninrightsubspansectionTLtensioninleftsubspansectionTutensioninconductoratuppersupportTltensioninconductoratlowersupport2006byTaylorFrancisGroup,LLC.6.Thehorizontalconductortensionisequalatbothsupports.Theverticalcomponentofconductortensionisgreaterattheuppersupportandtheresultanttension,Tu,isalsogreater.14.1.5IceandWindConductorLoadsWhenaconductoriscoveredwithiceand=orisexposedtowind,theeffectiveconductorweightperunitlengthincreases.Duringoccasionsofheavyiceand=orwindload,theconductorcatenarytensionincreasesdramaticallyalongwiththeloadsonangleanddeadendstructures.Boththeconductoranditssupportscanfail

unlessthesehightensionconditionsareconsideredinthelinedesign.TheNationalElectricSafetyCode(NESC)suggestscertaincombinationsoficeandwindcorrespondingtoheavy,medium,andlightloadingregionsoftheUnitedStates.Figure14.3isamapoftheU.S.indicatingthoseareas(NESC,1993).ThecombinationsoficeandwindcorrespondingtoloadingregionarelistedinTable14.1.TheNESCalsosuggeststhatincreasedconductorloadsduetohighwindloadswithouticebeconsidered.Figure14.4showsthesuggestedwindpressureasafunctionofgeographicalareafortheUnitedStates(ASCEStd788).Certainutilitiesinveryheavyiceareasuseglazeicethicknessesofasmuchastwoinchestocalculateicedconductorweight.Similarly,utilitiesinregionswherehurricanewindsoccurmayusewindloadsashighas34lb=ft2.AstheNESCindicates,thedegreeoficeandwindloadsvarieswiththeregion.Someareasmayhaveheavyicing,whereassomeareasmayhaveextremelyhighwinds.Theloadsmustbeaccountedforinthelinedesignprocesssotheydonothaveadetrimentaleffectontheline.Someoftheeffectsofboththeindividualandcombinedcomponentsoficeandwindloadsarediscussedinthefollowing.14.1.5.1IceLoadingTheformationoficeonoverheadconductorsmaytakeseveralphysicalforms(glazeice,rimeice,orwetsnow).Theimpactoflowerdensityiceformationisusuallyconsideredinthedesignoflinesectionsathighaltitudes.Theformationoficeonoverheadconductorshasthefollowinginuenceonlinedesign:.Iceloadsdeterminethemaximumverticalconductorloadsthatstructuresandfoundationsmustwithstand..Incombinationwithsimultaneouswindloads,iceloadsalsodeterminethemaximumtransverseloadsonstructures.MEDIUMHEAVYLIGHTMEDIUMLIGHTHEAVYLIGHTFIGURE14.3IceandwindloadareasoftheU.S.2006byTaylorFrancisGroup,LLC.7.TABLE14.1DenitionsofIceandWindLoadforNESCLoadingAreasLoadingDistrictsHeavyMediumLightExtremeWindLoadingRadialthicknessofice(in.)0.500.2500(mm)12.56.500Horizontalwindpressure(lb=ft2)449SeeFig.14.4(Pa)190190430Temperature(8F)0153060(8C)2010115Constanttobeaddedtotheresultantforallconductors(lb=ft)0.300.200.050.0(N=m)4.402.500.700.0.Inregionsofheavyiceloads,themaximumsagsandthepermanentincreaseinsagwithtime(differencebetweeninitialandnalsags)maybeduetoiceloadings.Iceloadsforuseindesigninglinesarenormallyderivedonthebasisofpastexperience,coderequirements,stateregulations,andanalysisofhistoricalweatherdata.Meanrecurrenceintervalsforheavyiceloadingsareafunctionoflocalconditionsalongvariousroutings.Theimpactofvaryingassumptionsconcerningiceloadingcanbeinvestigatedwithlinedesignsoftware.PA807070SeattleCI808070FI80C90OCa70mBismarckFargocoDuluthTaEASalemBillings70N90Minneapolis70RapidCitySaltLakeCity90BuffaloLansing90DavenportDetroitCheyenneDesMoinesChicago80PittsburghLincolnColumbus70SanFrancisco80DenverFresnoyKansasCitNRichmondSt.LouisALasVegasNorfolkELosAngelesDodgeCity100C110SanDiegoOKnoxvilleRaleighICAlbuquerqueAmarilloOklahomaCityTPhoenixColumbiaNLittleRockLAAtlantaBirmingham1107070TFortWorthAShreveportJacksonJackson1009080ALASKA8080050100707090NewOrleans110Tampa1100100200300400500MILESSCALE1:20,000,000Miami11080GULFOFMEXICO70110NOTES:10090BASICWINDSPEED70MPHSPECIALWINDREGION80100901.VALUESAREFASTESTMILESPEEDSAT33FT(10M)ABOVEGROUNDFOREXPOSURECATEGORYCANDAREASSOCIATEDWITHANANNUALPROBABILITYOF0.02.1101102.LINEARINTERPOLATIONBETWEENWINDSPEEDCONTOURSISACCEPTABLE.3.CAUTIONINTHEUSEOFWINDSPEEDCONTOURSINMOUNTAINOUSREGIONSOF110ALASKAISADVISED.FIGURE14.4WindpressuredesignvaluesintheUnitedStates.Maximumrecordedwindspeedinmiles/hour.(FromOverend,P.R.andSmith,S.,ImpulseTimeMethodofSagMeasurement,AmericanSocietyofCivilEngineers.Withpermission.)2006byTaylorFrancisGroup,LLC.8.TABLE14.2RatioofIcedtoBareConductorWeightWbareWiceACSRConductorDc,in.Wbare,lb=ftWice,lb=ftWbare#1=0AWG6=1Raven0.3980.14510.5594.8477kcmil26=7Hawk0.8580.65530.8452.31590kcmil54=19Falcon1.5452.0421.2721.6Thecalculationoficeloadsonconductorsisnormallydonewithanassumedglazeicedensityof57lb=ft3.Theweightoficeperunitlengthiscalculatedwiththefollowingequation:wice1:244tDct(14:17)wheretthicknessofice,in.Dcconductoroutsidediameter,in.wiceresultantweightofice,lb=ftTheratiooficedweighttobareweightdependsstronglyuponconductordiameter.AsshowninTable14.2forthreedifferentconductorscoveredwith0.5inradialglazeice,thisratiorangesfrom4.8for#1=0AWGto1.6for1590kcmilconductors.Asaresult,smalldiameterconductorsmayneedtohaveahigherelasticmodulusandhighertensilestrengththanlargeconductorsinheavyiceandwindloadingareastolimitsag.14.1.5.2WindLoadingWindloadingsonoverheadconductorsinuencelinedesigninanumberofways:.Themaximumspanbetweenstructuresmaybedeterminedbytheneedforhorizontalclearancetoedgeofrightofwayduringmoderatewinds..The

maximumtransverseloadsfortangentandsmallanglesuspensionstructuresareoftendeterminedbyinfrequenthighwindspeedloadings..Permanentincreasesinconductorsagmaybedeterminedbywindloadinginareasoflighticeload.Windpressureloadonconductors,Pw,iscommonlyspeciedinlb=ft2.TherelationshipbetweenPwandwindvelocityisgivenbythefollowingequation:Pw0:0025(Vw)2(14:18)whereVwthewindspeedinmilesperhour.Thewindloadperunitlengthofconductorisequaltothewindpressureload,Pw,multipliedbytheconductordiameter(includingradialiceofthicknesst,ifany),isgivenbythefollowingequation:Dc2tWwPw(14:19)1214.1.5.3CombinedIceandWindLoadingIftheconductorweightistoincludebothiceandwindloading,theresultantmagnitudeoftheloadsmustbedeterminedvectorially.Theweightofaconductorunderbothiceandwindloadingisgivenbythefollowingequation:qwwiwbwi2Ww2(14:20)2006byTaylorFrancisGroup,LLC.9.wherewbbareconductorweightperunitlength,lb=ftwiweightoficeperunitlength,lb=ftwwwindloadperunitlength,lb=ftww+iresultantoficeandwindloads,lb=ftTheNESCprescribesasafetyfactor,K,inpoundsperfoot,dependentuponloadingdistrict,tobeaddedtotheresultanticeandwindloadingwhenperformingsagandtensioncalculations.Therefore,thetotalresultantconductorweight,w,is:wwwiK(14:21)14.1.6ConductorTensionLimitsTheNESCrecommendslimitsonthetensionofbareoverheadconductorsasapercentageoftheconductorsratedbreakingstrength.Thetensionlimitsare:60%undermaximumiceandwindload,33.3%initialunloaded(wheninstalled)at608F,and25%nalunloaded(aftermaximumloadinghasoccurred)at608F.Itiscommon,however,forlowerunloadedtensionlimitstobeused.Exceptinareasexperiencingsevereiceloading,itisnotunusualtondtensionlimitsof60%maximum,25%unloadedinitial,and15%unloadednal.Thissetofspecicationscouldeasilyresultinanactualmaximumtensionontheorderofonly35to40%,aninitialtensionof20%andanalunloadedtensionlevelof15%.Inthiscase,the15%tensionlimitissaidtogovern.Transmissionlineconductorsarenormallynotcoveredwithice,andwindsontheconductorareusuallymuchlowerthanthoseusedinmaximumloadcalculations.Undersucheverydayconditions,tensionlimitsarespeciedtolimitaeolianvibrationtosafelevels.Evenwitheverydaylowertensionlevelsof15to20%,itisassumedthatvibrationcontroldeviceswillbeusedinthosesectionsofthelinethataresubjecttoseverevibration.Aeolianvibrationlevels,andthusappropriateunloadedtensionlimits,varywiththetypeofconductor,theterrain,spanlength,andtheuseofdampers.Specialconductors,suchasACSS,SDC,andVR,exhibithighselfdampingpropertiesandmaybeinstalledtothefullcodelimits,ifdesired.14.2ApproximateSagTensionCalculationsSagtensioncalculations,usingexactingequations,areusuallyperformedwiththeaidofacomputerhowever,withcertainsimplications,thesecalculationscanbemadewithahandheldcalculator.Thelatterapproachallowsgreaterinsightintothecalculationofsagsandtensionsthanispossiblewithcomplexcomputerprograms.Equationssuitableforsuchcalculations,aspresentedintheprecedingsection,canbeappliedtothefollowingexample:Itisdesiredtocalculatethesagandslackfora600ftlevelspanof795kcmil26=7ACSRDrakeconductor.Thebareconductorweightperunitlength,wb,is1.094lb=ft.Theconductorisinstalledwithahorizontaltensioncomponent,H,of6300lb,equalto20%ofitsratedbreakingstrengthof31,500lb.ByuseofEq.(14.2),thesagforthislevelspanis:1:094(6002)D7:81ft(2:38m)(8)6300ThelengthoftheconductorbetweenthesupportpointsisdeterminedusingEq.(14.6):8(7:81)2L600600:27ft(182:96m)3(600)2006byTaylorFrancisGroup,LLC.10.Notethattheconductorlengthdependssolelyonspanandsag.Itisnotdirectlydependentonconductortension,weight,ortemperature.Theconductorslackistheconductorlengthminusthespanlengthinthisexample,itis0.27ft(0.0826m).14.2.1SagChangewithThermalElongationACSRandAACconductorselongatewithincreasingconductortemperature.TherateoflinearthermalexpansionforthecompositeACSRconductorislessthanthatoftheAACconductorbecausethesteelstrandsintheACSRelongateatapproximatelyhalftherateofaluminum.Theeffectivelinearthermalexpansioncoefcientofanonhomogenousconductor,suchasDrakeACSR,maybefoundfromthefollowingequations(FinkandBeatty):AALASTEASEALEST(14:22)ATOTALATOTALEALAALESTASTaASaALaST(14:23)EASATOTALEASATOTALwhereEALElasticmodulusofaluminum,psiESTElasticmodulusofsteel,psiEASElasticmodulusofaluminumsteelcomposite,psiAALAreaofaluminumstrands,squareunitsASTAreaofsteelstrands,squareunitsATOTALTotalcrosssectionalarea,squareunitsaALAluminumcoefcientoflinearthermalexpansion,per8FaSTSteelcoefcientofthermalelongation,per8FaASCompositealuminumsteelcoefcientofthermalelongation,per8FTheelasticmoduliforsolidaluminumwireis10millionpsiandforsteelwireis30millionpsi.Theelasticmoduliforstrandedwireis

