Rail bridge and composite girder bridge analysis

3,954 views

Published on

An introduction of how to do rail bridge and composite girder bridge analysis with midas Civil

Published in: Technology, Business
2 Comments
11 Likes
Statistics
Notes
No Downloads
Views
Total views
3,954
On SlideShare
0
From Embeds
0
Number of Embeds
57
Actions
Shares
0
Downloads
407
Comments
2
Likes
11
Embeds 0
No embeds

No notes for slide

Rail bridge and composite girder bridge analysis

  1. 1. 111-1M I D A S I TBridging YourInnovations to Realities
  2. 2. Bridging Your Innovations to Realitiesmidas Civil2Rail Structure InteractionOverview1) Definition of Continuous Welded Rail (CWR)Rails are continuously welded and thus, the length of one rail is longer than 200m.ex > standard length rail (L=25m), longer rail (L=25~200m)2) Necessity of Continuous Welded RailTime[ms]DynamicamplificationQQ654321016 18 20 221412108642Wheel/rail impact forcesWheel impactforces occur- The reduced impact force in the rails increases the life span of the rails and improves the ride quality.- The decreasing noise and vibration by the reduced impact force is less impeding the ambient environment.3) Check Points for Continuous Welded Rail- When temperature rises: track deformation(buckling of rail)- When temperature drops: fracture failure
  3. 3. Bridging Your Innovations to Realitiesmidas Civil3Rail Structure InteractionTraction/Braking loadsabutment pierLongitudinal displacementsat top surface of deck endTemperature Train vertical loadsTrack-BridgeInteraction
  4. 4. Bridging Your Innovations to Realitiesmidas Civil4Rail Structure InteractionTrack-BridgeInteraction1) Axial Forcesin a ContinuouslyWeldedRail Track on Embankment(Thermal Load on the Rail)2) Axial Forcesin a ContinuouslyWeldedRail Track on Bridge(Thermal Load on the Bridge)Axial forces in the track on embankmentunder thermal loadingTrack/bridge interaction due tothermal loadingFixed end Movable endContinuous welded railAdditional railstressesAxial forcesin the railsDistance (m)Displacementintherails(mm)ResistanceTAEF ∆×××= α
  5. 5. Bridging Your Innovations to Realitiesmidas Civil5Rail Structure InteractionDesign Requirementsfor Track/Bridge Interaction AnalysisDesign Standards: UIC774-3, EN 1991-2Item LoadsDesignCriteriaGravel ballast bed Concrete bedAdditional railstressCompressive stress Thermal loadsTraction/braking loadsTrain vertical loadsR≥1500: 72N/mm2R≥700: 58N/mm2R≥600: 54N/mm2R≥300: 27N/mm292N/mm2Tensile stress 92N/mm2 92N/mm2Longitudinal relative displacement inbridge deckTraction/braking loads<5mm<30mm (when railexpansion device at bothends)Check the stability (theuplift force andcompression) of railfastenerlongitudinal displacement due to rotationof the deck end between deck and deck orbetween deck and pierTrain vertical loads <8mmCheck the stability (theuplift force andcompression) of railfastenerOpening displacement when split web atrail end takes place (applying cablesignaling system or zero-longitudinalresistance rail (ZLR) fastener)Thermal loads D=√(R2-(R-δ)2)Same as the gravel track
  6. 6. Bridging Your Innovations to Realitiesmidas Civil6Rail Structure InteractionDesign Loads- If all of the spans in the bridge consist of a continuous welded rail, thermal loads are applied to the bridge and rails or therails only.- If rail expansion joints are present on the bridge, thermal loads are applied to both the bridge and the rails.- Temperature variations in the rails and bridge are as follows:. Rails: in summer=+40℃, in winter=-50℃. Bridge: concrete structures=±25℃, steel structures= normal temperature area ±35℃, cold temperature area ± 45℃1) Thermal Loads2) Traction/Braking Loads- Traction/braking loads are uniformly distributed and applied to the two front positions of the rails. The magnitudeof load and the loaded length are as follows:- For the cases such as an exclusive subway track, light rail transit, etc where the design loads are different,transformed uniform loads which correspond to ¼ of the rail axial loads are used. The loaded length is equal toone maximum coach.- Traction/braking loads are applied concurrently with the associated vertical loads.- Traction/braking loads are applied to the positions that will cause the most unfavorable rail stresses or bridgedeformations.Type of TrackTractionloads braking loadsMagnitude of Load Loadedlength Magnitude of Load LoadedlengthHigh-speedrailway 33kN/m/track 33m 20kN/m/track 400mNormal railway 24kN/m/track 33m 12kN/m/track 300m
