Sven Snauwaert Steel railway bridges with one central arch

247 Pages·2017·8.43 MB·English

Steel railway bridges with one central arch
Sven Snauwaert
Supervisors: Prof. dr. ir. Hans De Backer, Prof. ir. Bart De Pauw
Counsellor: Dr. ir. Dries Stael
Master's dissertation submitted in order to obtain the academic degree of
Master of Science in Civil Engineering
Department of Civil Engineering
Chair: Prof. dr. ir. Peter Troch
Faculty of Engineering and Architecture
Academic year 2016-2017

Steel railway bridges with one central arch
Sven Snauwaert
Supervisors: Prof. dr. ir. Hans De Backer, Prof. ir. Bart De Pauw
Counsellor: Dr. ir. Dries Stael
Master's dissertation submitted in order to obtain the academic degree of
Master of Science in Civil Engineering
Department of Civil Engineering
Chair: Prof. dr. ir. Peter Troch
Faculty of Engineering and Architecture
Academic year 2016-2017
Acknowledgement
During this master dissertation I was able to enrich myself in a technical way as well as in a personal
way. I was lucky enough to work with bridges as a subject which is a dream topic for a lot of Civil
Engineers, and the admiration of these civil artworks stayed with me throughout the whole research.
However, sometimes it was hard to find a real defined end goal of this thesis, which made me from
time to time at a loss to know how to proceed. Although the process of executing the numerous
amount of simulations and data gathering was time consuming. The realisation of this report does
make me happy and proud. Nevertheless, I would not have been able to complete it without help.
Therefore I would like to thank some people who made the realisation of this dissertation possible.
Firstly I would like to thank Prof. dr. ir. Hans De Backer and Prof. ir. Bart De Pauw to give me the
opportunity to do this master dissertation for which I craved since the subjects were made available.
As well as the TUC RAIL company which provided the subject to the University of Ghent.
Thank you.
Secondly I want to thank both professors as well as Prof. dr. ir. Philippe Van Bogaert for the remarks
and guidelines during the interim presentations throughout the academic year. Although professor Van
Bogaert was actually not related to my dissertation, he did show his interests and shared his opinions
and ideas. These critical views were appreciated and allowed me to create a different point of
perspective on several aspects. Furthermore, they made it more clear to me on which elements I could
focus and go more into detail. In short, this feedback was very helpful and made it possible to make
this dissertation a better work.
Thank you.
Also, I want to thank professor De Pauw additionally to keep in contact with me despite of his busy
schedule. I realize that answering my é-mails and questions was an extra task added to your
professional and teaching activities. Therefore I want to show my gratitude.
Thank you.
Furthermore I would like to thank Dr. ir. Dries Stael to help me anytime I had questions or problems.
He was able to help in solving the struggles I had and comforted me when I had certain doubts about
the work I did. When I was stuck at a certain point, he provided me with new possible ideas. Also the
creation of the models and the simulations with the software program SCIA Engineer were not
possible without him. Although Dries did not need to be at the campus in Zwijnaarde for personal
business, he came anyway when I asked to. I know you have a lot of other activities going on. Hence,
I want to show my appreciation for the time you made free and the efforts you did to help and advise
me.
Thank you.
Lastly I want to thank my parents to give me the possibility to start my Civil Engineering studies and
provide me the support anytime I needed. Even throughout the difficult and stressful times over the
years they were there for me, irrespectively of their own problems. I also want to show my gratitude to
my brother who is closest to me and makes me laugh and comforts me anytime I need it. This helped
me to maintain the positive spirit, certainly while doing my master dissertation.
Thank you
De auteur geeft de toelating deze masterproef voor consultatie beschikbaar te stellen en delen van de
masterproef te kopiëren voor persoonlijk gebruik. Elk ander gebruik valt onder de bepalingen van het
auteursrecht, in het bijzonder met betrekking tot de verplichting de bron uitdrukkelijk te vermelden bij
het aanhalen van resultaten uit deze masterproef.

