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Rail Track Analysis User Manual

1. XC ka 9 centreline Bearing oZ Remaining Structure Piers Foundations Longitudinal Schematic Of The Model Transverse Cross Section Of Track Deck Bearing Syster Figure 2 Typical Model of Track Deck Bearing System The interaction between the track and the bridge is approximated in the UIC774 3 Code of Practice by a bilinear relationship as indicated in the following figure The resistance of the track to the longitudinal displacements for a particular track type is a function of both the relative displacement of the rail to the supporting structure and the loading applied to the track If the track is subjected to no train loads then the ultimate resistance of the track to relative movement is governed by the lower curve in the figure based on the track type Application of train loads increases the resistance of the track to the relative displacements and the upper curve should be used for the interaction between the track and bridge where these train loads are present unloaded resistance is still used for all other locations Resistance k of the track UIC774 3 Code of Practice Resistance of rail to sliding relative to sleeper Loaded Track Frozen ballast or track without ballast l Resistance of sleeper in ballast Loaded Track E Resistance of rail to sliding relative to sleeper Unloaded Track Frozen ballast or track without ballast Resistance of sleeper in ballast Unloaded Track
2. Neutral Axis Of Section Location Of Support Conditions Depth Of Section Figure 11 Eccentricity Definition for Geometric Properties and Depth of Section Element Orientations The orientations of the sectional properties should obey the element local axes indicated in the following figure where the double headed arrow indicates the element local x axis the single headed arrow indicates the element local y axis and the line without an arrowhead indicates the element local z axis For both the spans and the 10 The Rail Track Analysis Spreadsheet piers the element local y axis is orientated into the lateral direction for the bridge with the local z axis orientated vertically for the spans and in the longitudinal direction for the piers Span Element i Local Axes 7i Sa 4 Pier Element Local Axes 9S Figure 12 Beam Element Local Axes for Span and Pier Modelling 11 Rail Track Analysis User Manual Worksheet 4 Material Properties A Hd s Material Properties i m ure ame OE nac RE Hs IERI NT fe T ge rc en De ee a Fr en II GT D EN Material Properties Unis N mm kg 2 m K NIZ Structure Definition Material Properties Interaction and Expansion Joir E isessssuHNNESSSBSSISSSruyS Se e Figure 13 Material Properties Table for Structure The material properties worksheet should list all of the material properties required for the modelling of the
3. l u Frozen No Ballast Ballast Displacement u Figure 3 Resistance k of the Track per Unit Length versus Longitudinal Relative Displacement of Rails The values of displacement and resistance to use in these bilinear curves are governed by the track structure and maintenance procedures adopted and will be specified in the design specifications for the structure Typical values are listed in the Code of Practice for ballast frozen ballast and track without ballast for moderate to good maintenance According to the UIC774 3 Code of Practice there is no requirement to consider a detailed model of the substructure bearing pier foundation and bearing abutment foundation systems when standard bridges are considered instead this can be modelled simply through constraints and or spring supports that approximate the horizontal flexibility due to pier translational bending and rotational movement The LUSAS Rail Track Analysis option allows this type of analysis to be carried out where the behaviour of the bearing and the pier abutment foundation are individually specified but also provides the capability of explicitly modelling the bearing pier abutment foundation systems where each component is defined including the height and properties of the pier abutment Rail Track Analysis User Manual LUSAS Rail Track Analysis The Rail Track Analysis option in LUSAS provides the means to automate the finite element analyses required
4. 15 116 Position Initial Gap Position Initial Gap BEER TS SEE EIER Ea a tmu TT T pa 1 S LZ L BI 1 1 1 1 1 J LL 124 25 a 5 m is I2 p 1i EM 10 ee Ll oL EM 1 1 l1 lll e e ee gt lc EH V Lh es ee e taa ar Z 2a b bi Geometric Properties Material Properties Interaction and Expa Figure 14 Interaction Properties Between the Track Bridge and Expansion Joint Definition The main bilinear interaction effects for the track bridge interaction are defined in this worksheet along with additional properties associated with the rail track These include the eccentricity between the rail slab see Figure 11 and the Geometric Properties section and the presence of any rail expansion joints Eccentricity Between Rail Slab The eccentricity between the rail slab is used to define the distance between the nodal line or the rail track and the top of the bridge slab deck as indicated in Figure 11 In general all eccentricities will be positive in the modelling unless the neutral axis of the structure section is above the level of the rails This only happens for certain types of structures and the definitions of eccentricity should generally follow the sign conventions defined in the following figure 13 Rail Track Analysis User Manual Eccentricity Between Rail Slab ve Eccentricity Of Section ve
5. Nodal Line Of Track Rail Neutral Axis Of Section Location Of Support Conditions Depth Of Section Eccentricity Definitions Section Neutral Axis Below Rail Level Support At Base Eccentricity Of Section ve Eccentricity Between Rail Slab ve PEN MET aI ASWEEEE OMNEM Neutral Axis Of Section a ieee ales ie E or 8 ee II Nodal Line Of Track Rail ER A s c Location Of Support Conditions Depth Of Section Eccentricity Definitions Section Neutral Axis Above Rail Level Support At Base Figure 15 Sign Conventions for Eccentricity Definition The bilinear interaction properties are derived from the bilinear curves defined in the UIC774 3 Code of Practice Properties are entered for both the unloaded and loaded states with the contact stiffness defined in KN mm per metre length of track the lift off force onset of plastic yield defined in kN per metre length and the lift off springs defined as a small value so there is no stiffness once plastic yielding has started The values in Figure 14 are for unballasted track where uy 05mm K 40kN m Unloaded k 60kN m Loaded The contact stiffness is calculated directly from Contact Stiffness k Uo 14 The Rail Track Analysis Spreadsheet The transverse spring properties of the interaction should always be infinite as the analysis is two dimensional even though the elements are three dim
6. UIC 7743 Model HwashilRailOnly Units N m kg s C Figure 36 Yield In Track Bridge Interaction Due To Train Braking Load On Track 1 34 Combination of Separate Thermal And Rail Loading Looking now at the second track where the accelerating train is at the right hand end of the structure the interaction remains unloaded and so the rail axial force stress Observed it basically due to the bending of the bridge deck due to the action of the braking train load on the other track Because there is no direct loading to the track then the axial force in the rail displays a continuous variation over the span transition piers and therefore no reduction is observed in the combined diagram for this track LUSAS Modeller 14 0 B6 D Users GeoffiDocumentatiom P403a Increased Spans Rail Expansion Joints and Beam Piers for RairecaptsgDG Splut Scale 1 4 75114E3 Zoom 566 112 Eye 0 0 0 0 1 0 Nonlinear Analysis Loadcase 2 Increment 2 Load Factor 1 00000 Results File 1 Entity Stress Diagram Component Fx tr Q4eE 0B at EIU GP 6044 Title UIC 774 3 Model Hwashil Combined Thermal And Rail Units N m kg s C Figure 37 Zoomed Axial Force In Rails Due To Accelerating Train Loads On Track 2 Looking again at the yielding Figure 38 the difference between this track and the one with the braking train becomes obvious as without the action of any train load over the span transition for this track the yield is roughly symme
7. application of the train load changes the resistance state from unloaded to loaded without the loss of this initial rail stress caused by the relative movement The train load causes increased slip of the interaction based on the loaded resistance with the end of the force displacement curve for the unloaded resistance used as the starting point for the loaded resistance If it was modelled the departure of the train load would change the resistance state back to unloaded 38 Analysis Of Combined Thermal And Rail Loading Taking Account Of Effects Of Material Change Under Rail Loading Loaded Resistance Unde Thermal And Train Load Force Unloaded Resistance During Thermal Load Force strain corresponding to applied thermal loading no train Strain Figure 41 Representation Of Transition From Unloaded To Loaded In LUSAS The key is that the interaction resistance switches from unloaded to loaded the moment the rail load arrives thereby locking in any initial movement that has occurred under the thermal loading until that rail load departs The results from this form of analysis are shown in the following figures which give peak compressive rail stresses of Track 1 and 2 Thermal Only 46 06 N mm Track 1 Thermal and Train 79 08 N mm Track 2 Thermal and Train 92 58 N mm 39 Rail Track Analysis User Manual LUSAS Mode lle r 14D B6 D Wee rs GeomDocime station da Increased Spans Rall Ea
8. 06 360000 63959 46 42526 4 614 1224 4 26 614 1230 5 5 U 0 0 00434 1 3E 05 2 3E 06 360000 63959 46 42526 4 614 1230 5 27 617 1230 5 5 D 0 0 00434 1 3E 05 2 3E 06 440000 63958 37 52007 5 617 1230 5 28 617 1236 6 6 D 0 0 00414 1 5E 05 2 2E 06 440000 63958 37 52007 5 617 1236 6 29 620 1236 6 6 D 0 D 00414 1 5E 05 2 2E 06 520000 63958 63 61489 620 1236 6 30 620 1242 7 7 U 0 0 00384 1 7E 05 2E 06 520000 63958 63 61489 620 1242 7 31 623 1242 7 7 D 0 0 00384 1 7E 05 2E 06 600000 63958 57 70970 4 623 1242 7 32 623 1248 8 8 D 0 0 00374 1 9E 05 1 8E 06 600000 63958 57 70970 4 623 1248 8 33 626 1248 8 8 U 0 0 00374 1 9E 05 1 6E 06 680000 63958 58 80451 8 626 1248 8 34 626 1254 9 9 U 0 0 00355 2E 05 1 6E 06 680000 63958 58 80451 8 626 1254 9 629 1254 9 9 D 0 0 00355 2E 05 1 6E 06 760000 63958 58 89933 2 529 1254 9 I4 4 P Selection Sheet2 7 Sheet3 lal Sr Figure 25 Microsoft Excel Spreadsheet Generated by Processing Selection 23 Rail Track Analysis User Manual The results are currently output as displacements in the longitudinal X vertical Y and major bending rotations RZ along with axial forces Fx shear forces Fz and bending moments My These results can be further post processed in Microsoft Excel or a separate package to determine quantities such as the axial stress in the rails of the track The following figures show the axial stress in the rails for thermal effects onl
9. 1 MIN 0 1543E 07 at EIUGP 1595 1 Tite UIC 774 3 Mode UICTT 4 Hwar HIP Aa The mal Aad Rall Loads Applied Corctrre rte Uit N nE Z c Figure 40 Axial Force In Rails Due To Combined Thermal And Train Loads In Track 2 One Step 37 Rail Track Analysis User Manual Analysis Of Combined Thermal And Rail Loading Taking Account Of Effects Of Material Change Under Rail Loading The previous two analysis methods fail to take account of the train rail loading being applied to the rail when it has already undergone movement stresses due to thermal effects alone In this current form of analysis implemented into LUSAS the initial thermal effects are considered prior to the application of the train rail loading and the behaviour under this rail loading takes account of this history To illustrate the analysis consider the following When the train is not on the track the stresses in the rails are governed purely by the thermal effects For the Hwashil Viaduct the thermal effects due to the bridge only are considered and therefore the action of this causes the structure to move thus inducing relative movement between the track and the bridge and therefore an associated stress in the rail For this condition the unloaded resistance properties apply across the whole extent of the track As the train load arrives over a particular part of the bridge the initial relative movement of the track bridge from the thermal effects remains and therefore the