reduced.Themodulusforstrandedaluminumisassumedtobe8.6millionpsiforallstrandings.ThemoduliforthesteelcoreofACSRconductorsvarieswithstrandingasfollows:.27.5106forsinglestrandcore.27.0106for7strandcore.26.5106for19strandcoreUsingelasticmoduliof8.6and27.0millionpsiforaluminumandsteel,respectively,theelasticmodulusforDrakeACSRis:0:62470:1017EAS(8:6106)(27:0106)11:2106psi0:72640:7264andthecoefcientoflinearthermalexpansionis:68:61060:6247627:01060:1017aAS12:8106:41011:21060:726411:21060:726410:6106=FIftheconductortemperaturechangesfromareferencetemperature,TREF,toanothertemperature,T,theconductorlength,L,changesinproportiontotheproductoftheconductorseffectivethermalelongationcoefcient,aAS,andthechangeintemperature,TTREF,asshownbelow:LTLTREF(1aAS(TTREF))(14:24)2006byTaylorFrancisGroup,LLC.11.Forexample,ifthetemperatureoftheDrakeconductorintheprecedingexampleincreasesfrom608F(158C)to1678F(758C),thenthelengthat608Fincreasesby0.68ft(0.21m)from600.27ft(182.96m)to600.95ft(183.17m):L(167F)600:27(1(10:6106)(16760))600:95ftIgnoringforthemomentanychangeinlengthduetochangeintension,thesagat1678F(758C)maybecalculatedfortheconductorlengthof600.95ft(183.17m)usingEq.(14.8):r3(600)(0:95)D14:62ft8UsingarearrangementofEq.(14.2),thisincreasedsagisfoundtocorrespondtoadecreasedtensionof:w(S2)1:094(6002)H3367lb8D8(14:62)Iftheconductorwereinextensible,thatis,ifithadaninnitemodulusofelasticity,thenthesevaluesofsagandtensionforaconductortemperatureof1678Fwouldbecorrect.Foranyrealconductor,however,theelasticmodulusoftheconductorisniteandchangesintensiondochangetheconductorlength.Useoftheprecedingcalculation,therefore,willoverstatetheincreaseinsag.14.2.2SagChangeDuetoCombinedThermalandElasticEffectsWithmoduliofelasticityaroundthe8.6millionpsilevel,typicalbarealuminumandACSRconductorselongateabout0.01%forevery1000psichangeintension.Intheprecedingexample,theincreaseintemperaturecausedanincreaseinlengthandsagandadecreaseintension,buttheeffectoftensionchangeonlengthwasignored.Asdiscussedlater,concentriclaystrandedconductors,particularlynonhomogenousconductorssuchasACSR,arenotinextensible.Rather,theyexhibitquitecomplexelasticandplasticbehavior.Initialloadingofconductorsresultsinelongationbehaviorsubstantiallydifferentfromthatcausedbyloadingmanyyearslater.Also,hightensionlevelscausedbyheavyiceandwindloadscauseapermanentincreaseinconductorlength,affectingsubsequentelongationundervariousconditions.Accountingforsuchcomplexstressstrainbehaviorusuallyrequiresasophisticated,computeraidedapproach.Forillustrationpurposes,however,theeffectofpermanentelongationoftheconductoronsagandtensioncalculationswillbeignoredandasimpliedelasticconductorassumed.Thisidealizedconductorisassumedtoelongatelinearlywithloadandtoundergonopermanentincreaseinlengthregardlessofloadingortemperature.Forsuchaconductor,therelationshipbetweentensionandlengthisasfollows:HHREFLHLHREF1(14:25)ECAwhereLHLengthofconductorunderhorizontaltensionHLHREFLengthofconductorunderhorizontalreferencetensionHREFECElasticmodulusofelasticityoftheconductor,psiACrosssectionalarea,in.2Incalculatingsagandtensionforextensibleconductors,itisusefultoaddasteptotheprecedingcalculationofsagandtensionforelevatedtemperature.Thisaddedstepallowsaseparationofthermalelongationandelasticelongationeffects,andinvolvesthecalculationofazerotensionlength,ZTL,attheconductortemperatureofinterest,Tcdr.2006byTaylorFrancisGroup,LLC.12.ThisZTL(Tcdr)istheconductorlengthattainediftheconductoristakendownfromitssupportsandlaidonthegroundwithnotension.Byreducingtheinitialtensionintheconductortozero,theelasticelongationisalsoreducedtozero,shorteningtheconductor.Itispossible,then,forthezerotensionlengthtobelessthanthespanlength.ConsidertheprecedingexampleforDrakeACSRina600ftlevelspan.Theinitialconductortemperatureis608F,theconductorlengthis600.27ft,andEASiscalculatedtobe11.2millionpsi.UsingEq.(14.25),thereductionoftheinitialtensionfrom6300lbtozeroyieldsaZTL(608F)of:06300ZTL(60F)600:271599:81ft(11:2106)0:7264Keepingthetensionatzeroandincreasingtheconductortemperatureto1678Fyieldsapurelythermalelongation.Thezerotensionlengthat1678FcanbecalculatedusingEq.(14.24):ZTL(167F)599:81110:610616760600:49ftAccordingtoEqs.(14.2)and(14.8),thislengthcorrespondstoasagof10.5ftandahorizontaltensionof4689lb.However,thislengthwascalculatedforzerotensionandwillelongateelasticallyundertension.Theactualconductorsagtensiondeterminationrequiresaprocessofiterationasfollows:1.Asdescribedabove,theconductorszerotensionlength,calculatedat1678F(758C),is600.49ft,sagis10.5ft,andthehorizontaltensionis4689lb.2.

Becausetheconductoriselastic,applicationofEq.(14.25)showsthetensionof4689lbwillincreasetheconductorlengthfrom600.49ftto:46890Ll(167F)600:491600:84ft0:7264(11:21063.Thesag,D1(1678F),correspondingtothislengthiscalculatedusingEq.(14.8):r3(600)(0:84)Dl(167F)13:72ft84.UsingEq.(14.2),thissagyieldsanewhorizontaltension,H1(1678F),of:1:094(6002)H13588lb8(13:7)AnewtrialtensionistakenastheaverageofHandH1,andtheprocessisrepeated.TheresultsaredescribedinTable14.3.TABLE14.3InterativeSolutionforIncreasedConductorTemperatureIteration#Length,Ln,ftSag,Dn,ftTension,Hn,lbNewTrialTension,lbZTL600.55011.14435443535931600.83613.7359340142364740142600.80913.5364738312367438313600.79713.4367437532370237534600.79213.33702372722006byTaylorFrancisGroup,LLC.13.50004500Tension,Ibs40003700Ibs3500Catenary3000Elastic250020000.50.7511.251.5Slack/Elongation,ftFIGURE14.5Sagtensionsolutionfor600ftspanofDrakeat1678F.Notethatthebalanceofthermalandelasticelongationoftheconductoryieldsanequilibriumtensionofapproximately3700lbsandasagof13.3ft.Thecalculationsoftheprevioussection,whichignoredelasticeffects,resultsinlowertension,3440lb,andagreatersag,14.7ft.Slackisequaltotheexcessofconductorlengthoverspanlength.Theprecedingtablecanbereplacedbyaplotofthecatenaryandelasticcurvesonagraphofslackvstension.Thesolutionoccursattheintersectionofthetwocurves.Figure14.5showsthetensionversusslackcurvesintersectingatatensionof3700lb,whichagreeswiththeprecedingcalculations.14.2.3SagChangeDuetoIceLoadingAsanalexampleofsagtensioncalculation,calculatethesagandtensionforthe600ftDrakespanwiththeadditionof0.5inchesofradialiceandadropinconductortemperatureto08F.EmployingEq.(14.17),theweightoftheconductorincreasesby:wice1:244t(Dt)wice1:244(0:5)(1:1080:5)1:000lb=ftAsinthepreviousexample,thecalculationusestheconductorszerotensionlengthat608F,whichisthesameasthatfoundintheprevioussection,599.81ft.Theiceloadingisspeciedforaconductortemperatureof08F,sotheZTL(08F),usingEq.(14.24),is:ZTL(0F)599:81[1(10:6106)(060)]599:43ftAsinthecaseofsagtensionatelevatedtemperatures,theconductortensionisafunctionofslackandelasticelongation.Theconductortensionandtheconductorlengtharefoundatthepointofintersectionofthecatenaryandelasticcurves(Fig.14.6).Theintersectionofthecurvesoccursatahorizontaltensioncomponentof12,275lb,notveryfarfromthecrudeinitialestimateof12,050lbthatignoredelasticeffects.Thesagcorrespondingtothistensionandtheicedconductorweightperunitlengthis9.2ft.Inspiteofdoublingtheconductorweightperunitlengthbyadding0.5in.ofice,thesagoftheconductorismuchlessthanthesagat1678F.Thisconditionisgenerallytruefortransmissionconductorswhereminimumgroundclearanceisdeterminedbythehightemperatureratherthantheheavyloadingcondition.Smalldistributionconductors,suchasthe1=0AWGACSRinTable14.1,experienceamuchlargericetoconductorweightratio(4.8),andtheconductorsagundermaximumwindandiceloadmayexceedthesagatmoderatelyhighertemperatures.2006byTaylorFrancisGroup,LLC.14.130001250012,275Ibs12000Tension,IbsCatenary11500Elastic1100010500100009500900000.10.20.30.40.5Slack/Elongation,ftFIGURE14.6Sagtensionsolutionfor600ftspanofDrakeat08Fand0.5in.ice.Theprecedingapproximatetensioncalculationscouldhavebeenmoreaccuratewiththeuseofactualstressstraincurvesandgraphicsagtensionsolutions,asdescribedindetailinGraphicMethodforSagTensionCalculationsforACSRandOtherConductors(AluminumCompanyofAmerica,1961).Thismethod,althoughaccurate,isveryslowandhasbeenreplacedcompletelybycomputationalmethods.14.3NumericalSagTensionCalculationsSagtensioncalculationsarenormallydonenumericallyandallowtheusertoentermanydifferentloadingandconductortemperatureconditions.Bothinitialandnalconditionsarecalculatedandmultipletensionconstraintscanbespecied.ThecomplexstressstrainbehaviorofACSRtypeconductorscanbemodelednumerically,includingbothtemperature,andelasticandplasticeffects.14.3.1StressStrainCurvesStressstraincurvesforbareoverheadconductorincludeaminimumofaninitialcurveandanalcurveoverarangeofelongationsfrom0to0.45%.Forconductorsconsistingoftwomaterials,aninitialandnalcurveforeachisincluded.Creepcurvesforvariouslengthsoftimearetypicallyincludedaswell.Overheadconductorsarenotpurelyelastic.Theystretchwithtension,butwhenthetensionisreducedtozero,theydonotreturntotheirinitiallength.Thatis,conductorsareplasticthechangeinconductorlengthcannotbeexpressedwithasimplelinearequation,asfortheprecedinghandcalculations.Thepermanentlengthincreasethatoccursinoverheadconductorsyieldsthedifferenceininitialandnalsagtensiondatafoundinmostcomputerprograms.Figure14.7showsatypicalstressstraincurvefora26=7ACSRconductor(AluminumAssociation,1974)thecurveisvalidforconductorsizesrangingfrom266.8to795kcmil.A795

