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Preliminary Design of a Bowstring tied-arch deck
Pedro Pereira Clemente Andrade Gonçalves
October 2012
ABSTRACT
The present study aims the Preliminary Design for a Bowstring tied-arch solution for a bridge’s
deck.
A research about the historical context and construction methods of tied-arch bridges was
initially conducted, and a data base with an extensive list of the constructed Bowstring bridges up to
date was assembled, with the compilation of the i) general layout information, ii) geometric
characteristics and iii) main steel / concrete quantities.
A Preliminary Study of several Bowstring deck solutions was performed, as alternative solutions
for a real highway double box-girder bridge deck erected by the balanced cantilever method, in order
to choose one of them, to perform the deck pre-design.
The pre-design of the deck was then performed, namely the deck slab, the steel girders, the
steel arch and the hanger sections, as well as the installed forces.
The required and relevant safety verifications were performed at Preliminary Study level,
supported by a tridimensional structural analysis model, using the software SAP2000.
To finish, main quantities and estimated cost were evaluated for the proposed deck, solution
and a comparison of these results with other Bowstring tied-arch bridges and with the erected
box-girder bridges was performed.
Conclusions about the advantages and disadvantages of the proposed solution were finally
discussed.
Keywords: tied-arch bridges, Bowstring bridge, hangers, bridge design, deck analysis, arch instability
2
1. INTRODUCTION
Bridges have always been considered
as “works of art” in the Structural Engineering
domain. Amongst them, bridges with “upper
arch” highlight for their first-class aesthetics.
Numerous tied-arch bridges have been
designed and built over the last 50 years,
many of the Bowstring type. The term
“bowstring” is the outcome of the actual
behaviour for this kind of balanced structures.
The upper arch “bow”, always strongly
compressed, is internally balanced by the
tensioned deck, which works as a “string”.
From the conjugation of the two elements,
results the Bowstring tied-arch deck.
One of the forerunners of this solution,
Norwegian Engineer Per Tveit, proposed to
join the “Net” suspension system
(characterized by the crossed hangers
disposed in “net” arrangement). Since his first
built bowstring bridge deck in Steinkjer,
Norway, in 1963, to the astonishingly light and
slender Bolstadstraumen Bridge, 60 km
northwest of Bergen, Norway (Figure 1.1),
numerous decks of this type were design and
built.
Figure 1.1 – Bolstadstraumen Bridge in Norway
Similarly, in the railway bridges domain,
Bowstring tied-arch bridges have several
advantages and therefore have been design
and constructed. Although less slender than
motorway bridges of the same type, this kind of
decks allow spans higher than 100 m, without
the need of intermediate supports, and with a
sufficient stiff deck. Several railway decks,
namely for the high-speed railway networks in
Europe, China and Korea and Japan have,
therefore, adopted Bowstring tied-arch decks.
Also in Portugal, this kind of bridges has
been built throughout the years. Maybe the
major example is the recently opened to traffic
railway crossing of the Sado River (Figure 1.2).
It’s a unique structure, which combines two
railway lanes with a 480 m long continuous
composite box-girder deck, suspended by
three central arches of 160 m spans.
Figure 1.2 – Bridge over Sado River in Portugal
In the highway bridges domain several
recent structures were recent completed, for
small overpasses spans, to long span highway
river crossings. Two recent examples consist
of the Depot Street Bridge, concluded in the
USA in 2006, for crossing the Rogue River [1]
,
and the Pentele Bridge, concluded in Hungary
in 2007, for crossing the Danube River by the
new M8 Highway [2]
.
The first one presents a reinforced concrete
deck and arch, with lateral inclined Net
suspension and a 93 m span, as the second
has an orthotropic deck slab and a steel arch,
with lateral suspension and a 308 m span,
which evidence the potentialities of this kind of
3
structural solutions for medium spans, as for
spans longer than 300 m.
