PAPER Improving the Performance of Evaluation

Tadashi DESHIMARU,Improving the StructurePerfo randm aComponentsnce of R Laboratory,ail Fast Trackenin Structureg Syst Divisionem Ev aluation Shingo TAMAGAWA, Track Structures and Components Laboratory, Track Technology Division Masato NOGUCHI, Track Structures and ComponentsTadashi Laboratory, DESHIMA TrackRU Technology Division Track Structure and Components Laboratory, Track Structure Division Hiroo KATAOKA, Track Structures and Components Laboratory, Track Technology Division Shingo TAMAGAWA Masato NOGUCHI Hiroo KATAOKA RegardingTrack St rJapaneseuctures a ntestd C methodsompone nforts Lrailabo fasteningratory, Tr systems,ack Tech itn owaslogy confirmedDivision that the rail tilting angle obtained in a biaxial loading test did not agree with the angle calculatedRegarding using Japanese a conventional test methods rail tiltingfor rail analysis fastening model. systems, To address it was confirmedthis problem, that a the rail tilting angle obtained in a biaxial loading test did not agree with the， angle calculated us- ing calculationa conventional method rail fortilting biaxia analysisl loading model. using To an address FEM analysisthis problem, model a calculationwhere various method for stiffnessbiaxial loadingproperties using regarding an FEM the analysisrail fastening model, systems where can various be expressed stiffness as properties non-linearity regard， - ing wasthe railproposed fastening and systemsits validity can was be expressedconfirmed. as non-linearit In addition, y,a wasstudy proposed on the optimiz and itsation validity wasof confirmed. a method forIn addition,testing rail a studyrestraint on thewas optimization carried out ofthrough a method experimental for testing validation rail restraint wasunder carried various out through conditions. experimental validation under various conditions.

Key wordsKeywords: rail :fastening rail fastening systems, systems, performance performance verification, verification, FEM analysis, FEM analysis, rail tilting rail angel, tilting rail angle, restraint rail restraint

11.. InIntroductiontroduction

DDifferentifferent teststest sare a rconductede conduc tfored thefor purpose the pu ofrp confirmingose of con - ftheirm performanceing the per offor railma nfasteningce of ra systemsil faste nwhiching s yarest eamongms w htheich atrackre a mcomponentsong the t rusedack conom railwayponen ttracks.s used o Amongn railw theseay t rtests,acks . Ainm Japan,ong t hbiaxialese te staticsts, i andn J arepeatedpan, bi aloadingxial st testsatic arean dconducted repeated lforoad theing purposetests ar ofe cverifyingonducted the for performance the purpos eof o fthese veri fsystemsying th e pine rtermsform aofn cfatiguee of th durability.ese syste m s in terms of fatigue durabil- ity. Conventionally, the loading conditions for static and repeatedConv biaxialention aloadinglly, th etests, loa dusinging c oa nsingledition fastenings for sta systemtic and rset,epe areate determinedd biaxial lsooa thatdin gthe t erailsts tilting, usin angleg a s icalculatedngle fast usingening stheyst proposedem set, arailre tiltingdeter analysismined smodelo tha t[1 t-h4]e agreesrail t iwithltin gthe a nrailgle (a) Testing with single fastening system ctiltingalcul aangleted u obtainedsing the in p rtheop otest.sed r However,ail tilting it a wasnal yconfirmedsis mode l set [these1-4] atwogre erails w tiltingith th anglese rail dotilt noting agreeangl ein o practice.btained in the test. HoweTherefore,ver, it wa s in c o thisnfi r study,med t h thees e rail tw o tilting rail t angleilting caalculatedngles do nusingot ag r theee i proposedn practi c finitee. element method (FEM) model was comparedThere fwithore, ithen t hangleis st uobtaineddy, the rthroughail tilt ina guniaxial angle cloadingalculat - etestd u onsin ag test the track pro ptoo sverifyed fin theite validityelemen oft mthiset hproposedod (FEM analysis) mode l wmodelas co mwhenpar ead low wit stiffnessh the an fasteninggle obta isystemned th rwasoug applied.h a uni a x Iina l laddition,oading t ethest ovalidityn a tes oft t therac kbiaxial to ve rloadingify the conditionvalidity o forf t htestingis pro - ptoo s beed a appliednalysi s to m ao d singleel wh e railn a fasteninglow stiff n systemess fas t seten i calculatedng system wusingas a pthepl iproposeded. In a danalysisdition, modelthe va waslidit verifiedy of the bybi acomparingxial loadi nitg cwithond ithetio nresponse for test valuesing to obtainedbe appli ined a t biaxialo a sin loadinggle rail testifastngen oning say teststem track. set c alculated using the proposed analysis model (b) Testing on a test track was verified by comparing it with the response values ob- Fig. 1 Test apparatus for biaxial loading t2.ai nRailed in tilting a biax iangleal load anding t loadingesting on condition a test trac k . Fig. 1 Test apparatus for biaxial loading testing testing

There are two methods of static and repeated loading tests tconductedrack. using a track. 2conducted. Rail ti lt inin g Japan ang l fore a n verifyingd loadi n fasteningg condi ti systemon fatigue SStatictatic loadingloadin g tests te s arets a conductedre condu toct e examined to ex a responsesmine re - durability; one is conducted using a single fastening system set ssuchpon se ass su railch a displacements rail displac e andmen t railan d cliprail c stress.lip str es s. Rail Ra il and Tthhee otherre ar eis tconductedwo meth ousingds of as testtati trackc and as r eshownpeate din lFig.oad i1.ng ddisplacementisplacemen tduring durin gstatic sta tloadingic loadi ntestsg te isst sverified is veri fagainstied ag atheins t tWhenests c oan fasteningducted i nsystem Japa nof f other v sameerify itypeng f aiss tlaideni ncontinuouslyg system fa - trailhe lateralrail la displacementteral displa climiteme nvalue.t lim i t Theval ucombinede. The c railom bclipine d tonigu thee d utrackrab iatlit yregular; one iintervals,s conduc tae dsingle usin gfastening a singl esystem fasten seting rstressail c lisip verifiedstress i sby v echeckingrified by whether checki ntheg w plothet hrepresentinger the plot therep - swasyst eselected.m set a n d When the odifferentther is ctypesondu ofct efasteningd using asystems test t rareack rcombinationesenting th e is co insidembin a thetio n acceptance is inside t areahe a ofcc eptheta nGoodmance area o f auseds sh oonw na itrackn Fi gor. 1 when. Wh theen arail fa sprofiletenin gis s ynotst econstantm of th ein s athem e tdiagramhe Goo ddefinedman d ibyag rtheam types defin ofed spring by th esteels type sas o shownf sprin ing sFig.teel s ttrackype ilongitudinals laid conti ndirection,uously o asn tish etrue tra ofck a a jointedt regu lrail,ar i nteststerv areals , a2.s s hown in Fig. 2. a single fastening system set was selected. When different In static loading tests, the distributed force to be ap- types of fastening systems are used on a track or when the plied in tests using a single fastening system set is derived is not constant in the track longitudinal direc- from the design loads - load‘ A’ and load‘ B’ - based tion, as is true of a jointed rail, tests are conducted using a on beam theory on an elastic foundation. Load‘ A’ cor-

QR of RTRI, Vol. 59, No. 3, Aug. 2018 181 In static loading tests, the distributed force to be applied In static loading tests, the distributed force to be applied reinsp otestsndIns using tstatico a r aloadinga singlerely o fasteningctests,curr itheng distributedsystemload, w sethi lisforcee lderivedoa dto‘ beB ’from applied is t thehe 600 in tests using a single fastening system set is derived from the 600 mindesignor etests co m loadsusingmon - a ll ooadsinglead .‘A’ L fastening oandad‘ loadA’ system‘B’exe -r tbaseds seta fiso onr derivedc ebeam on t htheoryfrome tr athe conk 600 Elastic limit line design loads - load ‘A’ and load ‘B’ - based on beam theory on Elastic limit line wdesignhanic h elastic b loadsroa d foundation.e -n lsoad th e‘A’ tr and ac k Load loadgau ‘B’g ‘A’e w- basedh correspondsile l oonad beam‘ B to’ theory n aa r rarelyro wons Elastic limit line