  7. 7. Bridging Your Innovations to Realitiesmidas Civil7Rail Structure InteractionDesign Loads-For a high-speed railway, HL load does not includean impact factor. For a passenger locomotive, HLload can have a uniform load of 60kN/m.- For a normal railway, LS load and an equivalent loadcan be applied and an impact factor is notconsidered.- For an exclusive subway track, EL-18 load or an equivalentuniformly distributed load can be applied.- For a double or more track bridge, only two tracks will beloaded with train vertical loads.- For a multi-span continuous bridge, only the deck near thecritical positions will be loaded.3) Train Vertical Loads(b) Equivalent HL load(a) HL load(b) Equivalent LS load(a) LS load (L-load)95kN/m74kN/m
  8. 8. Bridging Your Innovations to Realitiesmidas Civil8Rail Structure InteractionLoad Combinations- Load combinations used for computing the rail stresses and the longitudinal loads acting on bearings- When computing the stresses and displacements in the rails for a continuous or simply supported bridge deck:α,β,γ=1- When using the computational analysis method, the interaction due to traction/braking loads and train verticalloads can be separately computed.ƩR = αR (Thermal loads) + βR(Traction/braking loads)+γR(Train vertical loads)
  9. 9. Bridging Your Innovations to Realitiesmidas Civil9Rail Structure Interaction1) Establishment of Criteria for Construction of Rail Expansion Joint on BridgeSectionRailExpansion JointCountermeasureThe limits to the axial force and displacementof a continuous welded rail on bridge are exceededbridgetrackSupport layoutSpan compositionStiffness of deckUse zero-longitudinal resistancerail fastenersEconomicefficiencyCompare the maintenance cost forrailexpansion joints with the cost of bridgeconstructionConditions for building rail expansion joints Minimum separated distance between expansion joints Separation distance from a turnout Separation distance from the terminus for a transitioncurve Separation distance from the terminus for a bell curve Requirements for building the bridge deck
  10. 10. Bridging Your Innovations to Realitiesmidas Civil10Rail Structure Interaction2) FlowchartRailExpansion JointCheck the axial forceand displacement inthe railsModify the support placementCheck the axial forceand displacement inthe railsModify the span compositionCheck the axial forceand displacement inthe railsModify the stiffness of deckCheck the axial forceand displacement inthe railsUse a zero-longitudinal resistance rail fastenerCheck the axial forceand displacement inthe railsConsider building REJ (rail expansion joint)Analyze the economicalefficiencySubmit the reportAllow the constructionof railexpansion jointContinueOKOKOKOKOKOKNGNGNGNGNGNGNGNGNGNG
  11. 11. Bridging Your Innovations to Realitiesmidas Civil11Rail Structure Interaction1) Computational Analysis- Considerations for modeling• Placement of bearings, the dimensions and properties of the deck and pier, the bending stiffness and the height of deck,the neutral axis of deck, and the lateral and bending stiffness of foundation.- Finite elements• Rail and bridge: Beam elements• Ballast or pad: nonlinear spring elements- Modeling method• Element length: 1~2m is recommended상판중립축궤도중심선Rigid LinkRigid LinkTrack-BridgeInteraction AnalysisEmbankment sectionBridge deckSpringfor the longitudinalresistance of ballast (Bilinear)RailRail expansion jointNeutral axis of bridge deckCenterline of trackBearingLongitudinal displacement of the rail1. Observed data2. Idealized bilinear curve (under train loading)3. Bilinear curve when train loading is not appliedLongitudinalresistance ofthe roadbed
  12. 12. Bridging Your Innovations to Realitiesmidas Civil12Rail Structure Interaction- The accuracy depends on the computational analysis methods.- The following two computational analysis methods are available:. Separate analysis: thermal loading, traction/braking loading and train verticalloading are separately considered.. Complete Analysis: thermal loading, traction/braking loading and train verticalloading are concurrently applied.- Depending on the global structural system, the separate analysis is more likely toproducethe greater axial forcesthan the staged analysis.AnalysisMethods
  13. 13. Bridging Your Innovations to Realitiesmidas Civil13Rail Structure InteractionSimplified Separate Analysis Complete AnalysisAnalysisMethods
  14. 14. Bridging Your Innovations to Realitiesmidas Civil14Rail Structure InteractionRailTrack AnalysisModel Wizard (Layout)Advanced:define the fixedendsfreelyandadjustthe spanlengthZLR: Specifythe zero-longitudinalresistance railfastener(the resistance of ballastissetto zeroforthe specifiedsections.)REJ: Place the rail expansionjointforeachtrackex ) 4@50,70:four decks with the length of 50m anda deck with the length of 70m. The total length ofbridge section is 270m.
