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1、BCR2A’09RailroadTrackDesignIncludingAsphaltTrackbedsPre-ConferenceWorkshopIntroductiontoRailroadTrackStructuralDesignDonUzarski,Ph.D.,P.E.uzarski@illinois.eduInteraction,VerticalLoadDistribution,andDeflectionsStressDistributionComponentsdonotfunctionindependently!Eachcomponentlayermustprotectt
2、heonebelow.2DeflectionProfileSource:SeligandWaters,TrackGeotechnologyandSubstructureManagement,19943Staticvs.DynamicLoads•Dynamicloadshigher–Accelerationfromspeed–Downwardrotationofwheel–Smallerwheels,fasterrotation,moreacceleration•Speed/wheelinfluence–Pv=P+θP(AREMA)wherePv=VerticalDynamicLoa
3、d(lbs)θ=D33xVDwx100D=Wheeldiameter(in)V=Speed(MPH)P=StaticLoad(lbs)–Largerwheelsimposelessinfluence•Additionaldynamicloadsfromimpactssuchascausedbywheelflatspots,raildiscontinuities(e.g.frogflangeways),tracktransitions(e.g.bridgeapproaches),trackcondition,etc.4DifferentWheelDiameters33inches36
4、inches38inches28inches36inches5TrackStiffness•Railisassumedtobeabeamonanelasticfoundation•ModulusofTrackElasticity,u(ork)(a.k.a.TrackModulus)u=P/Δwhereu=ModulusofTrackElasticity(lbs/in/in)P=Wheelloadperunitlengthofrail(lbs/in)Δ=UnitofTrackDeflection(in),less“play”ortrack“looseness”oru=P/Swhere
5、u=ModulusofTrackElasticity(lb/in/in)P=Wheelload(lbs)requiredtodeflectthetrack1inchononetieS=Tiespacing(in)6ClassicApproachtoTrackAnalysisandDesign•ContinuouslysupportedbeamNotes:a=tiespacing“s”w(x)=deflection“y”Source:Kerr,A.D.,FundamentalsofRailwayTrackEngineering,20037•TalbotequationsRailMom
6、ent:Mo=0.318Px1Deflection:Yo=0.391P/ux1RailSeatLoad:Qo=0.391PS/x1(Note:Qoa.k.a.Fmax)where:P=WheelLoad(lbs)u=TrackModulus(lbs/in/in)S=Tiespacing(in)x=(π/4)(4EI/u)¼(in)1EI=Flexuralrigidityofrailwith:E=ModulusofElasticityofRail(30x106psi)I=RailMomentofInertia(in4)8MasterDiagramSource:Hay,W.W.,Rai
7、lroadEngineering,19829LoadDeflectionsandBendingMomentsSource:Hay,W.W.,RailroadEngineering,198210DeterminationofRailSeatForces(QorF)Pressurep(x)[lb/in]CurveSource:Kerr,A.D.,FundamentalsofRailwayTrackEngineering,200311PressureDistribution