Report The Track bridge-interaction due to

Faculty of Civil Engineering Institute of Dynamic of Structure Prof. Dr.-Ing. Peter Ruge

Report

Title:

The Track bridge-interaction due to longitudinal loads.

By:

Yaseen Srewil

The lecturer:

Date:

Prof. Dr.-Ing. P. Ruge

30/04/2007

Faculty of Civil Engineering Institute for static and Dynamic Report of Special Lectures

TU .Dresden Rehab. Eng. Master Program

Content

Summary....................................................................................................................................2 1 Introduction...............................................................................................................................2 2 Ballast Track System .................................................................................................................2 3 Longitudinal action due to uniform tempearture change ....................................................3 4 Longitudinal action dsue to braking forces............................................................................4 5 Longitudinal action dsue to traction .......................................................................................5 6 The effect of bending of the supporting bridge deck ..........................................................6 7 Sudden change of ballast stifness ..........................................................................................7 8 Conclusion… .. .....................…………………………………………………………………………...8 9 acknldegment …………………………………………………………………………………………..9 10 References: ...............................................................................................................................9

1

01/04/2007 10:27:00

Faculty of Civil Engineering Institute for static and Dynamic Report of Special Lectures

TU .Dresden Rehab. Eng. Master Program

Summary The special lecture, which is given within frameworks of special lectures in Rehabilitation Engineering program in Dresden University of technical for third semester by prof. Ruge, was discussed the Track bridge railway interaction due to longitudinal loads. This lecture concentrated at the truth the interaction between Track and structure cannot be neglected specially for the rail continuously welded[1]. In addition, the steel bridge deck will expand under high temperature. Therefore, there is different between the railway before the bridge and railway behaviour on the bridge. This different behaviour should be considered in design process.

1 Introduction The interaction between rails and bridge aimed to recognize a safety and comfort standards of bridges and running train vehicles. The rails are continuous between a bridge and embankment at one or both ends of the structure, Even though the weight and geometry of trains on rails is exactly known, as for bridges the Railway Bridges load models do not describe actual loads. They have been selected in such a way that their effects, within dynamics increments, which are taken into account separately. The longitudinal rails forces have significant effect on railway bridge design, which resulted generally by: the uniform temperature change ( ∆t ), braking with braking forces ( P N ), changing of

[ m]

supporting structure or bending of the bridge deck[1], and sudden change of ballast stiffness when the train cross the bridge. The longitudinal action due to traction or braking will be resisted partly by the earthworks behind the abutment where the rails are continuous and the remainder through bridge bearings. The thermal variations, or bending of bridge deck, will produce indirect longitudinal at the bridge bearings. The longitudinal action shall also be taken into consideration when designing the bridge bearings, substructure and superstructure.[2] Moreover, the mutual influences of bridge and rail structural behaviour are known as Track/bridge interaction. In this report will discuss these phenomenons separately in detail. However, for the Ballasted Track “Classical Track” which will get overview on it.

2 Ballasted Track System The classical railway track consists of a flat framework made up of rails and sleepers which is supported on ballast. The ballast bed rests on a subballast layer that forms the transition layer to the formation[4]. Figure 1 and Figure 2 show

Figure 1 Track with it different components: rails, rialpads, fastening, sleepers, subballast, subgrade.[5]

2

01/04/2007 10:27:00

Faculty of Civil Engineering Institute for static and Dynamic Report of Special Lectures

TU .Dresden Rehab. Eng. Master Program

the construction principle of the classical track structure. Fastenings connect the rails and sleepers. These components and other structures such as switches and crossings are all considered as part of the track. The important development, since the begging of the railways, was after Second World War includes introduction of continuous welded rail, use of concrete sleepers, heavier rail-profiles, innovative elastic fastenings, mechanisation of maintenance, and introduction of advanced measuring equipment and maintenance management systems.