  15. 15. Bridging Your Innovations to Realitiesmidas Civil15Rail Structure InteractionTaperedSectionAssignmentSectionsat 0.1 of the total span length:Span_2Sectionsat 0.5 of the total span length:SpanSectionsat 0.9 of the total span length:Span_2TaperedOptionStart 0.1~Start 0.5: Z Axis CurvedType (Quadratic) , From (J-end)Start 0.5~Start 0.9: Z Axis CurvedType (Quadratic) , From (I-end)Define TaperedSectionRailTrack AnalysisModel Wizard (Section)
  16. 16. Bridging Your Innovations to Realitiesmidas Civil16Rail Structure Interaction1 . Lateral Resistance Data- Enter gravel ballast data and concrete ballast data.- For gravel ballast,the resistance of ballast isdifferentbetweenthe stresscheckand the displacementcheck.2. Define Condition- Selecteithergravel ballastor concrete ballast for the entire section.- Via the ‘Advanced’function,selecteithergravel ballast or concrete ballastbysections(Forundefinedsections,gravel ballastisused).3. Boundary TypesSpring Type Bearing Type123RailTrack AnalysisModel Wizard (Boundaries)
  17. 17. Bridging Your Innovations to Realitiesmidas Civil17Rail Structure Interaction4. ModelingbySections1) Embankment section5. Boundary ConditionsTaking into Account the Effective LengthThe resistance ofballast enteredshouldbe in kN/m and islongitudinal resistance.The resistance multipliedbythe effective lengthwill be usedin the model.2) Section connecting embankment and deck start point 3) Section connecting deck start and end pointsRailTrack AnalysisModel Wizard (Boundaries)
  18. 18. Bridging Your Innovations to Realitiesmidas Civil18Rail Structure Interaction1. Accelerating/braking/vertical train loadscan be freelyenteredbysectionsin a tabular format.The length and magnitude of load can be enteredwithreference tothe leftendof the model.-RunningDirection:the direction in which the train runs.Define either‘KeepRight’or ‘KeepLeft’.-TrainSection: Train sectionis recognizedwhenavertical load is entered. Whenavertical Load is excluded,define TrainSectionandapply LoadedCondition.- Load Type:For single track, in general,applyeitheraccelerating loadsor brakingloads. Fordouble track, apply acceleratingloads andbraking loadsforeachtrack. Asfar as train vertical loads are concerned, variousuniformloadscan be appliedby sectionsandtherefore HLload, which is mostfrequentlyused,canbe easilyrepresented.2. Filesare added for the moving load analysis- Number ofTrack LoadingLocations: the numberof movingtimesof train load.If “n” is entered,nfilesare added.- Location Incrementfor eachModel:the incrementof moving load pertrack. If “n” is entered,the trainmovesbyn and the boundaryconditionsare assignedtothe sectionto which the train load is applied.ex> If “Number of Track Loading Locations” is 3 and “Location Increment for Track” is 10, the train moves forward by 10m, 20m and 30m and three files are added.Case 1: Single Track Case 2: Double TrackRailTrack AnalysisModel Wizard (Load)
  19. 19. Bridging Your Innovations to Realitiesmidas Civil19Rail Structure InteractionRailTrack AnalysisModel Wizard1 .StressCheck Model OptionThisoptioncreatesa file to checkthe additionalstresses.-SimplifiedSeparate AnalysisModel-Complete Analysis2. DisplacementCheckModel OptionThisoptioncreatesa file to checkthe displacements. Inthisfile,the resistance of ballast applied at UnloadedConditionisdifferentforthe case ofgravelballast.In addition, this file is available only for SimplifiedSeparate AnalysisModel.- Relative LongitudinalDisplacementComponentdue toAccelerationandBrakingAlone- Relative LongitudinalDisplacementComponentdue toVerticalEffects-Relative LongitudinalDisplacementComponentatRailExpansionJoints- Rail Break GapSize
