Tensile
rprestressedconstructionoftensionstructures
;XinZHUO中1
;,
;Guo.faZHANG,KoichiroISHIKAWA2
;,
;Dao.anLOU3
;(DepartmentofCivilEngineering,ZhejiangUniversity,Hangzhou310027,China) ;(eDepartmentofArchitectureandCivilEngineering,FukuiUniversity,Fukui910.8507,Japan)
;(SZhejiangZhanchengConstructionGroupCo.,Ltd.,Hangzhou310005,China) ;E-mail:zhuoxin@zju.edu.cn
;ReceivedNov.27,2007;revisionacceptedJune2,2008
;1201
;嚣磐
;Abstract:Factorssuchaserrorsduringthefabricationorconstructionofstructuralcomponentsanderrorsofcalculationas.
;sumptlonorcalculationmethods,areverylikelytocauseseriousdeviationofmanystrings’actualprestressingforcesfromthe
;designedvaluesduringtensionstructureconstructionorserviceperiod,andfurthertothreatenthesafetyandreliabilityofthe
;structure.Aimingatrelativelylargeerrorsoftheprestressingforceofstringsinatensionstructureconstructionorserviceperiod,
;thispaperproposesanewfiniteelementmethod(FEM),the”tensileforcecorrectioncalculationmethod”.Basedonthemeasured
;prestressingforcesofthestrings.thisnewmethodappliesthestructurefromthezeroprestressingforcestatusapproachtothe
;measuredprestressingforcestatusforthefirstphase,andfromthemeasuredprestressingforcestatusapproachtothedesigned
;prestressingforcestatusforthesecondphase.Theconstructiontensileforcecorrectionvalueforeachstringcanbeobtainedby
;multi—iterationwithFEM.Usingtheresultsofcalculation,thestrings’tensileforcecorrectionbygroupandinbatchwillbe
;methodic,simpleandaccurate.Thisnewcalculationmethodcanbeappliedtotheprestressedcorrectionconstructionsimulation
;analysisfortensionstructures.
;Keywords:Tensionstructures,Prestressedconstruction,Highprecision ;doi:10.1631/jzus.A0720090Documentcode:ACLCnumber:TU3;TU7
;INTRODUCTION
;Tensionstructures.suchasprestressedspatia1
;gridstructuresandsuspend.dome.etc—combinethe
;rigidbeamsorrodswiththeflexiblestrings.The ;structuralefficienciesofsuchnewtypesofstructural ;systemsareenhancedbecausethestructuralrigidityis ;increasedandthedistributionofforcesinthewhole ;structureisimprovedbythestring’sprestressing
;force.Scholarshavestudiedtheanalysistheoriesand ;calculationmethodsforthisstructuresystem(Saiton ;Pf,.,1993;Kawaguchieta1.1993;ChenandLi, ;2005;Zhangeta1.,2004;2005).However,there—
;searchtopicsconcerningthemechanicsanalysisin ;thecourseofconstructionwerejustbegunafewyears ;Project(No.50678157)supportedbytheNationalNaturalScience ;FoundationofChina
;ago.Somestudiesputemphasisoninvestigationof ;experiments(Tagawaeta1.,1994;Yamagataeta1., ;l994;KawaguchiandAbe,l999;Miyasatoeta1., ;1999).SomestudiesfoCUSontheanalysistheories ;andthecalculationmethods(Saitoneta1..2001: ;Dongeta1.,2003:ZhuoandIshikawa,2004;Zhuo ;andYuan,2004;Zhuoeta1.,2004;LuandShen, ;2005).Thekeyforconstructingtensionstructuresis ;theprestressedconstructionofmanystrings.Itis ;unabletocalculateaccuratelythestring’sprestressing
;forceoftensionstructuresinthestructuraldesignor ;constructionsimulationanalysis,becausesuch ;non.idealfactorsastheerrorsofcalculationassump—
;tionorcalculationmethods.theerrorsoffabrication ;orconstructionofstructuralcomponents,theeffects ;ofconstructionortemperatureloads,andtheeffects ;Ofthematerialdeformationorfrictionofstructural ;components,etc.,areunavoidable.Thesenon—ideal
;
;1202Zhuootal/JZh~iangUnivSciA20089(9):1201—1207
;factorsareverylikelytocausetheactualprestressing ;forcesofmanystringsdeviatingseriouslyfromthe ;designedvaluesduringatensionstructureconstruc- ;tioncourseorserviceperiod,andthusthesafetyand ;reliabilityofthestructurewouldbethreaten.Inorder ;toachievehighprecisioncontroloftheprestressing ;forcesofthetensionstructure,theworkofconstruc- ;tioncorrectionisabsolutelynecessary.