The author gives permission to make this master dissertation available for consultation and to copy
parts of this master dissertation for personal use. In the case of any other use, the copyright terms
have to be respected, in particular with regard to the obligation to state expressly the source when
quoting results from this master dissertation.

June 2nd, 2017
Abstract

Steel railway bridges with one central arch
Author: Sven Snauwaert
Supervisors: Prof. dr. ir. Hans De Backer, Prof. ir. Bart De Pauw
Counsellor: Dr. ir. Dries Stael
Master's dissertation submitted in order to obtain the academic degree of Master of Science in Civil
Engineering.
Department of Civil Engineering
Chair: Prof. dr. ir. Peter Troch
Faculty of Engineering and Architecture
Academic year 2016-2017

Summary: No research has yet been done for steel (railway) bridges with one central arch. Such kind
of bridges would allow to create more aesthetically pleasing constructions as well as possibly more
economically ones. Therefore a parameter study will be done to create an idea of the possibilities of
this bridge type. To be able to do the intended study, a short literature research is done as well as a
determination of the different loads and load combinations to be considered according to the
Eurocode. The start-up of the parameter study consists of a three arched bridge designed by TUC
RAIL which functions as intermediate step between the classic tied arch bridges and the one arched
bridge. Hence, the first step is modelling the three arched bridge in the software program SCIA
Engineer. It can be noted that the design has a skewed deck. However, also a straight deck model is
made as the skewness already induces another behaviour of the bridge. Secondly a study is done for
the main parameters of this bridge once the model is ready. In this way an idea of the influence of
each parameter is obtained and the found results are partly compared with what is found in literature
for general steel tied arch bridges. These simulations are done to be able to do a comparison in the
later stage of the research with the results found for the bridge with one central arch. In a third step it
is wanted to know how the parameters influence each other. This is done as a design mind set for the
three arched bridge with each time maintaining the most optimal situation of the parameters. While for
the one arched bridge a combination of two parameters is each time done relative to the base model.
At the end of each of these chapters the general found conclusions are presented. The dissertation is
finalized with a comparison between the three arched bridge and the bridge with one central arch.
Followed by a short discussion of how the research can be consulted.
Keywords: Central arch, stiffness, arch rise, buckling, stress
Steel railway bridges with one central arch
Sven Snauwaert
Supervisor(s): Dr. ir. Dries Stael, Prof. ir. Bart De Pauw, Prof. dr. ir. Hans De backer
Abstract: A parameter study is done with the purpose of with one central arch. The results of the simulations are
gaining more information about steel railway bridges with one gathered and a deeper look is given into them to try to explain
central arch. This is done by starting with a three arched bridge the different bridge behaviours. Each time several conclusions
design by TUC RAIL, modelled in the software program SCIA are obtained at the end of the different parameter study parts
Engineer, which functions as an intermediate situation between a and these are given here.
classic tied arch bridge and a bridge with one central arch.
Furthermore, also a model for the one arched bridge is created.
II. LITERATURE STUDY - INFLUENCING PARAMETERS
Subsequently the most determining parameters are varied for
both types of bridges. This study is done for the parameters A short literature study is done at first, as mentioned before.
individually as well as a simultaneously variation of some. With And in this way a list of parameters to be simulated is found.
the latter to check whether the influence due to a certain
parameter on the bridge behaviour is altered by another one.
 Deck skewness angle
The results are discussed and explanations for different
 Central arch shape
behaviours are looked for.
 Arch rise to bridge span ratio (central and outer)
Keywords: Central arch, stiffness, arch rise, buckling, stress
 Arch moments of inertia I (central and outer)
z
I. INTRODUCTION  Central girder moment of inertia Iy
 Outer girder moment of inertia I
The classic tied arch bridge with two outer arches which are y
 Bridge length
laterally connected, is already widely used. However, the use