10. 9 291 0 O 1 2b 23 4 78E 73 2 16E 71 7 1E 15 1 7E 63 1 1E 64 19 35 9 I4 4 bih Rail 1 Rail 2 7 Spans la E TE I Al Sf S Job Title B E D E F 5 H J K L M N S Job Title IUIC 774 3 Model Sample Viaduct Gi Analysis Filename Sampleviaduct mys Analysis Directory EUIC Manual Analysis Date 14 09 05 1 Increment 1 Element Node Dist m Minimum Element Node Dist m X m 0 009679 3186 325 0 0061 1818 100 Y m 2 04E 05 3102 311 42E05 2962 288 4B9E06 016 297 47E 06 2902 278 Fx N 40000 602 1204 o 2501149 1478 2956 287 Fz N 8014395 1369 2738 251 B07257 1587 3174 323 My Nm 417037 4 984 1964 125 252649 1478 2956 207 17 602 1204 D U D D 0 00534 6 93E 08 26E 06 40000 64143 49 4548 25 602 1204 D 18 602 1206 1 1 U 0 0 00514 26E 06 2 5E 06 40000 64143 49 4646 26 602 1206 1 19 605 1206 1 1 U 0 0 00514 26E 06 26E 06 120000 63902 19 14065 4 605 1206 1 20 605 1212 2 2 D 0 0 00494 5 2E 06 26E 06 120000 63902 19 14065 4 605 1212 2 21 608 1212 2 2 D D 0 00494 5 2E 06 26E 06 200000 63973 27 23567 7 608 1212 2 22 608 1218 3 3 U 0 0 00474 7 7E 06 25E 06 200000 63973 27 23567 7 608 1218 3 23 611 1218 3 3 U 0 0 00474 7 7E 06 2 5E 06 280000 63954 95 33043 6 611 1218 3 24 611 1224 4 4 D 0 0 00454 1E 05 2 4E 06 280000 6395495 33043 6 611 1224 4 25 614 1224 4 4 U 0 0 00454 1E 05 2 4E
11. E321919 E3EC 108 3 E659 2 E3EEGSG d egest Q E3SB04E 3495 2 Z E3Z9F40 LUSAS ing ined Loadi From Comb ion Force Per Metre Length In Interacti Figure 77 Analysis 65 Rail Track Analysis User Manual Conclusions Three solution methods for carrying out the UIC track bridge interaction analyses have been investigated and differences observed in the assumed behaviour and results highlighted The key observations were as follows Separate Thermal And Rail Loading Analysis d d d Correct unloaded track resistance used for thermal effects across whole model Correct yielding of unloaded ballast frozen ballast no ballast track under thermal effects Incorrect yielding of loaded ballast frozen ballast no ballast track assuming that thermal effects are present only correct if there are no thermal effects Invalid combination of two nonlinear analyses results gives apparent increase in the resistance of the track due to stresses in ballast frozen ballast no ballast track from the unloaded thermal effects being ignored in the ultimate yield of the loaded analysis to correctly model the reduction of the resistance of the track before yielding occurs under loaded conditions the yield resistance for the loaded condition should be reduced by the amount of resistance already mobilised due to the thermal effects Separate analysis ignores the movement that has already occurred under
12. LUSAS analysis enforces the track resistance at which plasticity occurs instead of allowing the potential for an apparent increase in the track resistance equal up to the unloaded plus the loaded track resistance These differences have affected the peak compressive rail stresses in the track subjected to accelerating train loads with all three analyses predicting stresses in the range of 93 to 103 N mm Separate Train Load Added To Therm E fT ne LUSAS Analysis Apparent increase in resistance of loaded track x Force O fab Q D Q U zi D o o Limit of resistance of loaded track t Thermal Alone Limit of resistance of did track Strain Unloaded stiffness Thermal Figure 50 Illustration Of Behaviour Of Separate Analysis Vs LUSAS Analysis Looking now at the track rail that has the braking train on it the following figures show the same yield plots for this track rail resistance The immediate observation is the different yield behaviour observed for the LUSAS analysis Looking initially at the separate analysis and the concurrent thermal and rail loading analysis the yielding Observed in the thermal alone for the separate analysis Figure 51 shows close similarity to the yielding observed when the thermal and train loading are applied concurrently Figure 53 minimal yielding is observed under the action of the train load alone in the separate analysis Figure 52 45 Rail
13. SAS Modeller 140 86 O WseniGeattiDocumentationi P403a4 Increased Spans Rail Expansion Joint and Beam Piers for Rare 3p Scale 1 4 75114E3 Zoom 100 0 Eye 0 0 0 0 1 0 Nonlinear Analysis Load caze 1 Increment 1 Results File 0 Entity Stress Diagram Component Fx MAX 0 5599E 06 at Elt s P 10157 MIN O FOG5E 06 at Elt SP 158471 oo Title UIC 774 3 Model HwashilTemp nl Units M m kg z C Figure 29 Axial Force In Rails Due To Thermal Effects Only These thermal effects give a peak compressive rail stress of 46 06 N mm F A 0 7065E 06 0 0153389 Having carried out the thermal analysis the rail loading will be considered in a separate analysis both horizontal and vertical loading for the worst conditions This rail load analysis is again a nonlinear analysis but it has no knowledge of the history from the thermal effects and therefore assumes a zero strain initial state prior to the application of the load In addition to this unstrained condition the loaded resistance bilinear curve is used underneath the locations of the rail loading while the unloaded lengths of track use the unloaded resistance bilinear curve The results from the rail loading analyses are presented in the following two figures the first being the track that has the braking train loading and the second being the track that has the accelerating train loading 29 Rail Track Analysis User Manual LUSAS Modeller 14 0 B6 D Users Geoff
14. Spans Rail Expansion Joints and Beam Piers for R drec amp gptsy Dec p Scale 1 4 75114E3 Zoom 566 112 Eye 0 0 0 0 1 0 Nonlinear Analysis Loadcase 2 Increment 2 Load Factor 1 00000 Results File 1 Entity Stress omponent Fx MAX K ii ipe at EIU GP 75171 T i i 06 at El GP 159471 an TITRE etl E Zur DIA ii Title UIC 774 3 Model Hwashil Combined Thermal And Rail Units N m kg s C Figure 35 Zoomed Axial Force In Rails Due To Braking Train Loads On Track 1 33 Rail Track Analysis User Manual NOTE When viewing this axial force diagram it should be recognised that while the first two spans 2 25m each have identical geometry and pier bearing properties the first span segment of the first span does not carry any of the braking train load and this is contributing to the difference in the behaviours observed over the piers Looking at the yield in the track bridge interaction for this track Figure 36 the reason for the differences in axial force either side of the pier becomes clear as yielding has occurred to the left but not to the right of the span transition pier for these first two spans LUSAS Modeller 14 0 B6 D Users GeoffiDocumentation P403a Increased Spans Rail Expansion Joints and Beam Piers for R drec amp gptsy DG p Scale 1 4 75114E3 Zoom 267 297 Eye 0 0 0 0 1 0 Nonlinear Analysis Loadcase 2 Increment 2 Load Factor 1 00000 Results File 0 Entity Stress Title
15. amp ptevDeG Sp Scale 1 3 39E3 Zoom 710 202 Eye 0 0 0 0 1 0 Nonlinear Analysis Loadcase 2 Increment 2 Load Factor 1 00000 Results File 0 Entity Stress Title UIC 774 3 Model UIC774E13P403aBaseModeIR17 Units N m kg s C Figure 65 Yield Layout For Combined Thermal And Train Loading From LUSAS Nonlinear Analysis 56 Revisit Of UIC774 3 Test E1 3 Using The Separate And LUSAS Methods Of Analysis The following two plots show the forces in the interaction joints for the thermal and train loads from the separate analysis The thermal loading has caused yielding of the unloaded track interaction with a value of 20 kN m in accordance with the unloaded resistance but the train loads have only induced up to about 25 7 kN m over the structure Combining these two results means that the total force per unit length for the separate analysis is 45 7 KN m which is comparable to the LUSAS nonlinear solution of 40 4 kN m see Figure 68 Because the interaction is well below yield for the loaded interaction resistance of 60 kN m the two solution method effectively have identical solutions and their behaviour can be visualised in Figure 69 If however the train loading had induced interaction forces in the region of 40 kN m taking account of the track resistance already mobilised by the thermal loading instead of the observed 25 7 kN m then significant differences could be observed in the two analysis methods as the separate method would s
16. contains a list of the Microsoft Excel files to build the models from with one file per line If no directory structure is defined for the files then the current working directory will be assumed to contain the files otherwise they may exist at any directory level on the computer system If a spreadsheet file cannot be found or contains invalid data it will be skipped in the batch processing and an error reported in the UIC774 3 BuildModel log file created in the current working directory Blank lines are ignored and batch processing will terminate at the end of the batch text file The number of analyses in the batch process is unlimited 18 Rail Track Analysis Menu Options Bridgel xls SomeDirectory Bridge2 xls D Project Spreadsheet Bridge3 xls Figure 20 Example Batch Text File With Three Bridges To Build Q Element Size The element size to use in the Finite Element mesh should be specified in this box According to the UIC774 3 Code of Practice the maximum element size that is permitted in an analysis is 2 0m Clause 1 7 3 The dialog therefore allows element sizes of 0 lt Element Size lt 2 0m Note For large bridges and or embankments the use of small element sizes can generate excessively large models which take significant time to manipulate solve Use of element sizes below 1 0m should be used with caution Q Apply temperature and rail loads in same analysis Two analysis types are available from the model bu
17. defined and assigned to the model Centreline Centreline Centreline Track 1 Deck Track 2 Offset Track 1 Offset Track 2 Centreline Abutment Pier Offset Abutment Pier Offset Offset gt lt Bearing Bearng2 Offset Bearing CL Centreline Bearings Figure 28 Offsets of Tracks Bearings Piers from Centreline Of Deck 26 Introduction Appendix A Verification Testing Introduction This appendix includes some background to the calculation of the UIC774 3 track bridge interaction analyses in LUSAS It explains why results from running a LUSAS nonlinear analysis that considers all thermal and train effects for the test cases in question in one analysis does not over predict the rail stresses occurring under the combined thermal and rail loading unlike results from simplified hand calculations or from results from other finite element analysis software systems where thermal and train effects are carried out by running separate nonlinear analyses From the verification testing carried out we can say that Even though a computer program may be validated against the standard test cases in the UIC774 3 code of practice in situations when combined thermal and train loading from separate analyses gives track structure interaction forces that exceed the stated yield resistance of the track restraint system i e t
18. either one or two For two tracks one will take the braking load of a trainset and the other will take the acceleration load of a separate trainset The final input in this worksheet is the lengths of the left and right embankments These lengths should be sufficiently long to allow the trainset loading to be placed in the model and according to the UIC774 3 Code of Practice should be greater than 100m Clause 1 7 3 Left Embankment Right Embankment Figure 5 Left and Right Embankments in Model Rail Track Analysis User Manual Worksheet 2 Structure Definition A rz Structure Definition ee A EH Structure Definition Lecco e o SR S ET ee ee eee ESSE ESTER ETE Units Pier Height m Bearing springs on top of each pier kN mm Gap between Pier m Spring i i Bearing Gap i Support 1 Pier Pier Geo Pier Mat springs eee 1 Geo Mat foreach Height Assign Assign on top of i Assign i Assign pier i each pier i NUI Il ee A f 4 5 6 EES ES 110 EEE 112 113 114 15 16 18 19 20 21 122 23 24 25 28 31 an KIKI Figure 6 Structure Definition The structure definition worksheet allows the geometry of the bridge to be input span by span For each span the spreadsheet allows the definition of the left pier abutment up to eight internal piers and the right pier abutment each with their own support bearing characteristics The