kcmil26=7ACSRDrakeconductorhasabreakingstrengthof31,500lb(14,000kg)andanareaof0.7264in.2(46.9mm2)sothatitfailsatanaveragestressof43,000psi(30kg=mm2).Thestressstraincurveillustratesthatwhenthepercentofelongationatastressisequalto50%oftheconductorsbreakingstrength(21,500psi),theelongationislessthan0.3%or1.8ft(0.55m)ina600ft(180m)span.Notethatthecomponentcurvesforthesteelcoreandthealuminumstrandedouterlayersareseparated.Thisseparationallowsforchangesintherelativecurvelocationsasthetemperatureoftheconductorchanges.Fortheprecedingexample,withtheDrakeconductoratatensionof6300lb(2860kg),thelengthoftheconductorinthe600ft(180m)spanwasfoundtobe0.27ftlongerthanthespan.Thistensioncorrespondstoastressof8600psi(6.05kg=mm2).FromthestressstraincurveinFig.14.7,thiscorrespondstoaninitialelongationof0.105%(0.63ft).Asintheprecedinghandcalculation,iftheconductorisreducedtozerotension,itsunstressedlengthwouldbelessthanthespanlength.2006byTaylorFrancisGroup,LLC.15.35,00030,00025,000tesiStress,psipoom20,000lCnaFiesitpomCo15,000alitipminumIneepInitialAluCrreethrConeaepum6M1YeinCrumarAl10,000Yel10naFiteelialSInit5,000teelalSFin0.1.2.3.4.5UnitStrain,%EquationsforCurves(X=unitstrainin%Y=stressinpsi):351023Initialcomposite:X=4.0710+(1.2810)Y(1.1810)Y+(5.641015)YY=512+(8.617104)X(1.18104)X2(5.76104)X33InitialSteel:Y=(37.1510)X44243InitialAluminum:Y=512=(4.90210)X(1.1810)X(5.7610)X3FinalComposite:Y=(107.55X17.65)103FinalSteel:Y=(38.60X0.65)103FinalAluminum:Y=(68.95X17.00)1036MonthCreep:Y=(68.7510)X31YearCreep:Y=(60.6010)X310YearCreep:Y=(53.4510)XTestTemperature708Fto758FFIGURE14.7Stressstraincurvesfor26=7ACSR.Figure14.8isastressstraincurve(AluminumAssociation,1974)foranallaluminum37strandconductorranginginsizefrom250kcmilto1033.5kcmil.Becausetheconductorismadeentirelyofaluminum,thereisonlyoneinitialandnalcurve.14.3.1.1PermanentElongationOnceaconductorhasbeeninstalledataninitialtension,itcanelongatefurther.Suchelongationresultsfromtwophenomena:permanentelongationduetohightensionlevelsresultingfromiceandwindloads,andcreepelongationundereverydaytensionlevels.Thesetypesofconductorelongationarediscussedinthefollowingsections.14.3.1.2PermanentElongationDuetoHeavyLoadingBothFigs.14.7and14.8indicatethatwhentheconductorisinitiallyinstalled,itelongatesfollowingtheinitialcurvethatisnotastraightline.Iftheconductortensionincreasestoarelativelyhighlevelundericeandwindloading,theconductorwillelongate.Whenthewindandiceloadsabate,theconductor2006byTaylorFrancisGroup,LLC.16.35,00030,00025,000Stress,psi20,00015,000umminalAluumInitiminlu10,000lAnaFireepeparCCrereep1Yeear15,000thC10Yon6M0.1.2.3.4.5UnitStrain,%EquationsforCurves(X=unitstrainin%Y=stressinpsi):InitialAluminum:X=5.31103+(1.74105)Y(6.171010)Y2+(5.051014)Y3Y=136+(7.46104)X(8.51104)X2+(2.33104)X3FinalAluminum:Y=(85.20X16.14)1036MonthCreep:Y=(42.30103)X1YearCreep:Y=(38.20103)X10YearCreep:Y=(30.60103)XTestTemperature708Fto758FFIGURE14.8Stressstraincurvesfor37strandAAC.elongationwillreducealongacurveparalleltothenalcurve,buttheconductorwillneverreturntoitsoriginallength.Forexample,refertoFig.14.8andassumethatanewlystrung795kcmil37strandAACArbutusconductorhasaneverydaytensionof2780lb.Theconductorareais0.6245in.2,sotheeverydaystressis4450psiandtheelongationis0.062%.Followinganextremelyheavyiceandwindloadevent,assumethattheconductorstressreaches18,000psi.Whentheconductortensiondecreasesbacktoeverydaylevels,theconductorelongationwillbepermanentlyincreasedbymorethan0.2%.Alsothesagundereverydayconditionswillbecorrespondinglyhigher,andthetensionwillbeless.Inmostnumericalsagtensionmethods,nalsagtensionsarecalculatedforsuchpermanentelongationduetoheavyloadingconditions.14.3.1.3PermanentElongationatEverydayTensions(CreepElongation)Conductorspermanentlyelongateundertensionevenifthetensionlevelneverexceedseverydaylevels.Thispermanentelongationcausedbyeverydaytensionlevelsiscalledcreep(AluminumCompanyofAmerica,1961).Creepcanbedeterminedbylongtermlaboratorycreeptests,theresultsofwhichareusedtogeneratecreepcurves.Onstressstraingraphs,creepcurvesareusuallyshownfor6mo,1yr,and10yrperiods.Figure14.8showsthesetypicalcreepcurvesfora37strand250.0through1033.5kcmilAAC.InFig.14.8assumethattheconductortensionremainsconstantattheinitialstressof4450psi.Attheintersectionofthisstresslevelandtheinitialelongationcurve,6month,1year,and10yearcreep2006byTaylorFrancisGroup,LLC.17.curves,theconductorelongationfromtheinitialelongationof0.062%increasesto0.11%,0.12%,and0.15%,respectively.Becauseofcreepelongation,theresultingnalsagsaregreaterandtheconductortensionislessthantheinitialvalues.Creepelongationinaluminumconductorsisquitepredictable

asafunctionoftimeandobeysasimpleexponentialrelationship.Thus,thepermanentelongationduetocreepateverydaytensioncanbefoundforanyperiodoftimeafterinitialinstallation.Creepelongationofcopperandsteelconductorsismuchlessandisnormallyignored.Permanentincreaseinconductorlengthduetoheavyloadoccurrencescannotbepredictedatthetimethatalineisbuilt.Thereasonforthisunpredictabilityisthattheoccurrenceofheavyiceandwindisrandom.Aheavyicestormmayoccurthedayafterthelineisbuiltormayneveroccuroverthelifeoftheline.14.3.2SagTensionTablesToillustratetheresultoftypicalsagtensioncalculations,refertoTables14.4through14.9showinginitialandnalsagtensiondatafor795kcmil26=7ACSRDrake,795kcmil37strandAACArbutus,and795kcmilType16Drake=SDCconductorsinNESClightandheavyloadingareasforspansofTABLE14.4SagandTensionDatafor795kcmil26=7ACSRDrakeConductorSpan600ftNESCHeavyLoadingDistrictCreepisnotafactorFinalInitialResultantWeight,Temp,8FIce,in.Wind,lb=ft2K,lb=ftlb=ftSag,ftTension,lbSag,ftTension,lb00.504.000.302.50911.141015311.14101535415Al5415Al4738St4738St320.500.000.002.09444.54818511.0985123819Al4343Al4366St4169St200.000.000.001.0946.6873726.2778553871Al4465Al3501St3390St00.000.000.001.0947.5665176.8971473111Al3942Al3406St3205St300.000.000.001.0948.9854907.9561972133Al3201Al3357St2996St600.000.000.001.09410.444725a9.1254021321Al2526Al3404St2875St900.000.000.001.09411.87415710.364759634Al1922Al3522St2837St1200.000.000.001.09413.24372711.61424835Al1379Al3692St2869St1670.000.000.001.09414.29345613.5336490Al626Al3456St3022St2120.000.000.001.09415.24324115.2432410Al0Al3241St3239StaDesigncondition.2006byTaylorFrancisGroup,LLC.18.TABLE14.5TensionDifferencesinAdjacentDeadEndSpansConductor:Drake795kcmil26=7ACSRSpan700ftArea0.7264in.2CreepisafactorNESCHeavyLoadingDistrictFinalInitialWind,ResultantTemp,8FIce,in.lb=ft2K,lb=ftWeight,lb=ftSag,ftTension,lbSag,ftTension,lb00.504.000.302.50913.611131813.5511361320.500.000.002.09413.93922413.339643200.000.000.001.0948.2281617.60882400.000.000.001.0949.1973018.268115300.000.000.001.09410.7562429.397142600.000.000.001.09412.36542910.656300a900.000.000.001.09413.96480911.9955961200.000.000.001.09415.52433013.3750201670.000.000.001.09416.97396015.5343262120.000.000.001.09418.04372817.523837aDesigncondition.Conductor:Drake795kcmil26=7ACSRSpan1000ftArea0.7264in.2CreepisnotafactorNESCHeavyLoadingDistrictFinalInitialWind,ResultantTemp,8FIce,in.lb=ft2K,lb=ftWeight,lb=ftSag,ftTension,lbSag,ftTension,lb00.504.000.302.50925.981211625.9812116320.500.000.002.09426.30999025.5310290200.000.000.001.09418.72731817.25794000.000.000.001.09420.09682118.347469300.000.000.001.09422.13619720.046840600.000.000.001.09424.11568921.766300a900.000.000.001.09426.04527123.4958391200.000.000.001.09427.89492325.2054441670.000.000.001.09430.14455927.8249352120.000.000.001.09431.47436930.244544aDesigncondition.1000and300ft.Typicaltensionconstraintsof15%nalunloadedat608F,25%initialunloadedat608F,and60%initialatmaximumloadingareused.Withmostsagtensioncalculationmethods,nalsagsarecalculatedforbothheavyice=windloadandforcreepelongation.Thenalsagtensionvaluesreportedtotheuserarethosewiththegreatestincreaseinsag.14.3.2.1Initialvs.FinalSagsandTensionsRatherthancalculatethelinesagasafunctionoftime,mostsagtensioncalculationsaredeterminedbasedoninitialandnalloadingconditions.Initialsagsandtensionsaresimplythesagsandtensionsatthetimethelineisbuilt.Finalsagsandtensionsarecalculatedif(1)thespeciediceandwindloadinghasoccurred,and(2)theconductorhasexperienced10yearsofcreepelongationataconductortemperatureof608Fattheuserspeciedinitialtension.2006byTaylorFrancisGroup,LLC.19.TABLE14.6SagandTensionDatafor795kcmil26=7ACSRDrake600ftRulingSpanConductor:Drake795kcmil26=7ACSRSpan600ftArea0.7264in.2CreepisnotafactorNESCHeavyLoadingDistrictFinalInitialResultantWeight,2Temp,8FIce,in.Wind,lb=ftK,lb=ftlb=ftSag,ftTension,lbSag,ftTension,lb00.504.000.302.50911.141015311.1410153320.500.000.002.09411.54818511.098512200.000.000.001.0946.6873726.27785500.000.000.001.0947.5665176.897147300.000.000.001.0948.9854907.956197600.000.000.001.09410.444725a9.125402900.000.000.001.09411.87415710.3647591200.000.000.001.09413.24372711.6142481670.000.000.001.09414.29345613.5336492120.000.000.001.09415.24324115.243241aDesigncondition.TABLE14.7StringingSagTablefor795kcmil26=7ACSRDrake600ftRulingSpan600ftRulingSpanControllingDesignCondition:15%RBSat608F,NoIceorWind,FinalNESCHeavyLoadDistrictHorizontal649361935910564553975166495247534569Tension,lb2030405060708090100Temp,8FSpansSag,ftin.Sag,ftin.Sag,ftin.Sag,ftin.Sag,ftin.Sag,ftin.Sag,ftin.Sag,ftin.Sag,ftin.4003436383114143454749410363931141434548410504203931141434648410515343031141