2. OBJECTIVES
The main purposes identified for this
study, in order to carry out a Preliminary
Design of a Bowstring tied-arch bridge deck,
were the following:
Development of a data base including
the Bowstring tied-arch bridges
worldwide;
Preliminary study of multiple structural
solutions for this kind of construction,
and pre-design of the main structural
elements;
Study of the deck behavior for the
design actions, according to the
Eurocodes;
Obtain the main deck quantities and its
estimated cost for the proposed solution,
and compare these results with the
constructed structure and other
Bowstring tied-arch bridges; and
Conclusion assessment resuming
advantages and disadvantages of the
proposed deck solution.
3. BOWSTRING BRIDGES
AROUND THE WORLD
An extensive search has been
conducted in order to characterized every kind
of Bowstring tied-arch bridges that have been
built all over the years, and to built a data base
with extensive technical and geometric
information, such as the main span, the deck
slenderness, the ach height or hanger steel
weight.
The collected data allowed acquiring the
“know-how” to concentrate the information in
some charts that display some relations
between bridge spans, arch heights, function,
deck steel and concrete weight, aiming to
obtain same “state-of-the-art” rules for the
design of a Bowstring tied-arch deck.
Figure 3.1 – Relation between the arch height and
span length
The results of Figure 3.1 enables to
conclude that there is an increasing arch
height and approximately linear with the span,
and that it doesn’t matter in a significantly way,
if it concerns to a highway or railway bridge. It
also shows that the higher stiffness of the
deck, which is usually required in railway
bridges, is, in Bowstring decks, achieved
without raising up the arch, but rising the
stiffness of the deck slab, by the increasing the
steel used on hangers, arch sections and deck
girders.
Figure 3.2 – Relation between the total amount of
steel by m2 of deck slab, and the span
0 5
10 15 20 25 30 35 40 45 50 55 60 65
0 50 100 150 200 250 300 350 A
rch
he
igh
t [m
]
Span [m]
Motorway
Railway
High-speed Railway
Motorway/Railway
Motorway/Light Railway
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 50 100 150 200 250 300 350
Tota
l Qu
anti
ty o
f st
ee
l/m
2 o
f d
eck
sla
b [
kg/m
2 ]
Span [m]
Motorway
Railway
High-speed Railway
Motorway/Railway
Motorway/Light Railway
4
Observing the chart that displays the
ratio of the total among of steel used by m2 of
deck slab (Figure 3.2), the quantities of steel
used in a Bowstring solution grows
approximately in a linear way with the span,
but it is not independent of the bridge use,
since highway decks have, in general, less
steel than railway and road/railway decks with
the same span.
4. PRELIMINARY STUDY
The Preliminary Study was based on a
constructed continuous pre-stressed concrete
box-girder deck solution with variable height,
named Bridge over the Sorraia River, in
Portugal, which is part of the A13 highway.
This bridge consists in two separate decks,
with three spans (75 m + 120 m + 75 m) and a
total length of 270 m.
All the studies are planned to substitute
the main span of 120 m, with a Bowstring with
a single deck solution, extending the deck of
the side viaducts to the transition piers.
The deck’s cross section is composed
by four traffic lanes with 3.75 m each; 3.0 m
and 1.0 m for the roadsides, right and left
respectively; sidewalks 1.05 m wide; curbs;
safety guards; fascia beams and drainage
system.
Some of these elements were modified
by the 3D geometry of the hangers in order to
accomplish some regulations, and adopting
one deck instead of two, like adopting a New
Jersey traffic separator for the central
reservation.
4.1. GRAPHIC STUDY
At the beginning of the Preliminary
Study, some sketches were drawn to image
some of the possible ways to raise a Bowstring
tied-arch deck. After analyzing which ones
were viable and physically possible, there was
one which imposed itself for its innovation and
challenging design (Figure 4.1).
Figure 4.1 – Sketches for the proposed solution
Having the layout defined, it was
decided to choose a composite steel-concrete
deck, with a reinforced concrete deck slab,
crosswise steel girder attached on a central
longitudinal steel tube and lateral box-girder
beams, and a steel arch made of a tube with
high diameter and thickness, with interior
diaphragms.