19. for conducting bridge track interaction analyses in accordance with the UIC774 3 Code of Practice The key features are Q LUSAS finite element models are automatically built from general arrangement deck abutment pier properties expansion joints supports interaction effects and thermal and train loading data defined in a Microsoft Excel spreadsheet Batch capabilities allow both multiple structures to be built and multiple rail load configurations to be analysed to investigate the interaction effects on different structures the results of which can be enveloped to determine worst effects Rail and structure results are automatically extracted to Microsoft Excel for presentation and further processing The Rail Track Analysis Spreadsheet A Microsoft Excel spreadsheet is used to define the data from which a LUSAS finite element model is built and a track bridge interaction analysis carried out The spreadsheet is separated into a number of worksheets that relate to particular aspects of the Rail Track Analysis input requirements These worksheets cover Number of spans tracks and embankment lengths Structure Definition Geometric Properties Material Properties Interaction and Expansion Joint Properties Loading U U U U U U For each worksheet comments are included to advise on the appropriate input to the spreadsheet These can be seen when hovering the mouse cursor over the cell of interest The template for the input s
20. in the test case which is based on evaluating the effect of each part of the loading separately and are close to the rigorous answer of 182 4 N mm LUSAS Nonlinear Analysis The UIC774 3 E1 3 test case has been reanalysed using the LUSAS rail option and gives the following peak compressive rail stress for the thermal loading alone and the combined thermal and rail loading Thermal 150 21 N mm Thermal amp Rail 187 56 N mm Comparison of the results shows that the rail stresses are in excellent agreement for both parts of the analysis with the compressive rail stress having a percentage error of 2 83 when compared against the target rigorous solution of 182 4 N mm 53 Rail Track Analysis User Manual LUSAS Modeller 14 0 B6 D UserskGeoffiDocumentationPdO3a Increased Spans Rail Expansion Joints and Beam Piers for R dilrec amp pgtsV DG 3 Scale 1 3 39E3 Zoom 100 0 Eye 0 0 0 0 1 0 Nonlinear Analysis Loadcase 1 Increment 1 Results File 0 Entity Stress Diagram Component Fx MAX 0 1419E 07 at EIU GP 325 1 MIN 0 2304E 07 at EIU GP 423 1 Title UIC 774 3 Model UICF74E13P403aTempOnly Units N m kg s C Figure 61 Axial Force In Rails Due To Temperature In Bridge And Rail LUSAS Modeller 14 0 B6 D Users GeoffiDocumentation P403a Increased Spans Rail Expansion Joints and Beam Piers for Rarec amp g ter De 3 Scale 1 3 39E3 Zoom 100 0 Eye 0 0 0 0 1 0 Nonlinear Analysis Enveloping on ALL En
21. resistance is correctly modelled as the value determined from the loaded bilinear curve and therefore this potentially leads to reduced rail stresses observed in the analyses As the initial movement under pure thermal loading in the concurrent analysis uses the loaded track resistance this will give different results to the LUSAS rail option analysis Referring back to the Hwashil Viaduct analyses the rail stresses observed for the three analysis types are Separate Analysis Concurrent LUSAS Nonlinear Of Thermal And Thermal And Thermal And Train Train Loading Train Loading Loading With Material Change 94 99 85 6 79 08 Track Braking 7099 0 0 86 70 103 66 100 6 92 58 Track 2 Accelerating Table 1 Comparison Of Peak Compressive Rail Stresses in N mm For Different Analysis Methods Comparison of the results for the separate and LUSAS analyses shows that the peak compressive stress for the separate analysis is 1 2 times that of the LUSAS analysis for track 1 and 1 12 times for track 2 It should be noted however that the separate analysis could be giving an apparent increase in track resistance of up to 1 6 times that of the loaded track due to the combination of the nonlinear results The concurrent analysis gave results that are between the separate and LUSAS analysis as expected since the correct limit of loaded track resistance is modelled even though the thermal effects are only approximated One overall conclu
22. resistance that can be mobilised in the loaded condition is the main reason for the differences in the solutions obtained for the separate and LUSAS methods and demonstrates that the correct modelling of the interaction is critical to the solution Figure 55 Force In Interaction At Right Hand End Of Structure Where Peak Compressive Stresses Occur In The Rail Track 1 Separate Thermal Loading N m length 49 e U T co 10 oO Rail Track Analysis User Manual Hi At Right Hand End Of Structure Where Peak lon Force In Interact Figure 56 Compressive Stresses Occur In The Rail Track 1 Separate Train Loading N m length 3s 0z8 Smp 3 L8 al 397 8 ORD SSL Sg 38szL 957 3 2189 rap Sa Lele cep EarrSss COT SJELLE LA 3L60t Led 39826 0S 3 59 0575 3raa0 057 H H T U eaepss LE SAEZ ODES At Right Hand End Of Structure Where Peak lon Force In Interact Figure 57 Compressive Stresses Occur In THe Rail Track 1 LUSAS Nonlinear N m length 50 Revisit Of UIC774 3 Test E1 3 Using The Separate And LUSAS Methods Of Analysis Revisit Of UIC774 3 Test E1 3 Using The Separate And LUSAS Methods Of Analysis The standard UIC774 3 test E1 3 has been reanalysed using the following two approaches Q Separate analysis of thermal and rail loading effects Q LUSAS full nonlinear analysis The results of these two analyses are presented in the following sections and
23. should not be significantly modified nor the loadcase layout otherwise the application of the rail loading may fail 19 Rail Track Analysis User Manual Apply Rail Loads Dialog UIC774 3 Rail Loads 1 Original model filename BE Hail load model filename Rail load Microsoft Excel spreadsheet or batch test File Browse Cancel Help Figure 21 UIC774 3 Apply Rail Loads Dialog If the bridge model was built and solved with only the temperature loads Apply temperature and rail loads in same analysis turned off in model building dialog then this model can subsequently be used for applying rail load configurations using this dialog The dialog should not be used for models that have been built with both the temperature and rail loading applied and will report an error if attempted Q Original model filename If a single rail load configuration is to be analysed the original model filename should be entered into the box Alternatively the Browse button can be used to locate the original model file containing only the temperature loading For batch processing the original model filename is ignored Q Rail load model filename If a single rail load configuration is to be analysed the new filename for the model incorporating the temperature and rail loads should be entered into the box This filename can contain the path name for the model location directory must exist but should generally only have the filename defined w
24. structure and the unique ID numbers must include all of the material properties that have been assigned in the Structure Definition worksheet The elastic properties are all standard LUSAS values which should be entered in Newtons millimetres and kilograms The mass density p is not used in the analysis but is provided to allow the model to be solved with self weight loading and for it to be combined with the thermal train loading effects covered in these analyses Note The number of entries can be increased by adding data to the bottom of the table Data input will terminate on the first blank ID number in column B 12 The Rail Track Analysis Spreadsheet Worksheet 5 Interaction and Expansion Joint Properties A s interaction Joint Properties Between Rail Slab l x x T GERE T T SN C REST SUNT T n G RES E Interaction Joint Properties Between Rail Slab Units Bilinear springs characteristic kN mm m Eccentricity between rail slab m 2 3 Eccentricity between rail slab 4 Item Longitudinal Transverse Vertical 5 Contact Stiff infinite infinite 16 Unloaded Bilinear Springs characteristic Lift off force infinite infinite Lift off springs infinite infinite 8 Contact Stiff infinite infinite 9 Loaded Bilinear Springs characteristic Lift off force infinite infinite 10 Lift off springs infinite infinite EH 12 13 Get Expansion Joints Units Distance m Initial gap mm 14
25. the peak compressive rail stresses obtained albeit with the LUSAS value slightly lower Looking now at the separate analysis the yield layout for both the LUSAS and concurrent thermal train loading analyses are comparable 41 Rail Track Analysis User Manual with the yield layout for thermal effects alone Figure 45 with very little yield associated with the accelerating rail load analysis Figure 46 This is primarily due to the accelerating train only just entering the bridge with the majority of the loads over the right approach embankment which are vertical not horizontal LUSAS Modeller 14 0 B6 D Users GeoffiDocumentation P403a Increased Spans Rail Expansion Joints and Beam Piers for Rail reci ptszDG p Scale 1 4 75114E3 Zoom 267 297 Eye 0 0 0 0 1 0 Nonlinear Analysis Loadcase 1 Increment 1 Results File 0 Entity Stress Figure 45 Track Rail 2 Yield Due To Thermal Load On Track Alone LUSAS Modeller 14 0 B6 D Users GeoffiDocumentation P403a Increased Spans Rail Expansion Joints and Beam Piers for Rail reci pteyDG p Scale 1 4 75114E3 Zoom 267 297 Eye 0 0 0 0 1 0 Nonlinear Analysis Loadcase 2 Increment 2 Load Factor 1 00000 Results File 0 Entity Stress Y SEM T a Title UIC 774 3 Model HwashilRailOnly Units N m kg s C Figure 46 Track Rail 2 Yield Due To Accelerating Train Loads On Track 2 Separate Analysis 42 Analysis Of Combined Thermal And Rail Loading Taking Acc
26. two analyses with the separate analysis giving a train front position of 100m from the left abutment of the bridge and the LUSAS combined analysis giving a train front position of 110m from the left abutment of the bridge Referring back to test E1 3 similar plots can be generated for the yield and forces in the interaction These as with the E1 3 test show that the train loading is not bringing the force per metre length in the interaction close the loaded yield resistance of 60 kN m and therefore the separate analysis and LUSAS analysis methods agree even though the separate method potentially allows more track resistance to be mobilised than is allowed when the thermal and rail results are combined Separate 27 8 kN m LUSAS 26 1 kN m Figure 75 Force Per Metre Length In Interaction From Thermal Loading Separate Analysis 64 Of Analysis 36555 I D Revisit Of UIC774 3 Test H1 3 Using The Separate And LUSAS Methods Separate ing in Loadi From Trai ion Force Per Metre Length In Interact Figure 76 Analysis 318 8 86 38666 8 30 08 30 08 30 08 30 08 30 08 30 09 30 08 30 09 30 08 CERAM 31890 97 38869 7C E3S07F Bl 36 0985 EAS LOOP ls carpe bly car lores E3ECIS0 H EULER E3EO10 5 3818E8 36192 Cs 31 108 L BLS 285 go 852 TZE OSE lto 848 34 41 U 341089 395 48 U e3z0s0z Q 364 Q 3 0105