43464841151545644041434648411525457510450434648411525457510614604548411525457510616447048411515457510616467480410515457510616468611490515457510616468611725005356596164676117276510565960646761172767952058606367610727679815305116266610717579818554062656971757981858955064687074788084889156067611737771184889095570610727671083879094995807175798286811949810159074788185810939710010560077711848991969111041096107183879095910103109112620818681194991021071111166308899297101106110115111164088919691110510101141191236508119499103109112118122128660929710110711111612012613167095911105101111511111251211135680991031081121191231291341310690100106110116121127132138143700104101011411111251301361411482006byTaylorFrancisGroup,LLC.20.TABLE14.8TimeSagTableforStopwatchMethodReturnofWaveSag,3rdTime,5thTime,Sag,3rdTime,5thTime,Sag,3rdTime,5thTime,Sag,3rdTime,5thTime,in.secsecin.secsecin.secsecin.secsec51.93.2556.410.71058.814.715510.717.962.13.5566.510.81068.914.815610.818.072.33.8576.510.91078.914.915710.818.082.44.1586.611.11099.015.015810.918.192.64.3596.611.11099.015.015910.918.1102.74.6606.711.11109.115.116010.918.2112.94.8616.711.21119.115.216111.018.2123.05.0626.811.31129.115.216211.018.2133.15.2636.911.41139.215.316311.018.4143.25.4646.911.51149.215.416411.118.4153.35.6657.011.61159.315.416511.118.5163.55.8667.011.71169.315.516611.118.5173.65.9677.111.81179.315.616711.218.6183.76.1687.111.91189.415.616811.218.7193.86.3697.212.01199.415.716911.218.7203.96.4707.212.01209.515.817011.318.8214.06.6717.312.11219.515.817111.318.8224.06.7727.312.21229.515.917211.318.9234.16.9737.412.31239.616.017311.418.9244.27.0747.412.41249.616.017411.419.0254.37.2757.512.51259.716.117511.419.0264.47.3767.512.51269.716.217611.419.1274.57.5777.612.61279.716.217711.519.1284.67.6787.612.71289.816.317811.519.2294.67.7797.712.81299.816.317911.519.3304.77.9807.712.91309.816.418011.619.3314.88.0817.813.01319.916.518111.619.4324.98.1827.813.01329.916.518211.619.4335.08.3837.913.113310.016.618311.719.5345.08.4847.913.213410.016.718411.719.5355.18.5858.013.313510.016.718511.719.6365.28.6868.013.313610.116.818611.819.6375.38.8878.113.413710.116.818711.819.7385.38.9888.113.513810.116.918811.819.7395.49.0898.113.613910.217.018911.919.8405.59.1908.213.714010.217.019011.919.8415.59.2918.213.714110.317.119111.919.9425.69.3928.313.814210.317.119212.019.9435.79.4938.313.914310.317.219312.020.0445.79.5948.414.014410.417.319412.020.0455.89.7958.414.014510.417.319512.120.1465.99.8968.514.114610.417.419612.120.1475.99.9978.514.214710.517.419712.120.2486.010.0988.514.214810.517.519812.120.0496.010.1998.614.314910.517.619912.220.3506.110.21008.614.415010.617.620012.220.3516.210.31018.714.515110.617.720112.220.4526.210.41028.714.515210.617.720212.320.5536.310.51038.814.615310.717.820312.320.5546.310.61048.814.715410.717.920412.320.6Note:Tocalculatethetimeofreturnofotherwaves,multiplythetimeinsecondsforonewavereturnbythenumberofwavereturnsor,moresimply,selectthecombinationofvaluesfromthetablethatrepresentsthenumberofwavereturnsdesired.Forexample,thetimeofreturnofthe8thwaveisthesumofthe3rdand5th,whileforthe10thwaveitistwicethetimeofthe5th.Theapproximateformulagivingtherelationshipbetweensagandtimeisgivenas:2TD12:075(inches)NwhereDsag,in.Ttime,secNnumberofreturnwavescounted2006byTaylorFrancisGroup,LLC.21.TABLE14.9TypicalSagandTensionData795kcmil26=7ACSRDrake,300and1000ftSpansConductor:Drake795kcmil26=7ACSRSpan300ftArea0.7264in.2CreepisafactorNESCHeavyLoadingDistrictFinalInitialTemp,Wind,Weight,Sag,Tension,Sag,Tension,8FIce,in.lb=ft2K,lb=ftlb=ftftlbftlb300.009.000.051.4242.3767692.097664300.000.000.001.0941.9363641.667404600.000.000.001.0942.614725a2.046033900.000.000.001.0943.4635562.5747921200.000.000.001.0941.0030773.2537851670.000.000.001.0944.6026784.4927462120.000.000.001.0945.2023715.202371aDesigncondition.Conductor:Drake795kcmil26=7ACSRSpan1000ftArea0.7264in.2CreepisafactorNESCHeavyLoadingDistrictFinalInitialTemp,Wind,Weight,Sag,Tension,Sag,Tension,8FIce,in.lb=ft2K,lb=ftlb=ftftlbftlb300.009.000.051.42428.42629027.256558300.000.000.001.09427.26503625.705339600.000.000.001.09429.074725a27.365018900.000.000.001.09430.82446028.9847401200.000.000.001.09432.50423230.5644981670.000.000.001.09434.49

399032.5641752120.000.000.001.09435.75385135.143917aDesigncondition.Note:Calculationsbasedon:(1)NESCLightLoadingDistrict.(2)TensionLimits:a.InitialLoaded60%RBS@308Fb.InitialUnloaded25%RBS@608Fc.FinalUnloaded15%RBS@608F.14.3.2.2SpecialAspectsofACSRSagTensionCalculationsSagtensioncalculationswithACSRconductorsaremorecomplexthansuchcalculationswithAAC,AAAC,orACARconductors.Thecomplexityresultsfromthedifferentbehaviorofsteelandaluminumstrandsinresponsetotensionandtemperature.Steelwiresdonotexhibitcreepelongationorplasticelongationinresponsetohightensions.Aluminumwiresdocreepandrespondplasticallytohighstresslevels.Also,theyelongatetwiceasmuchassteelwiresdoinresponsetochangesintemperature.Table14.10presentsvariousinitialandnalsagtensionvaluesfora600ftspanofaDrakeACSRconductorunderheavyloadingconditions.Notethatthetensioninthealuminumandsteelcomponentsisshownseparately.Inparticular,someotherusefulobservationsare:1.At608F,withouticeorwind,thetensionlevelinthealuminumstrandsdecreaseswithtimeasthestrandspermanentlyelongateduetocreeporheavyloading.2.Bothinitiallyandnally,thetensionlevelinthealuminumstrandsdecreaseswithincreasingtemperaturereachingzerotensionat2128Fand1678Fforinitialandnalconditions,respectively.3.Atthehighesttemperature(2128F),whereallthetensionisinthesteelcore,theinitialandnalsagtensionsarenearlythesame,illustratingthatthesteelcoredoesnotpermanentlyelongateinresponsetotimeorhightension.2006byTaylorFrancisGroup,LLC.22.TABLE14.10TypicalSagandTensionData795kcmil26=7ACSRDrake,300and1000ftSpansConductor:Drake795kcmil26=7ACSR=SDSpan300ftArea0.7264in.2CreepisafactorNESCHeavyLoadingDistrictFinalInitialWind,Weight,Tension,Tension,Temp,8FIce,in.lb=ft2K,lb=ftlb=ftSag,ftlbSag,ftlb00.504.000.302.5092.9196952.889802320.500.000.002.0943.1375282.888188200.000.000.001.0941.2697331.26975600.000.000.001.0941.4883271.408818300.000.000.001.0941.9363641.667404600.000.000.001.0942.614725a2.046033900.000.000.001.0943.4635562.5747921200.000.000.001.0944.0030773.2537851670.000.000.001.0944.6026784.4927462120.000.000.001.0945.2023715.202371aDesigncondition.Conductor:Drake795kcmil26=7ACSRSpan1000ftArea0.7264in.2CreepisnotafactorNESCHeavyLoadingDistrictFinalInitialWind,Weight,Tension,Tension,Temp,8FIce,in.lb=ft2K,lb=ftlb=ftSag,ftlbSag,ftlb00.504.000.302.50930.071047930.0710479320.500.000.002.09430.56860729.948785200.000.000.001.09424.09569422.77602300.000.000.001.09425.38540623.905738300.000.000.001.09427.26503625.595362600.000.000.001.09429.074725a27.255038900.000.000.001.09430.82446028.8747581200.000.000.001.09432.50423230.4545131670.000.000.001.09434.36400532.8541872120.000.000.001.09435.62386535.053928aDesigncondition.Note:Calculationsbasedon:(1)NESCHeavyLoadingDistrict.(2)TensionLimits:a.InitialLoaded60%RBS@08Fb.InitialUnloaded25%RBS@608Fc.FinalUnloaded15%RBS@608F.14.4RulingSpanConceptTransmissionlinesarenormallydesignedinlinesectionswitheachendofthelinesectionterminatedbyastrainstructurethatallowsnolongitudinal(alongtheline)movementoftheconductor(Winkelman,1959).Structureswithineachlinesectionaretypicallysuspensionstructuresthatsupporttheconductorvertically,butallowfreemovementoftheconductorattachmentpointeitherlongitudinallyortransversely.14.4.1TensionDifferencesforAdjacentDeadEndSpansTable14.11containsinitialandnalsagtensiondatafora700ftanda1000ftdeadendspanwhenaDrakeACSRconductorisinitiallyinstalledtothesame6300lbtensionlimitsat608F.Notethatthe2006byTaylorFrancisGroup,LLC.23.TABLE14.11TypicalSagandTensionData795kcmilType16ACSR=SD,300and1000ftSpansConductor:Drake795kcmilType16ACSR=SDSpan300ftArea0.7261in.2CreepisafactorNESCHeavyLoadingDistrictFinalInitialWind,Weight,Tension,Tension,Temp,8FIce,in.lb=ft2K,lb=ftlb=ftSag,ftlbSag,ftlb300.009.000.051.4091.5999801.3112373300.000.000.001.0931.2697761.0311976600.000.000.001.0931.6076881.1610589a900.000.000.001.0932.1258061.3491591200.000.000.001.0932.6945721.5977131670.000.000.001.0933.1139572.2255452120.000.000.001.0933.5834353.173877aDesigncondition.Conductor:Drake795kcmilType16ACSR=SDSpan1000ftArea0.7261in.2CreepisafactorNESCHeavyLoadingDistrictFinalInitialWind,Weight,Tension,Tension,Temp,8FIce,in.lb=ft2K,lb=ftlb=ftSag,ftlbSag,ftlb300.009.000.051.40917.211025015.1011676300.000.000.001.09315.22898812.6910779600.000.000.001.09317.217950a13.989780900.000.000.001.09319.26710815.4488611200.000.000.001.09321.31642817.0380371670.000.000.001.09324.27564719.6969542120.000.000.001.09325.62535222.326136aDesigncondition.Note:Calculationsbasedon:(1)NESCLightLoadingDistrict.(2)TensionLimits:a.InitialLoaded60%RBS@308Fb.InitialUnloaded25%RBS@608Fc.FinalUnloaded15%RBS@608F.differencebetweenthe