) Yield line

an elastic foundation. Load ‘A’ corresponds to a rarely 2 the . Following the estimation of distributed ) 400 Yield line anoccurring elastic load, foundation. while load Load‘B’ is the ‘A’ more corresponds common load. to a rarely Load 2 ) 400 Yield line fooccurringrces, the load, rail whiletiltin loadg an ‘B’gle is i sthe d emorerive dcommon using tload.he r a il Load tilt- 2 400 Goodman occurring‘A’ exerts load, a force while on loadthe track ‘B’ is which the more broadens common the load. track gauge Load Goodman ‘A’ exerts a force on the track which broadens the track gauge GoodmanLine for 10 5 in‘A’whileg m exertsod e loadl aas force s ‘B’ho w narrowsonn ithen F tracki g the. 3 . which trackThis broadensi gauge.s calle d “ the Followingco tracknven tgaugeio n theal Line for 105 while load ‘B’ narrows the track gauge. Following the (N/mm 200 cycles 5 (N/mm Line for 10 mwhileestimationethod ” load an dof ‘B’ tdistributedh e narrowsrail til t forces,in theg a trackn thegle railc gauge.al ctiltingula te dangle Following by mise derivedan s the of 200 cycles estimation of distributed forces, the rail tilting angle is derived (N/mm 200 Goodman Line thestimationusingis me thetho drail of is distributed tiltingcalled model“ p rforces,ac astic showna lthe so lrailu inti o tiltingFig.n.” 3.W angle h Thisen ist h isderivede calledforce Goodman Line cycles using the rail tilting model as shown in Fig. 3. This is called Amplitude stresof Goodmanfor 107 cycles Line diusing“conventionalstrib uthete drail a ntilting dmethod” rai lmodel ti landtin asg the ashownn railgle ti ainltingr eFig. c aangle l3.cu l a Thiscalculatedted, isb icalledax ibyal Amplitude stresof for 107 cycles “conventional method” and the rail tilting angle calculated by Amplitude stresof 0 for 107 cycles lo“conventionalameansding cofon thisdit i methodomethod”ns for ist h andcallede t ethest “practical braily a tisltinging solution.”le angle faste calculatedni n g When syst ethebym 0 means of this method is called “practical solution.” When the 0 0 500 1000 1500 2000 semeansforcet are distributedaofls thiso de methodriv e andd, a isn rail dcalled th tiltinge r“practicalai l angle tiltin aregsolution.” a n calculated,gle is m Whene a biaxialsu rtheed 0 500 1000 15002 2000 force distributed and rail tilting angle are calculated, biaxial 0 500Mean stress1000 (N/mm15002 ) 2000 inforceloading the l distributedoa conditionsding tes t and uforn d railtheer t tiltingtesthat byco anglenad singleitio n are. fastening H calculated,ere, a ssystemm a biaxialll d setif- Mean stress (N/mm 2) loading conditions for the test by a single fastening system set Mean stress (N/mm ) feloadingrareen calsoe i nconditions derived, the ra iland fortil ttheing test railan gbytiltinle sa igsingles angleexp efastening ciste dmeasured bet systemwee nin t setthehe Fig.Fig. 2 2 TheThe GoodmanGoodman diagram diagram for for SUP9 SUP9 are also derived, and the rail tilting angle is measured in the Fig. 2 The Goodman diagram for SUP9 caareloadinglcu lalsoatio testnderived, a nunderd t hand ethat m thee condition.as urailre mtiltinen t g, Here, bangleut ian is smallp rmeasuredact differenceice th einr ethe iins Fig. 2 The Goodman diagram for SUP9 loading test under that condition. Here, a small difference in soloadingtheme raildev testitiltingati oundern .angles that is condition. expected between Here, a thesmall calculation difference and in Design load the rail tilting angles is expected between the calculation and Design load thethe railmeasurement, tilting angles but isin expectedpractice there between is some the deviation.calculation and Beam theory on (LoadDesign ‘A’ & Loadload ‘B’) the measurement, but in practice there is some deviation. Beam theory on (Load ‘A’ & Load ‘B’) the measurement, but in practice there is some deviation. elasticBeam theoryfoundation on (Load ‘A’ & Load ‘B’) elastic foundation 3. 3. R Railail t itiltinglting a nanalysisalysis m modelodel elastic foundation 3. Rail tilting analysis model Distributed force 3. Rail tilting analysis model Rail tilting model Distributed force 3.1 O utline of the proposed rail tilting analysis mod- Rail tilting model (perDistributed single fastening) force 3.1 Outline of the proposed rail tilting analysis Rail(Conventional) tilting model (per single fastening) 3.1e l Outline of the proposed rail tilting analysis (Conventional) (per single fastening) 3.1 Outline of the proposed rail tilting analysis (Conventional) model W model H W modelTo so l ve the problems described above, a non-linear H W Rail tilting angle H Rail tilting angle To solve the problems described above, a non-linear FEM (“PracticalRail tilting solution”) angle FEM Tora isolvel tilt theing problems analyti cdescribedal mode labove, [5] w aa snon pr-linearopose FEMd, as (“Practical solution”) rail tiltingTo solve analytical the problems model described[5] was proposed, above, a asnon shown-linear in FEM Fig. shrailow tiltingn in F analyticalig. 4. T hmodelis mo d[5]el wasena bproposed,les us to as r eshownprodu cine Fig.and F (“Practical solution”) rail4. tilting This modelanalytical enables model us [5] to was reproduce proposed, and as simulate shown in half Fig. a F F si4.m u l Thisate h modelalf a r enablesailway ustr a toc k reproduce consisti n andg o fsimulate twenty - halfsev e an F F 4.railway This track model consisting enables o usf twenty to reproduce-seven rail and fastening simulate systems half a F Biaxial loading condition rarailwayil fast etrackning consistingsystems aonf dtwenty a rai-lseven, and railits vfasteningalidity w systemsas con- Biaxial loading condition railwayand a rail, track and consisting its validity o fwas twenty confirmed-seven railwith fastening stiff rail systemspads, or (perBiaxial single loadingfastening condition system set) fiandrm ead rail, wit andh st itsiff validityrail pa dwass, oconfirmedr more sp withecifi stiffcall yrail, w hpads,en t orhe (per single fastening system set) andmore a rail,specifically, and its validity when the was rail confirmed pad constant with stiffwas rail110 pads, MN/m. or (per single fastening system set) ramoreil pa specifically,d constant whenwas 1 the10 MrailN pad/m. constantHowev ewasr, it 110is n MN/m.ot pos- moreHowever, specifically, it is not possiblewhen the to rail ignore pad theconstant effect wason the 110 rail MN/m. tilting siHowever,ble to ig nito isre not th epossible effect toon ignore the r atheil teffectilting on a nthegl erail, o ftilting stiff- Biaxial loading test using single However,angle, of it stiffness is not possible non-linearity to ignore in the low effect-stiffness on the rail rail support tilting Biaxial loading test using single nangle,ess n o ofn- l stiffnessinearity nonin l-olinearityw-stiff n ines s low ra-istiffnessl suppo r railt fa s supporttening Biaxialset loadingfastening test system using setsingle angle,fastening of systems. stiffness non Therefore,-linearity in inthis low study,-stiffness in consideration rail support of set fastening system set syfasteningstems. systems.Therefo r e Therefore,, in this sintu thisdy, study,in co nins iconsiderationderation of iofts set fastening system set fasteningits properties systems. the most Therefore, typical Japanese in this study, fastening in consideration systems were of Some deviation pitsro ppropertieserties th thee m mostost ttypicalypical Japanese Japane sfasteninge fasten systemsing sys weretems Some deviation itsapplied: properties D8 fasteningthe most typicalsystem Japanese used for fasteningJIS 60kg systems rail (Fig. were 5). Some deviation Rail tilting angle wapplied:ere app D8lied fastening: D8 fas tsystemening susedyste mfor u sJISed 60kgfor J I railS 6 (Fig.0kg r5).ail Rail tilting angle applied:This fastening D8 fastening system wassystem used used on afor slab JIS track 60kg and rail the (Fig. rail pad5). (obtainedRail tilting in angletesting ) (FThisig. 5fastening). This systfastemen iwasng susedyste onm wa aslabs u tracksed o andn a thesla railb tr padack (obtained in testing) Thisstiffness fastening was equal system to orwas above used 30 on MN/m. a slab track and the rail pad (obtained in testing) astiffnessnd the r awasil p equalad st itoffn ores aboves was 30eq uMN/m.al to o r above 30 MN/m. stiffnessIn this was model, equal lateralto or above springs 30 wereMN/m. set as horizontal springs, Fig. 3 Flowchart of the biaxial loading InIn t thishis model,model ,lateral later springsal spri nweregs w seter ase shorizontalet as ho rsprings,izontal Fig.Fig. 3 Flowchart 3 Flowchart of the biaxial of loading the biaxial condition loading and the and railIn this clip model, springs, lateral lower springs rail springs, were set and as horizontallower rail springs,support Fig.condition 3 and Flowchart the rail tilting of the angle biaxial in testing loading spandrin railgs, aclipnd springs,rail clip lower sprin railgs, lsprings,ower ra andil s plowerrings ,rail an supportd lower conditionrail tilting and angle the rail in testing tilting angle in testing andsprings rail wereclip springs, set as vertical lower springs.rail springs, In andparticular, lower railthe stiffnesssupport condition and the rail tilting angle in testing raspringsil sup pwereort s setpri asng verticals were ssprings.et as v e rt Inic aparticular,l springs the. I nstiffness partic- Loading springsof the rail were clip set springs as vertical and the springs. lower rail In springsparticular, are the set stiffnesseither as Loading uofla rthe, th raile s tclipiffn springsess of t andhe rtheail lowerclip s railprin springsgs and are th eset lo eitherwer r aasil (wheel load and lateral force) oflinear the railor bilinear clip springs in the and conventional the lower rail model, springs but arein the set proposedeither as (wheel loadLoading and lateral force) splinearring sor a bilinearre set einit htheer conventionalas linear o rmodel, biline butar iinn thethe proposed conven- (wheel load and lateral force) linearFEM ormodel bilinear and inshown the conventional in Fig. 6, they model, were but set in as the non proposed-linear. tiFEMonal mmodelodel ,and but shown in the inpr Fig.opos 6,ed theyFEM were mo dsetel aasn dnon sh-olinear.wn in Rail FEMAt the model beginning and shown of the in Fig. analysi 6, s,they the were offsets set as of non the- linear. initial Rail FAtig. the6, t h beginningey were s e oft a thes n o analysin-lineas,r . the At t offsetshe be g ofin n theing initialof the FasteningRail Atfastening the beginning force were of set the taking analysi intos, consideration the offsets ofthe thenon - initiallinear Fastening afasteningnalysis, tforcehe o fwerefsets set of takingthe in intoitia considerationl fastening f otherce non we-rlineare set system fasteningproperties force of this were stiffness. set taking into consideration the non-linear systemFastening tapropertiesking int oof c othisnsi stiffness.deration the non-linear properties of this system properties of this stiffness. st iffness. Consisting of 33.2.2 Validation Validation of of the the analysis analysis model model by by loading loading test test Consisting of 3.2 Validation of the analysis model by loading test Consisting27 fastening of 3.2 V alidation of the analysis model by loading test 27 fastening To evaluate the proposed analysis model, a loading 27systems fastening and a rail To evaluate the proposed analysis model, a loading systems and a rail analysisTo using evaluate the theproposed proposed model analysis in which model, loading a tests loading on a systems and a rail analysisTo e vusingalua tthee t proposedhe propo modelsed a nina lwhichysis m loadingodel, atests loa donin ag analysistest track using could the be proposedreproduced, model and inloading which tests loading on a tests test trackon a z atestnal ytracksis u couldsing tbehe reproduced, proposed mandod loadingel in w htestsich onloa ad testing tracktests z Rail clip z Rail clip ontestwere a ttracke sconducted,t t rcouldack c beo uso lreproduced,d that be rtheseepro dtwoanduce loadingdresults, and couldltestsoadi nonbeg atcompared. eteststs trackon a Lateral Railspring clip were conducted, so that these two results could be compared. Lateral spring wereA loading conducted, analysis so that using these the two conventional results could model be compared. was also Lateralspring spring teAs t loadingtrack w analysisere con d usingucted , the so conventionalthat these t w modelo res u waslts co alsould spring Acarried loading out analysisfor comparison. using the The conventional parameters modelapplied was to these also y x spring bcarriede comp outare ford. Acomparison. loading a n aThelys iparameterss using th appliede conv eton ttheseional x carriedanalyses out models for comparison. are indicated Thein Table parameters 1. applied to these y manalysesodel w amodelss also arecar indicatedried out info rTable com 1.pa rison. The param- y x analysesTo validatemodels arethis indicated FEM model, in Table FEM 1. loading analyses and eters Toap pvalidatelied to thisthe FEMse an model,alyses FEMmod eloadingls are ianalysesndicate dand in loadingTo validatetests on thisa test FEM track model, were FEMconducted. loading Theanalyses test track and Tloadingable 1. tests on a test track were conducted. The test track Lower rail Lower rail loadingwas composed tests on of a seventest track fastening were systemsconducted. and a The single test rail track on Lower rail Origin Lower rail wasT composedo validat eof t hsevenis F EfasteningM mod esystemsl, FEM andloa da isingleng an railaly sones Lowerspring rail Origin supportLower springrail wasthe tcomposedest bed as ofshown seven in fasteningFig. 7. Thesystems loading and conditionsa single rail were on spring Origin support spring athend ltoestad beding aste sshownts on ain t eFig.st t r7.a c k The we rloadinge cond uconditionscted. Th ewere test spring support spring thecommon test bed to as both shown the analysesin Fig. 7. and The the loading tests on conditions the test track.were trcommonack was toco bothmpo s theed o analysesf seven andfast e theni n testsg sy sonte m thes a testnd a track. sin- Fig. 4 Overview of the analysis model commonThe uniaxial to both loading the from analyses 0 to and100 thekN testswas carriedon the out test at track. each Fig. 4 Overview of the analysis model gThele ra uniaxialil on th eloading test be fromd as s0h toow 100n i nkN Fi gwas. 7. carried The lo outadi natg each con- Fig.Fig. 4 4 Overview of of the the analysis analysis model model diThetion uniaxials were c loadingommon from to b o0t hto t 100he a kNna lwasyses carried and th oute t eatst eachs on