27. 13 u EM T E S L L L 4 4 L L 1116 B 1117 m I4 4 b IM No Spans Tracks and EmbankLen Structure Definition Material Prope D Figure 8 Selection and Copying of Structure Definition Worksheet to Increase Number of Spans Copy and paste this section as many times as required at the end of the worksheet ensuring that the row formatting is not altered as indicated below If successful the span number should be correctly calculated for the added entries The number of spans in the first worksheet of the spreadsheet can now be increased to the number of spans added to the structure definition The Rail Track Analysis Spreadsheet B 2 TE E A1104 v Span 811114 SSS Sa Ln ar ar mE e EUER VERUS c ee E C a I ES Structure Definition Units Pier Height m Bearing springs on top of each pier kN mm Gap between Pier m an icd Geo Mat on top of E Assign Assign each pier d SERERE HE EHHERSEE ERE LER ELE EN No Spans Tracks and EmbankLen Structure Definition Geometric Properties Z Material Prope Figure 9 Pasting of Additional Spans to Ensure Formatting Maintained Worksheet 3 Geometric Properties EE E EGER RR NS ET TREE E P RR ee CE ERE RN IR II ET Depth of section to A Asy Asz support al Figure 10 Geometric Properties Table for Structure Rail Track Analysis User Manual The geomet
28. 14 0 B6 D Users GeoffiDocumentation P403a Increased Spans Rail Expansion Joints and Beam Piers for R ail 09T YUG Sp Scale 1 4 75114E3 Zoom 100 0 Eve 0 0 0 0 1 0 Nonlinear Analysis Combined Thermal And Rail Entity Stress Diagram Component Fx MAX 0 5641E 06 at EIU GP 1015 4 MIN 0 1457E 07 at EIU GP 1594 4 DIAGRAM Scale 1 0 5000E 01 Title UIC 774 3 Model Hwashil Combined Thermal And Rail Units N m kg s C Figure 32 Axial Force In Rails Due To Combined Thermal And Train Loads In Track 1 31 Rail Track Analysis User Manual LUSAS Modeller 14 0 B6 D Users GeotfiDocumentation P403a Increased Spans Rail Expansion Joints and Beam Piers for Railirec amp gtsy Ins Splut Scale 1 4 75114E3 Zoom 100 0 Eye 0 0 0 0 1 0 Nonlinear Analysis Combined Thermal And Rail Entity Stress Diagram Component Fx MAX 0 5661E 06 at EI GP 1016 4 MIN 0 1590E 07 at EIt GP 1595 4 DIAGRAM Scale 1 0 5000E 01 Title UIC 774 3 Model Hwashil Combined Thermal And Rail Units N m kg s C Figure 33 Axial Force In Rails Due To Combined Thermal And Train Loads In Track 2 Inspection of the two plots shows that there is a reduction in the axial force rail stresses over the first two span transition piers towards the left end of the structure for track 1 only subjected to the braking train The following figures show zoomed plots of the rail axial force for this location with the thermal diagram showing identical values e
29. 3 1199 300 33 6154 1362 2723 549 0 0 ilr 1 1 0 300 D 0 U 3E 15 1 56E 64 1 27E 65 1 1 D 18 1 2 1 299 0 O 8 4E 25 2 08E 73 1 18E 2 3E 15 1 56E 64 1 27E B5 1 2 1 19 3 2 1 299 0 O 9 4E 25 2 08E 73 1 18E 72 3 1E 15 22b B4 2 2E 65 3 2 1 20 3 7 2 298 0 0 1 9E 24 1 5E 73 2 BE 72 3 1E 15 2 2E 64 2 2E 65 3 7 2 21 5 7 2 298 D O 1 9E 24 1 5E 73 2 6E 72 3 3E 15 3 06E 64 1 88E b5 5 7 2 22 5 11 3 297 0 0 2 9E 24 1 29E 73 4 02E 72 3 3E 15 3 06E 64 1 88E b5 5 11 3 23 7 11 3 297 0 0 2 9E 24 1 29E 73 4 02E 72 3 5E 15 3 9E B4 2 2bE b5 2 11 3 24 7 15 4 296 0 0 4E 24 1 4E 73 5 5E 72 3 5E 15 3 9E 64 2 2E 65 7 15 4 25 9 15 4 296 D 0 4E 24 1 4E 73 5 5E 72 3 6E 15 4 87E 64 2 83E 55 9 15 4 26 9 18 5 295 0 0 5 2E 24 1 78E 73 7 41E 72 3 8E 15 4 97E 64 2 83E 65 9 18 5 27 11 18 5 295 U O 52bE 24 1 78E 73 7 41E 72 4 2E 15 6 2E 64 3 7E b5 11 18 5 28 11 23 6 294 0 0 5 5E 24 2 3E 73 8 8BE 2 42E 15 6 2E 64 3 7E 65 11 23 6 29 13 23 6 294 5 5E 24 23E 73 9 8E 72 48E 15 7 9E B4 4 87E 65 13 23 6 30 13 27 7 293 0 0 BE 24 2 88E 73 1 28E 71 4 6E 15 7 9E 64 4 97E 65 13 27 7 31 15 27 7 293 0 0 8E 24 2 88E 73 1 28E 71 5 4E 15 1E 63 6 3E 65 15 27 7 32 15 31 8 292 D 0 9 7E 24 3 7E 73 1 7E 71 5 4E 15 1E 63 5 3E 55 15 31 8 33 17 31 8 292 0 O 9 7E 24 3 7E 73 1 7E 71 6 2E 15 1 31E 63 8 25E 65 17 31 8 34 17 35 9 291 0 0 1 2bE 23 4 78E 73 2 15E 71 5 2bE 15 1 31E 63 8 25E 65 17 35 8 19 35
30. ElVGP 483 1 Title UIC 7743 Model UICF74H13P403 aT emp Only Units N m kg s C Figure 70 Axial Force In Rails Due To Temperature In Bridge And Rail To determine the worst location of the train load for compressive rail stresses the bridge has been analysed with the rail loading at 37 separate locations starting from the left abutment of the bridge and finishing 90m from the right abutment of the 60 Revisit Of UIC774 3 Test H1 3 Using The Separate And LUSAS Methods Of Analysis bridge train moving from left to right and these results enveloped The results of this analysis are presented in the following figure which give a peak compressive rail stress of 29 09 N mm LUSAS Modeller 14 0 B6 D Users GeoffiDocumentation P403a Increased Spans Rail Expansion Joints and Beam Piers for Ran reca pre UBG Sp Scale 1 3 5441E3 Zoom 100 0 Eye 0 0 0 0 1 0 Nonlinear Analysis Enveloping on ALL Enveloping Rail Load Envelope_MIN Entity Stress Diagram Component Fx MAX 186 5 at EIt GP 7371 MIN 0 44562E 06 at EIt GP 481 1 DIAGRAM Scale 1 0 5000E 01 Title UIC 774 3 Model UIC774H1SP403aTempOnly Units N m kg s C Figure 71 Envelope Of Axial Force In Rails Due To Rail Loading Manual combination of the peaks would give a peak compressive rail stress of 190 57 N mm ignoring locations of the peaks and combination of the results in LUSAS gives 190 56 N mm 61 Rail Track Analysis User Manual LUSAS Model
31. Rail Track Analysis User Manual LUSAS Version 14 2 Issue 1 LUSAS Forge House 66 High Street Kingston upon Thames Surrey KT1 IHN United Kingdom Tel 44 0 20 8541 1999 Fax 44 0 20 8549 9399 Email info lusas com http www lusas com Distributors Worldwide Copyright 1982 2008 LUSAS All Rights Reserved Table of Contents Table Of Contents Rail Track Analysis 1 Tess Ra estat DUC anna 1 WIC 74 3 Code of PracliCG iie eei orato coo te ee a ien Ease eee ied 1 LUSAS Rail Track Analysis neri i a ae 4 The Rail Track Analysis Spreadsh et ns 4 Worksheet 1 Spans and Embankment Lernpths tio eu 5 Worksheet 2 Stmiet re Definition oh osea deo en fen pu aba a nde bea recitata d dad tels 6 Worksheet 3 RT lic Properties ale 9 Worksheet 4o Material Proper Wes caren Reue 12 Worksheet 5 Interaction and Expansion Joint Properties essen 13 Worksheet o Thenmaland Iran Loading nee a ae u te adieu 16 Hall Track Analysis Menu Optlons u n een 17 Build Model Dale een ea EAI TATA EEEE AE eee epee ee eee re 18 Apply Rail boddsdJOralo8 s uisi unten 20 Extract Results To Microsoit Excel Dialog a au Aelia eens 2l Limitations OT USC een 26 Appendix A Verification Testing 27 luigi me M 27 prega mec M 27 Combination of Separate Thermal And Rail Loading s
32. Track Analysis User Manual Concentrating on the LUSAS analysis the front of the braking train load is just over the right end of the structure and the carriages cover most of the remaining bridge This has the effect unlike the accelerating track of changing nearly all of the resistance from unloaded to loaded for this track over the bridge and therefore the interaction is no longer under yield because the loaded resistance now governs plastic yield The LUSAS analysis however does not display the possible apparent increase in the resistance of the track that can be observed with the separate analysis method This means the track interaction around the front of the braking train resisting the movement of the rails cannot sustain the same level of loading and therefore yield to a larger extent than observed in the separate analysis thereby reducing the compressive stress in the rails underneath the train compare Figure 52 and Figure 54 where the yielding underneath the braking train is greater for the LUSAS analysis than in the separate rail load analysis LUSAS Modeller 14 0 B6 D Users GeoffiDocumentation P403a Increased Spans Rail Expansion Joints and Beam Piers for R ail recgBteEy DG p Scale 1 4 75114E3 Zoom 267 297 Eve 0 0 0 0 1 0 Nonlinear Analysis Loadcase 1 Increment 1 Results File 0 Entity Stress Title UIC 774 3 Model HwashilTempOnly Units N m kg s C Figure 51 Track Rail 1 Yield Due To Thermal Load On Track A
33. VGP 1595 4 Tite UIC 774 3 Model UICTT Hwe bP Aa Uit N mpgs C Figure 44 Axial Force In Rails Due To Combined Thermal And Train Loads In Track 2 The analyses produced using this method can give a lower peak compressive stress in the rails than observed using the other approaches but agrees closely with the published test cases using rigorous methods in UIC774 3 as observed in the following sections for test E1 3 and H1 3 Discussion The peak compressive stresses in track rail 2 which has the accelerating load and track rail 1 that is subjected to the braking train show differences in the peak compressive stress in the rails based on the position of the train loads used in the analysis As the loading and geometry of the models are identical the differences can only be associated with the track resistance modelling behaviour It has been noted previously in Section 0 above that the transition from unloaded resistance to loaded resistance is only incorporated into the LUSAS modelling so this track resistance is investigated by looking at the yield under the effects of the rail loading Looking first at the second track rail that has the accelerating load the yielding occurring from the three analyses are shown in the following figures Comparing the yield layout for the LUSAS analysis Figure 48 and the concurrent thermal train loading analysis Figure 47 shows that the overall yield behaviour is almost identical hence the similarity in
34. amp prezUBG p Scale 1 3 5441E3 Zoom 100 0 Eye 0 0 0 0 1 0 Nonlinear Analysis Loadcase 1 Increment 1 Results File O Entity Stress Diagram Component Fx MAX 0 1275E 07 at EIt GP 349 MIN 0 2477E 07 at EIU GP 48371 Title UIC 774 3 Model UIC774H13P4dO3aTemp nhy Units N m kg s C Figure 73 Axial Force In Rails Due To Temperature In Bridge And Rail LUSAS Modeller 14 0 B6 DAUsersGeoffiDocumentationP403a Increased Spans Rail Expansion Joints and Beam Piers for R 31 recapre 2 DBG p Scale 1 3 5441E3 Zoom 100 0 Eye 0 0 0 0 1 0 Nonlinear Analysis Enveloping on ALL Enveloping Envelope MIN Entity Stress Diagram Component Fx MAX 0 1370E 07 at EIU GP 345 1 MIN 0 2909E 07 at EI GP 483 1 DIAGRAM Scale 1 0 5000E 01 Title UIC 774 3 Model UIC774H13P4Q03a Base Model Units N m kg s C Figure 74 Axial Force In Rails Due To Combined Temperature And Enveloped Rail Loading 63 Rail Track Analysis User Manual Discussion As with the previous E1 3 test case the difference in the results due to the track resistance modelling between the two methods is minimal Combining the results of two nonlinear analysis while invalid gives almost identical results to the LUSAS analysis which correctly represents the transition from unloaded to loaded resistance on arrival of the train load The train load position that gives the worst compressive stress in the rail does however differ slightly between the
35. and end of the structure roller bearing where the peak compressive rail stresses are observed shows no sign of yield with yield only occurring over the left end and embankment Figure 64 and Figure 65 This indicates that the separate analysis while invalid due to the linear combination of two nonlinear analyses is giving the correct result and this only occurs because the interaction over the structure at this location is nowhere near yield LUSAS Modeller 14 0 B6 D Wsers GeoffiDocumentation P403a Increased Spans Rail Expansion Joints and Beam Piers for Rail reci ptsgDG p Scale 1 3 39E3 Zoom 513 577 Eve 0 0 0 0 1 0 Nonlinear Analysis Loadcase 1 Increment 1 Results File 0 Entity Stress Title UIC 774 3 Model UIC774E13P403aTempOnly Units N m kg s C Figure 63 Yield Layout For Thermal Loading Only 55 Rail Track Analysis User Manual LUSAS Modeller 14 0 B6 D UserGeoffiDocumentation P403a Increased Spans Rail Expansion Joints and Beam Piers for R dibrec amp ptsgDeG p Scale 1 3 39E3 Zoom 507 345 Eye 0 0 0 0 1 0 Nonlinear Analysis Loadcase 2 Increment 2 Load Factor 1 00000 Results File 0 Entity Stress Title UIC 774 3 Model UIC774E13P4O03 aR ailOnlyR16 Units N m kg s C Figure 64 Yield Layout For Train Loading Only From Separate Analysis LUSAS Modeller 14 0 B6 D UsersiGeoffiDocumentation P403a Increased Spans Rail Expansion Joints and Beam Piers for R dil rec
