land viaduct design dynamic behaviour-completed

8/2/2019 Land Viaduct Design Dynamic Behaviour-Completed

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Design Basis - Land Viaduct April 2009 Perunding FAISAL, ABRAHAM dan AUGUSTIN sdn bhd

LAND VIADUCT

DYNAMIC BEHAVIOUR

Prepared by :

Ir. Patrick C. AUGUSTIN

Perunding FAISAL, ABRAHAM dan AUGUSTIN sdn bhd


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1.GENERAL

The design of high-speed railway bridges is regulated in two different parts of Eurocode:

EN 1990- Annex A2 containing principal bridge performance criteria and EN 1991-2 containing the requirements

related to loading, dynamic increment of loading, requirements for a dynamic analysis.

EN 1991-2 provides a flow chart considering speed, bridge type, span arrangements, first bending and firsttorsional mode. For bridges with a behavior similar to a simply supported beam, a dynamic analysis might not be

necessary as indicated by a span and frequency depending diagram. For all other structures and speed greater than

200km/h a complete dynamic analysis is deemed necessary. [1]

2.Verification whether dynamic analysis is required

The requirements for determining a static or a dynamic analysis is required are shown in figure 1. The National

Annex may specify alternative requirements. The use of the flow chart in figure 1 is recommended. [2]

where:

Vis the Maximum Line Speed at the Site [km/h]

L is the span length [m]

n0 is the first natural bending frequency of the bridge loaded by permanent actions [Hz]

nT is the first natural torsional frequency of the bridge loaded by permanent actions [Hz]

v is the Maximum Nominal Speed [m/s](v/n0)lim is given in annex F


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Figure 1: Flow chart for determining whether a dynamic analysis is required


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NOTE 1 Valid for simply supported bridges with only longitudinal line beam or simple plate behavior with

negligible skew effects on rigid supports.

NOTE 2 For Tables F1 and F2 and associated limits of validity see annex F.

NOTE 3 A dynamic analysis is required where the Frequent Operating Speed of a Real Train equals a Resonant

Speed of the structure. See 6.4.6.6 and annex F.NOTE 4 dyn is the dynamic impact component for Real Trains for the structure given in 6.4.6.5(3).

NOTE 5 Valid providing the bridge meets the requirements for resistance, deformation limits given in EN 1990

A2.4.4 and the maximum coach body acceleration (or associated deflection limits) corresponding to a very good

standard of passenger comfort given in EN 1990 A2.

NOTE 6 For bridges with a first natural frequency n0 within the limits given by Figure 6.10 and a Maximum Line

Speed at the Site not exceeding 200km/h, a dynamic analysis is not required.

NOTE 7 For bridges with a first natural frequency n0 exceeding the upper limit (1) in Figure 6.10 a dynamicanalysis is required. Also see 6.4.6.1.1(7).

in order to use this flow chart, a spread sheet has been prepared as described further.


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Figure 2: 3D view of modeling in PROKON


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2.1.Double Tracking Bridge

2.1.1.Modeling and Analysis

The bridge view in modeling is as illustrated herein. (figure 2). This bridge has been modeled using PROKON

3D program. A modal analysis has been carried to find out maximum deflection in each direction and alsofrequencies of different modes.

The bridge is considered combination of 15 meter long spans with continuous beams.


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2.1.2. Results

The results of modal analysis is given afterwards in table 1.