182 QR of RTRI, Vol. 59, No. 3, Aug. 2018 tloadinghe test angletrack –. 45,Th e55 u andnia x65ia ldegrees, loadin gand fro them 0rail to tilting100 k anglesN was TableTable 1 1 Parameters Parameters applied to to the the analysis analysis models models loading angle – 45, 55 and 65 degrees, and the rail tilting angles cwerearrie measuredd out at eandach compared loading awithngl eeach - 4 5other., 55 a nd 65 degrees, Table 1 Parameters applied toFEM theFEM analysisPracticalPra cmodelstical wereloading measured angle – and 45, compared55 and 65 withdegrees, each and other. the rail tilting angles Table 1Item It e Parametersm UnitappliedUni t to theFEM analysis Practical models aloadingnd the angle rail t–i l45,tin 55g a andngl 65es degrees,were m eandas uthere drail an tiltingd com anglespared Table 1 ParametersItem appliedUnit to analysistheanal yanalysissis solutions omodelslution were measured and compared with each other. Fastening system - analysisFEMType DirectsolutionPractical 8 wwere3i.t3h Result emeasuredach ot hande rand. discussion compared with each other. FasteninItemg sy stem Unit- FEMT ype DirePracticalct 8 FasteningItem system Unit- analysisType Directsolution 8 3.3 Result and discussion RailRai l analysisJISJIS 60kg60kg solutionrrailail FasteningRail system - JISType 60kg Direct rail 8 3.33 .R3Figure e Resultsult 8a ncompares andd di sdiscussioncu sthesi orailn tilting angles obtained through FasteningSleeperSleepe systemrspan span mmm- m Type 6256Direct25 8 3.3 Result and discussion SleeperRail span mm JIS 62560kg rail analysesFigure and 8those compares obtained the throughrail tilting loading angles tests. obtained Both through the RailRa ipadRaill pa dwidth width mmm m JIS 60kg140140 rail RailRailRSleepera iclipl padclip span widths spanpan mmmmmmmm 116111406256 “practicalanalysesFigFigureur esolution and 8 8 cthose ocomparesm”p andaobtainedre sthe theth anglee rail throughra itilting lcalculated til tloading ianglesng a byn tests.obtainedg lthees proposedo b Botht throughain ethed Sleeper span mm 2 625 Figure 8 compares the rail tilting angles obtained through YoungYounRailg'’ss mmodulus clippadodu lspanwidthus o fof r a il kNmm/mmmm 201161406 tFEMh“practicalranalysesou ganalysish an a andsolutionly weres ethoses a largern” dandobtained th o thanthese o anglethe bthroughta anglein ecalculatedd tobtainedloadinghroug h by tests.lino athe thed i n proposedloadingg Both tes tthes . Rail pad width kN/mmmm 2 140206 analyses and those obtained through loading tests. Both the Young’sPRailoirailss oclipmodulusn ra spantio of mm- 2 0.3 116 - tests,FEM“practical at analysis “any solution loading were ”larger angle, and thanthe and ”angle the results angle calculated of obtained the proposed by in the the proposed loading FEM Rail clip span kN/mmmm 116206 Both the practical solution and the angle calculated by Second rail About 4 5 “practical solution” and the angle calculated by the proposed Young’sPoisson modulus ratio of m- m 2 0.3- 309 ×- 10 tanalysishtests,eFEM pro atpanalysis wereo anysed closer loadingF wereEM to alarger then angle,al testy thans is andresults w the e resultsr eangle obtainedlar g ofobtainede r the tonh aproposed then in t tesththee aloadingtrack n FEMgle Young’smoment modulustrong ofax is kN/mm2 206 FEM analysis were larger than the angle obtained in the loading SecondPoisson railAbout ratio kN/mm-4 0.3 206 - 5 othanbanalysisttests,ai nthee d atpractical i werenany th e loadingcloser l osolution.adi nto g angle,the te s testts , and aresultst a resultsny obtainedloa ofdi n theg aon nproposed gthele, testand track FEMre- of area rail About mm - 309×10 tests, at any loading angle, and results of the proposed FEM momentSecondPoisson strong ratioAbout axis mm-4 4 -0.3 512 × -1 045 thananalysisIt the was practical were considered closer solution. to that the test one results reason obtained for this on was the that test thetrack ofPoisson rail ratiowea k axis mm- 0.3- 309×10- sanalysisults of twerehe p closerropose tod theFE Mtest a resultsnalysi sobtained were c lonose ther t otest th tracke tes t ofmoment Secondarea strongAboutAbout axis 4 5 Second About mmmm4 - - 512×10309×104 6 rinfluenceesthanultsIt theo b was oft practicala i then considereded frictional on solution. the thattforcees t onet rgenerateda ck reason than forbyth econt this pra act wascti cbetween a thatl so l theu - ofTofmoment orail rareasio n st ifweakfnstrongesAbouts oaxisf r aaxisi l mmkNm4 m - - 2309×1035 × 105 than the practical solution. moment strong axis mm4 - 512×104 ttheioinfluencen .rail Itand was theof the consideredbase frictional plate shoulder that force one generatedcould reason not for beby ignored thiscont wasact in between thatthese the TorsionofIofni trailareaia lstiffness cl ampweaking Aboutof fo railraxisce kNmmkN - 3.94235×106 It was considered that one reason for this was that the of area About mm4 - 512×104 typestheinfluenceI trail ofw aandrails c of othefasteningn thes baseid frictionaler eplate dsystems th shouldera tforce o whichne generated rcoulde acontainso nnot f o bybe ra tignoredcontbaseplate.his actwa inbetweens ttheseh Ita t InitialTorsionofRa raili lclamping lo stiffnesswer sweaktif fforcen ofes axissrail mmkkNmmkNN/m4 m Fig-. 6- (a) 3.94 512×10235×1027.9 4 6 influence of the frictional force generated by contact between ofR arailil c lip weakUp waxisard kN/mm 0.58 6 twashtypesethe i nthought railf lofu eand nrailc ethat, the fasteningof basetforhe the platefr i systemscreasont ishoulderona l given whichfor couldce above, gcontaine nnoter theabe tae ignored tiltingdbaseplate. by cangleso inn tthese a c Itt RailTorsionInitial lower clamping stiffness stiffness forceof rail kN/mmkNmmkN Fig.6Fig.6 (a) -( b) 3.94 27.9235×10 the rail and the base plate shoulder could not be ignored in these Torsionstiffne sstiffnesss Do wofn wrailard kNmmkN/mm - 235×105.95 6 obtainedwastypes thought of through rail that, fastening loading for the systemstests reason were givenwhich smaller above,contain than the thosea baseplate.tilting obtained angles It RailInitialRail clip lower clampingUpward stiffness force kN/mmkN/mmkN Fig.6 (a) 3.940.58 27.9 btypesetwe eofn railthe fasteningrail and systemsthe bas ewhich plat econtain should ae rbaseplate. could no t Itbe InitialL aclampingteral stiffn forceess kkNN/m m Fig.6209 .(b)63 3.94 243.9 obtainedwas thought through that, loading for the testsreason were given smaller above, than the those tilting obtained angles stiffnessRailRail clip lower Downward Upwardstiffness kN/mmkN/mmkN/mm Fig.6 (a) 5.950.5827.9 iwasgfromno rthought ecalculation.d in t hthat,ese tfor yp ethes o reasonf rail fgivenasten iabove,ng sys thetem tiltings whi canglesh con - RailR aloweril supp stiffnessort lower kN/mm Fig.6Fig.6 (a) (b) 27.9 fromobtained calculation. through loading tests were smaller than those obtained stiffnessRailLateral clip stiffnessDownwardUpward kN/mmkkN/mmkN/mmN/mm 209.63300.0 243.9305.9500.58.0 tobtainedain aFrom ba throughse theseplate .resultsloading It w aof stests ttheho uwereaboveght smallert-hmentionedat, fo thanr th ethosecomparison, reas obtainedon giv eitn Rail clip stiffnUpwardess kN/mm Fig.6 (b) 0.58 fromFrom calculation. these results of the above-mentioned comparison, it RailstiffnessLateral support stiffnessDownward lower kN/mmkN/mm Fig.6209.63 (b) 243.95.95 afromisb o consideredve calculation., the til t thatin g a theng l proposedes obtai n FEMed th r analysisough lo a modelding t wasests stiffness Downward kN/mm 300.0 300.05.95 is consideredFrom these that results the of proposed the above FEM-mentioned analysis comparison, model was it RailLateralstiffness support stiffness lower kN/mm 209.63 243.9 wvalidated.ere smal l er than those obtained from calculation. Lateral stiffness kN/mmkN/mm 209.63300.0 243.9300.0 From these results of the above-mentioned comparison, it Rail stiffnesssupport lower validated.isF r consideredom th ese r thatesu lt thes o f proposedthe abov e FEM-men t analysisioned co m modelparis o wasn, Rail support lower kN/mm 300.0 300.0 is considered that the proposed FEM analysis model was stiffnessFastening kN/mm 300.0 300.0 it4 . i validated.s Methodconside re d for th at calculating the propose d loading FEM an a conditionslysis model w inas stiffness Uniaxial loading validated. systemFastening (0Uniaxial to 100 loadingkN) va4l i.d aMethodted. for calculating loading conditions in Rail biaxial loading tests Fixing jig Fasteningsystem (45,Uniaxial (055, to 65 100kN) degloading.) biaxial4. Method loading for tests calculating loading conditions in Fixing jig Fastening Uniaxial(45,(0 55,to loading100kN) 65 deg) Rail 4. Method for calculating loading conditions in system (0 to 100kN) biaxial loading tests Fixing jig system (45, 55, 65 deg) Rail biaxial4.1 Method loading for tests verifying loading conditions in Fixing jig (45, 55, 65 deg) Rail 4. Met hod for calculating loading conditions in bi- biaxial4.1 Method loading for verifying loading conditions in axial loading tests 4.1biaxial4.1 Method Method loading for for verifying verifying loading loading conditions conditions in in biaxial loading biaxialFollowing loading the validation of the proposed FEM model, the Rail support Sleeper span 625 mm *6 4.1 MFollowinge thod fo ther v validationerifying oflo thead iproposedng cond FEMitio nmodel,s in b thei- validity of the method for calculating the biaxial loading Rail support Sleeper span 625mm*6 validityaxFollowingia l of lo a thedi nthe methodg validation for calculatingof the proposed the biaxialFEM model, loading the conditionsFollowing for the the FEM validation model of was the also proposed confirmed. FEM model, the Rail support Sleeper span 625mm*6 conditionsvalidity of for the the methodFEM model for was calculating also confirmed. the biaxial loading Rail supportFig.Fig. 7 7 Loading LoadingSleeper test span on 625mm*6 thethe test test track track validityFigure 9 ofshows the the method comparison for calculating of responses the such biaxial as rail loading tilting Fig. 7 Loading test on the test track FigureconditionsFollo 9w showsin forg t hthe thee vFEM comparisonalida modeltion o wasfof t hresponses ealso pr oconfirmed.pos suched F Eas M rail m tiltingodel, tconditionshe validit yfor o fthe th FEMe me tmodelhod fo wasr ca alsolcul aconfirmed.tRailing the b iaxial load- Fig. 7 Resutl Loading45 test deg. on55 the deg. test65 deg.track Figure 9 showsBolt the & comparison Nut of responses such as rail tilting Fig. 7 LoadingResutl test45△ on deg. the55○ test deg. track65□ deg. Figure 9 shows the comparison of responsesRail such a s rail tilting Loading test Bolt & Nut Rail clip △ ○ □ Anchor bolt Rail FEMLoading AnalysisResutl test 45 deg. 55 deg. 65 deg. Rail clip Resutl 45 deg. 55 deg. 65 deg. Anchor bolt Bolt & Nut Rail FEMLoading Analysis test △ ○ □ Bolt & Nut Rail clip 0.04 Loading test △ ○ □ Rail clipBaseplate 0.04 FEM Analysis Anchor bolt FEM Analysis Anchor bolt Baseplate 0.030.04 0.040.03 Baseplate Baseplate 0.020.03 0.03 (rad.) 0.02

