Investigation of internal forces in the rail due to the interaction of CWR tracks and steel railway bridges with ballasted track superstructure

Abstract

The technical specifications of D.12/H of Hungarian State Railways specifies that a continuously welded rail track can be constructed through a bridge without being interrupted if the expansion length of the bridge is no longer than 40 m. If the expansion length is greater than 40 m, rail expansion joints have to be constructed.
The aim of the research is to create finite-element models with which the interaction of continuously welded rail track and steel railway bridges can be calculated and to provide technical solutions of track structures on bridges with ballasted track so rail expansion joints can be omitted.

Full text

POLLACK PERIODICA
An International Journal for Engineering and Information Sciences
DOI: 10.1556/606.2016.11.2.6
Vol. 11, No. 2, pp. 65–74 (2016)
www.akademiai.com
HU ISSN 1788–1994 © 2016 Akadémiai Kiadó, Budapest
INVESTIGATION OF INTERNAL FORCES IN THE
RAIL DUE TO THE INTERACTION OF CWR
TRACKS AND STEEL RAILWAY BRIDGES WITH
BALLASTED TRACK SUPERSTRUCTURE
1
Helga PAPP,
2
Nándor LIEGNER
1,2
Department of Highway and Railway Engineering, Faculty of Civil Engineering,
Budapest University of Technology and Economics, H-1521 Budapest, P.O.B. 91, Hungary,
e-mail:
1
papp.helga@epito.bme.hu,
2
liegner.nandor@epito.bme.hu
Received 11 November 2015; accepted 21 March 2016
Abstract: The technical specifications of D.12/H of Hungarian State Railways specifies that a
continuously welded rail track can be constructed through a bridge without being interrupted if
the expansion length of the bridge is no longer than 40 m. If the expansion length is greater than
40 m, rail expansion joints have to be constructed.
The aim of the research is to create finite-element models with which the interaction of
continuously welded rail track and steel railway bridges can be calculated and to provide
technical solutions of track structures on bridges with ballasted track so rail expansion joints can
be omitted.
Keywords: Steel railway bridge, Expansion joints, Ballasted track, Rail restraint,
Longitudinal stiffness
1. Introduction
In the paper a finite-element model has been developed to determine the axial forces
in the rail, bridge structure and the bearing in case of a two-span-bridge with an
expansion length of 40 m resulting from the change of temperature, braking or
acceleration of trains. Following this, the model has been converted into bridges with
70 m and 100 m expansion lengths with the purpose to find technical solutions, with
their application the resultant normal forces do not exceed - or exceed to a less extent -
those values resulting in bridges with expansion length of 40 m. By the application of
these solutions, the Continuously Welded Rail (CWR) track can be constructed through

66 H. PAPP, N. LIEGNER
Pollack Periodica 11, 2016, 2
the bridge without interruption. Only the joining of CWR tracks from earthworks to
steel railway bridges with ballasted track superstructure are discussed in this paper.
2. Laboratory testing of rail fastenings
Test series have been carried out in the Laboratory of the Department of Highway
and Railway Engineering, Budapest University of Technology and Economics, in order
to determine the longitudinal stiffness and the longitudinal rail restraint of different rail
fastenings to model the interaction of the rail and bridges precisely.
The tests were carried out according to standard EN 13146-1:2012 [1]. The test
arrangement is shown in Fig. 1. The concrete sleeper, the rail and the fastening
assembly were fixed to a horizontal base. A tensile load at a constant rate of 10 kN/min
was applied to one end of the rail, while the load and the displacement were measured.
When the rail slipped in the fastening, the load was reduced to zero rapidly and the rail
displacement was measured for two minutes. Without removing or adjusting the
fastening, the cycle was repeated further three times with three minute intervals in the
unloaded condition between each cycle.
The rail displacement was measured with inductive transducer of type Hottinger
Baldwin Messtechnik (HBM) WA20 mm, and the load was measured with force
transducer of type HBM C9B 50 kN. The data acquisition unit and measuring amplifier
was HBM Quantum MX 840, evaluation software was Catman AP. The sampling rate
of frequency was 10 Hz.
Fig. 1. Longitudinal rail restraint test (KS fastening)
The maximum load to produce an initial elastic displacement was determined in
each cycle. The value of the first cycle was discarded. The average of the second, third
and fourth cycle was calculated and considered to be the longitudinal rail restraint. The
fastening assembly is unable to take on higher forces, the rail will slip in the fastening
longitudinally.