  20. 20. Bridging Your Innovations to Realitiesmidas Civil20Rail Structure InteractionCaseStudiesForthe case of a high-speedrailwaywithgravel ballast and double track,the following propertiesare definedforrail, ballast and horizontalalignment:Track Item Property Unit Value RemarkRailUIC60Cross-sectionalarea A m2 7.669E-3Moment of inertia Iyy m4 30.363E-6BallastGravelballastLongitudinal resistance (Unloaded) kN/m 12.0~20.0 Stress check: 20.0Displacement check: 12.0Longitudinal resistance (Loaded) kN/m 60.0Limit displacement mm 2.0HorizontalalignmentTangent sectionGirder TypeSpan LengthEquivalent Modulusof ElasticityCross-sectional AreaMoment of InertiaNeutral Axis(Girder ReferenceLocation)Main Girder Height( m ) ( E : N/m2 ) ( A : m2 ) ( Iyy : m4 ) ( Izz : m4 ) ( d : m ) ( H : m )PC Box 40 2.8 x 1010 12.0 20.0 165.0 1.11 3.5PCBox girder bridge is chosenfor the high-speedrailwaytrack.The dimensionsof girderandthe geometricrelationbetweenthe girderandtrack are definedasfollows:The longitudinalresistance of deckis setto 1.5 x 106kN/m.
  21. 21. Bridging Your Innovations to Realitiesmidas Civil21Rail Structure InteractionForthe case of a high-speedrailwaywithgravel ballast and double track,the rail, ballast and horizontal alignmentare definedasfollows:Simple bridge typeContinuousbridge typeCaseStudies40m 40m 40m 40m 40m 40m 40m 40m 40m 40m80m 80m 80m 80m 80m
  22. 22. Bridging Your Innovations to Realitiesmidas Civil22Rail Structure InteractionAxial stressby temperature load (Simple spanbridge)Axial stressby temperature load (Continuousbridge)Because the simple bridge type gives the smaller additional stress than the continuous bridge type, the simple bridge type is adopted.CaseStudies-26.6 MPa-44.1MPa
  23. 23. Bridging Your Innovations to Realitiesmidas Civil23Rail Structure InteractionCaseStudiesAxial stressby temperature (+25°C) at UnloadedConditionAxial stressby temperature,traction and vertical train loads at LoadedCondition-35.6MPa-26.6 MPa
  24. 24. Bridging Your Innovations to Realitiesmidas Civil24Rail Structure InteractionCaseStudiesAxial stressby temperature,braking and vertical train loadswith differenttrain position
  25. 25. Bridging Your Innovations to Realitiesmidas Civil25Rail Structure InteractionCheckDisplacements- Restrict the deformations of the deck and the track to prevent the excessive relaxation of ballast.- Limits to the relative lateral displacements between the bridge deck and rails under traction/braking loads: 4mm or less- Exceptions are made for the cases where the zero-longitudinal resistance rail fastener is used and the special treatment isdone for the contact underneath the rails.2) Limits to the RelativeLongitudinal Displacements in the Bridge Deck3) Limits to the Longitudinal Displacements in the Deck End due to the Angle of Rotation- Limits to the longitudinal displacements in the deck end due to the rotation of the deck end under train verticalloads: 8mm or less1) RelativeDisplacements between the Rails and Bridge- Limits to the absolute longitudinal displacements between the bridge deck and pier or between the bridge deckand deck under traction/braking loads: 5mm or lessLimits to relative longitudinal displacements Limits to displacements due to rotation of deck endabutment pierLongitudinal displacementsat top surface of deck end