of a steel (railway) bridge with one central arch can introduce
These parameters are modified throughout the different
an aesthetically more pleasing view and possibly reduce the
simulations for the three arched bridge. Those which are still
cost of the bridge. Though, no research has yet been done for
possible to vary for the bridge with one central arch are
this kind of bridges. Therefore a parameter study is conducted
simulated as well in those models.
to create a general idea of the behaviour of this type of
It should be noted that the choice of which moment of
bridges.
inertia is varied is based on the most susceptible situations
A short literature study for tied arch bridges in general
found in literature. An idea of the tubular cross-sections used
results in the collection of the most determining parameters of
for both the arches and the girders is given in Figure 1.
the bridge model.
The study is started, based on a steel bridge design made by
TUC RAIL. This bridge has a steel orthotropic deck which
has a 45° skewness angle. The length is 48,3 m and a
perpendicular width of 18 m is considered to provide space
for three railway tracks. There are furthermore two outer
arches with a rise of 5 m and one larger central arch of which
a height of 8,74 m is present. This is used as start-up to have
Figure 1: Tubular cross-section for the arches and the girders
an idea of the behaviour of this intermediate type between
lateral braced tied arch bridges and bridges with one central
III. MODEL - LOADS
arch. No bracings are present anymore, but the outer arches
induce a stabilizing function on the total bridge behaviour.
A. SCIA Engineer model
First the implementation of the three arched bridge in the
software calculation program SCIA Engineer is realized. The base model which will be used as start for each
Secondly a study is done for the individual parameters of parameter variation is obtained in different steps.
this bridge. Which is executed for a model with a straight First a skewed deck is created as a single 2D ribbed slab
deck and also for one which keeps the skewed deck from the element in SCIA.
TUC RAIL model. The consideration of both is done due to Next the arches are modelled. These were initially built up
the fact that the skewness of the bridge deck will have an as piecewise linear elements between the hanger summits for
influence. Furthermore, it should be mentioned that there will ease of calculations in SCIA. However, these linear elements
be looked to the global behaviour of the bridge during the caused stress peaks at the transition points between the
study. And the variations of the parameters will be considered different parts. Which induced the need for smooth elements
relative to the base models. anyway.
Next a combined variation of several parameters is done to Thirdly the hangers connecting the arches and the
look for possible different induced behaviours of the bridge. orthotropic deck/longitudinal girders are modelled. Their
Lastly the outer arches are removed from the model and height is determined in a way that the arch going through their
combined parameter simulations are done for the steel bridge summits forms a parabolic shape. A short check for the
stresses in the hanger elements shows almost only tension. IV. PARAMETER STUDY - THREE ARCHED BRIDGE
Hence, the traditional tied arch behaviour is approximated
quite well, which approves the model. A. General
The longitudinal girders are added subsequently, and these
The different parameters mentioned earlier are now varied
form the tension ties between the arch springs for the different
for the straight and skewed three arched bridge base model.
arches. A visualisation of the three arched bridge base model
To have a good idea of the global behaviour of the bridge,
is given in Figure 2. The following elements can be found
several variables are checked for each simulation. An
when looked in the positive y-direction. There is the first outer
overview of the latter is given below.
arch, followed by one railway track and then the central arch.

Next there are two railway tracks and eventually the second
 Maximum central arch compression stress [MPa]
outer arch can be seen. Figure 3 shows the bridge with one
 Buckling check of the central arch [-]
central arch situation.
 Maximum outer arches compression stresses [MPa]
Lastly the discussion of the boundary conditions can be
 Buckling check of the outer arches [-]
done. It is chosen to set the rotations around al axes free at
 Maximum outer girders tension stresses [MPa]
both abutments. The translations at the left supports are all
 Maximum central girder tension stress [MPa]
fixed. While the one in the longitudinal direction is modelled

freely at the other abutment. It should be noted that a line
The stresses obtained from SCIA will be the principal ones
support along the whole edge is used instead of only at each
and the buckling checks will be presented by a buckling
longitudinal girder. However, simulations showed only small
coefficient given by the software.
differences in the results for the line and point support
For the ease of discussion the abbreviation "StD" is used for
situations.
the straight deck situation, while "SkD" indicates the skewed
deck model.
B. Deck skewness angle
The deck skewness angle has a decreasing influence on the

