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1、Engineering Structures 33(2011)18171827Contents lists available at ScienceDirectEngineering Structuresjournal homepage: modeling of joint effects in lattice transmission towersW.Q.Jianga,Z.Q.Wanga,G.McClureb,G.L.Wangc,J.D.GengdaEnergy&Power Engineering School,North China Electric Power University,Ba

2、oDing 071003,ChinabDepartment of Civil Engineering and Applied Mechanics,McGill University,Montreal,Canada H3A 2K6cGuizhou Electric Power Design Research Institute,Guizhou 550002,ChinadChina Electric Power Research Institute,Beijing 102401,Chinaa r t i c l ei n f oArticle history:Received 16 Septemb

3、er 2010Received in revised form19 February 2011Accepted 21 February 2011Available online 23 March 2011Keywords:Lattice transmission towerJoint eccentricityBolted joint slippageBearing capacityPushover analysisa b s t r a c tLatticeTransmissiontowersarevitalcomponentsofoverheadtransmissionlineswhichp

4、layanimportantrole in the operation of electrical power systems.Accurate prediction of the structural capacity of latticetowers under different failure modes is very important for accurate assessment of the reliability oftransmissionlinesandpowergrids,andfordesignofefficientfailurecontainmentmeasure

5、s.Traditionally,lattice towers are analyzed as ideal trusses or frame-truss systems without explicitly considering loadingeccentricities and slippage effects in bolted joints.Such effects are always observed in full-scale towertests and introduce great differences in the ultimate bearing capacity an

6、d failure modes obtained fromclassicallinearanalysismodels.Inthispaperexperimentalresultsavailablefromfull-scaleprototypetestsofasingle-circuit110kVandasingle-circuit220kVlatticetransmissiontowerssubjectedtodifferentloadcases are presented and compared with those obtained from four series of numeric

7、al models that includejoint eccentricity effects and different joint slippage models.The numerical simulation results confirmthat joint slippage dramatically increases the deformation of the lattice towers,while its influence onload-bearing capacity will vary in different load cases according to the

8、 magnitude of vertical loading andthe tower failure mode.Results from the pushover nonlinear static analysis of the towers consideringboth joint slippage and eccentricity are found in agreement with the experimental results.This type ofanalysis can be used to model joint effects in lattice towers.20

9、11 Elsevier Ltd.All rights reserved.1.IntroductionLattice steel transmission towers are widely used all overthe world as conductor supports in electric transmission grids.Classical lattice towers are self-supported and constructed ofangle section L-shape members typically connected with boltedjoints

10、.In many instances,these bolted connections introduceeccentricities between the load transferred at the joints and thelongitudinal principal axis of the member.Each tower comprisesseveral joint configurations in terms of geometry,continuity,presence of gusset plates,bolt arrangements and load transf

11、ereccentricity,which make these lattice structures difficult tobe analyzed with accuracy using classical linear methods evenwhen material nonlinearities are negligible.When loads areapproaching the towers capacity,however,both geometric andmaterial nonlinearities have combined effects that cannot be

12、traced with linear analysis.Most of the latticed towers presentlyCorresponding address:Department of Civil Engineering and Applied Mechan-ics,McGill University 817 Sherbrooke Street West Room 475F Montreal,Quebec,Canada H3A 2K6.Tel.:+1 514 398 6677;fax:+1 514 398 7361.E-mail address:ghyslaine.mcclur

13、emcgill.ca(G.McClure).in service around the world were designed using traditionalstress calculations obtained from linear elastic ideal truss analysis,whereby members were assumed to be concentrically loaded andpin-connected.Tower designers have long recognized that theresults of those ideal truss a

14、nalysis models cannot match full-scaletest results very well.Peterson 1 and Marjerrison 2 reportedthat during full-scale transmission lattice tower tests the analysisresults would grossly underestimate the measured deflections,whichmightbeaslargeasthreetimesthe theoreticallinearelasticdeflections.Th

15、ediscrepancybetweentheexperimentalresultsandthe analytical solutions has traditionally been compensated bysafety factors in member and connection design.However moreanalysis accuracy is necessary to assess realistic failure modesand tower capacity at ultimate loads.When the tower memberdeformations

16、remain in their elastic range,the discrepancybetween linear analysis models and actual tower response stemsfrom two main sources:(1)Second-order effects caused by jointeccentricity(as shown for example in Fig.1 where ey,ezare therespective eccentricity about local principal axes y and z),and(2)the o

17、ccurrence of slippage effects in bolted joints(see Fig.2),which leads to additional second-order effects.Joint effects in lattice transmission towers have been studiedfor several decades and are now well-understood.Knight and0141-0296/$see front matter2011 Elsevier Ltd.All rights reserved.doi:10.101