M

shapeFreq.(Hz) Period (s) Modal stiffn. Modal Mass Part Participation Fac Eff. Mass

(kg) (kg)

1 1.01 0.99 1.32E+005 3.26E+003 1.01 3.34E+006

2 1.11 0.9 1.06E+005 2.17E+003 1.1 2.63E+006

3 1.23 0.82 6.42E+004 1.08E+003 1.00E-003 1.09

4 1.9 0.53 1.39E+005 971.6 1.54E-001 2.30E+004

5 2.75 0.36 2.98E+005 998.1 2.88E-003 8.3

6 4.13 0.24 6.02E+005 892.8 2.62E-002 610.6

7 5.19 0.19 4.32E+005 406.1 9.29E-002 3.50E+003

8 5.29 0.19 4.94E+005 446.9 4.33E-002 835.8

9 5.42 0.18 1.42E+006 1.22E+003 4.56E-002 2.55E+003

10 5.47 0.18 4.58E+005 387.8 3.33E-002 429.6

Table 1: Analysis Output-NATURAL FREQUENCY FOR EACH MODE SHAPE

Mode shapes are represented herein.


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Figure3: Mode Shape No.1


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Figure 4: Mode Shape No.2


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Land Viaduct Behavior Vertical Deflection

Figure 10 Annex A2 of EN1990 2002 gives the envelopes for limiting deflections of Span Length vs Line Speed.

This is to ensure rider comfort. Very Good rider comfort conforms to Figure 10 which is associated with vertical

track acceleration of 1m/s2.

The double track project has been designed for a maximum line speed of 180kM/hr. It is assumed that at this

operating speed the rider comfort level will be good corresponding to a vertical track acceleration of 1.3m/s2.

At 2.0m/s2 deck accelerationrider comfort is assumed as acceptable.


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Figure 10: Maximum permissible vertical deflection for railway bridges with 3or more successive simply

supported spans corresponding to a permissible vertical acceleration of bv = 1 m/s in a coach for speed

V [km/h]


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For the Land Viaduct , assuming the maximum Line Speed to 180 km/h, d/L is 900. For continuous beams with

three or more spans the values of d/L given in figure 3 should be multiplied by 0.9 and Regarding good level of

comfort this figure is divided with 1.3, which results to:

d= dL

d

=900

Vb

Variablegivenfor morethan3 spancontinuousbeams

Figure 10:L

d =900

Vb = 1.3 (Comfort Level for good level of comfort at speed of 180 km/h is 1.3)

L

d=

900

1.30.9=623.08

L= 15 m

thus :

allowable=15000 /623.08 = 24 mm

Double Tracking maximum vertical deflection = 19 mm

The corollary to satisfying deflection is that it will also satisfy dynamic requirements. Nonetheless a spreadsheet

was written to determine if dynamic analysis was required following the Flowchart ,Figure 6.9 of Clause 6.4.4

Requirement for a static or dynamic analysis, EN 1991-2:2003 (E).


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2.1.3. Running the Flowchart for Electrified Double Tracking Bridge

Input data are provided as below:

V: The Maximum Line Speed at the Site [km/h] of double tracking is limited to 180 km/h.L: The span length [m] for double tracking is 15 m.

n0: The first natural bending frequency ( Mode 7 ) of the bridge loaded by permanent actions [Hz] is 5.19 Hz.

Maximum line speed is less than 200 km/h. Thus we move to right.(Figure 1).

The next step is defining type of bridge regarding span types. This bridge is of continuous spans however

following the flowchart one should refer to annex A2 of EN 1990:2002 to determine that deflections are in

allowable range to consider bridge as continuous span bridge.

Allowable vertical deflection for this particular bridge can be obtained from Figure A2.3 of EN 1990. [3]

- the span lengthL [m],

- the train speed V[km/h],

The last step is to calculate the dynamic impact factor of loads is defining the dynamic factor to impose on static

loads.


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Dynamic factor is defined according to this equations given in : 6.4.5.2 Definition of the dynamic factor , EN

1991-2:2003 (E).

Running the spread sheet it is found there is no need for dynamic analysis and dynamic factor should be imposed

on loads is 1.32 .

All this procedure has been summarized in a spreadsheet .

Another thing to point out is the difference between natural frequency and exciting frequency. Natural frequency

is 5.19 for this bridge while exiting frequency is as below:

V/Lvehicle=50/20=2.5 Hz , where a trin length of 20m has been assumed. For shorter trains , the exciting

frequency becomes higher and is further from the spectrum that can cause resonence.

