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111-1
M I D A S I T Bridging Your Innovations to Realities
Bridging Your Innovations to Realities midas Civil
2
Rail Structure Interaction
Overview
1) Definition of Continuous Welded Rail (CWR)
Rails are continuously welded and thus, the length of one rail is longer than 200m.
ex > standard length rail (L=25m), longer rail (L=25~200m)
2) Necessity of Continuous Welded Rail
Time[ms]
Dyn
amic
am
plif
icat
ion
6
5
4
3
2
1
016 18 20 221412108642
Wheel/rail impact forces
Wheel impact forces occur
- The reduced impact force in the rails increases the life span of the rails and improves the ride quality.
- The decreasing noise and vibration by the reduced impact force is less impeding the ambient environment.
3) Check Points for Continuous Welded Rail
- When temperature rises: track deformation (buckling of rail)
- When temperature drops: fracture failure
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Rail Structure Interaction
Traction/Braking loads
abutment pier Longitudinal displacements at top surface of deck end
Temperature Train vertical loads
Track-Bridge Interaction
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Rail Structure Interaction
Track-Bridge Interaction
1) Axial Forces in a Continuously Welded Rail Track on Embankment (Thermal Load on the Rail)
2) Axial Forces in a Continuously Welded Rail Track on Bridge (Thermal Load on the Bridge)
Axial forces in the track on embankment under thermal loading
Track/bridge interaction due to thermal loading
Fixed end Movable end
Continuous welded rail
Additional rail stresses
Axial forces in the rails
Distance (m) Disp
lace
men
t in
the
rails
(mm
)
Resis
tanc
e
TAEF ∆×××= α
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Rail Structure Interaction
Design Requirements for Track/Bridge Interaction Analysis
Design Standards: UIC774-3, EN 1991-2
Item Loads Design Criteria
Gravel ballast bed Concrete bed
Additional rail stress
Compressive stress Thermal loads Traction/braking loads Train vertical loads
R≥1500: 72N/mm2
R≥700: 58N/mm2
R≥600: 54N/mm2
R≥300: 27N/mm2
92N/mm2
Tensile stress 92N/mm2 92N/mm2
Longitudinal relative displacement in bridge deck Traction/braking loads
<5mm <30mm (when rail expansion device at both ends)
Check the stability (the uplift force and compression) of rail fastener
longitudinal displacement due to rotation of the deck end between deck and deck or between deck and pier
Train vertical loads <8mm
Check the stability (the uplift force and compression) of rail fastener
Opening displacement when split web at rail end takes place (applying cable signaling system or zero-longitudinal resistance rail (ZLR) fastener)
Thermal loads D=√(R2-(R-δ)2) Same as the gravel track
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Rail Structure Interaction
Design Loads
- If all of the spans in the bridge consist of a continuous welded rail, thermal loads are applied to the bridge and rails or the rails only. - If rail expansion joints are present on the bridge, thermal loads are applied to both the bridge and the rails. - Temperature variations in the rails and bridge are as follows:
. Rails: in summer=+40℃, in winter=-50℃ . Bridge: concrete structures=±25℃, steel structures= normal temperature area ±35℃, cold temperature area ± 45℃
1) Thermal Loads
2) Traction/Braking Loads - Traction/braking loads are uniformly distributed and applied to the two front positions of the rails. The magnitude of load and the loaded length are as follows:
- For the cases such as an exclusive subway track, light rail transit, etc where the design loads are different, transformed uniform loads which correspond to ¼ of the rail axial loads are used. The loaded length is equal to one maximum coach.
- Traction/braking loads are applied concurrently with the associated vertical loads. - Traction/braking loads are applied to the positions that will cause the most unfavorable rail stresses or bridge
deformations.
Type of Track Traction loads braking loads
Magnitude of Load Loaded length Magnitude of Load Loaded length
High-speed railway 33kN/m/track 33m 20kN/m/track 400m
Normal railway 24kN/m/track 33m 12kN/m/track 300m
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Rail Structure Interaction
Design Loads
-For a high-speed railway, HL load does not include an impact factor. For a passenger locomotive, HL load can have a uniform load of 60kN/m.