;Themechanicsanalysisoftensionstructuresin ;thecourseofconstructionhasbeenahotresearch
;topicinrecentyears.Researchhasbasicallysolved ;theissueofmechanicsanalysisandcalculation ;methodoftensionstructuresinthecourseofintro. ;ducinginitialprestressingforcesconstructionfSaiton ;Pfal.,200l;Dongelal.,2003;ZhuoandIshikawa, ;2004;ZhuoandYuan,2004;Zhuoela1.,2004;Luand ;Shen.2005).butnottheissueofanalysisandcalcu. ;1ationmethodofhighprecisioncontrollingof ;prestressingforcesfortensionstructuresbasedon ;measureddataduringconstructionorserviceperiod. ;Aimingatthetensionstructureswithbigerrorsin ;prestressingtorceduringconstructionorservicepe. ;riod,anewcalculationmethod,so.called”tensile
;forcecorrectioncalculationmethod”.isputforward
;inthispaper.Basedonthevaluesofthestrings’
;measuredprestressingforces,thetensileforcecor. ;rectionvalue,whichmeansthestring’stensileforce
;controlvaluesinactualconstructioncorrectionof ;eachstring,canbeobtainedbythiscalculation ;method.Thecalculationresultsshowedthatthe ;string’stensileforcecorrectionconstructionworkby
;groupandinbatchismethodic.simpleandaccurate. ;PRINCIPLE0FTENSILEF0RCEC0RRECT10N
;CALCULAT10NMETH0D
;Manystrings’measuredprestressingforcesina
;tensionstructurehavelargeerrors.andshouldbe ;carriedoutbygroupandinbatchconstructioncor- ;rectionmethod.Here,thegroup,asaspaceparameter, ;reterstosomestringstensionedatthesametime,and ;thebatch,asatimeparameter,referstothesequence ;olthestringstensioned.Thegroupsandthebatches ;shouldbedecidedonthedistributionofthestringsin ;thestructureandtheactualconstructionconditions. ;1neprestressedconstructioncorrectionanalysis ;isdividedintotwophases.Inthefirstphase,the ;analysisisstartedatthe”zeroprestressingforce
;status”ofthestructure.andendedatthe”measured
;prestressingforcestatus’’ofthestructurewith
;prestressingforceerrors.Thesubsistenttensileforce ;calculationvaluesofeachstringareforcedtomeet ;themeasuredvaluesthroughstructuralfiniteelement ;analysis.Inthesecondphase,thestartingpointof ;analysisisthe”measuredprestressingforcestatus”.
;andtheendingpointistheideal”designed
;prestressingforcestatus”ofthestructure.Theerror
;statuscontinuouslyapproachesandfinallyreaches ;theidealstatusthroughstructuralanalysisandcal- ;culation,sotheconstructiontensioncorrectionvalues ;ofeachstringcouldbeobtained.
;Thetraditionalconceptofprestressingforce ;shouldbechangedandfractionized,becausethe ;constructioncorrectionofstring’sprestressingforces
;inatensionstructureincludesthefactorsoftimeand ;space.Assumengroupsofstringsinatensionstruc. ;turetensionedinnbatches.Theparametersarede. ;finedasfollows:fl1constructioncontroltensileforce ;()—lheprestressingforceconstructioncontrol- ;lingvalueoftheithstringinthejthbatchtensioning ;construction;(2)subsistenttensileforce(,m)I—
;theprestressingforcevalueoftheithstringinthejth ;batchtensioningconstruction;(3)targettensileforce ;P()一inthefirstanalysisphase,itistheprestressing ;forcemeasuredvalueoftheithstringafterthestruc. ;tureconstructioncompletedorintheserviceperiod; ;inthesecondanalysisphase,itistheprestressing ;forcevalueoftheithstringwhichshouldmeet,i…e
;theprestressingforcedesignvalueofthestring. ;Wheremisthestepofanalysisphase,=l,2:kisthe ;stepofiteration,k=-l,2,3,…;freferstotheithstring,
;f=l,2,3….,n;jisthetensionconstructionsequence
;number,J=l,2,3….,n.
;Thetensileforcecorrectioncalculationusesthe ;iterationapproximationmethods.Thesecondphase ;analysisiscarriedoutafterthefirstphase.Theca1. ;culationprinciplesandmethodsofthetwoanalysis ;phasesarebasicallythesame.Theanalysismethods ;andthecalculationprocedurescouldbesummarized ;asfollows:
;(1)Forthefirstiteration.thestructuralgeomet. ;ricalnonlinearfiniteelementmethod(FEM1analysis ;isperformedintermsoftheconstructiontensioning ;sequence.Whencalculatingthestringsofthe,th ;groupinthebatchoftensioning
;,theconstructiOn
;
;Zhuoota1./JZhejiangUnivSciA20089《9):1201—1207
;controltensileforcesofstringsareforcedtobeequal ;tothetargettensileforces,i.e.,(1,)=Pi(m),and
;thesubsistenttensileforces(1,m)ofotherstrings ;whichhavebeentensionedinstructurearecalculated ;atthesametime.Allofthesubsistenttensileforcesof ;eachbatchofstringshavechangedexceptthatofthe ;lastbatchstringswhencalculatingthenthgroupof ;thelastbatchofthestrings.Thevalueoftensionforce ;changeofeachgroupofstringsis?(2,)=(1,)一
;(1,).
