Rail bridge and composite girder bridge analysis

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M I D A S I T
Bridging YourInnovations to Realities

Bridging Your Innovations to Realitiesmidas Civil
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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]
Dynamicamplification
Q
Q
6
5
4
3
2
1
0
16 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

3
Traction/Braking loads
abutment pier
Longitudinal displacements
at top surface of deck end
Temperature Train vertical loads
Track-BridgeInteraction

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Track-BridgeInteraction
1) Axial Forcesin a ContinuouslyWeldedRail Track on Embankment
(Thermal Load on the Rail)
2) Axial Forcesin a ContinuouslyWeldedRail Track on Bridge
(Thermal Load on the Bridge)
Axial forces in the track on 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)
Displacementintherails(mm)
Resistance
TAEF ∆×××= α

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Design Requirementsfor Track/Bridge Interaction Analysis
Design Standards: UIC774-3, EN 1991-2
Item Loads
DesignCriteria
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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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
Tractionloads braking loads
Magnitude of Load Loadedlength Magnitude of Load Loadedlength
High-speedrailway 33kN/m/track 33m 20kN/m/track 400m
Normal railway 24kN/m/track 33m 12kN/m/track 300m

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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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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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1) Establishment of Criteria for Construction of Rail Expansion Joint on BridgeSection
RailExpansion 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
Economicefficiency
Compare the maintenance cost forrail
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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2) Flowchart
RailExpansion Joint
Check the axial force
and displacement in
the rails
Modify the support placement
and displacement in
the rails
Modify the span composition
and displacement in
the rails
Modify the stiffness of deck
and displacement in
the rails
Use a zero-longitudinal resistance rail fastener
and displacement in
the rails
Consider building REJ (rail expansion joint)
Analyze the economical
efficiency
Submit the report
Allow the constructionof rail
expansion joint
ContinueOK
OK
OK
OK
OK
OK
NG
NG
NG
NG
NG
NG
NG
NG
NG
NG

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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-BridgeInteraction Analysis
Embankment section
Bridge deck
Springfor 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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- 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
producethe greater axial forcesthan the staged analysis.
AnalysisMethods

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Simplified Separate Analysis Complete Analysis
AnalysisMethods

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RailTrack AnalysisModel Wizard (Layout)
Advanced:define the fixedendsfreelyand
adjustthe spanlength
ZLR: Specifythe zero-longitudinalresistance rail
fastener(the resistance of ballastissetto zerofor
the specifiedsections.)
REJ: Place the rail expansionjointforeachtrack
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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TaperedSectionAssignment
Sectionsat 0.1 of the total span length:Span_2
Sectionsat 0.5 of the total span length:Span
Sectionsat 0.9 of the total span length:Span_2
TaperedOption
Start 0.1~Start 0.5: Z Axis CurvedType (Quadratic) , From (J-end)
Start 0.5~Start 0.9: Z Axis CurvedType (Quadratic) , From (I-end)
Define TaperedSection
RailTrack AnalysisModel Wizard (Section)

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1 . Lateral Resistance Data
- Enter gravel ballast data and concrete ballast data.
- For gravel ballast,the resistance of ballast isdifferentbetweenthe stress
checkand the displacementcheck.
2. Define Condition
- Selecteithergravel ballastor concrete ballast for the entire section.
- Via the ‘Advanced’function,selecteithergravel ballast or concrete ballastby
sections(Forundefinedsections,gravel ballastisused).
3. Boundary Types
Spring Type Bearing Type
1
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RailTrack AnalysisModel Wizard (Boundaries)

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4. ModelingbySections
1) Embankment section
5. Boundary ConditionsTaking into Account the Effective Length
The resistance ofballast enteredshouldbe in kN/m and islongitudinal resistance.
The resistance multipliedbythe effective lengthwill be usedin the model.
2) Section connecting embankment and deck start point 3) Section connecting deck start and end points
RailTrack AnalysisModel Wizard (Boundaries)

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1. Accelerating/braking/vertical train loadscan be freelyenteredbysectionsin a tabular format.
The length and magnitude of load can be enteredwithreference tothe leftendof the model.
-RunningDirection:the direction in which the train runs.Define either‘KeepRight’or ‘KeepLeft’.
-TrainSection: Train sectionis recognizedwhenavertical load is entered. Whenavertical Load is excluded,define TrainSectionandapply Loaded
Condition.
- Load Type:For single track, in general,applyeitheraccelerating loadsor brakingloads. Fordouble track, apply acceleratingloads andbraking loads
foreachtrack. Asfar as train vertical loads are concerned, variousuniformloadscan be appliedby sectionsandtherefore HLload, which is most
frequentlyused,canbe easilyrepresented.
2. Filesare added for the moving load analysis
- Number ofTrack LoadingLocations: the numberof movingtimesof train load.If “n” is entered,nfilesare added.
- Location Incrementfor eachModel:the incrementof moving load pertrack. If “n” is entered,the trainmovesbyn and the boundaryconditions
are assignedtothe sectionto which the train load is applied.
ex> If “Number of Track Loading Locations” is 3 and “Location Increment for Track” is 10, the train moves forward by 10m, 20m and 30m and three files are added.
Case 1: Single Track Case 2: Double Track
RailTrack AnalysisModel Wizard (Load)