Figure 2 principle of Track structure longitudinal section.[4]

3 The longitudinal action due to uniform temperature change The longitudinal action due to temperature variation shall determine according the Eurocode 1-1991-3:1995 & its commentary. For single-span bridges not more than 15 m long, carrying standard directly fastened track that is continuous over both ends of the deck, the characteristic value of the longitudinal action to be taken into account at the bearings is given by: Where: FTk = ±40LT (in kN) per track (FTk ): The characteristic value of the longitudinal action due to temperature variation that shall be taken into account at the bearing level. This action results from the expansion movement of the bridge relative to the continuous ballasted track.[2] • ( LT): is the expansion length in (m). For bridges carrying directly fastened track other than those covered by the formulae above, or for any bridge where the track has expansion devices at both ends of the deck then: FTk = 0 For bridge carrying ballasted track which is continuous over both ends of the deck and in which the fixed bearing is at one end, the characteristic value of the longitudinal action to be taken into account at the bearings is given by: L1 L2 FTk = ±8LT (in kN) per track. For bridge carrying ballasted track which is continuous over both ends of the deck and in Figure 3 Deck with the fixed bearing not located at one end [2] which the fixed bearing is not located at one end, •

3

01/04/2007 10:27:00

Faculty of Civil Engineering Institute for static and Dynamic Report of Special Lectures

TU .Dresden Rehab. Eng. Master Program

the characteristic value of the longitudinal action to be taken into account at the bearings is given by : FTk = ±8(L2 -L1) (in kN) per track see figure 3. For bridge carrying ballasted track with an expansion device adjacent to the moving end of the deck and continuous over the fixed bearing at the other end, the characteristic value of the longitudinal action to be taken into account at the bearings is given by: FTk = ± (400+5LT) (in kN) per track. This force is limited to 1100 KN per track.

4 The longitudinal action due to the barking forces . The braking forces which acting at the top of the rails in longitudinal direction of the rails commonly assumed as constant distributed forces (P) in section along each wagon as illustrated in Figure 4. The result that obtained from this assumption will be satisfied. The characteristic values of braking forces (P), which are applicable for all types of track Figure 4 Track-bridge system with constant braking force[2] construction, e.g. continues welded rails, with or without expansion devises, Is taken in theory as following: The braking force (P) is caused by the vertical trainload (Pv) multiplied by the frictional P ( x , t ) = PV ( x , t ).µ (t ) coefficient (µ) [3]: According to the German Railway code, this value is time-dependent with a peak during the last four second before train stops:

µ1 (t ) = µ max [0.0189 t ]

if :

µ 2 (t ) = µ max [0.016833 e 0.891626 ( t − 22 .3) + 0.404217 ]

0 .0 s ≤ t ≤ 22 .3 s 22 .3 s ≤ t ≤ 26 .3 s

µ

The maximum value max has to be fixed according to environmental conditions like wheel rail-contact, rain, ice, maintenance, and so on. A Fourier-series expansion for the frictional coefficient in figure 5 with an active period of T=26.3 seconds shows some first significant harmonics. [2]

Figure 5 Frictional Coefficient versus time [2]

4

01/04/2007 10:27:00

Faculty of Civil Engineering Institute for static and Dynamic Report of Special Lectures

TU .Dresden Rehab. Eng. Master Program

Other approaches can be use for calculating the barking forces on bridge, depending on the influence length ( La,b) for braking effects for the structure elements considered. The characteristic value of braking forces, which are applicable to all type of track construction, e.g. continuous welding rails or joint rails, with or without expansion devices, should be taken as following[6]:

Qlbk = 20 [kn / m ] .La ,b ≤ 6000 kn.

Qlbk (kn ) : The characteristic value of braking. La ,b ( m ) : The influence length for braking. For load models 71, SW/0, and load model HSLM, this according to the load models which are given in EN 1991-2 for railway loading. Qlbk = 35 kn / m .La ,b For load model: SW/2.

[

]

Qlbk = 2 .5[kn / m ] .La ,b

For load model “unloaded train”.

In special cases, like for lines carrying special traffic (restricted high-speed passenger traffic for example). The braking forces may be taken as equal to 25% of sum of axils-loads acting on the influence length of the action effect of the structural element considered with maximum value for Qlbk = 6000 kn . [6]

5 The longitudinal action due to traction. According to the same previous approaches, the traction is given longitudinal forces and these forces commonly considered as uniformly distributed over the corresponding influence length La ,b ( m ) for traction effect for the structural element considered.[6] The characteristic value in this case should be taken as following:

Qlak = 33[kn / m ] .La ,b ≤ 1000 kn. Qlak (kn ) The characteristic value of traction. La ,b ( m ) The influence length for traction. For load models 71, SW/0, SW/2, “unloaded train” and HSLM. As in case of barking forces, for line carrzing special traffic. The traction forces may be taken as equal to 25% of sum of axial-loads acting on the influence length ( La ,b ) of the action

Qlak

effect

for = 1000 kn. [6]

the

structural

element

considered

with

maximum

value

for

There are other considerations for above load such as the mulicomponent action when defining the characteristic value of traction and braking, for more information can find in the reference [6].