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Pollack Periodica 11, 2016, 2
The longitudinal stiffness of the fastening is defined as the ratio of the force
producing the initial elastic displacement and the elastic displacement.
The tests were carried out on rail fastenings of Vossloh KS (Skl-12), Vossloh W14,
K (Geo) and Pandrol Fastclip. The results of KS and K (Geo) are summarized in
Table I.
Table I
Longitudinal rail restraint and stiffness of rail fastenings
Type of fastening
Longitudinal rail
restraint per
fastening [kN]
Longitudinal
stiffness [N/mm]
KS, Skl-12 without any railpad 10.47 14 000
KS, Skl-12 with flat EVA railpad under the rail 12.56 14 000
KS, Skl-12 with flat EVA railpad under the rail
and the railclip over-tightened by moment of
250 Nm
16.58 36 000
K (Geo) fastening without railpad 20.52 40 000
K (Geo) fastening with EVA railpad, over-
tightened 26.51 51 400
A measured load - displacement diagram of KS fastening is illustrated in Fig. 2 in
case there was no railpad and Fig. 3 indicates a measured diagram in case there was a
railpad in the assembly and the railclip was over-tensioned with a moment of 250 Nm.
In the latter case the longitudinal rail restraint is obtained to be 16.58 kN, and the
longitudinal stiffness has been found to be 36 000 N/mm.
Fig. 2. Load - displacement diagram of Skl-12 fastening without any railpad under the rail
0
5
10
15
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
Load [kN]
Displacement [mm]

68 H. PAPP, N. LIEGNER
Pollack Periodica 11, 2016, 2
Fig. 3. Load - displacement diagram of Skl-12 fastening with flat EVA railpad
under the rail and the railclip over-tightened
3. FEM models
The finite-element software of AxisVM 12 was used for the model. In this software
two different types of beams are possible to be defined. In this paper the models
comprise two dimensional Euler-Bernoulli beams.
The model structures consist of one rail of section 60E1 and half of the cross-
sectional area of the bridge. For interest of the comparability of different models, each
model has got the same material and cross-sectional properties [2].
3.1. Bridge structure
In the beam modeling the half-cross-sectional area of the bridge are the following:
• cross-sectional area: 1000 cm
2
;
• elasticity modulus: 210 000 N/mm
2
;
• linear heat expansion modulus: 1.20·10
-5
1/°C.
The static model of the bridge is illustrated in Fig. 4. A fix support is located at the
left hand-side and there are moving supports at mid-span and at the right hand end,
therefore the expansion length of the bridge is equal to its structural length.
Fig. 4. The static model of the railway bridges
0
5
10
15
20
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Load [kN]
Displacement [mm]

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Pollack Periodica 11, 2016, 2
3.2. Modeling CWR ballasted tracks
It has been assumed in the models that a ballasted track with continuously welded
rail (CWR) joins the bridge at its both ends. The ballasted CWR tracks are modeled
with continuously elastically supported beams, whose properties are equal to those of
the rail section of 60E1:
• area of cross section: 7670 mm
2
;
• elasticity modulus: 215 000 N/mm
2
;
• linear coefficient of thermal expansion: 1.15·10
-5
1/°C.
The ballast bed has got a constant longitudinal resistance. The longitudinal
resistance of a consolidated and well maintained ballast can be 8 to 10 N/mm, whereas
that of a newly laid ballast can be considered to be 5 N/mm in respect of one rail. In
accordance with this, the limiting longitudinal load of the continuous support of the
ballasted track has been assumed to be 9 N/mm for the consolidated ballast and 5 N/mm
for the newly laid ballast [3].
3.3. Modeling the track - bridge interaction
The applied fastenings are modeled by non-linear springs (Table I) at a spacing of
0.60 m.
The ballast bed is modeled by discrete spring elements at a spacing of 0.30 m. In this
case the limiting longitudinal force of one spring element is 1.5 kN or 2.7 kN. Reducing
the spacing between the spring elements would result in great excess of computation
time and might lead to calculation errors.
The two sets of springs modeling the fastenings and the ballast are connected by a
stiff element that does not deform, but can displace together with connected elements
and convey internal forces. The model of the interaction of the bridge and the rail is
illustrated in Fig. 5 [4].
Fig. 5. The railway track - bridge interaction
3.4. Load cases and combinations
According to the technical specifications of D.12/H. of Hungarian State Railways
(MÁV), the neutral temperature of the rail is
C 23
o5
8
+
−
. The temperature of the rail can
reach even 60 °C in summer due to direct sunshine, and as low as -30 °C in winter. The
neutral temperature of the steel bridge is 10 °C that can be changed by ±40 °C under
extreme weather conditions [5].