  26. 26. Bridging Your Innovations to Realitiesmidas Civil26Rail Structure InteractionJapanese Shinkansen Railway Structure Design StandardConditionsAllowable openingdisplacements-rail: 60kg-buckling strength of rail:100tonf/rail69mmACI Manual of Concrete PracticeWheel radiusAllowable openingdisplacements16 in. (0.4m) or less 2in.(50mm)16 in. or higher 4in.(100mm)CheckDisplacements4) AllowableOpening Displacements when Opening Gap at Rail End takes place .- Allowable Opening Displacements According to International Standards- Allowable Opening Displacements According to Korean Standards. Railway Design Manual (Volume Track)1) Limits to the opening displacements, d, when the split web at railend takes place due to thermal loads in case of using cablesignaling system (not track circuit system):2 2( )d R R δ= − − 32xPe xEIβδ ββ−= 44kEIβ =2) Restrict the opening displacements of (1) when azero-longitudinal resistance rail fastener is builtWheel loadPCenter of wheel OVehicle velocity VWheel radius RVertical displacement δBending stiffness of rail EIBearing stiffness of trackKOpening displacement d
  27. 27. Bridging Your Innovations to Realitiesmidas Civil27Rail Structure InteractionRelative Longitudinal Displacementbytraction loadsCaseStudies
  28. 28. Bridging Your Innovations to Realitiesmidas Civil28Rail Structure InteractionCaseStudiesTip> If the deck is defined by Center-Top, the nodal displacements at deck top are produced andthese include the nodal displacements due to rotational angle. If the deck is defined by centroid,the nodal displacements at deck top can be computed using the following equation:Relative displacement due to rotation of the end= displacement Dx at neutral axis + distance from centroid to deck top x sin(Rot Ry)Relative Longitudinal Displacementbyvertical train loads
  29. 29. Bridging Your Innovations to Realitiesmidas Civil29Rail Structure InteractionFactorsAffecting the Axial Forcesin Track (1)1) Longitudinal Resistanceof TrackLongitudinal resistance of trackvs. longitudinaldisplacement of railBi-Linear behavior of longitudinal resistance of trackAllowable longitudinal resistance of track Note 1: Apply 20.0kN/m when checking the rail stresses and apply 12.0kN/m when checking the displacements in the structure Note 2: In the case when tests for longitudinal resistance are conducted, values derived from tests can be used.Type of Track Load CaseLimit displacement(mm)Longitudinalresistance of track(kN/m)RemarkGravel trackLoaded Case 2.0 12.0~20.0 Note 1Unloaded Case 2.0 60.0Concrete track or frozenballast trackLoaded Case 0.5 40.0 Note 2Unloaded Case 0.5 60.0
  30. 30. Bridging Your Innovations to Realitiesmidas Civil30Rail Structure InteractionFactorsAffecting the Axial Forcesin Track (1)Axial stresses of Ballast Bed in the longitudinal directionAxial stresses of Concrete Bed in the longitudinal directionUnloaded Condition (underthermal loads)Loaded Condition(traction/brakingloads and vertical loads added)Unloaded Condition (underthermal loads)Loaded Condition(traction/brakingloads and vertical loads added)Longitudinal axial stress is about 30% less in the ballast track than in the concrete track under the same conditions.
  31. 31. Bridging Your Innovations to Realitiesmidas Civil31Rail Structure Interaction2) Zero-Longitudinal Resistance Rail (ZLR) Fastener inthe BridgeSectionCharacteristic behavior of zero-longitudinal resistance rail fastener- The zero-longitudinal resistance rail fastener behaves similarly to the conventional rail fastener for the gravityload but generates a gap between the rail and the rail fastener not to introduce longitudinal resistance.<Gap between rail fastener and rail base> <Downslide of rigid body of rail fastener> <Vertical load-displacement diagram>FactorsAffecting the Axial Forcesin Track (2)Installing ZLR fastener can reduce about 29% of the axial stress.