4.2. PRE-DESIGN
Before performing the safety standard
verifications (Serviceability Limit State and
Ultimate Limit State), it was necessary to admit
dimensions for the deck elements (deck slab,
longitudinal and transversal beams, arch and
hangers).
The deck slab 30 cm thick was defined
according to the structural behaviour, use of
the bridge, deck materials and deck width.
5
For the main longitudinal beam it was
used the same tube section of the arch, a CHS
(Circular Hollow Section) with D = 1250 mm
and t = 25 mm, for aesthetic reasons mainly,
and two secondary longitudinal box-girders
beams were set on both cantilever tips, to stiff
the grid steel structure and better redistribute
the hangers forces through the deck.
Figure 4.2 – Transversal girders cross-section
The transversal beams were base on
important works like the Puente de la
Exposición in Valencia or Pont de
l’Observatoire in Liège (Figure 4.3), from the
famous architect Santiago Calatrava, leading
to a maximum and minimum cross-section
presented on Figure 4.2.
Figure 4.3 – Pont de l’Observatoire in Belgium
The chosen cross-section for the arch,
the same as the main longitudinal beam, was a
CHS (D = 2500 mm and t = 80 mm) since it’s
going to be heavily compressed and subjected
to high bending moments in every direction.
The arch height and the hangers were
designed simultaneously due to the fulfilment
of the 5.0 m minimum required gabarit over the
sidewalks kerb. Since there was a maximum
height (1/4 of the span) defined by the study of
other Bowstring cases, 30 m high was the
chosen solution. From that, several designs
were made for the hanger’s geometry, leading
to an inclined Net solution of Figure 4.4.
Figure 4.4 – Geometry of the hangers
4.3. MATERIALS AND ACTIONS
The materials adopted were the
concrete C35/45 for the deck slab; steel
reinforcement bars A500; steel grade
S420 NH/NHL [3]
for all deck girders and grade
S460 NH/NHL [3]
for the arch; and steel S355
or S460 for the hangers.
For every step of the design, the actions
(dead loads, hangers installed forces, live
loads and fatigue) were considered. With all
the permanent actions in play, it is able to
verify the ULS [4]
and fatigue [5]
, as well as the
ULS and stability of the arch.
5. SAFETY VERIFICATIONS
To determine the required area of
reinforcement in the concrete deck slab, the
shell bending moments were obtained by with
a 3D finite beam/shell elements analysis
model. The longitudinal slab cracking was
relevant to the slab behaviour, and a fictitious
6
modulus of elasticity was determined based on
the reinforcing bars rate and the slab
thickness. The cracking thickness was
obtained and is within the standard limits.
Since they aren’t subjected to highly
efforts and the main role is the desirable
behaviour of the deck slab, for the beams,
longitudinal and transversal, safety checks
were performed using simple calculations to
obtain the resisting bending moment,
considering in both cases a composite cross-
section (due to the benefits of the deck slab).
5.1. HANGERS
To obtain the cross-section area for the
hangers the rules regarding the SLS [4]
were
taking into consideration. It was stated that the
hangers cannot be compressed (namely for
the several possible patterns of the live load
action), and imposed as well that the
displacements along the slab can’t be too high
(below 200 mm).
Table 5.1 – Axial loads on the hangers
Nperm Nsob
Nk+ Nk
- NRd ΔN
cp ten sob+ sob-
Hanger [kN]
1 -499 967 371 -393 839 75 2208 1369
2 208 645 227 -217 1080 636 2208 1128
3 753 868 191 -111 1812 1509 2208 396
4 1148 501 300 -56 1949 1593 2208 259
5 1394 227 362 -29 1983 1592 2208 225
6 1512 194 387 -37 2093 1669 2208 115
7 1536 130 385 -40 2051 1625 2208 157
8 1513 -12 362 -26 1863 1474 2208 345
9 1509 288 316 -9 2113 1787 2208 95
10 1618 -97 261 -14 1781 1506 2208 426
11 1977 -347 273 -101 1902 1528 2208 306
12 1897 -631 503 -159 1769 1107 2208 439
13 1126 -603 319 -59 841 464 2208 1367
14 882 192 303 -24 1377 1050 2208 830
15 917 739 319 -53 1975 1603 2208 233
16 1057 256 326 -52 1639 1261 2208 569
17 1192 -92 331 -40 1431 1060 1773 342
18 1241 -357 334 -29 1218 855 1773 555
19 1122 -111 331 -24 1341 987 1773 432
20 761 -83 309 -35 986 643 1773 787
21 143 296 258 -59 697 380 1773 1076
22 -633 963 173 -84 503 246 1773 1270
23 -1207 1344 61 -96 198 41 1773 1575
A computation procedure was performed
with a group of matrixes to relate the influence
of each hanger on the others (Table 5.1). This
allowed finding the tensioning forces (defined
as the axial displacements for the hydraulic
jacks) needed to apply on each of the hangers.