36. ation is assumed to be zero in the analysis This can be adjusted by modifying the support conditions manually after a temperature only analysis has been performed see user interface discussions In addition to the general arrangement or the piers supports and bearings the gaps between the piers are also defined in this worksheet and should be a positive number greater than zero in metres The final entries in the worksheet relate to the geometric and material properties to assign to the spans Different properties can be assigned to each segment of the span but continuously varying properties cannot be modelled All of the geometric and material properties used in the structure definition must be defined in the geometric and material property worksheet tables described later in this manual Increasing the number of spans modelled If more than 100 spans are required the Microsoft Excel spreadsheet can be modified To do this scroll to the end of the Structure Definition worksheet and select the last complete span definition as indicated on the figure below Rail Track Analysis User Manual A FES ca eT a eel eT ee m ips M RENE Units Pier Height m Bearing springs on top of each pier kN mm Gap between Pier m A1093 v Span 811103 pec SS Structure Definition Mat ign i Assign 091 1092 1094 1095 1097 1100 1101 1102 1103 1104 1105 1106 ng 1108 11109 11110 11111 11112 111
37. d Spans Rail Expansion Joints and Beam Piers for R arec amp gtsy DG p Scale 1 3 39E3 Zoom 100 0 Eve 0 0 0 0 1 0 Nonlinear Analysis Enveloping on ALL Enveloping Rail Load Envelope MIN Entity Stress Diagram Component Fx MAX 537 7 at ElVGP 62 4 MIN 0 6233E 06 at EI GP 42371 DIAGRAM Scale 1 0 5000E 01 Title UIC 774 3 Model UICF74E13P403aTempOnly Units N m kg s C Figure 59 Envelope Of Axial Force In Rails Due To Rail Loading Manual combination of the peaks would give a peak compressive rail stress of 190 85 N mm ignoring locations of the peaks and combination of the results in LUSAS gives 190 82 N mm 52 Revisit Of UIC774 3 Test E1 3 Using The Separate And LUSAS Methods Of Analysis LUSAS Modeller 14 0 B6 D AUsersvGeoffiDocumentationXPdO3a Increased Spans Rail Expansion Joints and Beam Piers for Raireciggtsy DG Splut Scale 1 3 39E3 Zoom 100 0 Eye 0 0 0 0 1 0 Nonlinear Analysis Combination Temp And Rail Load Envelope Entity Stress Diagram Component Fx MAX 0 1473E 07 at EIt GP 327 41 MIN 0 2927E 07 at EIt GP 42371 DIAGRAM Scale 1 0 5000E 01 Title UIC 774 3 Model UIC774E13P4dO03aTemp Only Units N m kg s C Figure 60 Axial Force In Rails Due To Combined Temperature And Rail Loading Comparison of these results with the UIC774 3 code of practice test results shows that the result compares directly with the 190 07 N mm compressive rail stress from the simplified analysis
38. e track and the bridge as a result of temperature and train loading is within specified design limits UIC774 3 Code of Practice According to the Union Internationale des Chemins de fer International Union of Railways UIC774 3 Code of Practice the track structure interaction effects should be evaluated in terms of the longitudinal reactions at support locations rail stresses induced by the temperature and train loading effects in addition to the absolute and relative displacements of the rails and deck To assess the behaviour these interaction effects should be evaluated through the use of a series of nonlinear analyses where all thermal and train loads are taken into account These loads should be Q Thermal loading on the bridge deck LJ Thermal loading on the rail if any rail expansion devices are fitted LI Vertical loads associated with the trainsets Q Longitudinal braking and or acceleration loads associated with the trainsets Rail Expansion Joint Track Non linear Springs If Present Representing Ballast or Connection N N Bridge Deck Embankment Figure 1 Representation of Structural System for Evaluation of Interaction Effects Rail Track Analysis User Manual Non linear spring representing ballast connection E x S n Track rail Z t 7 centreline mni Deck
39. ensional but the vertical spring properties can be adjusted from this to include vertical deformation effects of the ballast If this type of analysis is carried out care must be taken to ensure that the spring remains in the elastic regime This is achieved by setting a very high value for the lift off force 1 0E12 kN mm per metre length for example and ensuring that the lift off springs are set to the same stiffness value as the contact stiffness Defining Rail Expansion Joints If rail expansion joints are present in the bridge then the information for these can be entered into the worksheet for each track The data input takes the form of a unique positive ID number that is placed in column B the positions and initial gaps The expansion joint data will be read from the spreadsheet until a blank ID entry is detected For each unique ID number an expansion joint can be defined for either track by entering the position in metres from the start of the left hand embankment and initial gap in millimetres A vw Interaction Joint Properties Between Rail Slab 4 Interaction Joint Properties Between Rail Slab Units Bilinear springs characteristic kN mm m Eccentricity between rail slab m 2 NEN 3 Eccentricity between rail slab 4 Item Longitudinal Transverse Vertical 5 Contact Stiff infinite infinite 16 Unloaded Bilinear Springs characteristic Lift off force infinite infinite Lift off springs infinite infini
40. erature of the bridge deck and rails relative to the reference temperature of the deck when the rail was fixed needs to be considered in accordance to the code of practice and design specifications The temperature loads for both the slab deck and the rail should be entered zero if not required in Celsius degrees centigrade where temperature rises are entered as positive values and temperature drops are entered as negative values The train loading is defined in terms of the type track position and magnitude The type may be Braking Acceleration or Vertical with the first character governing the type detection and allows a more descriptive definition to be entered if required The track to be loaded must indicate a valid track based on the data entered into the Number of Spans Tracks And Embankment Lengths worksheet described earlier The start and end positions of the loading should be defined in metres relative to the left hand end of the left embankment which is at position 0 0m and must remain within the overall length of the model including embankments refer to the Spans Tracks and Embankments worksheet which reports the total length of the model The final data required is the amount of load to apply to the rail in KN per metre length For vertical loads a positive value indicates that the load acts in a downward sense and for horizontal braking and accelerating loads a positive value indicates that the load acts towards the right embank
41. he ballast then the separate analysis method will potentially over predict the rail stresses unless the loaded track yield surface is reduced by the mobilised track resistance over the extent of the train loading Rail stress over predictions of up to 30 have been seen when thermal and train loading results are combined from separate analyses Description The rail track analysis UIC774 3 option in LUSAS allows the construction and solution of finite element models to study the interaction between the rail track and a bridge This forms an essential part of the design process as the stresses within the rails of the tracks must remain within specified limits based upon the design and the state of maintenance A number of calculation methods are available and each of these can lead to a slightly different solution for the combined thermal and rail loading condition Each of these methods except the hand calculation has been investigated in this technical note prior to carrying out the analysis in LUSAS using the rail track analysis option 27 Rail Track Analysis User Manual The Hwashil Viaduct a railway bridge in South Korea has been used for this testing with continuous welded rail CWR and thermal effects only present in the structure for the following analyses Q Combination of Separate Thermal And Rail Loading LJ Analysis Of Combined Thermal And Rail Loading One Step LJ Analysis Of Combined Thermal And Rail Loading Taking Acc
42. hich will then be saved in the current working directory This filename can be the same as the original model filename but should generally be different to allow the temperature loading model to be reused for another rail load configuration For batch processing the new rail load model filename is ignored Q Rail load Microsoft Excel spreadsheet or batch text file If a single rail load configuration is to be analysed for the specified bridge model the filename of the Microsoft Excel spreadsheet containing the required loading should be entered into the box Alternatively the Browse button can be used to locate the file Once the spreadsheet has been specified the OK button can be clicked to carry out the modification of the original bridge model to include the combined effects of the temperature and rail loading If multiple models and or multiple rail load configurations are to be analysed then only the batch text file which must have a txt file extension listing the information 20 Rail Track Analysis Menu Options required by the software should be entered into this box Alternatively the Browse button can be used selecting Batch text file txt as the file type For each model rail configuration analysis the batch text file should contain a separate line of data Each line should specify the original temperature model the new combined loading model to create and the Microsoft Excel spreadsheet that contains the rail configurat
43. iDocumentation P403a Increased Spans Rail Expansion Joints and Beam Piers for R ai reci tsv DG 3 Scale 1 4 75114E3 Zoom 100 0 Eye 0 0 0 0 1 0 Nonlinear Analysis Loadcase 2 Increment 2 Load Factor 1 00000 Results File 0 Entity Stress Diagram Component Fx MAX 0 3624E 06 at EI GP 751 71 MIN 0 7505E 06 at EIt GP 1584 1 Title UIC 774 3 Model HwashilRailOnly Units N m kg s C Figure 30 Axial Force In Rails Due To Braking Train Loads On Track 1 LUSAS Modeller 14 0 B6 D XUsersvGeoffiDocumentationP4dQ03a Increased Spans Rail Expansion Joints and Beam Piers for R dil recap ts DG 3 Scale 1 4 75114E3 Zoom 100 0 Eye 0 0 0 0 1 0 Nonlinear Analysis Loadcase 2 Increment 2 Load Factor 1 00000 Results File 0 Entity Stress Diagram Component Fx MAX 0 357 3E 06 at EII GP 6044 MIN 0 8834E 06 at EIU GP 1595 4 Title UIC 774 3 Model HwashilRailOnly Units N m kg s C Figure 31 Axial Force In Rails Due To AcceleratingTrain Loads On Track 2 30 Combination of Separate Thermal And Rail Loading From these results the peak compressive rail stresses for the two tracks are as follows Track 1 48 93 N mm Track 2 57 59 N mm A basic combination of the loading can be defined to add the results from the thermal and rail loading analyses together which gives the following track peak compressive stresses see following figures Track 1 94 99 N mm Track 2 103 66 N mm LUSAS Modeller
44. ilding dialog These are e The solution of the combined temperature and rail loading effects option turned on e The solution of just the temperature effects option turned off If only a single rail loading configuration is going to be analysed for a particular model then this option should be switched on If on the other hand a range of rail loading configurations needs to be applied to a model for different train positions with varying braking accelerating loading configurations then this option should be turned off to allow the rail loads to be applied separately by the Apply Rail Loads dialog described below Building a model to solve only temperature effects also allows the model to be updated prior to applying the rail loading A situation where this may be needed is the case of a mixed bridge type for example one having concrete and steel sections where the temperature loading of the bridge deck cannot be classified by the single temperature change available in the Microsoft Excel spreadsheet If only the temperature model is built additional temperature loading attributes can be defined and assigned to the temperature loadcase prior to the rail load application This will also allow the support conditions to be modified for pier foundations that require rotational stiffness rather than rigidity see the discussion of Structure Definition section of the Microsoft Excel spreadsheet Note The overall structure of the model