0.01(rad.) 0.02 Insulation shim Rail pad (30MN/m) 0.02 (rad.) 0.01 Rail pad (30MN/m) Rail tilting angle

(rad.) Insulation shim 0.010 Rail pad (30MN/m) Rail tilting angle 0.01 Fig.Insulation 5 Type shim directRail 8 pad(D8) (30MN/m) fastening system 00 20 40 60 80 100 Insulation shim Rail tilting angle Fig. 5 Type direct 8 (D8) fastening system Rail tilting angle 0 0 20 40 60 80 100 0 Load (kN) Fig.Fig. 5 Type Type direct direct 8FEM (D8) 8 (D8) analysis fastening fastening system system 0 20 40 60 80 100 Fig. 5 Type direct 8 (D8) fastening system 0 20(a) Practical40Load solution (kN)60 80 100 PracticalFEM analysis solution (a) PracticalLoad solution(kN) PracticalFEM analysis solution 0.04 Load (kN) -15 FEM analysis (a) Practical solution Practical-250 solution 0.04 (a) Practical solution -15 Practical-200-250 solution 0.030.04 -15 -150-200-250 0.040.03 -15 -250 -5 -100-150-200 0.020.03 -5 -200-100-50-150 (rad.) 0.030.02

-150 (rad.) -5 -100-500 0.010.02 -5 Load (kN) -100 (rad.) Load Load (kN) 5 500 0.020.01

-50 Rail tilting angle (rad.) Load Load (kN) -50 Load Load (kN) 510 0 -10 50 0 01 0 -1 -2 -3 Rail tilting angle 0.01