- For a normal railway, LS load and an equivalent load can be applied and an impact factor is not considered.
- For an exclusive subway track, EL-18 load or an equivalent uniformly distributed load can be applied.
- For a double or more track bridge, only two tracks will be loaded with train vertical loads.
- For a multi-span continuous bridge, only the deck near the critical positions will be loaded.
3) Train Vertical Loads
(b) Equivalent HL load
(a) HL load
(b) Equivalent LS load
(a) LS load (L-load) 95kN/m
74kN/m
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Rail Structure Interaction
Load Combinations
- Load combinations used for computing the rail stresses and the longitudinal loads acting on bearings
- When computing the stresses and displacements in the rails for a continuous or simply supported bridge deck: α,β,γ=1
- When using the computational analysis method, the interaction due to traction/braking loads and train vertical loads can be separately computed.
ƩR = αR (Thermal loads) + βR(Traction/braking loads)+γR(Train vertical loads)
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Rail Structure Interaction
1) Establishment of Criteria for Construction of Rail Expansion Joint on Bridge Section
Rail Expansion Joint
Countermeasure
The limits to the axial force and displacement of a continuous welded rail on bridge are exceeded
bridge
track
Support layout Span composition Stiffness of deck
Use zero-longitudinal resistance rail fasteners
Economic efficiency
Compare the maintenance cost for rail expansion joints with the cost of bridge construction
Conditions for building rail expansion joints
Minimum separated distance between expansion joints Separation distance from a turnout Separation distance from the terminus for a transition curve Separation distance from the terminus for a bell curve Requirements for building the bridge deck
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Rail Structure Interaction
2) Flowchart
Rail Expansion Joint Check the axial force and displacement in
the rails
Modify the support placement
Check the axial force and displacement in
the rails
Modify the span composition
Check the axial force and displacement in
the rails
Modify the stiffness of deck
Check the axial force and displacement in
the rails
Use a zero-longitudinal resistance rail fastener
Check the axial force and displacement in
the rails
Consider building REJ (rail expansion joint)
Analyze the economical efficiency
Submit the report Allow the construction of rail expansion joint
Continue OK
OK
OK
OK
OK
OK
NG
NG
NG
NG
NG
NG
NG
NG
NG
NG
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Rail Structure Interaction
1) Computational Analysis
- Considerations for modeling • Placement of bearings, the dimensions and properties of the deck and pier, the bending stiffness and the height of deck,
the neutral axis of deck, and the lateral and bending stiffness of foundation.
- Finite elements
• Rail and bridge: Beam elements
• Ballast or pad: nonlinear spring elements
- Modeling method
• Element length: 1~2m is recommended
상판중립축
궤도중심선
Rigid Link
Rigid Link
Track-Bridge Interaction Analysis
Embankment section Bridge deck
Spring for the longitudinal resistance of ballast (Bilinear)
Rail Rail expansion joint
Neutral axis of bridge deck
Centerline of track
Bearing
Longitudinal displacement of the rail
1. Observed data
2. Idealized bilinear curve (under train loading)
3. Bilinear curve when train loading is not applied
Longitudinal resistance of the roadbed
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Rail Structure Interaction
- The accuracy depends on the computational analysis methods.
- The following two computational analysis methods are available:
. Separate analysis: thermal loading, traction/braking loading and train vertical loading are separately considered.
. Complete Analysis: thermal loading, traction/braking loading and train vertical loading are concurrently applied.
- Depending on the global structural system, the separate analysis is more likely to produce the greater axial forces than the staged analysis.
Analysis Methods
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Rail Structure Interaction
Simplified Separate Analysis Complete Analysis
Analysis Methods
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Rail Structure Interaction
Rail Track Analysis Model Wizard (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.) REJ: Place the rail expansion joint for each track
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.