initialandnallimitsat608Fisapproximately460lb.Eventheinitialtension(equalat608F)differsbyalmost900lbat208Fand600lbat1678F.14.4.2TensionEqualizationbySuspensionInsulatorsAtatypicalsuspensionstructure,theconductorissupportedverticallybyasuspensioninsulatorassembly,butallowedtomovefreelyinthedirectionoftheconductoraxis.Thisconductormovementispossibleduetoinsulatorswingalongtheconductoraxis.Changesinconductortensionbetweenspans,causedbychangesintemperature,load,andtime,arenormallyequalizedbyinsulatorswing,eliminatinghorizontaltensiondifferencesacrosssuspensionstructures.14.4.3RulingSpanCalculationSagtensioncanbefoundforaseriesofsuspensionspansinalinesectionbyuseoftherulingspanconcept(Ehrenberg,1935Winkelman,1959).Therulingspan(RS)forthelinesectionisdenedbythefollowingequation:sS13S23Sn3RS(14:26)S1S2Sn2006byTaylorFrancisGroup,LLC.24.whereRSRulingspanforthelinesectioncontainingnsuspensionspansS1SpanlengthofrstsuspensionspanS2SpanlengthofsecondsuspensionspanSnSpanlengthofnthsuspensionspanAlternatively,agenerallysatisfactorymethodforestimatingtherulingspanistotakethesumoftheaveragesuspensionspanlengthplustwothirdsofthedifferencebetweenthemaximumspanandtheaveragespan.However,somejudgmentmustbeexercisedinusingthismethodbecausealargedifferencebetweentheaverageandmaximumspanmaycauseasubstantialerrorintherulingspanvalue.Asdiscussed,suspensionspansaresupportedbysuspensioninsulatorsthatarefreetomoveinthedirectionoftheconductoraxis.Thisfreedomofmovementallowsthetensionineachsuspensionspantobeassumedtobethesameandequaltothatcalculatedfortherulingspan.Thisassumptionisvalidforthesuspensionspansandrulingspanunderthesameconditionsoftemperatureandload,forbothinitialandnalsags.Forlevelspans,sagineachsuspensionspanisgivenbytheparabolicsagequation:w(Si2)Di(14:27)8HRSwhereDisagintheithspanSispanlengthoftheithspanHRStensionfromrulingspansagtensioncalculationsThesaginlevelsuspensionspansmayalsobecalculatedusingtheratio:whereDRSsaginrulingspanSuspensionspansvaryinlength,thoughtypicallynotoveralargerange.Conductortemperatureduringsaggingvariesoverarangeconsiderablysmallerthanthatusedforlinedesignpurposes.Ifthesaginanysuspensionspanexceedsapproximately5%ofthespanlength,acorrectionfactorshouldbeaddedtothesagsobtainedfromtheaboveequationorthesagshouldbecalculatedusingcatenaryEq.(14.29).Thiscorrectionfactormaybecalculatedasfollows:wCorrectionD2(14:28)6HwhereDsagobtainedfromparabolicequationwweightofconductor,lb=ftHhorizontaltension,lbThecatenaryequationforcalculatingthesaginasuspensionorstringingspanis:HSwSagcosh1(14:29)w2HwhereSspanlength,ftHhorizontaltension,lbwresultantweight,lb=ft14.4.4StringingSagTablesConductorsaretypicallyinstalledinlinesectionlengthsconsistingofmultiplespans.Theconductorispulledfromtheconductorreelatapointnearonestrainstructureprogressingthroughtravelersattachedtoeachsuspensionstructuretoapointnearthenextstrainstructure.Afterstringing,the2006byTaylorFrancisGroup,LLC.25.TABLE14.12TypicalSagandTensionData795kcmilType16ACSR=SD,300and1000ftSpanConductor:Drake795kcmilType16ACSR=SDSpan300ftArea0.7261in.2CreepisafactorNESCHeavyLoadingDistrictFinalInitialWind,Weight,Tension,Tension,Temp,8FIce,in.lb=ft2K,lb=ftlb=ftSag,ftlbSag,ftlb00.504.000.302.4862.19127742.0313757320.500.000.002.0742.25103771.9012256200.000.000.001.093.9113477.871415600.000.000.001.0931.0311962.9213305300.000.000.001.0931.2697761.0311976600.000.000.001.0931.6076881.1610589a900.000.000.001.0932.1258061.3491591200.000.000.001.0932.6945721.5977131670.000.000.001.0933.1139572.2255452120.000.000.001.0933.5834353.173877aDesignConditionConductor:Drake795kcmilType16ACSR=SDSpan1000ftArea0.7261in.2CreepisafactorNESCHeavyLoadingDistrictFinalInitialWind,Weight,Tension,Tension,Temp,8FIce,in.lb=ft2K,lb=ftlb=ftSag,ftlbSag,ftlb00.504.000.302.48620.651508920.3615299320.500.000.002.07420.611260719.3213445200.000.000.001.09312.201120510.891255200.000.000.001.09313.351024411.5611832300.000.000.001.09315.22898812.6910779600.000.000.001.09317.217950a13.989780900.000.000.001.09319.26710815.4488611200.000.000.001.09321.31642817.0380371670.000.000.001.09324.27564719.6969542120.000.000.001.09325.62535222.326136aDesigncondition.Note:Calculationsbasedon:(1)NESCHeavyLoadingDistrict.(2)TensionLimits:a.InitialLoaded60%RBS@08Fb.InitialUnloaded25%RBS@608FFinalUnloaded15%RBS@608F.conductortensionisincreaseduntilthesaginoneormoresuspensionspansreachestheappropriatestringingsagsbasedontherulingspanforthelinesection.Thecalculationofstringingsagsisbasedontheprecedingsagequation.Table14.13showsatypicalstringingsag

tablefora600ftrulingspanofDrakeACSRwithsuspensionspansrangingfrom400to700ftandconductortemperaturesof201008F.Allvaluesinthisstringingtablearecalculatedfromrulingspaninitialtensions,showninTable14.12usingtheparabolicsagequation.14.5LineDesignSagTensionParametersInlayingoutatransmissionline,therststepistosurveytherouteanddrawupaplanproleoftheselectedrightofway.Theplanproledrawingsserveanimportantfunctioninlinkingtogether2006byTaylorFrancisGroup,LLC.26.TABLE14.13TypicalSagandTensionData795kcmil37StrandAACArbutus,300and1000ftSpansConductor:Arbutus795kcmil37StrandsAACSpan300ftArea0.6245in.2CreepisafactorNESCHeavyLoadingDistrictFinalInitialWind,Weight,Tension,Tension,Temp,8FIce,in.lb=ft2K,lb=ftlb=ftSag,ftlbSag,ftlb300.009.000.051.1223.5635462.824479300.000.000.000.7462.9128892.064075600.000.000.000.7464.032085a2.802999900.000.000.000.7465.1316383.7922151200.000.000.000.7466.1313724.8617321670.000.000.000.7467.5111226.3813192120.000.000.000.7468.659757.651101aDesigncondition.Conductor:Arbutus795kcmil37StrandsAACSpan1000ftArea0.6245in.2CreepisafactorNESCHeavyLoadingDistrictFinalInitialWind,Weight,Tension,Tension,Temp,8FIce,in.lb=ft2K,lb=ftlb=ftSag,ftlbSag,ftlb300.009.000.051.12244.50318542.853305300.000.000.000.74643.66215841.712258600.000.000.000.74645.242085a43.322175900.000.000.000.74646.76201844.8921011200.000.000.000.74648.24195846.4220331670.000.000.000.74650.49187348.7219392120.000.000.000.74652.55180150.841860aDesigncondition.Note:Calculationsbasedon:(1)NESCLightLoadingDistrict.(2)TensionLimits:a.InitialLoaded60%RBS@308Fb.InitialUnloaded25%RBS@608Fc.FinalUnloaded15%RBS@608F.thevariousstagesinvolvedinthedesignandconstructionoftheline.Thesedrawings,preparedbasedontheroutesurvey,showthelocationandelevationofallnaturalandmanmadeobstaclestobetraversedby,oradjacentto,theproposedline.Theseplanprolesaredrawntoscaleandprovidethebasisfortowerspottingandlinedesignwork.Oncetheplanproleiscompleted,oneormoreestimatedrulingspansforthelinemaybeselected.Basedontheseestimatedrulingspansandthemaximumdesigntensions,sagtensiondatamaybecalculatedprovidinginitialandnalsagvalues.Fromthisdata,sagtemplatesmaybeconstructedtothesamescaleastheplanproleforeachrulingspan,andusedtographicallyspotstructures.14.5.1CatenaryConstantsThesaginarulingspanisequaltotheweightperunitlength,w,timesthespanlength,S,squared,dividedby8timesthehorizontalcomponentoftheconductortension,H.Theratioofconductorhorizontaltension,H,toweightperunitlength,w,isthecatenaryconstant,H=w.Forarulingspansagtensioncalculationusingeightloadingconditions,atotalof16catenaryconstantvaluescouldbedened,oneforinitialandnaltensionundereachloadingcondition.Catenaryconstantscanbedenedforeachloadingconditionofinterestandareusedinanyattempttolocatestructures.Sometypicalusesofcatenaryconstantsforlocatingstructuresaretoavoid2006byTaylorFrancisGroup,LLC.27.Min.SagMax.SagUpliftatTowerMin.SagMax.SagFIGURE14.9Conductoruplift.overloading,assuregroundclearanceissufcientatallpointsalongtherightofway,andminimizeblowoutorupliftundercoldweatherconditions.Todothis,catenaryconstantsaretypicallyfoundfor:(1)themaximumlinetemperature(2)heavyiceandwindloading(3)windblowoutand(4)minimumconductortemperature.Underanyoftheseloadingconditions,thecatenaryconstantallowssagcalculationatanypointwithinthespan.14.5.2WindSpanThemaximumwindspanofanystructureisequaltothedistancemeasuredfromcentertocenterofthetwoadjacentspanssupportedbyastructure.Thewindspanisusedtodeterminethemaximumhorizontalforceastructuremustbedesignedtowithstandunderhighwindconditions.Windspanisnotdependentonconductorsagortension,onlyonhorizontalspanlength.14.5.3WeightSpanTheweightspanofastructureisameasureofthemaximumverticalforceastructuremustbedesignedtowithstand.Theweightspanisequaltothehorizontaldistancebetweenthelowpointsandthevertexoftwoadjacentspans.Themaximumweightspanforastructureisdependentontheloadingconditionbeingaminimumforheavyiceandwindload.Whentheelevationsofadjacentstructuresarethesame,thewindandweightspansareequal.14.5.4UpliftatSuspensionStructuresUpliftoccurswhentheweightspanofastructureisnegative.Onsteeplyinclinedspans,thelowpointofsagmayfallbeyondthelowersupport.Thisindicatesthattheconductorintheuphillspanisexertinganegativeorupwardforceonthelowertower.Theamountofthisupwardforceisequaltotheweightoftheconductorfromthelowertowertothelowpointinthesag.Iftheupwardpulloftheuphillspanisgreaterthanthedownwardloadofthenextadjacentspan,actualupliftwillbecausedandtheconductorwillswingfreeofthetower.Thisusuallyoccursunderminimumtemperatureconditionsandmustbedealtwithbyaddingweightstotheinsulatorsuspensionstringorusingastrainstructure(Fig.14.9).14.5.5TowerSpottingGivensufcientlydetailedplanproledrawings,structureheights,wind=weightspans,catenarycon