Load Load (kN) 0 0.01 Load Load (kN) 5 50 0 Load Load (kN) 0 20 40 60 80 100 Displacement10 0 (mm)-10 1 0 -1 -2 -3 Rail tilting angle Load Load (kN) 5 50Displacement (mm) Rail Rail tilting angle 0 0 20 40 60 80 100 Displacement10 0 (mm)-10 Displacement1 0 -1 (mm)-2 -3 0 Load (kN) (a)10 Rail clip0 stiffness-10 (b) Lower1 0 rail-1 stiffness-2 -3 0 20 40 60 80 100 Displacement (mm) Displacement (mm) 0 (b)20 Proposed40Load FEM (kN)60 analysis80 100 Displacement(a) Rail clip stiffness (mm) (b)Displacement Lower rail stiffness (mm) Load (kN) Fig.(a) Rail6 Ccliponfiguration stiffness of(b) vertical Lower stiffness rail stiffness (b) ProposedLoad FEM(kN) analysis (a) Rail clip stiffness (b) Lower rail stiffness Fig. 8 Comparison of analyses and test Fig. 6 Configuration of vertical stiffness (b) Proposed FEM analysis Fig. 66 Configuration Configuration of vertical of vertical stiffness stiffness Fig.Fig. 8 8 ComparisonComparison(b) Proposedresults of of FEM analyses analyses analysis and and test test Fig. 6 Configuration of vertical stiffness Fig. 8 Comparisonresults of analyses and test Fig. 8 Comparison of analyses and test resultsresults QR of RTRI, Vol. 59, No. 3, Aug. 2018 183 angle, rail displacement and rail clip stress between the three ing conditions for the FEM model was also confirmed. differentangle, rail methods displacement applied. and rail To confirmclip stress the between validity the of three the Design load (Load ‘A’ & Load ‘B’) Figure 9 shows the comparison of responses such as Design load (Load ‘A’ & Load ‘B’) methoddifferent for methods calculating applied. biaxial loading To confirm conditions the validity by means of theof ramethodil tiltin forga ncalculatinggle, rail d ibiaxialsplace loadingment a nconditionsd rail cli pby s tmeansress b ofe- the proposed method, the conventional calculation method was Conventional method Proposed method twtheee nproposed the thr emethod,e differ theent conventional methods ap calculationplied. To c methodonfirm wasthe valsoalid iexaminedty of the forme comparison.thod for cal c u Thelati nbiaxialg biax loadingial load conditionsing condi- Conventional method Proposed method also examined for comparison. The biaxial loading conditions Beam theory tiobtainedons by m bye a eachns o f ofth e the p r twoopo s methodsed meth o wered, t h thene co n appliedventio n ina l obtained by each of the two methods were then applied in Beam theory Rail tilting FEM cbiaxialalcula ti loadingon me th testsod w usingas a ls ao singleexam in fasteninged for co systemmpar is set.on . Furthermore,biaxial loading biaxial tests load usinging testsa single on a fastening test track system were also set. - Load distribution analyRail tiltingsis model FEM The biaxial loading conditions obtained by each of the two conducted,Furthermore, applying biaxial design loading loads tests directly. on a test The track validity were of alsothe - Load distribution analysis model methods were then applied in biaxial loading tests using a proposedconducted, calculation applying designmethod loads was examineddirectly. by The comparing validity of the the Rail tilting angle single fastening system set. Furthermore, biaxial loading responseproposed values calculation obtained method from waseach examined test. by comparing the Rail tilting angle - Rail tilting angle teresponsests on a valuestest t robtainedack wer frome als oeach con test.duc te d, applying design - Rail tilting angle - -Distributed Rail tilting angleforce - -Rail Distributed rollover forcemoment lo ads directly. The validity of the proposed calculation - -Rail Rail rollover tilting angle moment 4.2 Calculation of load distribution and rollover - Rail rollover moment - Rail rollover moment m4.et2h oCalculationd was exami n ofed b loady co m distributionparing the r e andspon s rollovere values omomenbtained ftr o m each test. moment Biaxial loading condition 4.2 CIna lc theul a proposedtion of lo methodad di s fortri b calculatingution an d biaxial rollo v loadinger mo- (per singleBiaxial fastening loading conditionsystems set) conditions,mInen thet the proposed load distribution method for and calculating the rail rollover biaxial moment loading (per single fastening systems set) wereconditions, derived the using load the distribution proposed FEMand the analysis rail rollover model andmoment the were derived using the proposed FEM analysis model and the balanceIn th ofe forcespropo sundered m theeth loadingod for c pointalcul inat itheng FEMbiax imodelal loa dwasing Biaxial testing using single Biaxial testing on cconsidered.obalancendition ofs, forcest h Fige loure underad 10di stheshowstri loadingbut itheon balancepointand t inh e ofthe r aforces FEMil rol modellwhenover mwastheo- Biaxialfastening testing system using set single Biaxiala test testing track on mdesignconsidered.ent w eloadsre d e suchr Figureived as u s10 thein g shows wheelthe p rtheloadop obalances eandd F theE ofM lateralforcesanaly s forcewhenis m o aredthee l fastening system set a test track aappliedndesignd the onloadsba thela n srailcuche ohead. fas f o ther c e swheel und eloadr th eand lo athedin lateralg poin forcet in tarehe Comparison of responses applied on the rail head. (Rail tilting angle,Comparison rail displacement, of responses rail clip stress) FEM Atmo thedel centerwas c o ofns theide r railed. bottom Figur e of 1 0 the sh fasteningows the b systemalance (Rail tilting angle, rail displacement, rail clip stress) ounderf forc Ate thes w the h loadinge centern the point, d ofes theig n the raillo a distributed d bottoms such ofa s vertical thethe fasteningw h forceeel l o Wa systemd wasand under the loading point, the distributed vertical force W was Fig. 9 Method for verifying biaxial loading thderie lvedater asal thefor csume ar eof a thepp lreactionied on t hofe lowerrail h erailad .springs and rail Fig. Fig.9 Method 9 Method for verifying for verifying biaxial loading biaxial conditions loading re- clipderivedA springs,t th ase cthee andn tsume rthe o fof distributedth thee r areactionil bo horizontaltto ofm lowerof th forcee rail fas springstHe nwasing derivedsandyst reailm conditionssults results clip springs, and the distributed horizontal force H was derived conditions results uasnd theer sumthe lofoa thedin reactiong point ,of t hlaterale dis tsprings.ributed v Theerti crailal rolloverforce W wmomentasas theder sumi vMed was ofas the tderivedh ereaction sum in o considerationf of th laterale reac tsprings.ion of o fthese l o w Thee forces,r rrailail srolloverthepr irailngs Load Gauge aheightnmomentd ra iandl c Ml isop was son.p rderived in gs, a innd consideration the distribu ofte thesed hor forces,izonta lthe fo rrailce (WheelLoad load and Track height and so on. lateral(Wheel force) load and cornerGauge P e outerTrack H was derived as the sum of the reaction of lateral springs. Pp lateral force) sidecorner ep sideouter z Q T4.3he rai Methodl rollover m forome nt calculating M was deriv ed biaxial in cons ide loadingration of z side side 4.3 Method for calculating biaxial loading Q thconditionsese forces, th e rail height and so on. y conditions y d d h l r 4.3 MBiaxial etho dloading for c conditionsalculati nareg derivedbiaxia followingl loadin gthe c aboveondi- q d d Fastening system immediately h l r tBiaxialions loading conditions are derived following the above q P calculation. When the derived vertical and horizontal forces Fasteningunder loading system positionimmediately l R P P arecalculation. applied to Whenthe rail the head derived directly, vertical the railand rolloverhorizontal m omentforces l l z r under loading position x P R M Rl z r r becomesareB appliediax ia excessivel ltooa thedin grail and c oheadn thedit idirectly,o lateralns ar e force thede rrail iv doesne drollover fo’tl lo matchw momenting thethe x R c r acalculatedbbecomesove cal c lateral excessiveulatio force.n. andW h e Therefore, then t h laterale de rthe i forceve heightd v e doesn’tr tofic theal a matctestnd railh o therisi- M c H W , .., W , ...,W zdeterminedocalculatedntal force laterals ina re consideration force.applie d Therefore,to t h ofe ra the ithel h eheight balancead di ofr e cthe oftl y ,test betweenth erail ra isi l W -n 0 n W-n,..,W-1, W0, W1,...,Wn W H b rdistributedodeterminedllover m oforces m inen t considerationandbec railom erollovers ex ce ofs moment.s iv thee an balanced the la ofte ra betweenl force i b dodistributedesnIn’t addition,mat forcesch t hforcee and ca lLrailc0u ils arollover appliedted lat efrommoment.ral ftheorc opposite e . Ther sideefor ewhile, the i P : Wheel load (external force) heightIn o faddition, the test force rail Lis0 dise appliedtermin efromd in the con oppositesiderat isideon o whilef the Load A and Load B are applied because of the stabilization of QP :: LateralWheel loadforce (external (external force) force) btheaLoadla nbiaxialc eA o andf bloade Loadtw etestinge nB d areis tas rappliedi bshownuted becausef oinrc Fig.es a ofn11.d the r a Theistabilizationl ro lloadlove rL m0 isofo- eQp :: OffsetLateral of force point (external of action force) of wheel load mnormallytheent .biaxial 10 loadkN. testing Therefore, as shown the effect in Fig. of 11.these Theforces load is Lalso0 is e : Offset of point of action of wheel load hqp : Height of point of action of lateral force normallyIn add 10iti okN.n, f o r Therefore,ce L0 is a theppl ieffected fr oofm thesethe o forcespposit ise salsoide considered in this calculation. Ph q :: ReactionHeight of ofpoint rail ofclip action at gauge of lateral corner force (GC) wconsidehile BasedLoredad A onin a thisn thesed calculation.Lo calculationad B are a p methods,plied be c theau s biaxiale of th loadinge stabi- l PP：l :Reaction Reaction of of rail rail clip clip at at field gauge corner corner (FC) (GC) liconditionszatioBasedn of ttoh one be b i theseaappliedxia l calculationlo atod ate singlestin methods,g afastenings show then systemi n biaxial Fig . set1 1 loadin .were Theg r ： dP ：r DistanceReaction between of rail clip original at field position corner (FC)and rail clip (GC) localculatedconditionsad L0 is asn too shownr bema appliedlly in 1 0Table ktoN .a 2. singleT h Theere fasteningf designore, th axlee systemef floadect osetwasf t hwere setese l ： dd ：l DistanceDistance between between original original position position and and rail rail clip clip (FC) (GC) foatcalculatedr c150es i skN, als whichaso c shownons isid ea rinstandarde dTable in th 2. iloads c a The lforcu l designaconventionaltion. axle load lines, was and set r ： Wdr： ReactionDistance ofbetween lower rail original stiffness position (i= - nand～n ）rail clip (FC) at 150 kN, which is a standard load for conventional lines, and i the Bdesiasegnd forceson the ofse the ca lLoadculat Aio nand m Loadethod Bs, werethe balsoiax iderived.al load- ： ～ ） Wi (WReaction : Reaction of lower of lower rail stiffness rail stiffness (i= -n at originaln position) inLoadingtheg c designond it conditionsi oforcesns to ofb e thewere ap Loadp li deriveded A t oand a separately sLoadingl eB f awere s usingten alsoin g both derived.sys t theem 0 ： (W0 : Reaction of lower rail stiffness at original position) Loading conditions were derived separately using both the bi Distance between original position and Wi sproposedet were cmethodalculat eandd a thes s hconventionalown in Tab method.le 2. T h e design axle ： Rb ：i ReactionDistance of between lateral springoriginal of position fastening and system Wi (GC) loproposedad was s methodet at 1 5and0 k theN, conventionalwhich is a s method.tandard load for con- l ： R：l Reaction of lateral spring of fastening system (GC) ve ntional lines, and the design forces of the Load A and Rr Reaction of lateral spring of fastening system (FC) 4.4 Test result and discussion R ：Reaction of lateral spring of fastening system (FC) Lo4.4ad TestB we rresulte also danderiv discussioned. Loading conditions were derived c ：r Distance between original position and lateral spring ： separa tely using both the proposed method and the con- Wc ：DistributedDistance between vertical originalforce position and lateral spring Figure12 compares the rail tilting angle and rail ： ventioFigure12nal meth od compares. the rail tilting angle and rail HW：DistributedDistributed horizontal vertical force force displacement while loading using the three methods. The rail ： displacement while loading using the three methods. The rail MH：RailDistributed rollover horizontalmoment force tilting angle measured in the test using the proposed method was M：Rail rollover moment 4about.tilting4 Te halfs anglet r eofs measureduanglelt an measuredd dini sthecu testsins ithe ousingn test the track proposed test when method Load was A Fig. 10 Balance of forces under the loading about half of angle measured in the test track test when Load A Fig. 10 Balance of forces under the loading point in the and Load B were applied. The result was almost the same for pointFig. 10 in the Balance FEM modelof forces under the loading railand Fdisplacement. Loadigure B12 were com applied.p ares t h e The rai lresult tilti nwasg a almostngle a nthed rsameail d foris- pointFEM in themodel FEM model plrailace displacement.ment while l oading using the three methods. The

184 QR of RTRI, Vol. 59, No. 3, Aug. 2018 Gauge corner Track outer Gauge Track Gauge corner Track outer Gauge Track Test track FEM analysis Practical solution side side corner side outer side Test track FEM analysis Practical solution Gaugeside corner Trackside outer cornerGauge side outerTrack side Test track FEM analysis Practical solution Lside (Load A) sideL corner side e outerL (Load side B) 0.03 A e e 0 L0 e B 0.03 LA (Load A) e e L0 L e e L (Load B) L (Load A) θ L θ Lθ 0 e e L B(Loadθ B) 0.03 A θ A e e 0θ B θ 0A B θ B 0.02 θ A θ B θ A θ B 0.02 A B A B 0.02 h 0.01 h h 0.01 h (rad.) 0.01 h (rad.) h 0 (rad.) 0 0 Rail Rail tilting angle -0.01

Fig. 11 Schematization of biaxial loading conditions Rail tilting angle Fig. 11 Schematization of biaxial loading -0.01 Application of Application of Rail Rail tilting angle Application of Application of Fig. 11 Schematization of biaxial loading -0.01 Load A Load B Fig.conditions 11 Schematization of biaxial loading ApplicationLoad A of ApplicationLoad B of conditions Load A Load B conditions (a)(a) RailRail tiltingtilting angleangle (a) Rail tilting angle Table 2 Biaxial loading conditions to be applied to a Gauge corner side Track outer side single fastening system set Gauge corner side Track outer side Table 2 Biaxial loading conditions to be applied to 2 Gauge corner side Track outer side Table 2 Biaxial loading conditionsFEM to be Pappliedractical to 2 Tablea single 2 fastening BiaxialItems loading systemUn conditionsi tset to be applied to 21 a single fastening system set analysis solution 1 a single fastening system set FEM Practical 10 Items Load UnitkN FEM64.9 Practical40.1 0 LoadItems A Unit FEManalysis Practicalsolution Items Angle Unitdegr ee analysis36.3 solution39.5 (mm) 0-1 analysis solution (mm) -1 Load kN 64.9 40.1 (mm) -1 Load A LoadLoad kNkN 634.95.5 40.130.6 -2 LoadLoa dA B Load kN 64.9 40.1 -2 AngleAngle degreedegree 36.346.5 439.58.2 -2-3 Load A Angle degree 36.3 39.5 Rail displacement -3 Rail Rail displacement FEM Practical AngleLoad degreekN 36.335. 5 39.530.6 -3 Test track FEM Practical Height of the Rail displacement Load B Load kNmm 35.805 30.680 Test track analysisFEM Practicalsolution Loadloa dBin g poLoadsAngleition degreekN 35.46.55 30.648.2 Test track analysis solution Load B Angle degree 46.5 48.2 (b) Rail verticalanalysis displacementsolution Height ofAngle the degree 46.5 48.2 (b) Rail vertical displacement Height of the mm 80 80 (b) Rail vertical displacement Heightloading of position the mm 80 80 Fig. 12 Comparison of the rail tilting angle loading position mm 80 80 Fig.Fig. 12 12 Comparison Comparison of the of rail the tilting rail angletilting and angle rail verti- loading position Fig.and 12 rail Comparisonvertical displacement of the rail tilting angle and railcal vertical displacement displacement and rail vertical displacement