45. ion definition Each item on a line should be TAB delimited to allow spaces to be used in the filenames An example batch text file is shown below Bridgel mdl Bridgel RailConfigl mdl Bridgel RailConfigl xls Bridgel mdl Bridgel RailConfig2 mdl Bridgel RailConfig2 xls Bridgel mdl Bridgel RailConfig3 mdl Bridgel RailConfig3 xls Bridgel mdl Bridgel RailConfig4 mdl Bridgel RailConfig4 xls Bridge2 mdl Bridge2 RailConfigl mdl Bridge2 RailConfigl xls Bridge2 mdl Bridge2 RailConfig2 mdl Bridge2 RailConfig2 xls Bridge3 mdl Bridge3 RailConfigl mdl Bridge3 RailConfigl xls Figure 22 Sample Rail Loading Batch Text File In the above example three different bridge deck temperature models have been selected and four rail load configurations analysed for the first two rail load configurations for the second and one rail load configuration for the third The number of entries in the batch text file is unlimited and batch processing will terminate once the end of the file is reached If any analysis fails due to missing or invalid files an error will be reported to the UIC774 3 RailLoads log file in the current working directory Extract Results To Microsoft Excel Dialog UIC 774 3 Post Processor Filename Working folder e Current User defined Jave in A rusas all Projects Figure 23 UIC774 3 Post Processor Dialog A dedicated post processing dialog is provided that allows the automatic extraction of the results from the track bridge interacti
46. ither side of these piers for all of the spans in the model The reason for the reduction in the axial force becomes clear from the axial force diagram for the train braking load alone Figure 35 where the axial force has a positive peak over the span transition piers which is not symmetrical Looking at the transition from the first span to the second 27d pier from left abutment the axial force in the rail over the end of the first span is equal to a tension force of 362 4 kN while the axial force over the start of the second span is equal to a tension force of 344 7 kN Like for like comparison of the elements a certain distance from the pier for each span shows that the second span is consistently lower and this difference has caused the non symmetric nature of the combined axial force rail stress diagram over the span transition piers 32 Combination of Separate Thermal And Rail Loading LUSAS Modeller 14 0 B6 D Users Geoff iDocumentation P403a Increased Spans Rail Expansion Joints and Beam Piers for R ah 9 ptsvDao p Scale 1 4 75114E3 Zoom 566 112 Eye 0 0 0 0 1 0 Nonlinear Analysis Loadcase 1 Increment 1 Results File 0 Entity Stress Diagram Component Fx MAX 0 5599E 06 at E x Mi Title UIC 774 3 Model Hwashil Combined Thermal And Rail Units N m kg s C Figure 34 Zoomed Axial Force In Rails Due To Thermal Effects Only LUSAS Modeller 14 0 B6 D Users GeoffiDocumentation P403a Increased
47. ity Stress Tite UIC 774 3 Model UICTT HWS HIP Aa Uit N nZ C Figure 54 Track Rail 1 Yield Due To Braking Train Load On Track 1 LUSAS Combined Analysis 48 Analysis Of Combined Thermal And Rail Loading Taking Account Of Effects Of Material Change Under Rail Loading Looking at the behaviour of the track interaction for the separate analysis we can plot the values of the force per metre length for the track subjected to the braking train loads Figure 55 and Figure 56 show the forces per metre length for the thermal loading and the train braking loading for the separate analyses Clearly near the right hand abutment the force per metre length under the thermal loading is equal to 40kN m and due to the train loading is equal to 60kKN m Combination of these two results means that the track interaction has mobilised 100kN m in this region when it is actually only able to mobilise 60kN m based on the loaded track resistance bilinear curve the separate analysis method is giving an apparent increase in the loaded track resistance that can be mobilised before plastic yielding occurs This apparent increase in the loaded track resistance has the consequence of allowing the rail stresses to increase beyond the value that would occur if the true loaded track resistance was used as in the LUSAS modelling where the track resistance is correctly limited to the loaded value of 60KN m Figure 57 NOTE This difference in the amount of track
48. ler 14 0 B6 DAUsersGeoffiDocumentationXP403a Increased Spans Rail Expansion Joints and Beam Piers for Rareca prz UG Sp Scale 1 3 5441E3 Zoom 100 0 Eve 0 0 0 0 1 0 Nonlinear Analysis Combination Temp And Rail Envelope Entity Stress Diagram Component Fx MAX 0 1369E 07 at Elt GP 345 1 MIN 0 2923E 07 at Elt GP 48171 DIAGRAM Scale 1 0 5000E 01 Title UIC 774 3 Model UIC774H13P403aTemp nhyr Units N m kg s C Figure 72 Axial Force In Rails Due To Combined Temperature And Rail Loading Comparison of these results with the UIC774 3 code of practice test results shows that the result compares well with the 188 23 N mm compressive rail stress from the complex analysis in the test case LUSAS Nonlinear Analysis The UIC774 3 H1 3 test case has been reanalysed using the LUSAS rail option and gives the following peak compressive rail stress for the thermal loading alone and the combined thermal and rail loading Thermal 161 48 N mm Thermal amp Rail 189 65 N mm Comparison of the results shows that the rail stresses are in excellent agreement for both parts of the analysis with the compressive rail stress having a percentage error of 0 75 when compared against the target solution of 188 23 N mm 62 Revisit Of UIC774 3 Test H1 3 Using The Separate And LUSAS Methods Of Analysis LUSAS Modeller 14 0 B6 D Users GeoffiDocumentation P403a Increased Spans Rail Expansion Joints and Beam Piers for Rairec
49. lone 46 Analysis Of Combined Thermal And Rail Loading Taking Account Of Effects Of Material Change Under Rail Loading LUSAS Modeller 14 0 B6 D Users GeoffiDocumentation P403a Increased Spans Rail Expansion Joints and Beam Piers for R Jh H RLZYUHGS p Scale 1 4 75114E3 Zoom 267 297 Eye 0 0 0 0 1 0 Nonlinear Analysis Loadcase 2 Increment 2 Load Factor 1 00000 Results File 0 Entity Stress Title UIC 774 3 Model HwashilRailOnly Units N m kg s C Figure 52 Track Rail 1 Yield Due To Braking Train Loads On Track 1 Separate Analysis LUSAS Mode lle 14 0 86 D We rs GeomDocime tation da licreared Spans Rall pass lor Jolt aad Beam Pers or Rall STE TN Soliton TempardRallToge the hy IC 77 Hie BS LDO arm pac Scale 1 4 75114E3 Zoom 267 297 Eye 0 0 0 0 1 0 Nonlinear Analysis Loadcase 1 Increment 1 Results File 0 Entity Stress Tite UC 774 3 Model U CTT HWE HIP da The mal Aad Rall Loads applied Corcarre sty Uis N pos C Figure 53 Track Rail 1 Yield Due To Braking Train Loads On Track 1 Thermal And Rail Applied Concurrently 47 Rail Track Analysis User Manual LUSAS Mode ler 140 86 DWsers GeomDocume station da Increased Spans Rall Brass los Jolt aad Beam Pers or Rall Scrpt TN Soliton U Ses 77 Hwas HIP DS mairie 25 05 Scale 1 4 75114E3 Zoom 267 297 Eye 0 0 0 0 1 0 Nonlinear Analysis Loadcase 2 Increment 2 Load Factor 1 00000 Results File 0 Ent
50. ment 16 Rail Track Analysis Menu Options As many rail train loads as required can be defined in the spreadsheet with data input terminating when blank data is detected in the loading type column This allows more complex loading patterns to be defined such as those illustrated below LI A rj Al sj Loading EN mm l GI a 4 REAL 2 Se ES SS SENE ake SaaS a EE ESTIS SES BE IN E zu O 4 N 33m 27 E Acceleration Sm 30 Load Unis Temperature Celsius Load Position Length m Load kN m For Slab m Ate ijemperature Tack R r S Gerken tes i N H iy i ipe mount selection Position Position per unit Loaded i tobe for fo length length entr na I Vertical Carriag For Rails 157 kN m BOkN B kN xia m tots S Load v 14 4 gt NZ Geometric Properties Material Properties Interaction and Expansion Joint Loading IERI E Fi Figure 18 More Complex Train Loading Definition in Spreadsheet Rail Track Analysis Menu Options The Rail Track Analysis option is accessed through the Bridge menu by selecting the Rail Track Analysis UIC774 3 entry This menu entry provides the following three options Q Build Model Q Apply Rail Loads Q Extract Results To Excel 17 Rail Track Analysis User Manual Build Model Dialog UTC 774 3 Model Builder l Model filename FP Microsof
51. ness Thermal Figure 69 Illustration Of Behvaiour For UIC774 3 Standard Test E1 3 For Separate And LUSAS Analyses 59 Rail Track Analysis User Manual Revisit Of UIC774 3 Test H1 3 Using The Separate And LUSAS Methods Of Analysis The previous test case E1 3 is one of the key test cases that must be matched for computer programs carrying out this form of analysis with the results for both the separate method and the LUSAS method being in close agreement to the results required The deck type for this test is however a concrete slab underlain by I section steel beams which does not compare with the deck being used for Hwashil Viaduct For this reason the H1 3 test is also revisited and solved using the two methods of analysis Separate Analyses The analysis of the thermal effects due to the temperature in the bridge and rail are presented in the following figure These two thermal effects give a peak compressive rail stress of 161 48 N mm which compares well with the code of practice value of 169 14 N mm allowing for slight differences in material properties which have been estimated LUSAS Modeller 14 0 B6 D Users Geoffibocumentation P403a4 Increased Spans Rail Expansion Joints and Beam Piers for Railreca prz UBG Sp Scale 1 3 5441E3 Zoom 100 0 Eye 0 0 0 0 1 0 Nonlinear Analysis Loadcase 1 Increment 1 Results File 0 Entity Stress Diagram Component Fx MAX 0 1275E 07 at EIt GP 349 1 0 2477E 07 at
52. on analysis to a Microsoft Excel spreadsheet 21 Rail Track Analysis User Manual On start up the dialog will inspect the active model to ensure that these are results present and also detect whether the UIC774 3 groups defined during the model building process are present For this reason any manual editing of the model should be kept to a minimum and the Rail 1 Rail 2 and Spans groups should not be modified If all of the groups are found in the model separate worksheets are generated for the results in the tracks rails and spans If one or more of these groups are absent from the model then the dialog will attempt to use the current selection in Modeller to perform the post processing If the selection is used this must contain lines that have 3D engineering thick beam elements assigned to them Q Filename The filename for the Microsoft Excel spreadsheet that will be created should be entered into this box The filename must not have any directory structure specified as the file will be placed in the directory selected below Q Working folder Save In If the spreadsheet is to be saved in a directory other than the current working directory then the User defined option can be selected and the required directory entered into the box or browsed for using the button Output Format On clicking the OK button the post processor will extract the results from all of the results loadcases along with all envelopes without as
53. or the separate analysis the thermal effects use the unloaded curve and the behaviour of this part of the analysis is limited by the resistance of the unloaded track Under these conditions the analysis may give a location indicated by the Thermal Alone point on the unloaded curve Separate consideration of the train loading effectively places the origin of the loaded bilinear curve at this Thermal Alone position and any loading could potentially give the location indicated by the Separate Train Load Added To Thermal position This could give an apparent increase in the resistance of the track and therefore increase rail stresses in the loaded track Separate Train Load Added To Therm RN a Se en A Concurrent thermal and train loading loaded resistance cn resistance of loaded track Ck e d lt Limit of resistance of loaded tr Thermal Alone Limit of resistance of T track Strain Unloaded stiffness Thermal Figure 49 Illustration Of Behaviour Of Separate Analysis Vs Concurrent Thermal And Rail Loading 44 Analysis Of Combined Thermal And Rail Loading Taking Account Of Effects Of Material Change Under Rail Loading Similar comparisons can be made between the separate analysis and the LUSAS analysis Figure 50 While both of these effectively use the Thermal Alone location as an origin for the loaded resistance curve the key difference between the two approaches is that the