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RailTrack AnalysisModel Wizard
1 .StressCheck Model Option
Thisoptioncreatesa file to checkthe additionalstresses.
-SimplifiedSeparate AnalysisModel
-Complete Analysis
2. DisplacementCheckModel Option
Thisoptioncreatesa file to checkthe displacements. Inthisfile,the resistance of ballast applied at UnloadedConditionisdifferentforthe case of
gravelballast.In addition, this file is available only for SimplifiedSeparate AnalysisModel.
- Relative LongitudinalDisplacementComponentdue toAccelerationandBrakingAlone
- Relative LongitudinalDisplacementComponentdue toVerticalEffects
-Relative LongitudinalDisplacementComponentatRailExpansionJoints
- Rail Break GapSize

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CaseStudies
Forthe case of a high-speedrailwaywithgravel ballast and double track,the following propertiesare definedforrail, ballast and horizontal
alignment:
Track Item Property Unit Value Remark
Rail
UIC60
Cross-sectionalarea A m2 7.669E-3
Moment of inertia Iyy m4 30.363E-6
Ballast
Gravelballast
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
Girder Type
Span Length
Equivalent Modulus
of Elasticity
Cross-
sectional Area
Moment of Inertia
Neutral Axis
(Girder 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
PCBox girder bridge is chosenfor the high-speedrailwaytrack.
The dimensionsof girderandthe geometricrelationbetweenthe girderandtrack are definedasfollows:
The longitudinalresistance of deckis setto 1.5 x 10
6
kN/m.

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Forthe case of a high-speedrailwaywithgravel ballast and double track,the rail, ballast and horizontal alignmentare definedasfollows:
Simple bridge type
Continuousbridge type
CaseStudies
40m 40m 40m 40m 40m 40m 40m 40m 40m 40m
80m 80m 80m 80m 80m

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Axial stressby temperature load (Simple spanbridge)
Axial stressby temperature load (Continuousbridge)
Because the simple bridge type gives the smaller additional stress than the continuous bridge type, the simple bridge type is adopted.
CaseStudies
-26.6 MPa
-44.1MPa

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CaseStudies
Axial stressby temperature (+25°C) at UnloadedCondition
Axial stressby temperature,traction and vertical train loads at LoadedCondition
-35.6MPa
-26.6 MPa

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CaseStudies
Axial stressby temperature,braking and vertical train loadswith differenttrain position

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CheckDisplacements
- 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 RelativeLongitudinal 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) RelativeDisplacements 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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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)
CheckDisplacements
4) AllowableOpening Displacements when Opening Gap at Rail End takes place .
- Allowable Opening Displacements According to International Standards
- Allowable Opening Displacements According to Korean Standards
. Railway Design Manual (Volume Track)
1) Limits to the opening displacements, d, when the split web at 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= − − 3
2
xP
e x
EI
β
δ β
β
−
= 4
4
k
EI
β =
2) Restrict the opening displacements of (1) when a
zero-longitudinal resistance rail fastener is built
Wheel loadP
Center of wheel O
Vehicle velocity V
Wheel radius R
Vertical displacement δBending stiffness of rail EI
Bearing stiffness of trackK
Opening displacement d

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Relative Longitudinal Displacementbytraction loads
CaseStudies

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CaseStudies
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 Displacementbyvertical train loads

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FactorsAffecting the Axial Forcesin Track (1)
1) Longitudinal Resistanceof Track
Longitudinal resistance of trackvs. 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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Axial stresses of Ballast Bed in the longitudinal direction
Axial stresses of Concrete Bed in the longitudinal direction
Unloaded Condition (underthermal loads)
Loaded Condition
(traction/brakingloads and vertical loads added)
Unloaded Condition (underthermal loads)
Loaded Condition
(traction/brakingloads and vertical loads added)
Longitudinal axial stress is about 30% less in the ballast track than in the concrete track under the same conditions.

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2) Zero-Longitudinal Resistance Rail (ZLR) Fastener inthe BridgeSection
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>
Installing ZLR fastener can reduce about 29% of the axial stress.

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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
FactorsAffecting the Axial Forcesin Bridge (1)
- Type 1 - Type 2
- Type 3 - Type 4

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- Type 1
-Unloaded Condition : 26.48 MPa -Loaded Condition : 32.86 MPa
- Type 2

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- Type 3
- 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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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
RailStress(MPa)
2@40M_FMM_Vertical Load
Stiffness of Deck

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4) Support stiffness
K: Total stiffness of support
: relative displacement between the upperand lower parts of bearing
-Factors affecting the support stiffness K
Bending ofPier Rotation ofFoundation Displacement of Foundation

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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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Cases illustratingthe effects ofsupport layout ofbridge
- Case1: Simple bridge ( 1@30 8 Span)
Axial force is about 26% less for MFFM type (28.12 MPa) than in the FMFM type (38.08 MPa) when other conditions are identical.
- Case 2: 2 span continuous bridge (2@30 4 Span)
Axial force is about 45% less for MFM type (29.77 MPa) than in the FMM type (54.20 MPa) when other conditions are identical.
FMFM type MFFM type
MFM type FMM type
38.1 MPa 28.1 MPa
29.8 MPa 54.2 MPa

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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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1) Verificationof 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-BridgeInteraction Verification

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2) Validation against UIC774-3
Resultdue to temperature 35 degreescentigrade onbridge deck:
-30.47 Mpa
UIC774-3 recommendation:-30.67 MPa
Resultdue to temperature 35 degreescentigrade onbridge deckand
50 degreescentigrade onrails: -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 stressat 0 pointfrom right pierdue to train loading:181.38 Mpa
UIC774-3 recommendation:182.4 MPa
Maximumadditional stressesdue to train moving
loads:-195.05 MPa
Track-BridgeInteraction Verification

Rail bridge and composite girder bridge analysis

Rail bridge and composite girder bridge analysis

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Rail bridge and composite girder bridge analysis