600 600 Yield line ○ Test track 600 Yield line ○ Test track ElasticYield limitline line ○△ Test track Elastic limit line △ Proposed method (FEM analysis) ) ElasticGoodman limit line line Proposed method (FEM analysis) 2 △ ) 400 Goodman7 line ◇ Proposed Conventional method method (FEM (Practical analysis) solution) 2 400 ◇ ) Goodmanfor 107 cycles line Conventional method (Practical solution) 2 400 for 10 cycles ◇ for 107Goodmancycles Conventional method (Practical solution) Goodman 5 Goodmanline for 10 5 (N/mm 200 line for 105 (N/mm 200 linecycles for 10 (N/mm 200 cycles Measuring point Stress variation Stress variation cycles Measuring point Stress variation Stress variation Measuringof clip stress point Stress variation Stress variation 0 of clip stress 0 of clip stress 0 0 500 1000 1500 2000 0 500 1000 1500 2000 (Cross section of rail clip) 0 500 1000 15002 2000 (Cross section of rail clip) MeanMean stressstress (N/mm(N/mm2)) (Cross section of rail clip) Mean stress (N/mm2)

Fig.Fig. 1313 ComparisonComparison ofof thethe railrail clipclip stressstress duringduring loadingloading atat thethe gaugegauge cornercorner sideside Fig. 13 Fig. Comparison 13 Comparison of the of rail the cliprail clipstress stress during during loading loading at at the the gauge gauge corner corner sideside The reason for such a difference could be attributed in part rail tTheiltin reasong ang lfore m sucheas ua rdifferenceed in the could test ubes iattributedng the p rinop partose d t5.es tValidation track than tofhe thestre stests m emeasuthodred u sforing obtainingthe conven trailiona l to theThe effectreason offor frictionsuch a difference between thecould rail be andattributed the baseplate in part 5. Validation of the test method for obtaining rail mto et theho d effect was a ofb o frictionut half o betweenf angle m theea s railur e andd in thethe baseplatetest trac k 5.mrestraint Validationethod. force of the test method for obtaining rail toshoulder the effect in of the friction tests using between a single the rail fastening and the system baseplate set. restraint force tshoulderest whe n in L o thead A tests and usingLoad B a w singleere a p fasteningplied. T h systeme resul tset. wa s restraint Cons forceiderin g these results, the proposed method en- shoulderHowever, in overall, the tests regarding using the a single method fastening for calculating system biaxial set. aHowever,lmost th eoverall, same fregardingor rail di sthepla methodcemen tfor. calculating biaxial ablesIn u thiss t ochapter, reprod theuc eeffect actu ofal the tr atestck conditionscondition suchs mo asre theap - However,loading conoverall,ditions, regarding it is safe the to methodsay that forthe calculatingproposed method biaxial is In this chapter, the effect of the test conditions such as the loadingThe con readitions,son fo rit sisu csafeh a todi fsayfer ethatnce the co uproposedld be at tmethodributed is i n ploadingropInr ithisa tposition,e lchapter,y than the wthei tnumber heffect the ofc ofo nthe vfasteninge ntesttio conditionsna lsystem metho suchsetsd, a s andas is the testse e n loadingmore suitable conditions, than it the is conventionalsafe to say that method the proposed when judging method from is loading position, the number of fastening system sets and test pmoreart tsuitableo the e fthanfect theof fconventionalriction betw methodeen the when rail ajudgingnd the from base - loadingftemperature,rom t hposition,e co monp athetheris numberoresultn wi tofh of tthe hfasteninge railbia xrestraintia lsystem load forcein setsg t e testsandst r etestweresu lt s morethe comparisonsuitable than of the the conventional test results. method when judging from temperature, on the result of the rail restraint force tests were pthela tcomparisone shoulder ofin the th etest te sresults.ts usin g a single fastening system temperature,overified.n a test tr Aaon ctypek the. directresult 8of fastening the rail restraintsystem usedforce for tests JIS were 60kg the comparisonFigure 13 of shows the test the results. comparison of rail clip stress during verified. A type direct 8 fastening system used for JIS 60kg set. FigureHowe v13er ,shows overa thell, rcomparisonegarding t hofe railme tcliphod stress for c aduringlculat - verified.rail, comprising A type adirect rail pad 8 fastening with a steel system slide usedplate forof stiffnessJIS 60kg 60 loading.Figure 13 Here, shows the the rail comparison clip stress of measuredrail clip stress on theduring clip rail, comprising a rail pad with a steel slide plate of stiffness 60 iloading.ng biax i al Here, load i theng c railon d clipitio n stresss, it is measured safe to sonay thetha t clip th e raMN/m,il, comprising was adopted a rail padin each with verification a steel slide test. plate of stiffness 60 loading.fastened at Here, the gauge the railcorner clip side stress was measuredadopted for on comparison the clip MN/m, was adopted in each verification test. pfastenedropose dat m theet hgaugeod is cornermore sidesuit awasble adoptedthan th fore c comparisononventiona l MN/m,5 . Va waslid aadoptedtion o fin t eachhe t verificationest metho test.d fo r obtaining rail fastenedbecause at stressthe gauge measured corner atside this was point adopted is most for comparison severe. A mbecauseethod w stresshen j measuredudging f ro atm thisthe pointcomp a isr is moston o fsevere. the te s t Are - 5.1 re Effectstrain t offo rc loadinge position and number of becausecomparison stress of measuredrail clip stresses at this on point a Goodman is most diagram, severe. shows A 5.1 Effect of loading position and number of scomparisonults. of rail clip stresses on a Goodman diagram, shows 5.1 Effect of loading position and number of comparisonthat the stress of rail measured clip stresses in the on test a Goodmanusing the proposeddiagram, showsmethod fasteningfastening systemsystem setssets that Ftheig ustressre 13 measured shows th ine ctheom testpar iusingson o thef ra proposedil clip st rmethodess dur - I n this chapter, the effect of the test conditions such as thatagreed the stress more measured with results in the obtained test using on the proposed test track method than the fastening system sets iangreedg loa d moreing. withHer e results, the r a obtainedil clip s t onres s the m e testasu trackred o n than the thecli p the loIna dordering ptoo sdetermineition, the the nu influencember of fofas loadingtening spositionystem sonet s agreedstress moremeasured with using results the obtainedconventional on the method. test track than the In order to determine the influence of loading position on fstressasten measureded at the using gaug thee co conventionalrner side wa method.s adopt e d for compari- aresultsndIn t eorder sfromt te tomtests pdetermineer toat uobtainre, theo nrail influenceth restrainte resu loft force, oloadingf th threee r positionai ltests res twere ronai n t stress measuredConsidering using these the results, conventional the proposed method. method enables us results from tests to obtain rail restraint force, three tests were son bConsideringecause str ethesess m results,easure dthe a tproposed this poi methodnt is m enablesost sev eusre . resultsfcarriedorce fromte outsts tplacingwestser eto v obtainetherif iloaded rail. inA restraintthreetype differentdi rforce,ect 8 positions:threefaste ntestsing neutralweresyste m to reproduceConsidering actual these track results, conditions the proposed more method appropriately enables thanus carried out placing the load in three different positions: neutral Ato c reproduceompariso n actual of ra trackil cli p conditions stresses o moren a G appropriatelyoodman dia g thanram , carrieduposition,sed foutor andJplacingIS head 60k the gand r loada bottomil, cinom three ofpr ithes idifferentn rail.g a r a Figure ipositions:l pad 14 w ishowst neutralh a s thete e l towith reproduce the conventional actual track method, conditions as is moreseen from appropriately the comparison than position, and head and bottom of the rail. Figure 14 shows the swithhow thes t hconventionalat the stres method,s measu asre dis iseenn th efrom tes tthe us comparisoning the pro - position,sthreelide loadingpl andate headof positions st iandffne bottomss and 60 Fig.M ofN the15/m ,rail.shows wa s a Figurethedo ptestte 14d results. i nshows eac h the ve ri- withwith the theconventional biaxial loadingmethod, as test is seen results from on the a comparison test track. three loading positions and Fig. 15 shows the test results. pwithose d theme th biaxialod ag re loadinged mo re test w ith results resu lt ons o b at ai testned o track.n th e threefica tloadingiOfon thetes tthrpositions. ee obtained and Fig.results, 15 shows the rail the restraint test results. force closest with the biaxial loading test results on a test track. Of the three obtained results, the rail restraint force closest Of the three obtained results, the rail restraint force closest

QR of RTRI, Vol. 59, No. 3, Aug. 2018 185

to the target value was when the bottom of the rail was loaded. Furthermore, when considering real-life situations where rail Rail head

to the target value was when the bottom of the rail was loaded. axisFurthermore, force is generated when consideringby thermal expansion, real-life situations and in order where to rail Rail head 149 5to.1 the E targetffect valueof lo awasdin wheng po stheiti bottomon an dof n theum railbe rwas of loaded.fasten - ensureaxis thatforce i nis thegenerated tests toby obtainthermal railexpansion, restraint and force in order rail to Neutral axis

