1

Preliminary Design of a Bowstring tied-arch deck

Pedro Pereira Clemente Andrade Gonalves

October 2012

ABSTRACT

The present study aims the Preliminary Design for a Bowstring tied-arch solution for a bridges

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

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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).

Its 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

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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 doesnt 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

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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 decks 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.

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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

Exposicin in Valencia or Pont de

lObservatoire in Lige (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 lObservatoire 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 its

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 hangers 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

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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 arent 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 cant be too high

(below 200 mm).

Table 5.1 Axial loads on the hangers

Nperm Nsob

Nk+ Nk

- NRd N

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, its 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.

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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, well apply a live

loading to the deck slab (defined as 5kN/m2,

corresponding to LM4 [7]

), running a buckling

analysis to achieve a factor , 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 factors and respective critic loads

Position 1 2 3 4 5 6 7

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 doesnt

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 (s = 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 its 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

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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,

its 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 its obvious the beauty of this

kind of solutions, the crossed arch wasnt 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] Hajs, B., Halsz, L., Kara, K., Magyari, L.,

Rasztik, R., Sitku, L., Tth, E., Trger, H. (2008)

Bridges in Hungary From the Roman heritage

until todays giants, Budapest: Katalin Kara e

Ern Tth Deng (translated by gnes 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

Szkely)

[3] CEN: European Committee for Standardization.

(2005). Eurocode 3 - Design of steel structures -

Part 1-1: General rules and rules for buildings

(version consulted Eurocdigo 3 Projecto de

estruturas de ao Parte 1-1: Regras gerais e

regras para edifcios) - 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 Eurocdigo

3 Projecto de estruturas de ao 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]