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Rail Structure Interaction
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)
Define Tapered Section
Rail Track Analysis Model Wizard (Section)
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Rail Structure Interaction
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. 2. 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
1
2 3
Rail Track Analysis Model Wizard (Boundaries)
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Rail Structure Interaction
4. Modeling by Sections
1) Embankment section
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.
2) Section connecting embankment and deck start point 3) Section connecting deck start and end points
Rail Track Analysis Model Wizard (Boundaries)
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Rail Structure Interaction
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.
-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.
Case 1: Single Track Case 2: Double Track
Rail Track Analysis Model Wizard (Load)
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Rail Structure Interaction
Rail Track Analysis Model Wizard
1 .Stress Check Model Option This option creates a file to check the additional stresses. -Simplified Separate Analysis Model -Complete Analysis
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 - Relative Longitudinal Displacement Component due to Vertical Effects -Relative Longitudinal Displacement Component at Rail Expansion Joints - Rail Break Gap Size
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Rail Structure Interaction
Case Studies
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
UIC60
Cross-sectional area A m2 7.669E-3
Moment of inertia Iyy m4 30.363E-6
Ballast
Gravel ballast
Longitudinal resistance (Unloaded) kN/m 12.0~20.0 Stress check: 20.0 Displacement check: 12.0
Longitudinal resistance (Loaded) kN/m 60.0
Limit displacement mm 2.0
Horizontal alignment
Tangent section
G irder Type Span Length Equivalent Modulus
of Elasticity Cross-
sectional Area Moment of Inertia Neutral Axis
(G irder Reference Location)
Main Girder Height
( m ) ( E : N/m2 ) ( A : m2 ) ( Iyy : m4 ) ( Izz : m4 ) ( d : m ) ( H : m )
PC Box 40 2.8 x 1010 12.0 20.0 165.0 1.11 3.5
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:
The longitudinal resistance of deck is set to 1.5 x 106 kN/m.
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Rail Structure Interaction
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
Continuous bridge type
Case Studies
40m 40m 40m 40m 40m 40m 40m 40m 40m 40m
80m 80m 80m 80m 80m
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Rail Structure Interaction
Axial stress by temperature load (Simple span bridge)
Axial stress by temperature load (Continuous bridge)
Because the simple bridge type gives the smaller additional stress than the continuous bridge type, the simple bridge type is adopted.
Case Studies
-26.6 MPa
-44.1MPa
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Rail Structure Interaction
Case Studies Axial stress by temperature (+25°C) at Unloaded Condition
Axial stress by temperature, traction and vertical train loads at Loaded Condition
-35.6MPa
-26.6 MPa
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Rail Structure Interaction
Case Studies Axial stress by temperature, braking and vertical train loads with different train position
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Rail Structure Interaction
Check Displacements
- Restrict the deformations of the deck and the track to prevent the excessive relaxation of ballast. - Limits to the relative lateral displacements between the bridge deck and rails under traction/braking loads: 4mm or less - Exceptions are made for the cases where the zero-longitudinal resistance rail fastener is used and the special treatment is
done for the contact underneath the rails.
2) Limits to the Relative Longitudinal Displacements in the Bridge Deck
3) Limits to the Longitudinal Displacements in the Deck End due to the Angle of Rotation - Limits to the longitudinal displacements in the deck end due to the rotation of the deck end under train vertical
loads: 8mm or less
1) Relative Displacements between the Rails and Bridge
- Limits to the absolute longitudinal displacements between the bridge deck and pier or between the bridge deck and deck under traction/braking loads: 5mm or less
Limits to relative longitudinal displacements Limits to displacements due to rotation of deck end
abutment pier Longitudinal displacements at top surface of deck end
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Rail Structure Interaction
Japanese Shinkansen Railway Structure Design Standard
Conditions Allowable opening displacements
-rail: 60kg -buckling strength of rail: 100tonf/rail
69mm
ACI Manual of Concrete Practice
Wheel radius Allowable opening displacements
16 in. (0.4m) or less 2in.(50mm)
16 in. or higher 4in.(100mm)
Check Displacements
4) Allowable Opening Displacements when Opening Gap at Rail End takes place .