Rail head Furthermore, when considering real-life situations where rail

ing system sets 149

displacement is in the same longitudinal direction, the line along

15 axisensure force is that generated in the by tests thermal to obtain expansion, rail restraintand in order force to rail Neutral axis

which external force is exerted should be the same as that of the 77.8

displacement is in the same longitudinal direction, the line along 149 railensure fasteningIn o thatrde r irestraintnto thedet e testsr mforce.in e to t h obtain Ase i naf lresult ue railnc e restraintofof theloa drail in force grestraint po si railtio n Neutral axis 15

which external force is exerted should be the same as that of the 77.8 odisplacementn results fr isom in thetes tsames to longitudinalobtain rail direction,restrain tthe fo linerce ,along thre e Bottom of rail

test, it became clear that the bottom of the rail was the most 15 rail fastening restraint force. As a result of the rail restraint Unit [mm] twhichests w externalere ca rforceried isou exertedt placi nshouldg the be lo thead samein th rase ethat di foffe rtheen t 77.8 suitabletest, loadingit became position. clear that the bottom of the rail was the most Bottom of rail prailos ifasteningtions: ne restraintutral p oforce.sition , Asan da hresultead aofn dthe b orailtto mrestraint of th e suitableNext, railloading restraint position. force tests using both a single fastening Fig. 14 Loading positionUnit [mm] rtest,ail. it F becameigure 1 4clear sho wthats t hthee t bottomhree lo aofd itheng prailosi twasion sthe an dmost Fig . Bottom of rail system setNext, and railseven restraint fastening force system tests using sets bothwere aconducted single fastening to Unit [mm] 1suitable5 show loadings the te position.st result s . Fig. 14 Loading position graspsystem the effect set and of number seven fastening of sets of systemfastening sets system were onconducted the test to ONext,f the railthr restraintee obta iforcened rtestsesu lusingts, th bothe ra ail single restr afasteningint forc e Fig. 14 Loading position result.grasp the Figure effect 16 of comparesnumber of testsets of results. fastening The system difference on the test Fig. 14 Loading position betweencsystemlosest sett theo tandh averagese tsevenarget of fasteningva theselue w resultsa systems wh wasen sets t 0.6he were bkN.ott oconducted m When of th testse rtoa il 2nd loading 3rd loading graspresult. the effect Figure of number 16 compares of sets of testfastening results. system The on the difference test werewas lo conductedaded. Fu r usingtherm ao re single, whe n fastening conside ri systemng rea l- set,life s theitu - 5 2nd loading 3rd loading result.between Figure the averages 16 compares of these test results results. was 0.6 The kN. difference When tests Target value differenceations wh iner raile ra restraintil axis f oforcerce i causeds gene rbyat changinged by the componermal expntsan - 4 5 betweenwere the conducted averages usingof these a results single was fastening 0.6 kN. system When set,tests the 2nd loading 3rd loading insio n the, a n fasteningd in ord er sets to e betweennsure th a trialst in th wase t es withints to ob 0.9ta in kN. ra il 3 Target value weredifference conducted in rail using restraint a singleforce caused fastening by changing system compone set, the nts 5 4 Therefore,restraint fito risc esafe rai lto d sayisp lthatace mtheen abovet is in-mentioned the same difference longitud i- (kN) in the fastening sets between trials was within 0.9 kN. 2 Target value inndifferencea l restraint direct iin o forcen rail, th restraint e wasline alsoa lforceon causedg wcausedhic h by eby x individualt changingernal for ccompone differencese is exerntste d 4 3 Therefore, it is safe to say that the above-mentioned difference (kN) in the fastening sets between trials was within 0.9 kN. 1 2 betweenshoinul d restraint bsets.e th e forceThesesame wasaresultss t h alsoa tmade o causedf th cleare r a by ilthat f individualas theten iinfluenceng r differencesestr aofin t 3 (kN) Therefore, it is safe to say that the above-mentioned difference Rail restraint force 0 thefor cbetweennume. Abers a of sets.r erailsu lfastening t Theseof the results rsystemail r emades setstrai noncleart ttestes thatt results,, it thebec awasinfluenceme very clea rof 2 1 tinh a restraintt the bo t forcetom o wasf th e also ra il caused was t h bye m individualost suit a differencesble loadin g Head Neutral axis Bottom small. Rail restraint force 0 betweenthe num sets.ber of These rail fastening results made system clear sets that on test the results, influence was of very 1 possmall.ition. HeadLoadingNeutral Position axis Bottom the number of rail fastening system sets on test results, was very Rail restraint force 0 5.2 EffectNext, r aofil railrest rpadaint temperatureforce tests usi n g both a single fas- Loading Position small. Fig. 15 RailHead restraintNeutral force axis andBottom loading tenin g system set and seven fastening system sets were c on5.du2c tEffected to g rofas railp th epad effe temperaturect of number o f sets of fastening positionFig.Fig. 15 15 Rail Railrestraint Loading restraint force Positionand force loading and position loading EN (European Norm) 13146-1 defines the test temperatures5.ys2t eEffectm on t hof fore railt whenest rpade railsu ltemperaturet . restraint Figure force16 c o testsm pa r arees t conducted,est result s. Fig.position 15 Rail restraint force and loading The d iffeENre nc (Europeane between t Norm)he ave ra 13146ges o-f1 t he definesse res ult thes w a tests whichtemperature is not the case for whenfor test rail methods restraint in Japan. force tests Therefore, are conducted, rail 5 0.6 kNEN. W (Europeanhen tests w Norm)ere co nd 13146ucted- 1u sin definesg a sin g thele f as testten - position restraintwhich force is not tests the casewere for conducted test methods at various in Japan. temperatures Therefore, to rail itemperatureng system s foret, whenthe d i railffer e restraintnce in r forceail re testsstra in aret f o conducted,rce cause d 5 verifyrestraint its effect. force tests were conducted at various temperatures to 4 bwhichy cha isn notgin theg c ocasemp oforne testnts methods in the infa sJapan.tenin g Therefore,sets betw railee n verifyFigure its 17 effect. shows the test apparatus. The test rail with an 5 4 trestraintrials w aforces wi ttestshin 0were.9 k Nconducted. There fator evarious, it is stemperaturesafe to say t htoa t 3 electric heaterFigure was 17 showsfastened the to test a type apparatus. direct 8 fastening The test railsystem, with an tverifyhe ab itsov eeffect.-men ti oned difference in restraint force was also 4 andelectric rail restraintheater was forc fastenede tests to werea type conducteddirect 8 fastening while system, the 3 causeFigured by i17nd ishowsvidua thel d itestffer eapparatus.nces bet w e Theen stestets rail. T withhese anre - 2 temperatureand rail of restraint the surface forc ofe the tests rail were pad was conducted measured while to be the selectricults m heaterade c lwasear fastenedthat the to i naf typeluen directce of t8h fasteninge numbe system,r of ra il 3 2 abletemperature to adjust it graduallyof the surface to the of target the railtemperature. pad was measured to be 1 fandast enFigure railing s restraint y 18ste m shows se forcts theoen t tests testest r results.e weresults , conductedw Whenas ver y the sm while fasteningall. the able to adjust it gradually to the target temperature. 2 1 conditionstemperature were of theconstant surface by of adjusting the rail thepad axlewas formeasuredce of the to rail be 0 Figure 18 shows the test results. When the fastening Rail restraint force (kN) 5able.2 Etof fadjustect o fit rgraduallyail pad ttoe mthep etargetratu temperature.re fasteningconditions bolts, were no constant significant by adjusting relationship the axle were for confirmedce of the rail 1 0 Figure 18 shows the test results. When the fastening Rail restraint force (kN) Single fastenig Seven fastenig betweenfastening the rail bolts, pad no temperature significant and relationship the rail restraint were confirmed force system systems conditionsEN (E wereurop constantean No rbym )adjusting 13146-1 the de axlefine sfor tcehe ofte thest trailem - 0 betweenbetween 10 to the 45 rail degrees pad temperatureCelsius, which and is thea wider rail restraintrange than force Rail restraint force (kN) Single fastenig Seven fastenig pfasteningerature f bolts,or wh e non r significantail restra in relationshipt force tes ts were are confirmedconducted , system systems definedbetween in the 10 EN. to 45 Therefore, degrees Celsius, with reference which is to a SBR wider rail range pads, than (a) Second loading wbetweenhich is thenot railthe padcase temperaturefor test me t andhod s the in railJap a restraintn. The r forceefore , Single fastenig Seven fastenig the definedeffect of in the the temperature EN. Therefore, on the withrail restraintreference force to SBR was rail very pads, system systems rbetweenail rest 10ra itont 45fo rdegreesce test sCelsius, were cwhichondu ciste ad widerat va rangerious thantem - 5 (a) Second loading smallthe while effect the of theeffect temperature of friction on between the rail restraintthe rail andforce the was rail very pdefinederatur ines theto vEN.eri fy Therefore,its effect. with reference to SBR rail pads, padsmall was relatively while the dominant. effect of friction between the rail and the rail 4 5 (a) Second loading the effectFigur ofe 1the7 s temperaturehows the te onst theapp railara restrainttus. Th eforce test was rai lvery wit h pad was relatively dominant. 5 asmalln el ewhilectric htheea teffecter w aofs ffrictionastene dbetween to a t ythepe raildir eandct 8 the fa srailten - 3 4 6. Conclusions ipadng swasyst erelativelym, and dominant.rail restr a int force tests were conducted 4 6 . Conclusions 2 3 w hilAe tFEMhe te analysismperat uwasre o carriedf the s uoutrf ausingce of thethe proposed rail pad railwa s 3 tiltingm6.e Conclusionsas uanalysisred to bmodele abl eon t oa alowdju-stiffnessst it gr araildu asupportlly to tfasteninghe targe t 1 2 temp eraAtu FEMre. analysis was carried out using the proposed rail systemtilting and analysis the validity model of on the a lowproposed-stiffness analytical rail support model fastening was 2 1 confirmedFAi gFEMur followinge 1analysis8 sho wcomparison swas th e carried test with r eouts utest lusingts .results W thehe fromproposedn th euniaxial fa srailten - 0