5

01/04/2007 10:27:00

Faculty of Civil Engineering Institute for static and Dynamic Report of Special Lectures

TU .Dresden Rehab. Eng. Master Program

6 The effect of bending of the supporting bridge deck. The bending of the supporting bridge deck consider as one of longitudinal forces causes, where the rail and bridge-deck are coupled throw the ballast or fastening system. The longitudinal forces caused by the bending of structure which results of applying the live load. The system illustrates in the figure 6. For donating the longitudinal displacement of the upper surface will be used the following symbol [1]; Zb, Zn, and Za; The natural axis and left-hand side elastic support of the bridge respectively. The displacement of neutral axis and the slope of the bending line w´(x) define the deformation Zb. Z b ( x ) = Z n + w′( x ) h0 . The rail stress due to bending id influenced by relative location of the neutral axis η and the relative maximum vertical displacement δ.

h η= 0, hu

) w δ = , L

L ) w = w ( x = ). 2

For single-span beam of bending stiffness EI under constant live load q0 the deflection of natural axis is described by famous formula:

w( x ) =

Figure 6 Bending of the supporting structure [2]

q 0 L4φ x x x ( − 2 ( ) 3 + ( ) 4 ). Where, Φ is a dynamic magnification factor [2] 24 EI L L L

Using the last equation, the maximum deflection at the centre of the span can be given

L 5 q 0 L4φ ) w = w ( x = ) = , as: 2 16 24 EI

→δ =

5 q 0 L3φ 384 EI

The relative maximum deflection follows. using the last equation, the slope of bending line can be formulated in terms of δ.

w ′( x ) =

16 x x δ (1 − 6( ) 2 + 4 ( ) 3 ). 5 L L

This equation can be rewritten in term of a local element coordinate xj such as illustrate in figure 7.

16 x x δ (1 − 6( ) 2 + 4 ( ) 3 ). 5 L L 0 ≤ x ≤ lj w ′( x ) =

Figure 7 Embedded rail element of length lj described by local coordinate xj. [2]

There are two cases: 6

01/04/2007 10:27:00

Faculty of Civil Engineering Institute for static and Dynamic Report of Special Lectures

•

TU .Dresden Rehab. Eng. Master Program

Elastic coupling[1]

Provided that the elastic coupling between rail and bridge is retained, the additional the displacement of the rail due to bending of the structure is described by differential equation.

EA z ′R′ − c1 ( z R − z B ) = 0

C1; stiffness is used since the track is loaded by live load q0.

By solving the differential equation, can be evaluated the bending of the structure parameter. •

Plastic situation (slip)[1]

For this case the additional displacement of the rail described by the following differential equation.

EA z ′R′ = − q ( x ). The coupling between rail and structure is not effective anymore. A longitudinal restoring force q(x) acts on the rail which depends on the available elastic deformation capacity due to the complete preceding loading process. The situation ‘bending (plastic)’ is thus completely analogous to the loading case ‘∆T (plastic)’. Assuming a linear variation of longitudinal resistance q(x) between nodal values, the element stiffness matrix Kj and righthand side vector rj the vector of unknown variable.

7 Sudden change of ballast stiffness The sudden change of ballast stiffness when the train crosses the bridge causes considerable longitudinal forces on the bridge. Many studies about the ballast behaviour are done to determine the actual behaviour of ballast and its stiffness where the coupling element between rail and bridge depends on whether the track is loaded or not. Then, the value of the parameter C [N/m2] (the distribution stiffness) change suddenly when a train reaches the bridge. This leads to an additional restoring force, acting on both a rail and structure[1].

∆ q = − ∆ c.u D ,

∆ c = c1 − cu .