- Allowable Opening Displacements According to International Standards
- Allowable Opening Displacements According to Korean Standards
. Railway Design Manual (Volume Track)
1) Limits to the opening displacements, d, when the split web at rail
end takes place due to thermal loads in case of using cable
signaling system (not track circuit system):
2 2( )d R R δ= − − 32xP
e xEI
βδ ββ
−= 4
4
k
EIβ =
2) Restrict the opening displacements of (1) when a
zero-longitudinal resistance rail fastener is built
Wheel load P
Center of wheel O
Vehicle velocity V
Wheel radius R
Vertical displacement δ Bending stiffness of rail EI
Bearing stiffness of track K Opening displacement d
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Rail Structure Interaction
Relative Longitudinal Displacement by traction loads
Case Studies
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Rail Structure Interaction
Case Studies
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 rotation of the end
= displacement Dx at neutral axis + distance from centroid to deck top x sin(Rot Ry)
Relative Longitudinal Displacement by vertical train loads
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Rail Structure Interaction
Factors Affecting the Axial Forces in Track (1) 1) Longitudinal Resistance of Track
Longitudinal resistance of track vs. longitudinal displacement of rail Bi-Linear behavior of longitudinal resistance of track
Allowable longitudinal resistance of track
Note 1: Apply 20.0kN/m when checking the rail stresses and apply 12.0kN/m when checking the displacements in the structure Note 2: In the case when tests for longitudinal resistance are conducted, values derived from tests can be used.
Type of Track Load Case Limit displacement (mm)
Longitudinal resistance of track
(kN/m) Remark
Gravel track Loaded Case 2.0 12.0~20.0 Note 1
Unloaded Case 2.0 60.0
Concrete track or frozen ballast track
Loaded Case 0.5 40.0 Note 2
Unloaded Case 0.5 60.0
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Rail Structure Interaction
Factors Affecting the Axial Forces in Track (1) Axial stresses of Ballast Bed in the longitudinal direction
Axial stresses of Concrete Bed in the longitudinal direction
Unloaded Condition (under thermal loads) Loaded Condition
(traction/braking loads and vertical loads added)
Unloaded Condition (under thermal loads) Loaded Condition
(traction/braking loads and vertical loads added)
Longitudinal axial stress is about 30% less in the ballast track than in the concrete track under the same conditions.
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Rail Structure Interaction
2) Zero-Longitudinal Resistance Rail (ZLR) Fastener in the Bridge Section
Characteristic behavior of zero-longitudinal resistance rail fastener
- The zero-longitudinal resistance rail fastener behaves similarly to the conventional rail fastener for the gravity load but generates a gap between the rail and the rail fastener not to introduce longitudinal resistance.
<Gap between rail fastener and rail base> <Downslide of rigid body of rail fastener> <Vertical load-displacement diagram>
Factors Affecting the Axial Forces in Track (2)
Installing ZLR fastener can reduce about 29% of the axial stress.
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Rail Structure Interaction
1) Expansion Length
- Maximum expansion length recommended by UIC774-3 for a single deck railway bridge with gravel ballast not needing REJ (rail expansion joint)
. 60m: Steel structure with gravel ballast track (the maximum length is 120m when a support exists in the middle) . 90m: Steel or concrete bridge with gravel ballast track and concrete slab (the maximum length is 180m when a support exists in the middle) . For the ballastless track, detailed analysis should be conducted.