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Pollack Periodica 11, 2016, 2
European Standard EN 1991-2, [3] requires that the braking effect of the trains onto
the rails be substituted by a longitudinally uniformly distributed load of 20 kN/m per
two rails that is 10 kN/m per one rail through a total length of 300 m. It has a maximum
value of 6000 kN on the bridge. The acceleration of the trains is to be taken into
consideration by an evenly distributed longitudinal load of 33 kN/m with a total value
of 1000 kN [6]. Of the two effects, it is the braking that produces higher force, therefore
this is critical [7], [8].
The combinations of loads comprise of the kinematic load of change of temperature
in winter, that in summer and the braking effect over a distance of 300 m. In order to
determine the position of loads generating the greatest normal force in the structures, the
braking force has been moved from the position indicated in Fig. 6a gradually in steps
of 10 m through the positions to the position shown in Fig. 6b. Braking to the left and to
the right are mirrors of each other. Each braking load position has been combined with
kinematic load of change of temperature both in summer and in winter.
Fig. 6. Special positions of braking load
If the rail temperature is lower than the neutral temperature, tensile force will arise
in the rail that may result - in case of a too high value - in fracture of the rail. If it is
higher than the neutral temperature then compressive force will be induced that may
lead - in extreme case - to buckling of the track. The latter is more dangerous in respect
of traffic safety [9].
4. Normal forces in bridges with expansion length of 40 m
As it has already been mentioned in the introduction, according to technical
specifications of D.12/H. of MÁV, continuously welded rail track can be joined to the
bridge structure without a rail expansion joint if the expansion length of the bridge is
equal or less than 40 m, therefore the normal forces generated in the structural elements
are permitted [10], [11]. As a consequence, as first step normal forces were determined
in the rail, bridge structure and the bearing. The computations have been carried out in
the following cases:
• ballast resistance of 5 N/mm/rail and 9 N/mm/rail;
• KS, Skl-12 rail fastening with longitudinal rail restraint of 10.47 kN, 12.56 kN
and 16.58 kN;
• K (Geo) fastening with longitudinal rail restraint of 20.52 kN and 30.00 kN.

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Pollack Periodica 11, 2016, 2
As the distance between the rail fastenings is 0.6 m in the model, the 30.0 kN
longitudinal rail restraint of a discrete fastening will result in a specific rail resistance of
30 kN/0.6 m = 50 kN/m.
The longitudinal stiffness of the fastenings is summarized in Table I.
Table II summarizes the results obtained in case of a ballast resistance of
5 N/mm/rail, and Table III indicates those with 9 N/mm/rail of ballast resistance.
Table II
Maximum normal forces in case of bridge with ballasted track and expansion length of 40 m,
ballast resistance of 5 N/mm
Longitudinal rail
restraint per
fastening [kN]
Maximum normal force [kN]
Bridge structure Fixed bearing CWR track
10.47 ±200 ±200 +1861/-1614
12.56 ±200 ±200 +1862/-1616
16.58 ±200 ±200 +1867/-1621
20.52 ±200 ±200 +1871/-1624
30.00 ±200 ±200 +1879/-1632
Table III
Maximum normal forces in case of bridge with ballasted track and expansion length of 40 m,
ballast resistance of 9 N/mm
Longitudinal rail
restraint per
fastening [kN]
Maximum normal force [kN]
Bridge structure Fixed bearing CWR track
10.47 ±359 ±359 +1557/-1311
12.56 ±359 ±359 +1560/-1314
16.58 ±359 ±359 +1568/-1322
20.52 ±359 ±359 +1572/-1325
30.00 ±359 ±359 +1578/-1331
It can be concluded form Table II and Table III that with increasing ballast
resistance the internal normal forces will be higher in the beam representing the bridge
and in the bearing and will be lower in the rail. It has also been obtained that the lower
the rail restraint is the lower the normal forces are in the rail.
Normal internal forces were also determined in case the railway track superstructure
is constructed with wooden sleepers and the sleepers are directly fixed to the bridge
structure without any ballast bed. The normal internal forces in this case have been
obtained to be remarkably higher than in case of a ballasted superstructure. Taking these
values into consideration and the maximum limit values of 3000 kN of braking force
per one rail, Table IV summarizes the maximum permissible normal forces [12].