;(2)Fortheseconditeration,theconstruction ;controltensileforcevalueofeachgroupofstringsin ;thefirstiterationismodifiedbycompensatingthe ;valueoftensionchange.Theconstructioncontrol ;tensileforceofthestringsintheseconditerationis ;(2,)=(1,)+A(2,).
;Theconstructioncontroltensileforcesofthe ;stringsareforcedtoequalto(2,m)andthesubsis—
;tenttensileforcesofotherstringstensionedinstruc—
;ture(2,m)arecalculatedatthesametime.After ;calculatingthenthgroupofthelastbatchofthe ;strings,thetensileforcechangeofeachgroupof ;stringsisA(3,)=(2,)一(2,).
;Theresultsofiterationsk=3,4….canbeob—
;tainedintermsofthesameprinciple.
;(3)Attheendofthekthiteration,ifPi(m)一
;Yi)?印,i…ethedifferencebetweentheactual
;valueandthedesignedvalueofthestring’stensile
;forceislessthanacertainvalue.theiterationcouldbe ;terminated.Theflowchartofcalculationmethodis ;showninFig.1.
;Theresultsofthekthiterationinthefirstanaly—
;sisphasearelistedinTable1.Thesubsistenttensile ;forcesofthelastrow,F1”(1),”1),
;(1),…,(1),equalthemeasuredtension
;valuesofeachstring,PI(1),P2(1)….,(1)….,(1).
;Theresultsofthekthiterationinthesecond ;analysisphasearelistedinTable2.Theresultsonthe ;diagonals,(2),T2(庀,2),…,(庀,2),…,”(2),
;aretheconstructioncontroltensileforcevaluesofthe ;stringsofgroupsl,2,…,n.Thesevaluesarethe
;constructiontensioncorrectionvaluesofactualcon—
;structioncorrectiontensioningbygroupandinbatch, ;whicharethemajorresultsthatthenewcalculation ;methodinthispaperseeksfor.Thelastrow,F1”(2),
;F2”(,2)….,(,2)….,(,2),presentsthefinal
;subsistenttensileforcevaluesofthestringswhichare ;equaltotheirdesignedtensionvalues,Pl(2),P2(2)….,
;Pf(2),…,P”(2),respectively,withtheconstruction
;1203
;correctiontensioningmethodbygroupandinbatch. ;Thisisthefinaltargetofthecalculationmethodin ;thispaperaswellasthehighprecisioncontrolof ;prestressedconstructionfortensionstructures. ;Fig.1Flowchartoftensileforcecorrectioncalculation ;method
;Table1Resultsofthefirstanalysisphase
;Table2Resultsofthesecondanalysisphase ;
;1204Zhuoetal/dZhejiangUnivSciA20089(~.1201—1207
;ILLUSTRATIVEEXAMPLEANDDISCUSSIONS
;Overviewoftheproject
;Aprestressedspatialgridstructureprojectwith ;27mspan,24mlengthand24mheightisshownin ;Fig.2.Thedistancestothefirstquarterplaneandthe ;lastquarterplaneareboth2m.Thenodesareofbolt ;sphericalnodetype.Therodsaretwotypesofsteel ;tubeswith216.3mmx7.0mmandll4.3mmx6.0mm ;circularhollowsections(CHSs),andtheYoung’s
;modulusofthesteelwas200GPa.Wallstringsof ;groups1-6withmaximumprestressingforceof500 ;kN,symmetricallydistributedattwosidesofthe ;structure,aretopotentiatethesidewallsofthespatial ;gridstructure.Stringsconnectedtothelowernodeof ;thegridstructurearefortensioninginconstruction. ;Roofstringsofgroups7；12withmaximum
;prestressingforceof650kN,aretoreinforcethetop ;ofthestructure.Thestring’sgroupnumbersare
;showninFig.2a.
;ARertheintemalforcetestsofthestructure ;carriedouttheprestressedconstruction,largeerrors ;betweentheactualprestressingforcesandthede—
;signedvalueswerefoundinmanystrings.andcon. ;structioncorrectionontheprestressingforcesofthe ;stringsshouldbecarriedout.TheactualvaluesP(11 ;andthedesignedPi(2)valuesoftheprestressing ;fcIrcesofactivewallstringsandroofstringsare ;showninTable3.