Figure 2: SCIA Engineer base model for the three arched bridge compression stress in the central arch from 45° onwards to
larger angles, more skewed deck. The same can be said for the
buckling coefficient of the arch. Also the central girder feels
this beneficial influence. However, the variables checked in
the other elements are only slightly influenced
C. Shape of the central arch
Figure 3: SCIA Engineer base model for the bridge with one central
It is clear that a parabolic shape of the arch has a beneficial
arch
behaviour relative to a circular shaped arch.
B. The loads
D. Central arch rise to span ratio (RTS)
The appropriate loads to which the bridge is subjected have
The central arch rise to span ratio variation shows an
to be determined before the simulations with the created
interval in which the stability of the central arch has an
models can be done properly. These are found by applying the
optimum around a ratio of 0,18-0,25, see cross-section two in
Eurocode documents. [1],[2]
Figure 4. The smaller the buckling coefficient, the more stable
The permanent loads given below are all directed vertical.
the arch is. Furthermore, the straight deck is less favourable
 Self weight of the elements for the central arch buckling coefficient than the skewed deck.
 Self weight of the train tracks and supporting ballast
Buckling check of the central arch
The variable loads are however directed along all three main
axes. These are varied in location and combined in a way that 2,0
tlhatet emr ioss dt odneete brmasiendi nogn ltohaed r ucloems binin tahteio Enus rcoacno dbee. Acrne aotveedr.v Tiehwe [ tn-] 11,,68
e1,4
of the considered loads is given: ic
 Vertical train traffic load - Load Model 71 iffeoc11,,02
g0,8
 Traffic induced traction and brake loads n
ilk0,6
 Temperature induced loads (ΔTD = 35 K) cu0,4
 Wind load in the y-direction B0,2
0,0
It should be mentioned that the variable loads related to 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8
train traffic are multiplied with a classification factor of 1,2 Central arch rise to span ratio [-]
for the considered bridge. This is because it is part of the train
Cross-section 1 Cross-section 2 Cross-section 3
traffic connection between Bruges and the harbour of
Cross-section 4 Cross-section 5
Zeebruges. Hence, the trains which will cross this bridge are
more heavy than the traditional cases considered in the
Eurocode. Figure 4: Buckling check of the central arch in function of the central
arch rise to span ratio (StD)
The following chapters contain the conclusions obtained
throughout the different parameter studies.
The same progress can be seen for the compression stress in in cross-sections induces a decrease in compression stress and
the central arch, be it that the optimum interval is shifted a smaller increase in stress once the optimum rise is exceeded.
somewhat to the larger rise to span ratio values of 0,35-0,45. No large differences could be noted for the other variables
The outer arches as well as the outer girders do not feel the when a simultaneous variation of the central arch parameters
influence of the variations in the central arch rise. is done.
While the tension in the central girder shows a slight
decrease at first which is followed by an increase as the rise to G. Outer arch moment of inertia I
z
span ratio increases. The optimum is found around a ratio of
A decrease in the compression stress in the outer arches is
0,452 which approximately corresponds with the optimal
created when their I is increased. The buckling coefficients
z
ratios for the central arch compression stress.
show some random jumps at first. Which is due to the fact that
the self weight of the cross-sections becomes larger, while the
E. Central arch moment of inertia Iz stiffness around the y-axis is kept quasi constant. This is
An increasing central arch moment of inertia induces a solved by varying the height of the arch cross-sections
decrease in buckling susceptibility of the central arch towards accordingly with their width. A decreasing buckling
an asymptote, see Figure 5. The horizontal axis on the figure susceptibility of the outer arches can then be found as their
shows the ratio of the moment of inertia of the considered cross-section increases. Both variables seem, just like for the
cross-section relative to the initial one in the base model. central arch where its cross-section was changed, to go to an
asymptote for large cross-sections.
Buckling check of the central arch
The central arch does not show variations in its checked
variables due to a change in outer girder cross-section. This is
1,4
[ tn-] 1,2 sohuotewr n airnc hF igcurores s6-,s ewchtieorne. thAe lSsoT Sn oca scehsa inngdeics atien a lvoanrgiiattuiodnin ianl
e1,0
iciffe0,8 girder tension stress are found.
oc g0,6 Buckling check of the central arch
n0,4
ilk
cuB00,,02 [ tn-] 00,,67
0 100 200 300 400 500 600 eic0,5
Central arch moment of inertia Iz ratio [%] iffe0,4
o
Straight deck Skewed deck c g0,3
Figure 5: Buckling check of the central arch in function of the central nilkcuB00,,12
0,0
arch moment of inertia I ratio
z 0 20 40 60 80 100 120
Also the compression stress shows this kind of decrease, but Rise to rise ratio [%]
in a less pronoun way.
STS 25 STS 50 STS 75 STS 100
The outer arches do not feel an influence of the increase in
central arch cross-section. Their compression stress as well as
Figure 6: Buckling check of the central arch in function of the outer
their buckling coefficient remains quasi constant. Also the
arch rise to central arch rise ratio for different outer arch cross-
tension stress in the longitudinal girders does not vary.
sections (StD)
F. Simultaneous variation in central arch rise to span ratio
H. Outer arch rise to span ratio
and central arch moment of inertia I
z
The second outer arch shows a decrease in its compression
The conclusion for the variation of the rise to span ratio
stress as the outer arch rise increases. While much less
influence on the stability of the central arch is valid
influence can be found for the compression stress in the first
throughout the simultaneous variation of the central arch
outer arch.
cross-section. However, a horizontal curve is more and more
Both arches show furthermore a decrease in buckling
seen for both decks as the cross-section increases. Which
coefficient, but the advantageous influence is not that large.
indicates that the central arch rise variation has less and less
A decrease towards an asymptote can be seen for the
influence on the central arch stability.
buckling check and the compression stress verification of the
The whimsical behaviour of cross-section four in Figure 4,
central arch, see Figure 6. The asymptote is reached around
is due the increase in cross-sectional self weight, while the
the 50% situation. This shows that a higher outer arch rise to
resisting moment of inertia I against this load is kept quasi
y central arch rise ratio than 50% does not come with any
the same. Therefore cross-section five is introduced. Its cross-
benefits anymore in possible reduction of the central arch
sectional width to height ratio is the same as for the initial
cross-section
cross-section. Hence, the same relative moment of inertia as
The other elements do not show an influence. However, the
cross-section four is used, but with a larger stiffness around
influence of totally removing the outer arches shows a large
the y-axis. It should be noted that the influence of this
disadvantageous peak in all of the checked variables.
different buckling behaviour is less pronoun present for the