stants,andminimumgroundclearances,structurelocationscanbechosensuchthatgroundclearanceis2006byTaylorFrancisGroup,LLC.28.maintainedandstructureloadsareacceptable.Thisprocesscanbedonebyhandusingasagtemplate,planproledrawing,andstructureheights,ornumericallybyoneofseveralcommercialprograms.14.6ConductorInstallationInstallationofabareoverheadconductorcanpresentcomplexproblems.Carefulplanningandathoroughunderstandingofstringingproceduresareneededtopreventdamagetotheconductorduringthestringingoperations.Theselectionofstringingsheaves,tensioningmethod,andmeasurementtechniquesarecriticalfactorsinobtainingthedesiredconductorssaggingresults.ConductorstringingandsaggingequipmentandtechniquesarediscussedindetailintheIEEEGuidetotheInstallationofOverheadTransmissionLineConductors,IEEEStd.5241992.Somebasicfactorsconcerninginstallationarecoveredinthissection.Becausetheterminologyusedforequipmentandinstallationproceduresforoverheadconductorsvariesthroughouttheutilityindustry,alimitedglossaryoftermsandequipmentdenitionsexcerptedfromIEEEStd.5241992isprovidedinthechapterappendix.AcompleteglossaryispresentedintheIEEEGuidetotheInstallationofOverheadTransmissionLineConductors.14.6.1ConductorStringingMethodsTherearetwobasicmethodsofstringingconductors,categorizedaseitherslackortensionstringing.Thereareasmanyvariationsofthesemethodsasthereareorganizationsinstallingconductors.Theselectedmethod,however,dependsprimarilyontheterrainandconductorsurfacedamagerequirements.14.6.1.1SlackorLayoutStringingMethodSlackstringingofconductorisnormallylimitedtolowervoltagelinesandsmallerconductors.Theconductorreel(s)isplacedonreelstandsorjackstandsatthebeginningofthestringinglocation.Theconductorisunreeledfromtheshippingreelanddraggedalongthegroundbymeansofavehicleorpullingdevice.Whentheconductorisdraggedpastasupportingstructure,pullingisstoppedandtheconductorplacedinstringingsheavesattachedtothestructure.Theconductoristhenreattachedtothepullingequipmentandthepullcontinuedtothenextstructure.Thisstringingmethodistypicallyusedduringconstructionofnewlinesinareaswheretherightofwayisreadilyaccessibletovehiclesusedtopulltheconductor.However,slackstringingmaybeusedforrepairormaintenanceoftransmissionlineswhereruggedterrainlimitsuseofpullingandtensioningequipment.Itisseldomusedinurbanareasorwherethereisanydangerofcontactwithhighvoltageconductors.14.6.1.2TensionStringingAtensionstringingmethodisnormallyemployedwheninstallingtransmissionconductors.Usingthismethod,theconductorisunreeledundertensionandisnotallowedtocontacttheground.Inatypicaltensionstringingoperation,travelersareattachedtoeachstructure.Apilotlineispulledthroughthetravelersandisused,inturn,topullinheavierpullingline.Thispullinglineisthenusedtopulltheconductorfromthereelsandthroughthetravelers.Tensioniscontrolledontheconductorbythetensionpulleratthepullingendandthebullwheeltensionretarderattheconductorpayoutendoftheinstallation.Tensionstringingispreferredforalltransmissioninstallations.Thisinstallationmethodkeepstheconductorofftheground,minimizingthepossibilityofsurfacedamageandlimitingproblemsatroadwaycrossings.Italsolimitsdamagetotherightofwaybyminimizingheavyvehiculartrafc.14.6.2TensionStringingEquipmentandSetupStringingequipmenttypicallyincludesbullwheelordrumpullersforbacktensioningtheconductorduringstringingandsaggingtravelers(stringingblocks)attachedtoeveryphaseconductorandshieldwireattachmentpointoneverystructureabullwheelorcrawlertractorforpullingtheconductorthroughtravelersandvariousotherspecialitemsofequipment.Figure14.10illustratesatypicalstringingandsaggingsetupforastringingsectionandtherangeofstringingequipmentrequired.2006byTaylorFrancisGroup,LLC.29.2006byTaylorFrancisGroup,LLC.SLYVIOUDPREAGGETORSDUCNOTE:CONDUCTORSTOANCHORS(1)CONDELETEDFORCLARITY17168172347D16Y8C17GUHENRED6WQUI1REBA620ITEONSN22416NYGUHENDSIIDWHEEDENR87SPAEMIDICESITRWUIREEQTGEQUIRR1816SPLGRIDNROPEWHEIREDSYN.12REQU8211922S9UNDGROOF810VELERSIDESOSSING97TRABOTHDCRION3RGIZSECT2216EENE241612101325SAG1411711ES6162MILIMUMNXMAETWEEER1yBAVELDS6GuHENEDTRROUNN15WQUIRGEWHUIREDREREQTELSIPULFIGURE14.10Tensionstringingequipmentsetup.30.FIGURE14.11Basketgrippullingdevice.Provisionforconductorsplicingduringstringingmustbemadeattensionsiteormidspansitestoavoidpullingsplicesthroughthetravelers.Duringthestringingoperation,itisnecessarytousepropertoolstogripthestrandsoftheconductorevenlytoavoiddamagingtheouterlayerofwires.Twobasictypesorcategoriesofgripsarenormallyusedintransmissionconstruction.Therstisatypeofgripreferredtoasapocketbook,suitcase,bolted,etc.,thathingestocompletelysurroundtheconductorandincorporatesabailforattachingtothepullingline.ThesecondtypeissimilartoaChinesengergripandis

oftenreferredtoasabasketorKellemgrip.Suchagrip,showninFig.14.11,isoftenusedbecauseofitsexibilityandsmallsize,makingiteasilypulledthroughsheavesduringthestringingoperation.Whatevertypeofgrippingdeviceisused,aswivelshouldbeinstalledbetweenthepullinggripandpullinglineorrunningboardtoallowfreerotationofboththeconductorandthepullingline.Atravelerconsistsofasheaveorpulleywheelenclosedinaframetoallowittobesuspendedfromstructuresorinsulatorstrings.Theframemusthavesometypeoflatchingmechanismtoallowinsertionandremovaloftheconductorduringthestringingoperation.Travelersaredesignedforamaximumsafeworkingload.Alwaysensurethatthissafeworkingloadwillnotbeexceededduringthestringingoperation.Sheavesareoftenlinedwithneopreneorurethanematerialstopreventscratchingofconductorsinhighvoltageapplicationshowever,unlinedsheavesarealsoavailableforspecialapplications.(inches)(cm)10040MinimumSheaveDiameter(Ds)atBaseofGroove35(inches)MinimumRadius(Rg)atBaseofGroove(cm)Rg,4Layer7530Rg,1or2Layer1.43.5Rg,3Layer1.23251.02.5Min.Rg50200.8215SheaveDiameter0.61.5GrooveRadius25100.411.01.52.02.5(inches)2.53.7556.25(cm)ConductorDiameter(Dc)FIGURE14.12Recommendedminimumsheavedimensions.2006byTaylorFrancisGroup,LLC.31.Travelersusedintensionstringingmustbefreerollingandcapableofwithstandinghighrunningorstaticloadswithoutdamage.Propermaintenanceisessential.Veryhighlongitudinaltensionloadscandevelopontransmissionstructuresifatravelershouldfreezeduringtensionstringing,possiblycausingconductorand=orstructuredamage.Signicantlevelsofrotationresistancewillalsoyieldtensiondifferencesbetweenspans,resultinginincorrectsag.Properselectionoftravelersisimportanttoassurethattravelersoperatecorrectlyduringtensionstringingandsagging.Thesheavediameterandthegrooveradiusmustbematchedtotheconductor.Figure14.12illustratestheminimumsheavediameterfortypicalstringingandsaggingoperations.Largerdiametersheavesmayberequiredwhereparticularlysevereinstallationconditionsexist.14.6.3SaggingProcedureItisimportantthattheconductorsbeproperlysaggedatthecorrectstringingtensionforthedesignrulingspan.Aseriesofseveralspans,alinesection,isusuallysaggedinoneoperation.Toobtainthecorrectsagsandtoinsurethesuspensioninsulatorshangvertically,thehorizontaltensioninallspansmustbeequal.Figures14.13through14.18depicttypicalparabolicmethodsandcomputationsrequiredPlumpClippingClippingPlumpMarkOffsetOffsetMarkConductorinTravelersConductorinSuspensionClampsH1H0SagCorrectionDeadend(Typ.)SnubStructureH2SeeDetailAForVectorDiagram(ZeroClippingOffset)H0OfConductorTensionAtTravelerSuspensionY1SeeDetailBForVectorDiagramOfConductorTensionAtH3SuspensionClampH0Y2Suspension(Y2Y1)H4H0SuspensionH0VECTORDIAGRAMH5SuspensionDetailADetailBGuysH3H4H0H0SuspensionVVSnubStructureV1V1TV1V1(ZeroClippingOffset)TT1VVHorizontalTensionsH0AreEqualNOTE:H3=H4+W(Y2Y1)SaggingTensionsTT1AreUnequalW=ConductorWtStringingTensionsTAreEqualPerUnitLengthFIGURE14.13Clippingoffsetillustration.2006byTaylorFrancisGroup,LLC.32.4000C203500BSAG25S30002500A3035200040FormulasforEquivalentSpanLengthEquiv.DeadendSpan=2CA45Equiv.SuspensionSpan=AC5015002(AddtoHoriz.SpacingtoObtainEquivalentSpanLength)3604VerticalSpacingofSupports(B)7051000HorizontalSpacingofSupports(A)80900EquivalentSpanCorrection2.590800101001570020560025307.540101505005012.5601580204001002520015037.52002025030025062.530075300ForspansbetweenasuspensionanddeadendSuspensiontower,usesuspensionspancorrection.350DeadendSpanExample:AssumespanwithA=1000ft,Span200B=100ftifdeadendspan,correction=10ft(seeabove).Ifsuspensionspan,correction=4002.5ft(seeabove).Equivalentspan=1000ft+correction.Readchartsagforequivalentspanlength.500Sagisbasedonparabolicfunctions.Sagisbasedonparabolicfunctions.Ifsagexceeds5%ofspan,donotIfsagexceeds5%ofspan,donotusethischart.usethischart.100FIGURE14.14Nomographfordetermininglevelspanequivalentsofnonlevelspans.forsaggingconductors.Factorsthatmustbeconsideredwhensaggingconductorsarecreepelongationduringstringingandprestressingoftheconductor.Creepelongationduringstringing:Uponcompletionofconductorstringing,atimeofuptoseveraldaysmayelapsebeforetheconductoristensionedtodesignsag.Sincetheconductortensionduringthestringingprocessisnormallywellbelowtheinitialsaggingtension,andbecausetheconductorremainsinthestringingsheavesforonlyafewdaysorless,anyelongationduetocreepisneglected.The2006byTaylorFrancisGroup,LLC.33.ProcedureExamples10001900Determinefromnomographthecontrolfactorof800transitsetupusedinsaggingtheconductorExample1:Whensaggingbycalculatedtarget700(seeexamplesontheright).setting.(SeeFig.217)600FormostaccurateresultsinsaggingtheconductorT=40.09B=60.0500thisvalueof