  32. 32. Bridging Your Innovations to Realitiesmidas Civil32Rail Structure Interaction1) Expansion Length- Maximum expansion length recommended by UIC774-3 for a single deck railway bridge with gravel ballast not needingREJ (rail expansion joint). 60m: Steel structure with gravel ballast track (the maximum length is 120m when a support exists in the middle). 90m: Steel or concrete bridge with gravel ballast track and concrete slab(the maximum length is 180m when a support exists in the middle). For the ballastless track, detailed analysis should be conducted.- Illustrations of expansion lengthsL 2LFactorsAffecting the Axial Forcesin Bridge (1)- Type 1 - Type 2- Type 3 - Type 4
  33. 33. Bridging Your Innovations to Realitiesmidas Civil33Rail Structure InteractionFactorsAffecting the Axial Forcesin Bridge (1)- Type 1-Unloaded Condition : 26.48 MPa -Loaded Condition : 32.86 MPa-Unloaded Condition : 11.45 MPa -Loaded Condition : 14.07 MPa- Type 2
  34. 34. Bridging Your Innovations to Realitiesmidas Civil34Rail Structure InteractionFactorsAffecting the Axial Forcesin Bridge (1)- Type 3-Unloaded Condition : 26.52 MPa -Loaded Condition : 42.05 MPa-Unloaded Condition : 21.12 MPa -Loaded Condition : 26.43 MPa- Type 4Axial stresses in the longitudinal direction under the same conditions:Type 2 (14.07 MPa) < Type 4 (26.43 MPa) < Type 1 (32.86 MPa) < Type 3 (42.05 Mpa)
  35. 35. Bridging Your Innovations to Realitiesmidas Civil35Rail Structure InteractionFactorsAffecting the Axial Forcesin Bridge (2)2) Span length3) Bending stiffness of the deck and the deck height- Train vertical loads can cause the longitudinal deformations in the girder, and the span length is the factorcausing the track/bridge interaction.- Because of the bending of deck, train vertical loads on bridge can cause interactions.- The bending of deck induces longitudinal deflections at top surface of the deck end and therefore causes therelaxation of gravel track.-The effect of bending in deck end1.0 EI 1.5 EI 2.0 EI0-5-10-15-20-25-30-350.1 Ko0.5 Ko1.0 Ko2.0 Ko10 KoRailStress(MPa)2@40M_FMM_Vertical LoadStiffness of Deck
  36. 36. Bridging Your Innovations to Realitiesmidas Civil36Rail Structure InteractionFactorsAffecting the Axial Forcesin Bridge (3)4) Support stiffnessK: Total stiffness of support: relative displacement between the upperand lower parts of bearing-Factors affecting the support stiffness KBending ofPier Rotation ofFoundation Displacement of Foundation
  37. 37. Bridging Your Innovations to Realitiesmidas Civil37Rail Structure InteractionFactorsAffecting the Axial Forcesin Bridge (4)5) Effects of support layout of bridgeAxial forces by FF-MM type Axial forces by FM type-Types of bearingFFFF typeFM typeFMMF typeFMM typeMFM typeMFMM type
  38. 38. Bridging Your Innovations to Realitiesmidas Civil38Rail Structure InteractionFactorsAffecting the Axial Forcesin Bridge (4)Cases illustratingthe effects ofsupport layout ofbridge- Case1: Simple bridge ( 1@30 8 Span)Axial force is about 26% less for MFFM type (28.12 MPa) than in the FMFM type (38.08 MPa) when other conditions are identical.- Case 2: 2 span continuous bridge (2@30 4 Span)Axial force is about 45% less for MFM type (29.77 MPa) than in the FMM type (54.20 MPa) when other conditions are identical.FMFM type MFFM typeMFM type FMM type38.1 MPa 28.1 MPa29.8 MPa 54.2 MPa
  39. 39. Bridging Your Innovations to Realitiesmidas Civil39Rail Structure InteractionFactorsAffecting the Axial Forcesin Bridge (4)6) Axial forces affected by span compositionCase 1 : 78.75 MPa > Case 2 : 60.63 MPa > Case 3 : 59.72 MPaAxial force is 24.2% less for Case 3 than in Case 1.78.7 MPa 60.6MPa59.7 MPa
  40. 40. Bridging Your Innovations to Realitiesmidas Civil40Rail Structure Interaction1) Verificationof computational analysis- A computer program that performs the track/bridge interaction should be validated against the test cases specified in theAppendix 1.7.1 of UIC774-3. Percentage errors may be up to 10% and up to 20% for safety side.Standard dimensions recommended by UIC774-3Result table for a simple span bridge specified in UIC774-3Track-BridgeInteraction Verification
  41. 41. Bridging Your Innovations to Realitiesmidas Civil41Rail Structure Interaction2) Validation against UIC774-3Resultdue to temperature 35 degreescentigrade onbridge deck:-30.47 MpaUIC774-3 recommendation:-30.67 MPaResultdue to temperature 35 degreescentigrade onbridge deckand50 degreescentigrade onrails: -150.17 MpaUIC774-3 recommendation:156.67 MPaValidation of the maximum additional stresses due to train moving loadsValidation of thermal loadsAdditional stressat 0 pointfrom right pierdue to train loading:181.38 MpaUIC774-3 recommendation:182.4 MPaMaximumadditional stressesdue to train movingloads:-195.05 MPaTrack-BridgeInteraction Verification

×