skewed deck.
A simultaneous variation of the outer arch rise and outer
The same decreasing-optimum-increasing behaviour is
arch cross-sectional moment of inertia I does not lead to a
present for the compression stress in the central arch, for each z
change in behaviour of the different elements relative to the
cross-section as the rise to span ratio increases. The increase
individual parameter variations.
I. Central girder moment of inertia I Compression stress in the central arch
y
An increase in stiffness around the y-axis of the central For the StD an optimum in compression stress is present for
girder induces a stabilizing effect on the central arch as well the rise to span ratios of about 0,35-0,45. Just like for the three
as a reduction of the compression stress in it. This is however arched bridge. The decrease in stress between the most severe
only valid if a very large increase in moment of inertia is situation and the optimum is about 60%.
realized. To give an idea, an increase of about 1200% in I A different behaviour is noticed for the skewed deck. Over
y
relative to the initial situation caused a decrease in buckling there a decrease for the smaller rise to span ratios can be seen
coefficient of about 10% and 15% for the compression stress. and from a ratio of about 0,352-0,452 onwards, an asymptote
The other elements do not show variations. Except for the can be found, see Figure 7. Over here the downward jump
central girder itself which feels a decrease in tension stress as from the largest compression stress to the value for the
its cross-section increases. asymptote is about 40%.
Compression stress in the central arch
J. Outer longitudinal girder moment of inertia I
y
Some small drops can be seen in the buckling check and ]a 455000
compression stress verification of the arches. But other than P
M400
that no influence is seen, except in the tension stress in the [ s350
s
outer longitudinal girders themselves. This stress decreases er300
towards an asymptote as their cross-section increases. ts n250
ois200
se150
A simultaneous variation in both the outer and central r
p100
m
longitudinal girders did not induce any changes from what is o 50
C
told above. The conclusion found in literature about the axial 0
longitudinal girder stiffness not having a large influence on 0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8
the general bridge behaviour is therefore confirmed. Central arch rise to span ratio [-]
STS Iy 44 STS Iy 100 STS Iy 166 STS Iy 221
K. Bridge length