72 H. PAPP, N. LIEGNER
Pollack Periodica 11, 2016, 2
5. Railway bridges with expansion length greater than 40 m
An expansion joint has to be constructed between the ballasted CWR track and the
bridge if the expansion length of the bridge is greater than 40 m and as a consequence
the bridge can change its length due to change of temperature, however the longitudinal
forces resulting from braking of the trains whose maximum value is ±3000 kN on one
rail according to standard of Eurocode 1991-2 have to be taken on by the fixed bearing
of the bridge.
Table IV
Maximum permissible normal forces
Structure Maximum permissible normal force
Fixed bearing +3000 kN -3000 kN
Bridge structure +3000 kN -3000 kN
CWR track +2009 kN -1761 kN
Computations have been done to determine the normal forces in the rail, in the beam
representing the bridge and fixed bearing with the assumption that the rail expansion
joints are omitted at both ends of the bridge with an expansion length of 70 m and
100 m.
5.1. Railway bridges with expansion length of 70 m
The results of the computations carried out on bridges with expansion length of
70 m without any rail expansion joints are summarized in Table V.
Table V
Maximum values of normal forces in case of bridges with expansion length of 70 m without any
rail expansion joints, ballast resistance of 5 N/mm/rail and 9 N/mm/rail
Ballast
resistance
Longitudinal rail
restraint per
fastening [kN]
Maximum normal force [kN]
Bridge structure Fixed bearing CWR track
5 kN/mm
10.47 ±350 ±350 +1883/-1636
16.58 ±350 ±350 +1898/-1652
20.52 ±350 ±350 +1903/-1657
30.00 ±350 ±350 +1909/-1663
9 kN/mm
10.47 ±629 ±629 +1729/-1482
16.58 ±629 ±629 +1745/-1499
20.52 ±629 ±629 +1751/-1505
30.00 ±629 ±629 +1761/-1515
Based on the values of Tables V, the normal forces in the rail, the bridge and the
fixed bearing are lower than the maximum permissible forces summarized in Table IV.

INTERACTION OF CWR TRACKS AND STEEL RAILWAY BRIDGES 73
Pollack Periodica 11, 2016, 2
Increasing the expansion length from 40 m to 70 m will result in an excess force in the
rail of 1.5% in case of 5 N/mm of ballast resistance and 13% in case of 9 N/mm ballast
resistance. The longitudinal rail restraint hardly influences the normal forces.
Continuously welded rail track can be constructed through bridges with ballasted
track and an expansion length of 70 m without rail expansion joints even if the rail
fastening has got a longitudinal rail restraint of 30 kN that will result in a specific rail
resistance of 30 kN/0.6 m = 50 kN/m. The normal forces in this case will be less than
those in Table IV. In case of an expansion length of 70 m, the rail expansion joints can
be omitted.
5.2. Railway bridges with expansion length of 100 m
The results of these calculations carried out on bridges with expansion length of
100 m and without any rail expansion joints are summarized in Table VI. It can be
determined that with the application of a rail fastening with a rail restraint of 50 kN, the
normal internal forces will not exceed the permissible values.
Table VI
Maximum values of normal forces in case of bridges with expansion length of 100 m
without any rail expansion joints, ballast resistance of 5 N/mm and 9 N/mm
Ballast
resistance
Longitudinal rail
restraint per
fastening [kN]
Maximum normal force [kN]
Bridge structure Fixed bearing CWR track
5 kN/mm
10.47 ±500 ±500 +1918/-1671
16.58 ±500 ±500 +1934/-1687
20.52 ±500 ±500 +1939/-1693
30.00 ±500 ±500 +1948/-1702
9 kN/mm
10.47 ±899 ±899 +1870/-1623
16.58 ±899 ±899 +1890/-1644
20.52 ±899 ±899 +1898/-1652
30.00 ±899 ±899 +1911/-1665
Continuously welded rail track can be constructed through bridges with ballasted
track and expansion length of 100 m without rail expansion joints if the rail fastening
has got a longitudinal rail restraint of 30 kN, supposing that ballasted CWR track is
joined at both ends of the bridge. In these cases rail expansion joints can be omitted.
6. Conclusions
Research has been carried out with the purpose to find technical solutions to
construct continuously welded rail through bridges with expansion length of greater
than 40 m without interruption that joins ballasted CWR tracks at both ends. The
maximum permissible normal forces have been determined in the structural elements.
It has been obtained that if the expansion joints are omitted at both ends of a bridge
with ballasted track and the expansion length of the bridge is 100 m, the normal forces

74 H. PAPP, N. LIEGNER
Pollack Periodica 11, 2016, 2
in the modeled structural elements will not exceed those force generated in a bridge
with an expansion length of 40 m and with wooden sleepers directly fastened to it.
It can be concluded that a ballasted track is more advantageous in respect of track-
bridge longitudinal interaction than a bridge with wooden sleepers directly fastened
to it.
Based on the developed calculations the rail expansion joints can be omitted and the
CWR track can be constructed through a bridge without being interrupted up to an
expansion length of 100 m in case of ballasted bridges. Lower internal forces will be
generated from longitudinal loads than in case of a bridge with wooden sleepers with an
expansion length of 40 m.
Acknowledgements
This work has been undertaken as a part of the 11
th
Miklós Iványi International
PhD & DLA Symposium held at the Faculty of Engineering and Information
Technology, University of Pécs.
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