54. ount Of Effects Of Material Change Under Rail Loading LUSAS Mode ler 14D B6 D Wee rs Geom Doctme station da licreased Spans Rall pars loa Jolt aad Beam Pers tr Rall ScripteXTN Sol itioatTempiadRallToge the P IC 77 H 6 BI AT erm puc Scale 1 4 75114E3 Zoom 267 297 Eye 0 0 0 0 1 0 Nonlinear Analysis Loadcase 1 Increment 1 Results File 0 Entity Stress Tite UC 774 3 Model U CTT HG HIP da The mal Aad Rall Loads applied Corcarre sty Uit Nm kgs C Figure 47 Track Rail 2 Yield Due To Accelerating Train Loads On Track 2 Thermal And Rail Applied Concurrently LUSAS Node ler 140 86 D Wee rs GeottDocume station HR Increased Spans Rall pans be Joh ard Beam Pers Dr Rall Sorpt TN Soliton USR CTT tees IP amon ne 29 2006 Scale 1 4 75114E3 Zoom 267 297 Eye 0 0 0 0 1 0 Nonlinear Analysis Loadcase 1 Increment 1 Results File 0 Entity Stress Tite UC 774 3 Model UICTT Hee LIP de Uit Nm sc Figure 48 Track Rail 2 Yield Due To Accelerating Train Load On Track 2 LUSAS Combined Analysis 43 Rail Track Analysis User Manual Looking at what is effectively happening in these analyses Figure 49 the concurrent loading analysis uses the loaded resistance throughout the analysis and follows the loaded stiffness curve from the origin and potentially gives the location indicated on the plastic part of this curve as illustrated with a force in the interaction limited to the resistance of the loaded track F
55. ount Of Effects Of Material Change Under Rail Loading In addition two of the UIC standard test cases have also been reinvestigated to demonstrate that these results can be matched even if the analysis type is potentially invalid prior to providing guidance and conclusions on this type of analysis These analyses were Q Revisit Of UIC774 3 Test E1 3 Using The Separate And LUSAS Methods Of Analysis Q Revisit Of UIC774 3 Test H1 3 Using The Separate And LUSAS Methods Of Analysis Combination of Separate Thermal And Rail Loading In this form of analysis two or more separate analyses are carried out with each analysis considering a different loading regime to the structure This is the simplest form of analysis of the track bridge interaction as it assumes that superposition is valid for a nonlinear system and according to the UIC774 3 code of practice can generally overestimate the rail stresses with percentage errors up to 20 to 30 be it through hand calculation or computer methods This analysis procedure is replicated in LUSAS by performing two separate nonlinear analyses The first considers only the thermal effects and uses the unloaded resistance bilinear curve for modelling the interaction between the track and bridge The results of this analysis are identical for the two tracks in the model and so only the results for the first track are presented in the following figure 28 Combination of Separate Thermal And Rail Loading LU
56. preadsheet is located in the lt Lusas Installation Folder Programs WSscriptsNUser directory Initially this template contains data that reproduces the E1 3 UIC test case model outlined in the code of practice as an illustration and should be edited and saved to the working directory in order to carry out analyses Note All of the data entered into the Microsoft Excel spreadsheet should be in metric units The required units are indicated in the various sections of the spreadsheet and should be adhered to for the correct modelling of the interaction analysis When the model is built all input will be converted to SI units of N m kg C and s The Rail Track Analysis Spreadsheet Worksheet 1 Spans and Embankment Lengths Al m z Spans and Embankment EST ES RIEN ENTE E F G H J Kj Spans and Embankment _ Units m Number of Spans cc Number of Tracks u E Left embankment length n Right embankment length T 4 V WNNo Spans Tracks and Embank Len Structure Definition Z Geometric Properties Z Material Prope Figure 4 Definition of Number of Spans Tracks and Embankment Lengths This worksheet defines the global arrangement details of the bridge structure The number of spans is initially limited to 100 but can be increased by modifying the Structure Definition worksheet as outlined in the following section The number of tracks can be set as
57. ric properties worksheet should list all of the section properties required for the modelling of the structure and the unique ID numbers must include all of the geometric properties that have been assigned in the Structure Definition worksheet The properties should be entered in metres and are all standard LUSAS values except the Depth of Section to Support entry that is needed by the model building to ensure the support conditions occur at the correct elevation Eccentricity All eccentricity in the modelling is defined relative to the nodal line of the track rail and therefore a positive eccentricity will place a section below this line as indicated in the following figure If an eccentricity is entered for the geometric property of the rail then the neutral axis of the rail will be offset from this nodal line based on the positive sense described For this reason the eccentricity of the rail should generally be set to zero for all cases Notes The number of entries can be increased by adding data to the bottom of the table Data input will terminate on the first blank ID number in column B The depth of section should not be defined for geometric properties assigned to piers The eccentricity between the rail slab indicated in the figure is defined later in the interaction worksheet and should not be defined as a geometric property Eccentricity Of Section Eccentricity Between Rail Slab ve Sense ve Sense Nodal Line Of Track Rail
58. se can include the physical modelling of the piers by entering data into the pier height geometric and material assignment columns or be left blank if the behaviour of the combined pier foundation system is to be incorporated into the spring support only Note The pier properties for the last pier of one span must exactly match the properties defined for the next span or an error will be reported when the Microsoft Excel spreadsheet is used to carry out the analysis When the pier foundation system is modelled as a spring this spring can be calculated by combining the component movements associated with the pier as indicated below and described further in the UIC774 3 Code of Practice Ova Op On O where d displacement at top of support due to elastic deformation d displacement at top of support due to rotation of the foundation The Rail Track Analysis Spreadsheet d displacement at top of support due to horizontal movement of the foundation dy relative displacement between the upper and lower parts of bearing Only included if bearings effects lumped into support conditions and the total spring stiffness 1s calculated from K E in kN mm total BU E H H H H pH E Figure 7 Component Behaviour for Calculating Support Stiffness Note Ifthe piers are modelled in the analysis the rotation of the found
59. sion is obvious from these test case analyses and discussions made in this appendix When a combined thermal and train loading from a separate analysis gives interaction forces that exceed the stated yield resistance then the separate analysis method will potentially over predict the rail stresses unless the loaded track yield surface is reduced by the mobilised track resistance over the extent of the train loading References Ul UIC Code 774 3 R Track bridge Interaction Recommendations for Calculations 2001 Union Internationale des Chemins de fer Paris France 67 Rail Track Analysis User Manual 68
60. sistance properties are active under the thermal loading over the extent of the train loading The results from the analysis are shown in the following figures and give the following results for the track peak compressive stresses Track 1 85 6 N mm Track 2 100 6 N mm NOTE For this analysis the reduction in axial force rail stress is not observed at the span discontinuities towards the left end of the structure 36 Analysis Of Combined Thermal And Rail Loading One Step LUSAS Mode lle r 14 0 86 D AUse reGeoffiDocime station da Increased Spans Rall pans loa Jolt and Beam Pers tr Rall Scripts TN SolrtioiTemp adRallTogetie nU CTT Hide IP APT dh pac Scale 1 4 75114E3 Zoom 100 0 Eye 0 0 0 0 1 0 Nonlinear Analysis Loadcase 1 Increment 1 Results File 0 Entity Stress Diagram Component Fx MAX 0 6136E 06 at EIU GP 1042 4 MIN 0 1313E 07 at EIt GP 1594 4 Tite UC 774 3 Model UICTT Hwa HIP DS The mal Aad Rall Loads applied Coictrre rtie Uit Nm Z C Figure 39 Axial Force In Rails Due To Combined Thermal And Train Loads In Track 1 One Step LUSAS Mode ler 1 D B6 D MJse reGeomDoctme tation da Increased Spans Rall pans loa Joh aid Beam Pers tr Rall Scripts TN SolitiorTempeadRallTogetke MU ICT H ei OP aT aac Scale 1 4 75114E3 Zoom 100 0 Eye 0 0 0 0 1 0 Nonlinear Analysis Loadcase 1 Increment 1 Results File 0 Entity Stress Diagram Component Fx MAX 0 5479E 06 at ElVYGP 1501
61. sociation and basic combinations defined in the model file If multiple results files are loaded on top of the model for example if multiple rail load configurations have been analysed and the results loaded into Modeller for enveloping post processing then the results loadcases for all these results files will be extracted into the Microsoft Excel spreadsheet Microsoft Excel is currently limited to 256 columns in a worksheet and this limits the results processing to only 20 loadcases envelopes combinations If this limit is exceeded the results post processor will allow the extraction of the envelopes combinations into one Microsoft Excel spreadsheet and all of the results loadcases into a separate spreadsheet with the limit of 20 The results output format is indicated in the following two figures 22 Rail Track Analysis Menu Options I Al z Job Title EET a ERE ST UST F G H J K L M N 0 Fs Job Title IUIC 774 3 Model Sample Viaduct Analysis Filename SampleViaduct mys Analysis Directory EUIC Manual Analysis Date 14 09 05 1 Increment 1 Element Node Dist m Minimum Element Node Dist m X mjO 004346 3080 eoz ao 1894 ispY m 204E05 3104 611 42E05 2984 588 Rot RZ ad 489E 06 308 597 47E06 2904 578 Fx N 559944 1 1015 2028 435 706543 1594 3188 625 Fz N 1341331 1367 2729 550 134 116 1962 2723 549 My Nm 2374929 60
62. sses 28 Analysis Of Combined Thermal And Rail Loading One Step 36 Analysis Of Combined Thermal And Rail Loading Taking Account Of Effects Of Material Change Under Rail Loading eeeeeeeeeeeeeeeeeeeeeeeeeeeenn 38 Bi ei dio MT dia 41 Revisit Of UIC774 3 Test E1 3 Using The Separate And LUSAS Methods Of Analysis 51 Separe BOIS BE este ee ae cus etal stes idee eier ib e eec utu 51 LEUSASINoOnneac o SS LS oto oae ea takes a ess sque oca Lo caa LOC ass ier 53 Dis Son ern ee in esse DS Revisit Of UIC774 3 Test H1 3 Using The Separate And LUSAS Methods Of Analysis 60 SPE Analyse Sissi adi datu tdi desde otia pte at S bacs Dp ial otio E NL A d ad 60 LASS AS NOMINAL AMAL SIS een 62 Discussion E 64 CODCIUSIODS 55 ross cs cts E ERR DNI RR RA DK UI DE EE RES 66 Separate Thermal And Rail Loading Analysis iicet tete a esee E dE Red 66 Concurrent Thermal And Rail Loading Analysis essen 66 LUSAS Nonlinear Thermal And Rail Analysis With Material Change sese 66 nire mem 67 Table Of Contents Introduction Rail Track Analysis Introduction The passage of one or more trains crossing a rail bridge causes forces and moments to occur in the rails that in turn induce displacements in the supporting bridge deck bearings and piers As part of the design process for rail bridges it is necessary to ensure that any interaction between th
