Rail Track Analysis Wizard

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1 Rail Track Analysis Wizard M I D A S I T 111-1

2 01 Rail Track Analysis Wizard The Rail Track Analysis Wizard builds a model that is used for checking the additional stresses and the displacements due to the track/bridge interaction. 1) Build a Model for Simplified Separate Analysis - Case 1: thermal load case when the train loads are not applied - Case 2: accelerating/braking and train vertical load cases when the resistance of ballast has the modified boundary conditions for the sections which the train loading is on 2) Build a Model for Stage Analysis or Complete Analysis - Unloaded stage: only thermal loads are applied and train loads are not applied yet. Ballast has the resistance of Unloaded Condition for the entire sections. - Loaded stage: accelerating/braking loads and train vertical loads are included. Ballast has the resistance of Loaded Condition for the sections where the train loads are applied. 3) Build a Model for Moving Load Analysis At the loaded stage of staged analysis, the train is moved by a certain length to find the locations where additional stresses occur. Stages are added whenever the boundary conditions are changed as the train moves.

3 02 Rail Track Analysis Theory Simplified Separate Analysis Stage Analysis/Complete Analysis In the separate application of thermal loading, the lateral resistance of ballast initially follows the Unloaded stiffness curve and is limited to the Limit of resistance of unloaded track. In other words, the ballast resists with the Unloaded stiffness up to the Thermal Alone. Separate analysis of train loading is followed and combined with the thermal load analysis results so as to obtain the final analysis results. The analysis resumes from the Thermal Alone and the lateral resistance follows the Loaded stiffness curve and reaches the Separate Train Load Added to Thermal. This gives an increase in the resistance of the ballast, which equals the Apparent Increase in resistance of loaded track, results in a greater yielding load than in the Loaded state and therefore increases the stresses in the rails. Like the separate analysis, in the consideration of thermal loading, the resistance is limited to the Thermal Alone. The main difference between the two analyses is that Construction Stage Analysis of midas Civil applies the train loading maintaining the deflection and the internal forces caused by the thermal loading and replaces the Unloaded stiffness resistance with the Loaded stiffness. The analysis resumes from the Thermal Alone with the Loaded stiffness. But the lateral resistance is limited by the Limit of resistance of loaded track from the origin, not from the Thermal Alone, and arrives at the Construction Stage Analysis (Deformed position).

4 03 Layout Advanced: define the fixed ends freely and adjust the span length ZLR: Specify the zero-longitudinal resistance rail fastener (the resistance of ballast is set to zero for the specified sections.) ex ) 4@50,70: four decks with the length of 50m and a deck with the length of 70m. The total length of bridge section is 270m. REJ: Place the rail expansion joint for each track

5 04 Section Define Tapered Section Tapered Section Assignment Sections at 0.1 of the total span length: Span_2 Sections at 0.5 of the total span length: Span Sections at 0.9 of the total span length: Span_2 Tapered Option Start 0.1~Start 0.5: Z Axis Curved Type (Quadratic), From (J-end) Start 0.5~Start 0.9: Z Axis Curved Type (Quadratic), From (I-end)

6 05 Boundary 1 1. Lateral Resistance Data - Enter gravel ballast data and concrete ballast data. - For gravel ballast, the resistance of ballast is different between the stress check and the displacement check Define Condition - Select either gravel ballast or concrete ballast for the entire section. - Via the Advanced function, select either gravel ballast or concrete ballast by sections (For undefined sections, gravel ballast is used). 3. Boundary Types Spring Type Bearing Type

7 05 Boundary 4. Modeling by Sections 1) Embankment section 2) Section connecting embankment and deck start point 3) Section connecting deck start and end points 5. Boundary Conditions Taking into Account the Effective Length The resistance of ballast entered should be in kn/m and is longitudinal resistance. The resistance multiplied by the effective length will be used in the model.

8 06 Load 1. Accelerating/braking/vertical train loads can be freely entered by sections in a tabular format. The length and magnitude of load can be entered with reference to the left end of the model. Case 1: Single Track Case 2: Double Track -Running Direction: the direction in which the train runs. Define either Keep Right or Keep Left. -Train Section: Train section is recognized when a vertical load is entered. When a vertical Load is excluded, define Train Section and apply Loaded Condition. - Load Type: For single track, in general, apply either accelerating loads or braking loads. For double track, apply accelerating loads and braking loads for each track. As far as train vertical loads are concerned, various uniform loads can be applied by sections and therefore HL load, which is most frequently used, can be easily represented. 2. Files are added for the moving load analysis - Number of Track Loading Locations: the number of moving times of train load. If n is entered, n files are added. - Location Increment for each Model: the increment of moving load per track. If n is entered, the train moves by n and the boundary conditions are assigned to the section to which the train load is applied. ex> If Number of Track Loading Locations is 3 and Location Increment for Track is 10, the train moves forward by 10m, 20m and 30m and three files are added.