Thus natural and exciting frequencies are far apart and resonance will not happen.

D i B i L d Vi d t A il 2009 P di FAISAL ABRAHAM d AUGUSTIN d bhd


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3. FATIGUE

The verification on the need for a dynamic analysis showed that it was unnecessary. However this exercise was

carried a step further to show that fatigue is never a problem.

3.1 Requirements for satisfying fatigue for bridge structure is given in

BRITISH STANDARD BS 5400-4: 1990, Steel, concrete and composite bridges

Part 4: Code of practice for design of concrete bridges

Clause 4.7 Fatigue. The effect of repeated live loading on the fatigue strength of a bridge should be considered

in respect of reinforcing bars that have been subjected to welding; details of compliance criteria

are given in Part 10.

Welding may be used to connect bars subjected to fatigue loading provided that:

a) the connection is made to standard workmanship levels as given in Part 7;

b) the welded bar is not part of a deck slab spanning between longitudinal and/or transverse members and

subjected to the effect of concentrated wheel loads in a traffic lane;

c) the detail has an acceptable fatigue life determined in accordance with Part 10;

d) lap welding is not used.

Design Basis Land Viaduct April 2009 Perunding FAISAL ABRAHAM dan AUGUSTIN sdn bhd


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For unwelded reinforcing bars, the stress range under load combinations 1 to 5 for the serviceability

limit state should be limited to 325 N/mm2 for grade 460 bars and to 265 N/mm2 for grade 250 bars.

3.2 Examination of Stresses in Land Viaduct Structure

Clause 4.7 Stress Calculations to derive the stresses in the reinforcement are carried out in accordance to Clause

5.3.2 Resistance moment of beams and Clause 5.3.2.1 Analysis of sections.

The common method of calculating these stresses is the routine used when calculating crack widths in structures.

When crack width are satisfied , the stresses usually satisfy Clause 4.7 .



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Design Basis Land Viaduct April 2009 Perunding FAISAL, ABRAHAM dan AUGUSTIN sdn bhd

3.3 Crack Width Calculations for Land Viaduct Structure

The Land Viaduct has short spans. The governing ultimate design bending moments are almost entirely due to the

application of the derailment load which are higher than the normal train loads.. Therefore it is not surprising that

the fatigue stress limits are easily satisfied for Grade 460 bars and also within the limits of Grade 250 bars.

It is also to be noted that concrete stresses are in a very comfortable zone.

A brief summary is appended below for the most heavily loaded beams which are found in the first span with. The

complete results given in the appendix.

RESULTS FROM SERVICEABILITY LIMIT STATE ANALYSIS

BEAM 1 OF VIADUCT SPAN1 BEAM 2 SPAN 1 LAND VIADUCT

Depth to Neutral Axis 289.24 mm Depth to Neutral Axis 311.34mm

Concrete Stresses Concrete Stresses

Stre ss a t top P er mis sible Stre ss a t top m is sible

-section N/mm2 -section N/mm2

5.05 20 5.2466 20

Depth Stress Permissible Depth Stress P ermissible

mm N/mm2 N/mm2 mm N/mm2 N/mm2

1 1235 -173.87 -345 1 1235 -163.19 -345

2 1195 -166.52 -345 2 1200 -157 -345

0.13611 mm 0.11538mm

Cross Cross

N/mm2 N/mm2

1 1

Layer Layer

Design crack width Design crack width

Reinforcement stresses ( tension-negative, compression-positive )



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g p g

4.References

1. M. Heiden & H. Bokan et al. Dynamic Effects of Railway Bridges for High Speed Usage: Application

Example Steel- Composite Truss Bridge, Congresso de Construccao Metalica e Mista, Lisboa, December

2003

2. EN 1991-2:2003, Action on Structures- Part 2: Traffic Loads on Bridges

3. EN 1990:2002, Annex A2

land viaduct design dynamic behaviour-completed

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