Large differences in the compression stresses as well as the Figure 7: Compression stress in the central arch in function of the
buckling coefficients can be seen. A decrease in bridge length central arch rise to span ratio for different outer girder cross-sections
shows a more beneficial situation for the three arches. Also (SkD)
the tension stresses in the outer girders follow this
Tension stress in the outer longitudinal girders
advantageous progress.
The variation in central arch rise to span ratio does not
induce a variation in the tension stress in the outer girders in
V. PARAMETER STUDY - BRIDGE WITH ONE CENTRAL ARCH both bridge models.
The outer arches are now removed and a parameter study is
done on the bridge with one central arch. The same geometry Tension stress in the central longitudinal girder
and cross-sections are kept furthermore, so the values of the The tension stress in the central longitudinal girder for the
variables increase as there are less load bearing elements StD decreases when the rise to span ratio increases with an
present. Four parameters are actually left to be varied, see asymptote from a rise to span ratio of about 0,362 onwards.
paragraphs A to D which follow, and each time two of these For a small outer girder cross-section, no asymptotic zone is
were simulated together. Below, the influence of each present, but a crescent decrease in tension stress can be found.
parameter on the checked variables is discussed. If the general For the skewed deck an optimum is present for the tension
induced behaviour is altered when another parameter is stress in the central longitudinal girder, see Figure 8. This
simulated simultaneously, then this will be mentioned. The occurs around a rise to span ratio of 0,20 which corresponds
mentioned general behaviour concerns the situation for the with the optimum for the buckling check of the central arch.
base model for which one parameter is varied.
Tension stress in the central girder
A. Central arch rise to span ratio
500
Buckling check of the central arch 450
An optimum can be seen for the rise to span ratios of about ]aP 400
M350
0,18-0,25 for the buckling coefficient of the central arch. This [ s300
is valid for both the StD and the SkD and was also found for ser250
the three arched bridge. ts n200
o
Both decks show a decrease of the influence of the rise to is150
n
span ratio as the central arch cross-section increases. For large eT100
50
cross-sections almost no variation in buckling coefficient can
0
be seen for a variation in rise to span. Also, when the outer
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8
girder cross-section is increased, the influence of varying the Central arch rise to span ratio [-]
central arch rise to span ratio decreases. So the optimum is
less emphatically present. Lastly, the increase in central girder STS Iy 44 STS Iy 100 STS Iy 166 STS Iy 221
moment of inertia induces smaller influences of the rise to
span ratio variations for the SkD. Figure 8: Tension stress in the central longitudinal girder in function
of the central arch rise to span ratio for different outer girder cross-
sections (SkD)