rail bridge and composite girder bridge analysis

111-1

M I D A S I T Bridging Your Innovations to Realities

http://www.youtube.com/watch?v=h0X_MgU2cLs&list=PLEpoLspUgorbwzHg5AFTrdqPy2HHPvK-U

Bridging Your Innovations to Realities midas 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]

Dyn

amic

am

plif

icat

ion

QQ

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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Traction/Braking loads

abutment pier Longitudinal displacements at top surface of deck end

Temperature Train vertical loads

Track-Bridge Interaction


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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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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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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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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 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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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


the rails

Modify the stiffness of deck


the rails

Use a zero-longitudinal resistance rail fastener


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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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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- 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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Simplified Separate Analysis Complete Analysis

Analysis Methods


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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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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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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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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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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 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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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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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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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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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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Case Studies Axial stress by temperature, braking and vertical train loads with different train position


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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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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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Relative Longitudinal Displacement by traction loads

Case Studies


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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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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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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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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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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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- Type 1

-Unloaded Condition : 26.48 MPa -Loaded Condition : 32.86 MPa


- Type 2


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Factors Affecting the Axial Forces in Bridge (1) - 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

Rai

l Stre

ss (

MP

a)

2@40M_FMM_Vertical Load

Stiffness of Deck


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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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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 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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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) 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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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

http://www.youtube.com/watch?v=h0X_MgU2cLs&list=PLEpoLspUgorbwzHg5AFTrdqPy2HHPvK-U

rail bridge and composite girder bridge analysis

Technology

longer rail

continuouslyweldedrail

mpa case

ex standard length rail

reduced impact force

train loading

train movingloads

temperature drops