system and the validity of the proposed analytical model was Rail restraint (kN)force loadingitiltingng co nanalysis dtestsitio nons modelwa etestre ctrack.onon sat alow n Int -b stiffnessaddition,y adjus railt ibiaxialng support the loading ax lfasteninge fo testsrce o f 1 0 confirmed following comparison with test results from uniaxial Single fastening Seven fastening tsystemhe rai land fa stheten validitying bol tofs, theno proposedsignifica nanalyticalt relatio nmodelship waswer e Rail restraint (kN)force wereloading conducted tests on by a test applying track. loading In addition, conditions biaxial calculated loading tests 0 system systems throughcconfirmedonfirm bothed followingb ethetw eproposeden comparisonthe rFEMail p a analysiswithd te mtestp ande resultsra ttheure fromconventional and uniaxial the ra i l Single fastening Seven fastening rloadingesweretrai n testst con fo rductedonce ab teste tw by track.e e applyingn 1 0 Into addition, 4 loading5 degr biaxiale conditionses Ce loadinglsiu s calculated, w testshic h Rail restraint (kN)force system systems model;through results both from the proposed these tests FEM were analysis compared and the with conventional those Single(b) fastening Third loadingSeven fastening obtainediweres a w conid efromrducted ra ntrialsg e byt h ona applyingn a d testefin track.e d loading in t h Thesee conditionsEN .tests Th eresults re calculatedfore were, wit h system systems rthroughefemodel;ren cbothe t resultso theSB Rproposed fromrail p thesea FEMds, t tests hanalysise e f werefec tand o comparedf tthehe conventionaltem p withera tu thoser e Fig.Fig. 16 16 Effect Effect of of number number(b) Third of loading fastening sets sets thenobtained compared from with trials those on o btaineda test track. from biaxial These loading tests results tests on were aomodel; n test th e track,r resultsail re whichs t fromrai n clearlyt theseforce tests demonstratedwas v wereery s comparedm a thatll w h thei l withe proposedth e thoseeffec t Fig. 16 Effect(b) of Third number loading of fastening sets oobtainedf fthenricti ocompared nfrom bet wtrialsee withn onth those ea rtestai lo abtainedtrack.nd th efrom Theserail biaxialp testsad w resultsloadingas rela were ttestsivel yon obtainingrail tilti nrailg a restraintnalysis forcemod ewerel on conducteda low-stif underfness variousrail su ptestpo rt methoda test can track, reproduce which clearly actual demonstrated track conditions that the proposed more dthenom icomparednant. with those obtained from biaxial loading tests on conditionsfasteFig.ning 16 relatingsy s teEffectm to a ndifferentd ofth enumber v afactorslidity ofsuchof fasteningth ase ploadingropos setse position,d analyt i- appropriatelymethod canthan the reproduce conventional actual method. track conditions more obtaining rail restraint force were conducted under various test a test track, which clearly demonstrated that the proposed numbercal mo dofe lfastening was con systemfirmed setsfoll ousedwin gand co mtemperatureparison w ofith rail te st appropriatelyIn addition, inthan order the toconventional optimize the method. test method, tests for obtainingconditions rail restraintrelating toforce different were factorsconducted such under as loading various position, test method can reproduce actual track conditions more pads,resu landts f rtheom effects uniax iofal theseload ifactorsng tes tweres on clarified.a test tra c k. In addi- In addition, in order to optimize the test method, tests for conditionsnumber relatingof fastening to different system factors sets used such and as loadingtemperature position, of rail 6appropriately. Conclusi othanns the conventional method. tion, biaxial loading tests were conducted by applying load- numberpads, ofand fastening the effects system of these sets factors used andwere temperature clarified. of rail In addition, in order to optimize the test method, tests for ing conditions calculated through both the proposed FEM pads, and the effects of these factors were clarified. A FEM analysis was carried out using the proposed analysis and the conventional model; results from these

186 QR of RTRI, Vol. 59, No. 3, Aug. 2018

Masato NOGUCHI In addition, inMasato order NOGUCHIto optimiz e the test method, tests Rail Heater Photo Researcher, Track Structures and Components Loading in Rail Heater for Photoobtain ing raiResearcher,l restraint Track force Structures were co nanddu cComponentsted under Loading in Laboratory, Track Technology Division longitudinal various test condiLaboratory,tions relat iTrackng to Technologydifferent f aDivisionctors su ch as longitudinal Research Areas: Rail Fastening System, direction loading position, nResearchumber o f Areas:fasten in Railg sy st Fasteningem sets u se Syd stem,and direction Switch & Crossing Transduce temperature of rSwitchail pad &s, Crossingand the effects of these factors Transduce Thermometer r were clarified. Thermometer Fastening system r Hiroo KATAOKA Fastening system Hiroo KATAOKA Photo Laboratory Head, Track Structures and Photo Laboratory Head, Track Structures and Components Laboratory, Track Technology Fig.Fig. 17 1717 Test Test Test apparatus apparatus apparatus References Components Laboratory, Track Technology Division Division Research Areas: Rail Fatigue Life, Continuous [1] Timoshenko, ResearchS. & Lan Areas:ger, B Rail. F., “ FatigueStress Life,es in Continuous Railroad 6 6 Welded Rail, Track-bridge Interaction 6 6 Track,” TranWeldeds. of A SRail,ME Track APM-bridge 54-26 Interaction, Vol.54, p p.277- Bolt axis force Bolt axis force 302, 1932.

4 4 [2] Sato, Y.,“ On the Lateral Strength of Railway Track,” 4 4 Railway Technical Research Report, Vol.110, February Rail restraint force (kN) 2 Rail restraint forceTemperature 2 1960 (in Japanese). (kN) 2 2 rangeTemperature in EN range in EN [3] Hoshino. Y.,“ A Practical Solution for the Torsion (Tilt- 0 0 0 0 ing) of Rail,” Journal of Japan Society of Civil Engi- Rail Rail restranit force Bolt Bolt axis force(kN)

Rail Rail restranit force 0 10 20 30 40 50 neers, Vol.210, pp.33-46, 1973 (in Japanese). 0 10 20 30 40 50 Bolt axis force(kN) Rail pad temperature (deg.) [4] Yamamoto, T., Umeda, S. & Kanamori, T.,“ Relation- Rail pad temperature (deg.) ship between Spring Coefficient of Fastening Device Fig. 18 Effect of rail pad temperature and Rail Overturning Angle,” Quarterly Report, Vol.22 Fig. 18 Effect of rail pad temperature Fig. 18 Effect of rail pad temperature No.4, pp.153-156, April 1981. te sts were compared with those obtained from trials on a [5] Tamagawa, S., Kataoka, H & Deshimaru. T.,“ Practical tes t track. These tests results were then compared with Model for Rail Tilting and Its Application to Perfor- thReferencesoReferencesse obtaine d from biaxial loading tests on a test track, mance Test of Rail Fastening System,” Journal of Ja- wh ich clearly demonstrated that the proposed method can pan Society of Civil Engineers, Vol.73 No.2, pp.330-343, [1] Timoshenko, S. & Langer, B. F., “Stresses in Railroad Track,” rep[1]ro dTimoshenko,uce actual tS.ra &ck Langer, condit iB.on F.,s m “Stressesore app inro pRailroadriately Track,”than 2017 (in Japanese). Trans. of ASME APM 54-26, Vol.54, pp.277-302, 1932. theTrans. conv eofn tASMEional m APMetho 54d. -26, Vol.54, pp.277-302, 1932. [2] Sato, Y., “On the Lateral Strength of Railway Track,” [2] Sato, Y., “On the Lateral Strength of Railway Track,” Railway Technical Research Report, vol.110, February 1960. Railway Technical Research Report, vol.110, February 1960. (in Japanese). (in Japanese). [3] Hoshino. Y., “A Practical Solution for the Torsion (Tilting) Au[3]th oHoshino.rs Y., “A Practical Solution for the Torsion (Tilting) of Rail,” Journal of Japan Society of Civil Engineers, Vol.210, of Rail,” Journal of Japan Society of Civil Engineers, Vol.210, pp.33-46, 1973. (in Japanese). pp.33 -46, 1973. (in Japanese). [4] Yamamoto, T.,Tadashi Umeda, DESHIIMARU S. & Kanamori, T., “Relationship Masato NOGUCHI [4] Yamamoto, T., Umeda, S. & Kanamori, T., “Relationship between Spring S Coefficientenior Rese ar ofch e Fasteningr, Track S t Deruc-tviceures a andnd Rail Researcher, Track Structures and Components between SpringC o Coefficientmponents L a ofb o Fasteningratory, Tra c Dek T-evicechn o andlog y Rail Overturning Angle,” Quarterly Report, Vol.22 No.4, pp.153- Laboratory, Track Technology Division Overturning Angle,”Divisi o Quarterlyn Report, Vol.22 No.4, pp.153- 156, Apri l 1981. Research Areas: Rail Fastening System, 156, April 1981.R esearch Areas: Rail Fastening System, Rail [5] Tamagawa, S.,Fa ti Kataoka,gue Life H & Deshimaru. T., “Practical Switch & Crossing [5] Tamagawa, S., Kataoka, H & Deshimaru. T., “Practical Model for Rail Tilting and Its Application to Performance Test Model for Rail Tilting and Its Application to Performance Test of Rail Fastening System,” Journal of Japan Society of Civil of Rail FasteningShingo System,” TAMAGAWA Journal, Pofh .DJapanr. Society of Civil Hiroo KATAOKA Engineers, Vol.73 No.2, pp.330-343, 2017. (in Japanese). Engineers, Vol.73As sNo.2,istant pp.330Senior- R343,ese a2017.rcher ,(in Tr aJapanese).ck Structu res Senior Chief Researcher, Laboratory Head,

and Components Laboratory, Track Track Structures and Components Laboratory, Technology Division Track Technology Division

Authors Research Areas: Rail Fastening Systems, Research Areas: Rail Fatigue Life, Continuous Authors Continuous Welded Rail Welded Rail, Track-bridge Interaction

Tadashi DESHIIMARU Tadashi DESHIIMARU Photo Senior Researcher, Track Structures and Photo Senior Researcher, Track Structures and Components Laboratory, Track Technology Components Laboratory, Track Technology Division Division Research Areas: Rail Fastening System, Rail Research Areas: Rail Fastening System, Rail Fatigue Life Fatigue Life

Shingo TAMAGAWA, Ph.Dr. Shingo TAMAGAWA, Ph.Dr. Photo Assistant Senior Researcher, Track Structures Photo Assistant Senior Researcher, Track Structures and Components Laboratory, Track and Components Laboratory, Track Technology Division Technology Division Research Areas: Rail Fastening Systems, Research Areas: Rail Fastening Systems, Continuous Welded Rail Continuous Welded Rail

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