- C1 [N/m2] for unloaded track. - C2 [N/m2] for loaded track.

uD in the equation above is the relative deformation of the coupling element due to all preceding loading cases. Which define as following:

uD = u R − u B

) for[u R − u B ] p u

) uD = sign(uR − uB )u

) for uR − uB ≥ u,

a limitation of ∆q is given:

) ) − ∆ c.u ≤ ∆ q ≤ ∆ c.u

Figure 8 Longitudinal Track-bridge interaction system omdel (a). (b) coupling element uB >uR- [2]

This additional restoring force should be analysed as a separate loading case in connection with bending of the bridge deck due 7

01/04/2007 10:27:00

Faculty of Civil Engineering Institute for static and Dynamic Report of Special Lectures

TU .Dresden Rehab. Eng. Master Program

to live load and braking. Thus, relieving load -∆q should be consider prior to subsequent temperature change, if assumed that the train has left the bridge again. The additional displacement of the rail is described in elastic coupling case by the differential equation as the following[1]:

EA z ′R′ − c1 ( z R − z B ) = − ∆ q Where, c1 the stiffness of loaded ballast. And the additional displacement of the bridge due to the sudden change of ballast stiffness is constant. The additional displacement of rail due to the sudden change of ballast stiffness in plastic situation is described by the following differential equation.[1]

EA z ′R′ − = − ∆ q ( x ) − q ( x ) The relationship between the resistance and displacement for ballast track can be presented as illustrate in figure 9 [7] [1]. The diagram illustrate that the stiffness as soon as the load increases. In winter the ballast, behave like concrete due to ice action between it.

Figure 9 Resistance/Displacement relationship for ballasted track. [2]

8 Conclusion •

The longitudinal forces computation is very significant and should be taken into account separately and the coupled track –bridge analysis is required due to the interaction between the track and structure.

•

Eurocode recommended an independent treatment of the loading cases temperature change ,bending of the supporting structure and braking traction action taking into account nonlinear stiffness law and the subsequent summation of the results.

•

It is possible to use the result of single- track bridge model for double-track bridge with an abutment stiffness KA2 using KA = KA2/2 in the calculation.

8

01/04/2007 10:27:00

Faculty of Civil Engineering Institute for static and Dynamic Report of Special Lectures

TU .Dresden Rehab. Eng. Master Program

9 Acknowledgment I would like to thank Prof. Ruge and the co-workers in the institute of Static and Dynamic, for the efforts to organize these very useful lectures.

10 References: [1]

[2] [3]

[4] [5] [6]

[7]

[8]

[9]

P. Ruge. & C. Birk.: Longitudinal forces in continuously welded rails on bridgedecks due to nonlinear track–bridge interaction. University of TU Dresden, Faculty of civil engineering, Elsevier Ltd. Computers and Structure (2006). ENV 1991-3 - Eurocode 1 Basis of design and actions on structures . Part 3 Traffic loads on bridges . J. Toth.; P. Ruge.: Spectra assessment of mesh adaptation for the analysis of dynamical longitudinal behavior of Railway bridges, Research Journal: Archive of Applied Mechanics, 71, (Springer, Berlin, Germany), 453-462 (2001) Esveld, Coenraad.: Modern Railway Track, 2nd edit. M RT- Production, the Netherlands, 2001. Iwnicki, Simon (eds.).: HandBook Of Railway Vehicle Dynamic, CRC, Taylor & Francis Group. 2006. Sanpaolesi, Luca. & Croce, Pietro. (eds.).: Design of Bridge, Guide to basic of bridge design related to Eurocodes supplemented by practical example. Leonardo da Vinci pilot project, Pisa, 2005. Monnickwndam, Alan.: Track-Bridge interaction and Direct Track fixing, 3rd Network Rail sponsored supplier Conf. on The Maintenance and Renewal of Bridges, Bristol, 2006 , p 61-64. Johansson, A & Nielsen, J C O.: Out-of-round railway wheels- wheel-rail contact forces and track response derived from field tests and numerical simulations. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit. Professional Engineering publishing, 217 (2003), pp 135-146. V. Markine. & C. Esveld.: ANALYSIS OF LONGITUDINAL AND LATERAL BEHAVIOUR OF A CWR TRACK USING A COMPUTER SYSTEM LONGIN. TU Delft University, Railway department.

9

01/04/2007 10:27:00