18、6/j.engstruct.2011.02.0221818W.Q.Jiang et al./Engineering Structures 33(2011)18171827yOzxeyezOFig.1.Example of joint eccentricities.Santhakumar 3 conducted tests on a full-scale quadrant of thelowest panel of a transmission tower and compared the measuredresults with the classical analysis results.T

19、hey pointed out thatthe secondary stresses caused by bolted joint effects could besignificant enough to cause failure of leg members even undernormal working-load conditions.Chan et al.46 comparedthe experimental failure loads of single angle struts with thosepredicted by design code equations and n

20、umerical analysis results,and concluded that more reasonable ultimate load predictions canbe obtained by considering both the effects of joint fixity,whichincrease member capacity compared to the ideal pinned-jointconditions,and eccentricity which reduces capacity compared toideal centric loading.In

21、 order to obtain more accurate predictions of lattice steeltransmission tower response using finite element analysis,Leeand McClure 7 derived an L-Section beam finite element whichsuccessfully predicts the response and ultimate capacity of anglemembers used in lattice towers with consideration of lo

22、adingeccentricities and bounding conditions as well as material andgeometrical nonlinearities 8.Similar advanced modeling studieswere completed by Al-Bermani and Kitipornchai 9,10.Howeverthe tower deformations predicted by these numerical models stillPPPP(a)Before slippage.(b)After slippage.Fig.2.Bo

23、lted joint slippage effects.Fig.3.110 kV height-adjustable suspension tower.W.Q.Jiang et al./Engineering Structures 33(2011)181718271819Fig.4.220 kV anti-icing suspension tower.Fig.5.220 kV tower during full-scale testing.Fig.6.220 kV tower failure(load case 2flexural).did not agree with test result

24、s and the discrepancy was attributedto joint slippage effects.Kitipornchai et al.11 developed generic instantaneous andcontinuous bolt-slippage models for typical lattice tower joints.Their modeling work indicated that although joint slippagesignificantly affects the predicted tower deformation,it h

25、as littleinfluence on the stress analysis results and almost no effect on thepredicted ultimate capacity of lattice towers.Ungkurapinan 12and his collaborators 13 carried out an experimental studyto derive more accurate joint-slippage models.They conductedexperiments on angle shapes connected by typ

26、ical single-leg andlap-splice bolted joints and developed empirical mathematicalexpressions to describe slip and loaddeformation behavior;thesejoint-slip models have been used in the present study(see Fig.10).1820W.Q.Jiang et al./Engineering Structures 33(2011)18171827yxzOFig.7.Local coordinate syst

27、em for diagonal members.More recently a study by Ahmed et al.14 concluded that jointslippage has a significant influence on tower behavior by eitherreducing its load-carrying capacity or increasing deflections underworking loads.However,it should be noted that member shapeandjointeccentricityeffects

28、werenotincludedintheirmodelsandtower failure analysis results were not verified by experimentalresults.As indicated above,a number of researchers have studiedjoint effects on lattice transmission tower response,but to dateno published research has reported a complete study combininglatticetoweranaly

29、sisincludingbothjointeccentricityandslippageeffects,and verification by full-scale tower test results.In thispaper all these joint effects are successfully accounted for instatic pushover failure analysis of two lattice steel transmissiontowers using USFOS(Ultimate Strength for Offshore Structures)c

30、ommercial software 15,and the numerical results are comparedwith full-scale experimental measurements and observationsfrom static prototype tests conducted in 2007 and 2009 at theChina Electric Power Research Institute in Beijing.It should beemphasized here that full details of the tested prototypes

31、 cannotbe published since they are proprietary.2.Full-scale tower testing2.1.110 kV height-adjustable suspension towerThe first series of full-scale test results used in the study wereobtained from static tests on a 25-m tall 110 kV height-adjustabletransmission tower used in subsidence-prone area d

32、ue to coalmining.The tower height can be adjusted by using different bodyextension lengths.The outline of the tower geometry is shownin Fig.3(a)and the loading case applied during the tests is listedin Table 1(loading points are identified on Fig.3(b),and thecorresponding deflections of points A,B,C

33、,D,E,F and G(identifiedon Fig.3(a)were recorded(shown in Fig.11)after each loadlevel.This load case test is to verify the tower capacity followinga conductor breakage.The loading directions in Fig.3 refer tolongitudinal(L),transverse(T),and vertical(V).It is seen inTable 1 that only the longitudinal

34、 unbalanced load resulting fromconductor breakage at Loading Point 5 is applied progressively,from 50%to 95%of the design load,while the gravity loads atthe intact cable suspension points(Loading Points 14)are onlyapplied in the final loading stage.The maximum experimentalload,which is used as the r

35、eference value in comparisons withnumerical predictions,reached 95%of the design load in thiscase.Note that the tower did not collapse during the test,so themaximum experimental load is not the collapse load.2.2.220 kV anti-icing suspension towerThe second full-scale test results used in the study w