5.2. ARCH
When subjected to bending and axial
force, it’s linearly checked is according to,
(5.1)
A major challenge comes out when
dealing with the stability of the arch, since the
expression used for the safety check should
be:
(5.2)
(5.3)
The interaction factors, the resisting
moments and axial loading, and the reduction
coefficient due to buckling are calculated
according with the EC3 – part 1 [3]
. But, to
obtain the buckling coefficients was necessary
to determine the critic load of the structure,
which was performed loading of the structure
(to obtain the normalized slenderness),
meaning the load that will lead to the first deck
instability.
7
Figure 5.1 – 1st mode of the arch buckling
A group of Belgian engineers [6]
proposed a simple method to obtain that load.
Using a 3D structural model as close as
possible to the real bridge, we’ll apply a live
loading to the deck slab (defined as 5kN/m2,
corresponding to LM4 [7]
), running a buckling
analysis to achieve a factor λ, that will
reproduce the number of times which the
loading pattern needs to increase to cause the
1st mode of instability (Figure 5.1).
That loading pattern is defined by the
Designer, and can correspond to the whole
deck slab area loaded, or just half of it (Figure
5.2) [8]
.
Figure 5.2 – Overloading patterns
Table 5.2 – λ factors and respective critic loads
Position 1 2 3 4 5 6 7
λ 4,594 4,969 5,164 5,194 4,86 5,118 4,966
NEd [kN] -65852 -61021 -56804 -57325 -60722 -57148 -60135
NFE,el [kN] 302526 303215 293333 297745 295111 292482 298632
Note that the smallest factor doesn’t
exactly correspond to the smallest critic load
as shown in Table 5.2.
Verifying the three safety checks, it is
possible to notice that none of them meet the
desirable safety requirements:
To surpass this problem, the answer
goes through modifying the arch cross-section,
by increasing its diameter to the minimum of
3000 mm. Then the same calculation made so
far, has to be redone, ensuring the safety of
the arch.
6. QUANTITIES AND
ESTIMATED BUDGET
The main quantities were evaluated. The
amount of concrete and steel (bars, sections
and pre-stressing), was directly obtained from
the total volume of the deck slab in m3
(concrete), and steel plates and tubes
considering (γs = 78kN/m3). The results are
presented in Table 6.1, Figure 6.1 and Table
6.2.
The estimated budget was based on two
actual budgets: one from the case study, the
other from a general Bowstring tied-arch
bridge. On them it’s possible to retrieve
information about the unitary cost for the
concrete C35/45 and for the different kind and
range of steels.