;Analysisofcalculationresults
;Whenapplyingthetensioningconstructioncor—
;rectionmethodbygroupandinbatch,thetensioning ;sequencenumberwassetthesameasthestringgroup ;number.Twosymmetricalwallstringsconstitutedone ;groupandweretensionedinsequencefrom1to6. ;androofstringsweretensionedinsequencefrom7to ;12.Theconstructionsimulationanalysisofthe ;structureappliedthetensileforcecorrectioncalcula. ;tionmethodsubmittedinthispaper,andfouritera. ;tionsweredoneintermsofthecalculationprocedure ;andformulaeofthefirstandthesecondanalysis ;phases.Duetothelimitedspaceofthispaper,onlythe ;strings’calculationresultsoffouriterationsinthefirst ;andsecondanalysisphaseswerelistedinTable4and ;Table5,respectively,showingthat:
;(1)Attheendofthefirstanalysisphase.the ;calculationvaluesofprestressingforcesofallstrings ;inTable4havemettheirmeasuredvaluesinthe ;fa1
;Fig.2Structuralsketchandstring.(a)Perspective ;view;(b)Frontview
;iP1)(kN)P2)(kN)iPi(1)(kN)Pi(2)(kN)
;1123.003007323.00450
;2209.263008209.26450
;3325.673009425.67450
;4340.5830010409.58450
;5292.5030011492.50450
;6243.0030012343.00450
;Note:iisthestring’snumber;Pf(1)isthemeasuredvalueofthe
;prestressingforceofthefthstringafterthestructureconstructionis
;completedorintheserviceperiod;尸2)isthedesignvalueofthe ;prestressingforceofthefthstring.
;structurestatuswiththeprestressingforceerrors.And, ;attheendofthesecondanalysisphase,thecalculation ;valuesofprestressingforcesofallstringsinTable5 ;havemettheirdesignedvaluesintheidealstructure ;statuswithoutanyerrors.
;f21Theinitialsubsistenttensileforcesofall ;stringslistedinTable3,123.00,209.26,325.67, ;340.58,292.50,243.00,323.00.209.26,425.67, ;409.58,492.50,343.00kN,arethemeasuredtensions ;inTable4whenkis4.Thesubsistenttensileforcesof ;allstringsmeettheirtargettensileforcesafteranaly. ;sisandcalculationbyapplyingthecalculation ;methoddescribedinthisPaDer.Accordingtothese—
;quencefrom1to12whichisidenticaltothecalcula.
;tlon,applyingthecalculationresultsof
;
;Zhuoeta1./JZhejiangUnNSciA20089(9):1201?1207
;Table4Calculationresultsinthefirstanalysisphase ;kjString’stension(kN)
;i=12345678910l1
;112:QQ
;2l10.15209.26
;3103.07200.40325.67
;499.41194.423l1.29409.58
;5102.80195.46306.67401.11292.50
;6108.05198.06304.09395.44277.16243.00
;7127.58214.183l1.01398.51274.01236.31323.00
;8138.28218.75315.96401.66273.76234.27301.62209.26 ;9146.19227.09322.76410.33279.99239.17288.85189.67425.67 ;10148.99231.86330.71416.93288.93248.66285.06180.42401.72409.58 ;l1143.38230.74338.28429_32301.84276.64295.60184.62388.73384_30492.50 ;12137.58227.95341.00435.60317.41294.57305.95190.96384.56373.12457.17343.0
0
;1108.42
;296.72190.57
;389.97182.13310.34
;486.55176.53296.86383.56
;589.64l77.48292.59375.81267.59
;693.78179.53290.59371.33255.48191.43
;.7114.34196.50297.88374.57252.16184_39340.05
;8126.00201.47303.27378.00251.89182.17316.80227.56 ;9134.67210.63310.73387.51258.72187.53302.80206.09466.78 ;10137.73215.83319_38394.69268.46197.87298.66196.01440.72446.04 ;l1131.72214.63327.50407.96282.28227.84309.96200.51426.79418.96527.83 ;12125.922l1.84330.22414.23297.83245.71320.29206.82422.63407.79492.56343.00
;11Q:1
;293.95188.00
;387_30179.68305.78
;483.92174.14292.47378.90
;586.96175.07288.28371.31262.24
;691.04177.09286.31366.89250_32188.72
;7111.77194.20293.67370.15246.97181.62342.78
;8123.55199.23299.11373.62246.69179.38319.26230.01 ;9132.27208.44306.61383.20253.57184.78305.17208.39469.82 ;10135.34213.67315_31390.40263.35195.16301.02198.28443.66447.82 ;l1129.33212.46323.42403.67?