controlfactorshouldnotbebelowthe2S=49.1curveshownbelow.400t=59.12Inallcasesacontrolfactorof1.00isideal(ForT=t).3300A=1400.04(Tt)=19.1291.00ControlFactorS=49.12005Controlfactor=0.99(Fromnomograph).90ControlFactorShouldNotLie6.80inShadedAreaExample2:Whensaggingbyhorizontallineofsight.78(SeeFig.218).7000.10.20.30.40.50.60.7910010B=60.0990B/AS=49.19T+B80T70B.M6001020A=1400.09403050(Tt)=Bforhorizontallineofsight60502070=60.0ControlFactor4080S=49.190(Tt)30Controlfactor=0.91(Fromnomograph)30ConductorSag(S)954020995060Example3:Whensaggingbycalculatedangleofsight.(SeeFig.218)7080B=60.0T=59.129B9010S1100S=49.199ST=40.08(Angleofsight)7TA=1400.06(Tt)=Atanf(+B)_5200f=Angleofsight.+f=Whenangleisabovehorizontal.4f=Whenangleisbelowhorizontal.AB=Verticaldistancebetweenpointsofsupport3003+B=Whensupportaheadishigher.B=Whensupportaheadislower.400S1S1(Tt)22ControlFactor===1Inexample,f=+184021ortanf=+0.02920SS(4S)2500A=1400.0600T=Distancetransitissetbelowconductorsupport.B=+60.0700t=Correspondingdistancetargetissetbelowoppositesupport.S=49.1S=Conductorsagdeterminedfromstringingcharts.800Then(Tt)=1400.0(+0.02920)(+60.0)=19.12S1=Correspondingsagofpointoftangencyofconductorandlineofsight.90011000Controlfactor=0.99(Fromnomograph)S=ChangeofsagsS1=ChangeofsagS1Sagisbasedonparabolicfunctions.Ifsagexceeds5%ofspan,donotusethischart.FIGURE14.15Nomographfordeterminingcontrolfactorforconductorsagging.conductorshouldbesaggedtotheinitialstringingsagslistedinthesagtables.However,iftheconductortensionisexcessivelyhighduringstringing,ortheconductorisallowedtoremainintheblocksforanextendedperiodoftime,thenthecreepelongationmaybecomesignicantandthesaggingtablesshouldbecorrectedpriortosagging.Creepisassumedexponentialwithtime.Thus,conductorelongationduringtherstdayundertensionisequaltoelongationoverthenextweek.Usingcreepestimationformulas,thecreepstraincanbeestimatedandadjustmentsmadetothestringingsagtablesintermsofanequivalenttemperature.Also,shouldthisbecomeaconcern,SouthwiresWireandCableTechnologyGroupwillbehappytoworkwithyoutosolvetheproblem.Prestressingconductor:Prestressingissometimesusedtostabilizetheelongationofaconductorforsomedenedperiodoftime.Theprestressingtensionisnormallymuchhigherthantheunloadeddesigntensionforaconductor.Thedegreeofstabilizationisdependentuponthetimemaintainedatthe2006byTaylorFrancisGroup,LLC.34.BtSTf(Angleofsight)AT+Bt_METHOD1:Tanf=AB+2TS(2+M)METHOD2:Tanf=Af=Angleofsight+fWhenangleisabovehorizontalfWhenangleisbelowhorizontalt=Verticaldistancebelowsupporttolineofsight.(SeeFig.217).T=Verticaldistancebelowsupportfortransit.S=SagA=HorizontaldistancebetweenpointsofsupportobtainedfromstructurelistorplanprofileB=Verticaldistancebetweenpointsofsupportobtainedfromplanprofile,towersitedatasheetsorfieldmeasurement.+Bwhensupportaheadishigher.Bwhensupportaheadislower.M=DeterminedfromcureonFig.217.EXAMPLES:Given:A=1400.0S=49.1@608FB=+60.0S=51.2@908FT=40.0T=59.12@608FT=63.76@908FMETHOD1METHOD2T+Bt_B+2TS(2+M)Tanf=Tanf=AA40.060.059.1260.0+(40.0)(2)(49.1)(2+0.019)Tanf608F==0.02920Tanf608F==0.029191400.01400.0f608F=+184021f608F=+18401940.060.063.7660.0+(40.0)(2)(51.2)(2+0.027)Tanf908F==0.02589Tanf908F==0.025871400.01400.0f908F=+182859f908F=+1828555Changeinangleffor58F=(184021182859)5(30)=08154Changeinangleffor58F=(184019182855)(30)=08154Sagisbasedonparabolicfunctions.Ifsagexceeds5%ofspan,donotusethischart.FIGURE14.16Conductorsaggingbycalculatedangleofsight.prestresstension.Afterprestressing,thetensionontheconductorisreducedtostringingordesigntensionlimits.Atthisreducedtension,thecreeporplasticelongationoftheconductorhasbeenslowed,reducingthepermanentelongationduetostrainandcreepforadenedperiodoftime.Bytensioningaconductortolevelsapproaching50%ofitsbreakingstrengthfortimesontheorderofaday,creepelongationwillbetemporarilyhalted(Cahill,1973).Thissimpliesconcernsaboutcreepduringsubsequentinstallationbutpresentsbothequipmentandsafetyproblems.14.6.3.1SaggingbyStopwatchMethodAmechanicalpulseimpartedtoatensionedconductormovesataspeedproportionaltothesquarerootoftensiondividedbyweightperunitlength.Byinitiatingapulseonatensionedconductorandmeasuringthetimerequiredforthepulsetomovetothenearesttermination,thetension,andthus2006byTaylorFrancisGroup,LLC.35.EXAMPLESGiven:TBA=1400.0SB=60.0T=40.0S=49.1@608FtS=51.2@908FMETHOD1t=(2ST)2AT=6.325METHOD1:t=(2ST)2S608F=7.007METHOD2:t=2ST+SM2S608F=14.014t608F=59.12t=Verticaldistancebelowsupportfortarget.T=Verticaldistancebelowsupportfortransit.S=Sag.S908F=7.155A=Horizontaldistancebetweenstructuresobtainedfrom

structurelistorplanprofile.2S908F=14310B=Verticaldistancebetweenpointsofsupportobtainedfromplanprofile,towersitedatasheetsorfieldmeasurement.t908F=63.76M=Determinedfromcurvebelow.Changeintfor58F=(63.7659.12)(30)=0.775CURVEFORDETERMININGVALUEOFM0.14ForfindingvalueoftargetsettingtseeMethodsMETHOD212,orangleofsightf(SeeFig.216).t=2ST+SMRatioR=(T/S).0.12M=2+2(T/S)4T/ST/S608F=0.815M608F=0.019ForcheckingvalueofsagS(seeFig.219).2S608F=98.20.10RatioR=(T/t).t608F=59.13M=2+2(T/t)4T/tT/S908F=0.781M908F=0.0270.082S908F=102.4FactorMt908F=63.7850.06Changeintfor58F=(63.7659.13)(30)=0.780.040.02Sagisbasedonparabolicfunctions.Ifsagexceeds5%ofspan,donotusethischart.0.000.00.60.81.01.21.41.6RatioRFIGURE14.17Conductorsaggingbycalculatedtargetmethod.thesagoftheconductor,canbedetermined.Thisstopwatchmethod(OverendandSmith)hascomeintowideuseevenforlongspansandlargeconductors.Theconductorisstruckasharpblownearonesupportandthestopwatchisstartedsimultaneously.Amechanicalwavemovesfromthepointwheretheconductorwasstrucktothenextsupportpointatwhichitwillbepartiallyreected.Iftheinitiatingblowissharp,thewavewilltravelupanddownthespanmanytimesbeforedyingout.TimesagtablessuchastheoneshowninTable14.14areavailablefrommanysources.Speciallydesignedsaggingstopwatchesarealsoavailable.Thereectedwavecanbedetectedbylightlytouchingtheconductorbuttheprocedureismorelikelytobeaccurateifthewaveisbothinitiatedanddetectedwithalightropeovertheconductor.Normally,thetimeforthereturnofthe3rdor5thwaveismonitored.Traditionally,atransitsaggingmethodhasbeenconsideredtobemoreaccurateforsaggingthanthestopwatchmethod.However,manytransmissionlineconstructorsusethestopwatchmethodexclusively,evenwithlargeconductors.2006byTaylorFrancisGroup,LLC.36.BT+BST(LevelSight)B.M1.0AT=S(1B/4S)2=SKT=Verticaldistanceoftransitbelowlowersupportfortakinglevelsight.A=Horizontaldistancebetweenpointsofsupportobtainedfromstructurelistofplanprofile.0.9B=Verticaldistancebetweenpointsofsupportobtainedfromplanprofile,towersitedatasheetsorfieldmeasurement.S=Sag.K=(1B/4s)2Determinedfromcurvebelow.EXAMPLEA=1400.00.8B=60.0S=49.1@608FS=51.2@908FB/S=60.0/49.1=1.22@608FB/S=60.0/51.2=1.17@908FK=0.482@608FK=0.501@908F0.7T=(49.1)(0.482)=23.66@608FT=(51.2)(0.501)=25.65@908F5()ChangeinTfor58F=(25.6523.66)30=0.330.6KFactor0.50.40.3Formostaccurateresults,usethatpartofcurvedrawninsolidline.0.20.10.00.00.51.01.52.02.53.03.54.0Ratio(B/S)Sagisbasedonparabolicfunctions.Ifsagexceeds5%ofspan,donotusethischart.FIGURE14.18Conductorsaggingbyhorizontallineofsight.14.6.3.2SaggingbyTransitMethodsIEEEGuideStd.5241993liststhreemethodsofsaggingconductorwithatransit:CalculatedAngleofSight,CalculatedTargetMethod,andHorizontalLineofSight.Themethodbestsuitedtoaparticularlinesaggingsituationmayvarywithterrainandlinedesign.2006byTaylorFrancisGroup,LLC.37.TABLE14.14TypicalSagandTensionData795kcmil37StrandAACArbutus,300and1000ftSpansConductor:Arbutus795kcmil37StrandsAACSpan300ftArea0.6245in.2CreepisafactorFinalInitialWind,Weight,Tension,Tension,Temp,8FIce,in.lb=ft2K,lb=ftlb=ftSag,ftlbSag,ftlb00.504.000.302.1253.9760333.756383320.500.000.001.6964.3543863.785053200.000.000.000.7461.5853191.39605500.000.000.000.7462.0042081.595268300.000.000.000.7462.9128892.064075600.000.000.000.7464.032085a2.802999900.000.000.000.7465.1316383.7922151200.000.000.000.7466.1313724.8617321670.000.000.000.7467.5111226.3813192120.000.000.000.7468.659757.651101aDesigncondition.Conductor:Arbutus795kcmil37StrandsAACSpan1000ftArea0.6245in.2CreepisafactorNESCHeavyLoadingDistrictFinalInitialWind,Weight,Tension,Tension,Temp,8FIce,in.lb=ft2K,lb=ftlb=ftSag,ftlbSag,ftlb00.504.000.302.12545.1159.5344.506033320.500.000.001.69645.80467944.684794200.000.000.000.74640.93230038.89241800.000.000.000.74642.04224040.032350300.000.000.000.74643.66215841.712258600.000.000.000.74645.242085a43.322175900.000.000.000.74646.76201844.8921011200.000.000.000.74648.24195846.4220331670.000.000.000.74650.49187348.7219392120.000.000.000.74652.55180150.841860aDesigncondition.Note:Calculationsbasedon:(1)NESCLightLoadingDistrict.(2)TensionLimits:a.InitialLoaded60%RBS@08Fb.InitialUnloaded25%RBS@608Fc.FinalUnloaded15%RBS@608F.14.6.3.3SaggingAccuracySaggingaconductorduringconstructionofanewlineorinthereconductoringofaoldlineinvolvesmanyvariablesthatcanleadtoasmalldegreeoferror.IEEEStd.5241993suggeststhatallsagsbewithin6in.ofthestringingsagvalues.However,asidefrommeasurementerrorsduringsagging,errorsinterrainmeasurementandvariationsinconductorproperties,loadingconditions,andhardwareinstallationhaveledsomeutilitiestoallowupto3ftofmargininadditiontotherequiredminimumgroundclearance.14.6.3.4ClippingOffsetsIftheconductoristobesaggedinaseriesofsuspensionspans