Table 6.1 – Volume of concrete
Gross area [mm2] Volume Weight
[m3/m] [m3] [kN/m3] [kN] [ton]
7830000 7,83 916 25 22892 2336
8
Figure 6.1 – Quantities of steel in ton
Table 6.2 – Proposed solution estimated budget
Uni Quantity Uni. Cost Total
Concrete C35/45 m3 916 150,00 € 137.354,48 €
Steel bars A500 kg 190252 1,00 € 190.252,34 €
Profiles S420 NH/NLH kg 1429170 5,00 € 7.145.848,36 €
Profiles S460 NH/NLH kg 683652 6,00 € 4.101.914,34 €
Hangers S355 kg 83586 10,00 € 835.858,89 €
Hangers S460 kg 29122 15,00 € 436.829,11 €
12.848.057,52 €
Total Cost = 4100 €/m2
The case study budget is known
rounded up as 2.000.000 €, with a total cost
approximately equal to 577 €/m2 (including
equipment and labor). Comparing to the value
obtained for the proposed Bowstring solution,
it’s around 7 times lower. It was expected to
exceed it, but not by so much. There are some
solutions that could resolve this matter:
Bowstring design with a central arch with
central suspension, or two lateral arches
with lateral suspension;
Reduction of the class of the steel used
in the deck girders;
Reduction of the deck slab thickness.
7. CONCLUSIONS
Although it’s obvious the beauty of this
kind of solutions, the crossed arch wasn’t the
best decision for this case. Nonetheless, it was
a good choice to show that is a viable solution
(regardless the unsuccessful safety checks of
the arch) and maybe the best one in some
cases.
Figure 7.1 – Relation between the arch height and
span length (with solution proposed)
Figure 7.2 – Relation between the quantity of total
steel by m2 of deck slab and span (with proposed
solution)
Both charts show us that the design is
inside the reasonable values: the height of the
arch at the highest level, the quantity of steel
used in a high level, close to the amount used
in railway bridges with similar spans.
8. REFERENCES
[1] Bridgehunter.com | Depot Street Bridge, available in:
http://bridgehunter.com/or/jackson/depot-street/
[23/11/201]
[2] Hajós, B., Halász, L., Kara, K., Magyari, L.,
Rasztik, R., Sitku, L., Tóth, E., Träger, H. (2008)
Bridges in Hungary – From the Roman heritage
until today’s giants, Budapest: Katalin Kara e
Ernő Tóth Deng (translated by Ágnes Koroknai
190 (8%)
843 (35%) 586 (24%)
684 (28%)
113 (5%) Steel bars
Longitudinal girders
Transversal girders
Arch
Hangers Total = 2416 ton
0 5
10 15 20 25 30 35 40 45 50 55 60 65
0 50 100 150 200 250 300 350
Arc
h h
eig
ht
[m]
Span [m]
Motorway
Railway
High-speed Railway
Motorway/Railway
Motorway/Light Railway
Proposed Solution
0
500
1000
1500
2000
2500
3000
3500
4000
4500
0 50 100 150 200 250 300 350
Tota
l Qu
anti
ty o
f st
ee
l/m
2 o
f d
eck
sla
b [
kg/m
2 ]
Span [m]
Motorway
Railway
High-speed Railway
Motorway/Railway
Motorway/Light Railway
Proposed Solution
9
Székely)
[3] CEN: European Committee for Standardization.
(2005). Eurocode 3 - Design of steel structures -
Part 1-1: General rules and rules for buildings
(version consulted Eurocódigo 3 – Projecto de
estruturas de aço – Parte 1-1: Regras gerais e
regras para edifícios) - prEN 1993-1-1, Lisboa:
LNEC
[4] CEN: European Committee for Standardization.
(2005). Eurocode 3 - Design of steel structures -
Part 1-11: Design of structures with tension
components - prEN 1993-1-11
[5] CEN: European Committee for Standardization.
(2005). Eurocode 3 - Design of steel structures -
Part 1-9: Fatigue (version consulted Eurocódigo
3 – Projecto de estruturas de aço – Parte 1-9:
Fadiga) - prEN 1993-1-9, Lisboa: LNEC
[6] Outtier, A., De Backer, H., Schotte, K., Stael, D.,
Van Bogaert, P., (2010) Design methods for
buckling of steel tied arch bridges, LSIECU
[7] CEN: European Committee for Standardization.
(2003). Eurocode 1 - Actions on structures - Part
2: Traffic loads on bridges - EN 1991-2:2003,
Brussels, Belgium: CEN
[8] Tveit, P. (2006) An Introduction to the Network Arch,
available in: http://home.uia.no/pert/backup/
[13/11/2011]