36、ereobtained from static tests on a 36-m tall 220 kV anti-icingL-Section BeamL-Section BeamL-Section BeamL-Section BeamNonlinear SpringNonlinear SpringSpring(a)Lap-splice Bolted Joint(b)Single-leg Bolted Joint(c)Crossed Diagonal MemberFig.8.Typical bolted-joint connections.PPPP(a)Bearing.(b)Normal.PP

37、(c)Maximum.Fig.9.Different bolt/hole construction clearance configurations.W.Q.Jiang et al./Engineering Structures 33(2011)181718271821SLOPEDEFORMATION(mm)ACBPQRLOAD(kN)(a)Single-leg bolted joint.LOAD(kN)(b)Lap-splice bolted joint.Fig.10.Ungkurapinan joint slippage model 12,13.suspension tower for u

38、se in areas exposed to atmospheric icing.The outline of the tower geometry is shown in Fig.4(a).Forthis tower,two load cases are used which are listed in Tables 2and 3(the loading points are identified on Fig.4(b)where themaximum experimental load applied is 100%of the design load.The corresponding

39、deflections of points A,B,C,D,E,F,G and H(identified on Fig.4(a)were recorded(shown in Figs.12 and 13)after each load level.The tests using these two load cases are toverify the torsional and bending capacity of the tower when theline is subjected to unbalanced conductor loads with glaze iceaccretio

40、n equivalent to 30-mm radial thickness.For load case 2(Table 3)the tower is mainly bent about thetransverse direction due to longitudinal load imbalance,and theload was gradually increased until tower collapse.Fig.5 shows the220 kV tower during testing and Fig.6 shows the collapsed towerat the end o

41、f this test.The failure mode was the inelastic bucklingof the tower main legs and the ensuing global loss of stability andoverturning of the superstructure.3.Numerical simulation of tower tests3.1.Tower modelingIn the numerical model,the individual members are repre-sented by angle shapes with prope

42、r spatial orientation with re-spect to their local principal directions(see Fig.7),and themember eccentricities eyand ezare specified in accordance with1822W.Q.Jiang et al./Engineering Structures 33(2011)18171827(a)50%load.(b)75%load.(c)90%Load.(d)95%Load.Fig.11.110 kV tower longitudinal displacemen

43、t.Table 1Experimental conductor breakage loading for the 110 kV tower.PointDirectionLoad(kN)Ground wire1Transverse0.000Longitudinal0.000Vertical1.8202Transverse0.000Longitudinal0.000Vertical1.820Conductor3Transverse0.000Longitudinal0.000Vertical5.0004Transverse0.000Longitudinal0.000Vertical5.0005Tra

44、nsverse0.000Longitudinal15.750Vertical5.000the prototype design detailed drawings.The free(unconnected)leg of all diagonal members was assigned along the local y-axis asshown in Fig.7.Each member is meshed with a single materiallynonlinear beam element available in USFOS 15,based on plastichinge the

45、ory.In this formulation,plastic hinges may be introducedatbothendsandmidspanofeachmember.Whentheanalysisindi-catestheonsetofyieldinginamember,aplastichingeisinsertedatthe corresponding element node.If yielding is taking place at mid-span of the element,the member is automatically split into twonew s

46、ub-elements connected by a plastic hinge and the stiffnessmatrix for the two sub-elements is assembled.The steel materialpropertiesspecifiedinthenumericalmodelarethenominalvaluesused in design:a Youngs modulus of 200 GPa and a yield stress ofTable 2Experimental loading for the 220 kV tower(load case

47、 1torsional).PointDirectionLoad(kN)Ground wire1Transverse6.000Longitudinal31.298Vertical31.4682Transverse6.832Longitudinal33.015Vertical22.243Conductor3Transverse9.220Longitudinal46.380Vertical75.9304Transverse9.220Longitudinal46.380Vertical75.9305Transverse8.447Longitudinal48.494Vertical75.930Wind

48、loadWT1Transverse4.800WT2Transverse4.400WT3Transverse0.800WT4Transverse1.200WT5Transverse2.400WT6Transverse1.600WT7Transverse3.200235 MPa for all members except the main legs of the 220 kV tower,which are made of a stronger steel grade with a yield stress of345MPa.Thetowermodelsareassumedtobefixedon

49、arigidbase.Fig.8 shows the three typical bolted joint configurationsused in the lattice towers and their respective mechanical modelimplemented in the analysis.Taking for example the diagonalmember with a single-leg bolted joint to the tower main leg(seeW.Q.Jiang et al./Engineering Structures 33(201

50、1)181718271823(a)50%load.(b)75%load.(c)90%load.(d)100%load.Fig.12.220 kV tower longitudinal displacement(load case 1torsional).Table 3Experimental loading for the 220 kV tower(load case 2flexural).PointDirectionLoad(kN)Ground wire1Transverse6.000Longitudinal31.298Vertical31.4682Transverse6.000Longit