- Illustrations of expansion lengths
L 2L
Factors Affecting the Axial Forces in Bridge (1)
- Type 1 - Type 2
- Type 3 - Type 4
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Rail Structure Interaction
Factors Affecting the Axial Forces in Bridge (1)
- Type 1
-Unloaded Condition : 26.48 MPa -Loaded Condition : 32.86 MPa
-Unloaded Condition : 11.45 MPa -Loaded Condition : 14.07 MPa
- Type 2
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Rail Structure Interaction
Factors Affecting the Axial Forces in Bridge (1) - Type 3
-Unloaded Condition : 26.52 MPa -Loaded Condition : 42.05 MPa
-Unloaded Condition : 21.12 MPa -Loaded Condition : 26.43 MPa
- Type 4
Axial stresses in the longitudinal direction under the same conditions: Type 2 (14.07 MPa) < Type 4 (26.43 MPa) < Type 1 (32.86 MPa) < Type 3 (42.05 Mpa)
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Rail Structure Interaction
Factors Affecting the Axial Forces in Bridge (2)
2) Span length
3) Bending stiffness of the deck and the deck height
- Train vertical loads can cause the longitudinal deformations in the girder, and the span length is the factor causing the track/bridge interaction.
- Because of the bending of deck, train vertical loads on bridge can cause interactions.
- The bending of deck induces longitudinal deflections at top surface of the deck end and therefore causes the relaxation of gravel track.
-The effect of bending in deck end 1.0 EI 1.5 EI 2.0 EI
0
-5
-10
-15
-20
-25
-30
-35
0.1 Ko
0.5 Ko
1.0 Ko
2.0 Ko
10 Ko
Rai
l Stre
ss (
MP
a)
2@40M_FMM_Vertical Load
Stiffness of Deck
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Rail Structure Interaction
Factors Affecting the Axial Forces in Bridge (3)
4) Support stiffness K: Total stiffness of support
: relative displacement between the upper and lower parts of bearing
-Factors affecting the support stiffness K
Bending of Pier Rotation of Foundation Displacement of Foundation
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Rail Structure Interaction
Factors Affecting the Axial Forces in Bridge (4)
5) Effects of support layout of bridge
Axial forces by FF-MM type Axial forces by FM type
-Types of bearing
FFFF type
FM type
FMMF type
FMM type
MFM type
MFMM type
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Rail Structure Interaction
Factors Affecting the Axial Forces in Bridge (4)
Cases illustrating the effects of support layout of bridge - Case1: Simple bridge ( 1@30 8 Span)
Axial force is about 26% less for MFFM type (28.12 MPa) than in the FMFM type (38.08 MPa) when other conditions are identical.
- Case 2: 2 span continuous bridge (2@30 4 Span)
Axial force is about 45% less for MFM type (29.77 MPa) than in the FMM type (54.20 MPa) when other conditions are identical.
FMFM type MFFM type
MFM type FMM type
38.1 MPa 28.1 MPa
29.8 MPa 54.2 MPa
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Rail Structure Interaction
Factors Affecting the Axial Forces in Bridge (4)
6) Axial forces affected by span composition
Case 1 : 78.75 MPa > Case 2 : 60.63 MPa > Case 3 : 59.72 MPa
Axial force is 24.2% less for Case 3 than in Case 1.
78.7 MPa 60.6MPa
59.7 MPa
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Rail Structure Interaction
1) Verification of computational analysis - A computer program that performs the track/bridge interaction should be validated against the test cases specified in the
Appendix 1.7.1 of UIC774-3. Percentage errors may be up to 10% and up to 20% for safety side.
Standard dimensions recommended by UIC774-3
Result table for a simple span bridge specified in UIC774-3
Track-Bridge Interaction Verification
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Rail Structure Interaction
2) Validation against UIC774-3
Result due to temperature 35 degrees centigrade on bridge deck: -30.47 Mpa
UIC774-3 recommendation: -30.67 MPa
Result due to temperature 35 degrees centigrade on bridge deck and 50 degrees centigrade on rails: -150.17 Mpa
UIC774-3 recommendation: 156.67 MPa
Validation of the maximum additional stresses due to train moving loads
Validation of thermal loads
Additional stress at 0 point from right pier due to train loading: 181.38 Mpa UIC774-3 recommendation: 182.4 MPa
Maximum additional stresses due to train moving loads: -195.05 MPa
Track-Bridge Interaction Verification