wherethespanlengthsarereasonablycloseandwheretheterrainisreasonablylevel,thentheconductorissaggedusingconventionalstringingsagtablesandtheconductorissimplyclippedintosuspensionclampsthatreplacethetravelers.Ifthe2006byTaylorFrancisGroup,LLC.38.tBSTfAT+t2METHOD1:S=()2BttMMETHOD2:S=+228S=Sagt=Verticaldistancebelowsupporttolineofsight.=T+BAtanfwhenanglefisabovehorizontal._=T+B+Atanfwhenanglefisbelowhorizontal._T=Verticaldistancebelowsupportfortransit.B=Verticaldistancebetweenpointsofsupportobtaniedfromplanprofile,towersitedatasheetsorfieldmeasurement.+Bwhensupportaheadishigher.Bwhensupportaheadislower.A=Horizontaldistancebetweenpointsofsupportobtainedfromstructurelistorplanprofilef=AngleofsightM=DeterminedfromcureonFig.2.17.EXAMPLESGiven:A=1400.0T=40.0B=60.0f=+184021@608F(FieldMeasured)METHOD1METHOD2Note:WhenusingMethod2,value,Tshouldliebetween3/4S4/3ST+t2S=()BttM2S=+228t=40.0+60.01400.0tan184021t=59.12=59.12t/2=29.56t=7.689T/2=20.0M=0.061T=6.325(59.12)(0.061)S608F=49.1S608F=20.0+29.568S608F=49.1Sagisbasedonparabolicfunctions.ifsagexceeds5%ofspan,donotusethischart.FIGURE14.19ConductorsaggingforcheckingsagS.conductoristobesaggedinaseriesofsuspensionspanswherespanlengthsvarywidelyormorecommonly,wheretheterrainissteep,thenclippingoffsetsmayneedtobeemployedinordertoyieldverticalsuspensionstringsafterinstallation.ClippingoffsetsareillustratedinFig.14.19,showingaseriesofsteeplyinclinedspansterminatedinasnubstructureatthebottomandadeadendstructureatthetop.Thevectordiagramillustratesabalanceoftotalconductortensioninthetravelersbutanimbalanceinthehorizontalcomponentoftension.2006byTaylorFrancisGroup,LLC.39.14.7DeningTermsBlockAdevicedesignedwithoneormoresinglesheaves,awoodormetalshell,andanattachmenthookorshackle.Whenropeisreevedthroughtwoofthesedevices,theassemblyiscommonlyreferredtoasablockandtackle.Asetof4sreferstoablockandtacklearrangementutilizingtwo4inchdoublesheaveblockstoobtainfourloadbearinglines.Similarly,asetof5sorasetof6sreferstothesamenumberofloadbearinglinesobtainedusingtwo5inchortwo6inchdoublesheaveblocks,respectively.Synonyms:setof4s,setof5s,setof6s.BullwheelAwheelincorporatedasanintegralpartofabullwheelpullerortensionertogeneratepullingorbrakingtensiononconductorsorpullinglines,orboth,throughfriction.Apullerortensionernormallyhasoneormorepairsarrangedintandemincorporatedinitsdesign.Thephysicalsizeofthewheelswillvaryfordifferentdesigns,but17in.(43cm)facewidthsanddiametersof5ft(150cm)arecommon.Thewheelsarepowerdrivenorretardedandlinedwithsingleormultiplegrooveneopreneorurethanelinings.Frictionisaccomplishedbyreevingthepullinglineorconductoraroundthegrooveofeachpair.ClippinginThetransferringofsaggedconductorsfromthetravelertotheirpermanentsuspensionpositionsandtheinstallingofthepermanentsuspensionclamps.Synonyms:clamping,clipping.ClippingoffsetAcalculateddistance,measuredalongtheconductorfromtheplummarktoapointontheconductoratwhichthecenterofthesuspensionclampistobeplaced.Whenstringinginroughterrain,clippingoffsetmayberequiredtobalancethehorizontalforcesoneachsuspensionstructure.Grip,conductorAdevicedesignedtopermitthepullingofconductorwithoutsplicingonttings,eyes,etc.Itpermitsthepullingofacontinuousconductorwherethreadingisnotpossible.Thedesignsofthesegripsvaryconsiderably.GripssuchastheKlein(Chicago)andCrescentutilizeanopensidedrigidbodywithopposingjawsandswinglatch.Inadditiontopullingconductors,thistypeiscommonlyusedtotensionguysand,insomecases,pullwirerope.Thedesignofthecomealong(pocketbook,suitcase,fourbolt,etc.)incorporatesabailattachedtothebodyofaclampwhichfoldstocompletelysurroundandenvelopetheconductor.Boltsarethenusedtoclosetheclampandobtainagrip.Synonyms:buffalo,Chicagogrip,comealong,Crescent,fourbolt,grip,Klein,pocketbook,sevenbolt,sixbolt,slipgrip,suitcase.Line,pilotAlightweightline,normallysyntheticberrope,usedtopullheavierpullinglineswhichinturnareusedtopulltheconductor.Pilotlinesmaybeinstalledwiththeaidofngerlinesorbyhelicopterwhentheinsulatorsandtravelersarehung.Synonyms:leadline,leader,Pline,strawline.Line,pullingAhighstrengthline,normallysyntheticberropeorwirerope,usedtopulltheconductor.However,onreconstructionjobswhereaconductorisbeingreplaced,theoldconductoroftenservesasthepullinglineforthenewconductor.Insuchcases,theoldconductormustbecloselyexaminedforanydamagepriortothepullingoperations.Synonyms:bullline,hardline,lightline,sockline.Puller,bullwheelAdevicedesignedtopullpullinglinesandconductorsduringstringingoperations.Itnormallyincorporatesoneormorepairsofurethaneorneoprenelined,powerdriven,singleormultiplegroovebullwheelswhereeachpairisarrangedintandem.Pullingisaccomplishedbyfrictiongeneratedagainstthepullinglinewhichisreevedaroundthegroovesofapairofthebullwheels.Thepullerisusuallyequippedwithitsownenginewhichdrivesthebullwheelsmechanically,

hydraulically,orthroughacombinationofboth.Someofthesedevicesfunctionaseitherapullerortensioner.Synonym:puller.Puller,drumAdevicedesignedtopullaconductorduringstringingoperations.Itisnormallyequippedwithitsownenginewhichdrivesthedrummechanically,hydraulically,orthroughacombinationofboth.Itmaybeequippedwithsyntheticberropeorwireropetobeusedasthe2006byTaylorFrancisGroup,LLC.40.pullingline.Thepullinglineispayedoutfromtheunit,pulledthroughthetravelersinthesagsectionandattachedtotheconductor.Theconductoristhenpulledinbywindingthepullinglinebackontothedrum.Thisunitissometimesusedwithsyntheticberropeactingasapilotlinetopullheavierpullinglinesacrosscanyons,rivers,etc.Synonyms:hoist,singledrumhoist,singledrumwinch,tugger.Puller,reelAdevicedesignedtopullaconductorduringstringingoperations.Itisnormallyequippedwithitsownenginewhichdrivesthesupportingshaftforthereelmechanically,hydraulically,orthroughacombinationofboth.Theshaft,inturn,drivesthereel.Theapplicationofthisunitisessentiallythesameasthatforthedrumpullerpreviouslydescribed.Someofthesedevicesfunctionaseitherapullerortensioner.ReelstandAdevicedesignedtosupportoneormorereelsandhavingthepossibilityofbeingskid,trailer,ortruckmounted.Thesedevicesmayaccommodateropeorconductorreelsofvaryingsizesandareusuallyequippedwithreelbrakestopreventthereelsfromturningwhenpullingisstopped.Theyareusedforeitherslackortensionstringing.Thedesignationofreeltrailerorreeltruckimpliesthatthetrailerortruckhasbeenequippedwithareelstand(jacks)andmayserveasareeltransportorpayoutunit,orboth,forstringingoperations.Dependinguponthesizesofthereelstobecarried,thetransportingvehiclesmayrangefromsingleaxletrailerstosemitruckswithtrailershavingmultipleaxles.Synonyms:reeltrailer,reeltransporter,reeltruck.RunningboardApullingdevicedesignedtopermitstringingmorethanoneconductorsimultaneouslywithasinglepullingline.Fordistributionstringing,itisusuallymadeoflightweighttubingwiththeforwardendcurvedgentlyupwardtoprovidesmoothtransitionoverpolecrossarmrollers.Fortransmissionstringing,thedeviceiseithermadeofsectionshingedtransverselytothedirectionofpullorofahardnoserigiddesign,bothhavingaexiblependulumtailsuspendedfromtherear.Thiscongurationstopstheconductorsfromtwistingtogetherandpermitssmoothtransitionoverthesheavesofbundletravelers.Synonyms:alligator,bird,birdie,monkeytail,sled.SagsectionThesectionoflinebetweensnubstructures.Morethanonesagsectionmayberequiredinordertoproperlysagtheactuallengthofconductorwhichhasbeenstrung.Synonyms:pull,setting,stringingsection.Site,pullThelocationonthelinewherethepuller,reelwinder,andanchors(snubs)arelocated.Thissitemayalsoserveasthepullortensionsiteforthenextsagsection.Synonyms:reelsetup,tuggersetup.Site,tensionThelocationonthelinewherethetensioner,reelstandsandanchors(snubs)arelocated.Thissitemayalsoserveasthepullortensionsiteforthenextsagsection.Synonyms:conductorpayoutstation,payoutsite,reelsetup.SnubstructureAstructurelocatedatoneendofasagsectionandconsideredasazeropointforsaggingandclippingoffsetcalculations.Thesectionoflinebetweentwosuchstructuresisthesagsection,butmorethanonesagsectionmayberequiredinordertosagproperlytheactuallengthofconductorwhichhasbeenstrung.Synonyms:0structure,zerostructure.Tensioner,bullwheelAdevicedesignedtoholdtensionagainstapullinglineorconductorduringthestringingphase.Normally,itconsistsofoneormorepairsofurethaneorneoprenelined,powerbraked,singleormultiplegroovebullwheelswhereeachpairisarrangedintandem.Tensionisaccomplishedbyfrictiongeneratedagainsttheconductorwhichisreevedaroundthegroovesofapairofthebullwheels.Sometensionersareequippedwiththeirownengineswhichretardthebullwheelsmechanically,hydraulically,orthroughacombinationofboth.Someofthesedevicesfunctionaseitherapullerortensioner.Othertensionersareonlyequippedwithfrictiontyperetardation.Synonyms:retarder,tensioner.Tensioner,reelAdevicedesignedtogeneratetensionagainstapullinglineorconductorduringthestringingphase.Someareequippedwiththeirownengineswhichretardthesupportingshaftfor2006byTaylorFrancisGroup,LLC.41.thereelmechanically,hydraulically,orthroughacombinationofboth.Theshaft,inturn,retardsthereel.Someofthesedevicesfunctionaseitherapullerortensioner.Othertensionersareonlyequippedwithfrictiontyperetardation.Synonyms:retarder,tensioner.TravelerAsheavecompletewithsuspensionarmorframeusedseparatelyoringroupsandsuspendedfromstructurestopermitthestringingofconductors.Thesedevicesaresometimesbundledwithacenterdrumorsheave,andanothertraveler,andusedtostringmorethanoneconductorsimultaneously.Forprotectionofconductorsthatshouldnotbenickedorscratched,thesheavesareoftenlinedwithnonconductiveorsemiconductiveneopreneorwithnonconductiveurethane.Anyoneofthesematerialsactsasapaddingorcushionfortheconductorasitpassesoverthesheave.Travelergroundsmustbeusedwithlinedtravelersinordertoestablishanelectricalground.Synonyms:block,dolly,sheave,stringingblock,stringingsheave,stringingtraveler.WinderreelAdevicedesignedtoserveasa

recoveryunitforapullingline.Itisnormallyequippedwithitsownenginewhichdrivesasupportingshaftforareelmechanically,hydraulically,orthroughacombinationofboth.Theshaft,inturn,drivesthereel.Itisnormallyusedtorewindapullinglineasitleavesthebullwheelpullerduringstringingoperations.Thisunitisnotintendedtoserveasapuller,butsometimesservesthisfunctionwhereonlylowtensionsareinvolved.Synonyms:takeupreel.ReferencesCahill,T.,DevelopmentofLowCreepACSRConductor,WireJournal,July1973.Ehrenburg,D.O.,TransmissionLineCatenaryCalculations,AIEEPaper,CommitteeonPowerTransmissionDistribution,July1935.Fink,D.G.andBeaty,H.W.,StandardHandbookforElectricalEngineers,13thed.,McGrawHill.IEEEGuidetotheInstallationofOverheadTransmissionLineConductors,IEEEStandard5241993,IEEE,NewYork,1993.GraphicMethodforSagTensionCalculationsforACSRandOtherConductors,AluminumCompanyofAmerica,1961.MinimumDesignLoadsforBuildingsandOtherStructures,AmericanSocietyofCivilEngineersStandard,ASCE788.NationalElectricalSafetyCode,1993edition.Overend,P.R.andSmith,S.,ImpulseTimeMethodofSagMeasurement.StressStrainCreepCurvesforAluminumOverheadElectricalConductors,AluminumAssociation,1974.Winkelman,P.F.,SagTensionComputationsandFieldMeasurementsofBonnevillePowerAdministration,AIEEPaper59900,June1959.2006byTaylorFrancisGroup,LLC.42.2006byTaylorFrancisGroup,LLC.

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