63. t Excel spreadsheet PO or batch text file Browse NOTE LUSAS model will be built and run in the current working directory Current Working directory C Lusas140 Projects Element size 10 Apply temperature and rail loads in same analysis Figure 19 UIC774 3 Model Builder Dialog Q Model filename The model filename for the analysis should be entered into the box if batch processing is not being used see below The file should not contain any directory specification as all models will be placed in the current working directory indicated on the dialog Q Microsoft Excel spreadsheet or batch text file If batch processing is not being used and a single model is being created the filename of the Microsoft Excel spreadsheet that will be used to define the analysis must be entered into the box including file extension If no directory structure is specified the spreadsheet should be located in the current working directory Alternatively the Browse button may be used to locate the spreadsheet If batch processing of multiple models is being performed then a batch text file listing the Microsoft Excel spreadsheets to use for defining the models should be entered into the box must have a txt file extension The batch text file can be entered explicitly into the dialog or located using the Browse button and selecting Batch text file txt as the file type The format of the batch text file 1s indicated below and simply
64. te 8 Contact Stiff infinite infinite 19 Loaded Bilinear Springs characteristic Lift off force infinite infinite 10 Lift off springs infinite infinite 111 112 13 ERIT Expansion Joints Units Distance m Initial gap mm 14 EH 16 Position Initial Gap Position Initial Gap u ne end 8 L 9 S 20 1 5 z EE ll 1 5 L5 Mo ee ee BI 0 0 00 0 L 2 1208 1 5 BI 5L z Eee I loo uc ccs raa caet BA 1 1 1 1 a EE ee eee eee amc M s el OCS a 1414 pix Geometric Properties Material Properties Interaction and Expa q 4 mnc Figure 16 Sample Expansion Joint Definitions 15 Rail Track Analysis User Manual Worksheet 6 Thermal and Train Loading u a Se AT H l J K L M NZ Unig Temperature Celsius Load Position Length m Load kN m A EH En Loading 2 For Slab Starting End Amount beds per unit length length For Rails I4 4 b MA Geometric Properties Material Properties Interaction and Expansion Joint Loading Jal Figure 17 Definition of Thermal and Train Loading for Structure The temperature effects in the rails for a continuously welded rail CWR track do not cause a displacement of the track and do not need to be considered UIC774 3 Clause 1 4 2 For all other tracks the change in temp
65. the thermal effects when the load from the train acts on the rails Concurrent Thermal And Rail Loading Analysis d d Incorrect loaded track resistance used for thermal effects under location of train loads Incorrect yielding of ballast frozen ballast no ballast track under thermal effects as loaded track resistance used Correct track resistance for yielding under the train loading Movement due to thermal effects alone only approximated LUSAS Nonlinear Thermal And Rail Analysis With Material Change d d Correct unloaded track resistance used for thermal effects across whole model Correct yielding of unloaded ballast frozen ballast no ballast track under thermal effects Correct yielding of loaded ballast frozen ballast no ballast track under action of combined thermal and train loading effects as track resistance correctly modelled yield occurs at the correct loading no apparent increase in the yield value Q Instantaneous change from unloaded to loaded track resistance correctly takes account of movement that has already occurred under thermal effects alone 66 References Referring back to Figure 49 and Figure 50 the key issue with the separate analysis approach is the ability for the track resistance to be overestimated by the combination of the two nonlinear analyses and potentially cause the rail stresses to be overestimated In the concurrent loading and LUSAS rail option analyses the limit of track
66. then discussed briefly Separate Analyses The analysis of the thermal effects due to the temperature in the bridge and rail are presented in the following figure These two thermal effects give a peak compressive rail stress of 150 21 N mm which compares well with the code of practice value of 156 67 N mm allowing for slight differences in material properties which have been estimated LUSAS Modeller 14 0 B6 D Userns GeoffiDocumentation P403a Increased Spans Rail Expansion Joints and Beam Piers for R arec gtsvDee Splut Scale 1 3 39E3 Zoom 100 0 Eye 0 0 0 0 1 0 Nonlinear Analysis Loadcase 1 Increment 1 Results File 0 Entity Stress Diagram Component Fx MAX 0 1419E 07 at EIU GP 32571 MIN 0 2304E 07 at EIOP 423 41 Title UIC 774 3 Model UIC774E13P4dO03aTemp Only Units N m kg s C Figure 58 Axial Force In Rails Due To Temperature In Bridge And Rail To determine the worst location of the train load for compressive rail stresses the bridge has been analysed with the rail loading at 31 separate locations starting from 51 Rail Track Analysis User Manual the left abutment of the bridge and finishing 90m from the right abutment of the bridge train moving from left to right and these results enveloped The results of this analysis are presented in the following figure which give a peak compressive rail stress of 40 64 N mm LUSAS Modeller 14 0 B6 D Wsers GeoffiDocumentation P403a Increase
67. till allow a further 20 kN m track resistance to be mobilised before the onset of plastic yielding and the separate analysis would potentially over predict the rail stresses occurring This potentially means that even though a computer program is validated against the standard test cases in the UIC774 3 code of practice it may be predicting excessive rail stresses if it does not correctly take account of the loaded track resistance that can be mobilised Figure 66 Force Per Metre Length In Interaction From Thermal Loading Separate Analysis 57 Rail Track Analysis User Manual EIISTEZ ZZ Separate in Loading From Tra ion Force Per Metre Length In Interacti Figure 67 Analysis eao 09 e30 03 30 03 e30 03 E30 US 30 UR C3CERIDITS ed8rrr Ory EE LE SLA 35917 bey 389 0 8C X 38157 bey ELL Ld EL2L8SC BLA egt 9 La E2LC9p bly 36007 Eh 23999 dr EJFSEE U La LUSAS ined Loading From Comb ion Force Per Metre Length In Interacti Figure 68 Analysis 58 Revisit Of UIC774 3 Test E1 3 Using The Separate And LUSAS Methods Of Analysis essApparent boaded Yield Separate Analysis Far NEE kx ES E Separate Train Load Added To Thermal And LUSAS Analysis ack is Loaded Yield LUSAS Analysis o yg Force Loaded Stiffness Thermal Alone Limit of resistance of unloaded track Strain Unloaded stiff
68. trical and occurring across the transition between spans colour change indicates changing yield direction This yield over the whole region of the span transition is the whole reason why a smooth behaviour is observed in the rail force stress in the second track as opposed to the first track that has the braking train load 35 Rail Track Analysis User Manual LUSAS Modeller 14 0 B6 D Users GeoffiDocumentation P403a Increased Spans Rail Expansion Joints and Beam Piers for RailrecipBtsvDaG p Scale 1 4 75114E3 Zoom 267 297 Eye 0 0 0 0 1 0 Nonlinear Analysis Loadcase 2 Increment 2 Load Factor 1 00000 Results File 0 Entity Stress Title UIC 774 3 Model HwashilRailOnly Units N m kg s C Figure 38 Yield In Track Bridge Interaction Due To Train Acceleration Load On Track 2 Analysis Of Combined Thermal And Rail Loading One Step In this form of analysis a single nonlinear analysis is carried out where the thermal and rail loading are applied concurrently to the model In terms of the track bridge interaction the resistance bilinear curves used in the modelling are determined by the positioning of the rail loading so that loaded properties are used where the rail loading is applied and unloaded properties everywhere else As with the separate method highlighted above this analysis ignores any initial straining of the track bridge interaction under pure thermal loading and therefore assumes that the loaded re
69. veloping Envelope MIN Entity Stress Diagram Component Fx MAX 0 1474E 07 at EIt GP 32771 MIN 0 2877 E 07 at EIt GP 423 1 DIAGRAM Scale 1 0 5000E 01 Title UIC 774 3 Model UIC774E13P403a Envelope Over All Train Loads Units N m kg s C Figure 62 Axial Force In Rails Due To Combined Temperature And Enveloped Rail Loading 54 Revisit Of UIC774 3 Test E1 3 Using The Separate And LUSAS Methods Of Analysis Discussion For this test case the difference in the results due to the track resistance modelling between the two methods is minimal Combining the results of two nonlinear analysis while invalid gives almost identical results to the LUSAS analysis which correctly represents the transition from unloaded to loaded resistance on arrival of the train load The train load position that gives the worst compressive stress in the rail does however differ slightly between the two analyses with the separate analysis giving a train front position of 75m from the left abutment of the bridge and the LUSAS combined analysis giving a train front position of 80m from the left abutment of the bridge Looking at the yield behaviour it becomes clear why the two methods agree so closely for this UIC774 3 standard test case and not for the Hwashil Viaduct For both analyses the rail stresses and interaction yield over the single span bridge due to thermal loading are identical Figure 63 On consideration of the train loading the right h
70. y and combined effects for a sample structure Thermal Effects Only m Cv lt E o o co hen ded 0 s x t Distance m Figure 26 Thermal Effects Only in Rails 24 Rail Track Analysis Menu Options Combined Thermal And Train Effects G lt E 7 0 o G S x lt Distance m Figure 27 Combined Effects of Temperature and Train Loading in Rails 25 Rail Track Analysis User Manual Limitations of Use OO wv Since the analysis is two dimensional even though three dimensional elements are used the offsets are not modelled for the bearing section centrelines nor for the section rail centrelines see figure below Currently all centrelines are coincident with the centreline of the deck Curved bridges cannot be modelled Only up to two tracks can be considered Rail stresses and graphs are not calculated directly These however can easily be calculated by evaluating Force Area and plots can be generated from the data extracted to the Microsoft Excel results spreadsheets Thermal loading for mixed steel and concrete bridges in the same model cannot be generated through the input spreadsheet The model can however be modified to include these different thermal loads if no rail loading is applied when the model is built and the resulting LUSAS model modified manually Care should be taken carrying this out and generally only additional temperature loading attributes should be
71. z bi Joh aad Beam Pers Dr Rall ScriptsXTN Soltiorc Use sy CTT Hwes HIP Oa mde 27 2006 Scale 1 4 75114E3 Zoom 100 0 Eye 0 0 0 0 1 0 Nonlinear Analysis Loadcase 1 Increment 1 Results File 0 Entity Stress Diagram Component Fx MAX 0 5599E 06 at ElVYGP 1015 4 MIN O 7065E 06 at Elt GP 1594 4 Tite UC 774 3 Model UICTT Hwass IP ea Uit Nm zc Figure 42 Axial Force In Rails Due To Thermal Only LUSAS Mode ler 140 86 D Wee re GeofiDoctme taton da Increased Spans Rall Eaz ios Joh aad Beam Pers br Rall Scripts TN Sol tior USASYJ 17 Hwas IP Da madhe 27 205 Scale 1 4 75114E3 Zoom 100 0 Eye 0 0 0 0 1 0 Nonlinear Analysis Loadcase 2 Increment 2 Load Factor 1 00000 Results File 0 Entity Stress Diagram Component Fx MAX 0 5649E 06 at EIt GP 1015 1 Tite UIC 774 3 Model UICTT 4Hwas bP Aa Uit N nZ C Figure 43 Axial Force In Rails Due To Combined Thermal And Train Loads In Track 1 40 Analysis Of Combined Thermal And Rail Loading Taking Account Of Effects Of Material Change Under Rail Loading LUSAS Mode lle r 14D B6 D sere GeomDocume taton da herad Spans Rall pass los Joht aad Beam Pers tor Rall Scripts TN Sol oy LUSESWICTT HWS HIP Da mde Z7 2005 Scale 1 4 75114E3 Zoom 100 0 Eye 0 0 0 0 1 0 Nonlinear Analysis Loadcase 2 Increment 2 Load Factor 1 00000 Results File 0 Entity Stress Diagram Component Fx MAX 0 5665E 06 at EI GP 1016 1 MIN 0 1420E 07 at EI

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