9 07 Wizard Option 1.Stress Check Model Option This option creates a file to check the additional stresses. - Simplified Separate Analysis Model xxx_temp.mcb xxx_train.mcb - Complete Analysis xxx_complete.mcb 2. Displacement Check Model Option This option creates a file to check the displacements. In this file, the resistance of ballast applied at Unloaded Condition is different for the case of gravel ballast. In addition, this file is available only for Simplified Separate Analysis Model. - Relative Longitudinal Displacement Component due to Acceleration and Braking Alone xxx_add1_relativedisp.mcb - Relative Longitudinal Displacement Component due to Vertical Effects xxx_add2_rotationangle.mcb - Relative Longitudinal Displacement Component at Rail Expansion Joints xxx_add3_expansionjoint.mcb - Rail Break Gap Size xxx_add4_railbreakgapsize.mcb

10 08 Project Application For the case of a high-speed railway with gravel ballast and double track, the following properties are defined for rail, ballast and horizontal alignment: Track Item Property Unit Value Remark Rail Ballast Horizontal alignment UIC60 Cross-sectional area A m E-3 Moment of inertia Iyy m E-6 Gravel ballast Longitudinal resistance (Unloaded) Longitudinal resistance (Loaded) kn/m 12.0~20.0 Stress check: 20.0 Displacement check: 12.0 kn/m 60.0 Limit displacement mm 2.0 Tangent section PC Box girder bridge is chosen for the high-speed railway track. The dimensions of girder and the geometric relation between the girder and track are defined as follows: Girder Type Span Length Equivalent Modulus of Elasticity Crosssectional Area Moment of Inertia Neutral Axis (Girder Reference Location) Main Girder Height ( m ) ( E : N/m 2 ) ( A : m 2 ) ( Iyy : m 4 ) ( Izz : m 4 ) ( d : m ) ( H : m ) PC Box x The longitudinal resistance of deck is set to 1.5 x 10 6 kn/m.

11 08 Project Application For the case of a high-speed railway with gravel ballast and double track, the rail, ballast and horizontal alignment are defined as follows: Simple bridge type 40m 40m 40m 40m 40m 40m 40m 40m 40m 40m Continuous bridge type 80m 80m 80m 80m 80m

12 08 Project Application Simple bridge type Continuous bridge type Because the simple bridge type gives the smaller additional stress than the continuous bridge type, the simple bridge type is adopted.

13 08 Project Application (Additional Compressive Stresses) Unloaded Condition Additional stresses in the rails when the temperature of 25 degrees centigrade is applied to the deck Additional compressive stress MPa Other software MPa Loaded Condition Additional stresses in the rails when the train loads (accelerating/braking and vertical loads) are applied Additional compressive stress MPa Other software MPa

14 08 Project Application (Additional Tensile Stresses) Unloaded Condition Additional stresses in the rails when the temperature of -25 degrees centigrade is applied to the deck Additional tensile stress MPa Other software MPa Loaded Condition Additional stresses in the rails when the train loads (accelerating/braking and vertical loads) are applied Additional tensile stress MPa Other software MPa

15 08 Project Application (Moving Loads) Additional compressive stresses Track 1 Track 2 Additional tensile stresses Track 1 Track 2 Maximum additional compressive stress: MPa in Track 1 Maximum additional tensile stress: MPa in Track 2

16 08 Project Application (Relative Displacements of the Rails and Deck) Track1 (accelerating load + vertical load) Steps for plotting relative displacements 1) Activate Disp_Deck1~n of Structure Group 2) Select All and copy the node numbers 3) Right-click on the Node Table and select Selection/Filtering from Context Menu. Filter the x coordinates of nodes and Copy All. 4) Copy the x coordinates into Excel 5) Select All the Deck on view 6) Via the Results>Displacements, produce the nodal displacements of Deck and Copy All 7) Copy the displacement results into Excel Track2 (braking load + vertical load) 8) Activate Disp_Track1 of Structure Group 9) Select All and copy the node numbers 10) Right-click on the Node Table and select Selection/Filtering from Context Menu. Filter the x coordinates of nodes and Copy All. 11) Copy the x coordinates into Excel 12) Select All the Track1 on view 13) Via the Results>Displacements, produce the nodal displacements of Track1 and Copy All 14) Extract the results of Track2 by repeating steps 8~13 15) Draw via the Excel graph function -Relative displacement due to accelerating load = 0.67 mm < 4 mm -Relative displacement due to braking load = 0.79 mm < 4 mm. OK. OK

17 08 Project Application (Relative Displacement due to Rotation of the End) Steps for plotting relative displacements 1) Activate Disp_Deck1~n of Structure Group 2) Select All and copy the node numbers 3) Right-click on the Node Table and select Selection/Filtering from Context Menu. Filter the x coordinates of nodes and Copy All. 4) Copy the x coordinates into Excel 5) Select All the Deck on view 6) Via the Results>Displacements, produce the nodal displacements of Deck and Copy All 7) Copy the displacement results into Excel Tip> If the deck is defined by Center-Top, the nodal displacements at deck top are produced and these include the nodal displacements due to rotational angle. If the deck is defined by centroid, the nodal displacements at deck top can be computed using the following equation: -Relative displacement due to vertical load = 3.30 mm < 8 mm. OK Relative displacement due to rotation of the end = displacement Dx at neutral axis + distance from centroid to deck top x sin(rot Ry)

18 08 Project Application (Rail Expansion Joint) Additional stresses in the rails due to thermal loads when expansion joints are laid Rail stress in unmovable section = E xαx T = N/mm 2 x 1.2 x 10-5 x 40 C = MPa Maximum compressive stress in the rails = MPa Maximum additional compressive stress in the rails = MPa Displacements due to thermal loads when expansion joints are laid Left rail = mm (forward) Right rail = mm (backward) Displacement in the expansion joint = mm (contraction)

19 08 Project Application (Opening Displacement Due to Split Web at Rail End) When cable signaling system or zero-longitudinal resistance rail fastener is used, it is necessary to check the opening displacements due to split web at rail end. It is assumed that split web takes place at 705m, which is near the position where the maximum tension of the rails occurs. The highest negative (-) temperature loads are applied to the bridge and rails in order to generate the greatest additional tensile stress in the rails. (The temperature in rail is -50 degrees centigrade and the temperature in bridge is -25 degrees centigrade.) Opening displacement when split web at rail end takes place = mm (33.98 mm mm) < 69 mm OK

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