Comportamiento y diseño de puentes extradosados.pdf

8/10/2019 Comportamiento y diseo de puentes extradosados.pdf

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Behaviour and Design of

EXTRADOSED BRIDGES

by

Konstantinos Kris Mermigas


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Behaviour and Design of Extradosed Bridges

Konstantinos Kris MermigasMaster of Applied Science

Graduate Department of Civil EngineeringUniversity of Toronto2008

ABSTRACT

The purpose of this thesis is to provide insight into how different geometric parameters such as tower

height, girder depth, and pier dimensions influence the structural behaviour, cost, and feasibility of an

extradosed bridge.

A study of 51 extradosed bridges shows the variability in proportions and use of extradosed bridges,

and compares their material quantities and structural characteristics to girder and cable-stayed bridges.

The strategies and factors that must be considered in the design of an extradosed bridge are discussed.

Two cantilever constructed girder bridges, an extradosed bridge with stiff girder, and an extradosed

bridge with stiff tower are designed for a three span bridge with central span of 140 m. The structural

behaviour, materials utilisation, and costs of each bridge are compared. Providing stiffness either in the


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ACKNOWLEDGEMENTS

I would like to thank Professor Gauvreau for the opportunity to study under his guidance and be part ofa dynamic and ambitious bridge research group. Professor Gauvreau has served as an inspiration and

mentor to me in my career.

Thanks to my research colleagues for their insightful discussions and feedback: Mike Montgomery,

Jimmy Susetyo, Ivan Wu, Jeff Erochko, Lydell Wiebe, Brent Visscher, Jamie McIntyre, Lulu Shen, Eileen

Li, Sandy Poon, Davis Doan, and especially Jason Salonga.

Finally, thanks to my family and Mary Jane for encouraging and supporting me through my graduate

studies.


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TABLE OF CONTENTS

ii A BSTRACT

iii A CKNOWLEDGEMENTS

iv T ABLE OF C ONTENTS

viii LIST OF F IGURES

xiii LIST OF T ABLES

1 1 W HAT M AKES A B RIDGE E XTRADOSED ?

1 1.1 Introduction

2 1.2 Objectives and Scope

3 1.3 Historical Context

13 1.4 General Studies on Extradosed Bridges

15 2 R EVIEW OF E XISTING E XTRADOSED B RIDGES

15 2.1 Study of Extradosed Bridges

15 2.2 Trends in Extradosed Bridges to Date


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41 3 D ESIGN AND C ONSTRUCTION OF E XTRADOSED B RIDGES

41 3.1 Loads

41 3.1.1 Live Load

44 3.1.2 Temperature

46 3.2 Design Concepts

46 3.2.1 Stiffness of Cables and Girder

48 3.2.2 Stiffness of Superstructure and Substructure

50 3.2.3 Prestressing Methodology

52 3.3 Conceptual Design

52 3.3.1 Fixity of the Girder to the Piers

53 3.3.2 Side Span Length

53 3.3.3 Tower Height and Girder Depth

56 3.4 Stay Cables and Anchorages

56 3.4.1 Cable Arrangement

60 3.4.2 Stay Cable Protection

60 3.4.3 Anchorages in Girder

61 3 4 4 Cable Anchorage in Towers: Saddles or Anchorages?


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88 4 D ESIGN OF C ANTILEVER C ONSTRUCTED G IRDER B RIDGE , E XTRADOSED

BRIDGE WITH S TIFF G IRDER , AND EXTRADOSED B RIDGE WITH S TIFF TOWER

89 4.1 Design Assumptions

89 4.1.1 Material Properties and Detailing

90 4.1.2 Analysis and Limit States Verification

91 4.1.3 Temperature Gradient

92 4.1.4 Construction Sequence and Segment Construction Cycle

93 4.2 Cantilever Constructed Girder Bridge

93 4.2.1 Layout and Cross-Section

93 4.2.2 Longitudinal Prestressing

96 4.2.3 Verification at SLS and ULS

97 4.3 Extradosed Bridge with Stiff Deck

97 4.3.1 Layout and Cross-Section

98 4.3.2 Longitudinal Prestressing

100 4.3.3 Comparison with Bending Moments in a Girder Bridge

102 4.3.4 Detailed Model

102 4.3.5 Verification at SLS and ULS


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122 D RAWINGS123 CANT-S1. Cantilevered PT Bridge - General Arrangement

124 CANT-A-S2. Cantilevered PT Bridge, Mixed Tendons - P.T. Tendon Duct Locations

125 CANT-A-S3. Cantilevered PT Bridge, Mixed Tendons - P.T. Layout126 CANT-B-S2. Cantilevered PT Bridge, Internal Tendons - P.T. Tendon Duct Locations & Typical

Reinforcement

127 CANT-B-S3. Cantilevered PT Bridge, Internal Tendons - P.T. Layout

128 EXTG-S1. Extradosed Bridge, Stiff Girder - General Arrangement

129 EXTG-S2. Extradosed Bridge, Stiff Girder - P.T. Tendon Duct Locations & Typical Reinforcement

130 EXTG-S3. Extradosed Bridge, Stiff Girder - P.T. Layout

131 EXTT-S1. Extradosed Bridge, Stiff Tower - General Arrangement

132 EXTT-S2. Extradosed Bridge, Stiff Tower - P.T. Tendon Duct Locations & Typical Reinforcement

133 EXTT-S3. Extradosed Bridge, Stiff Tower - P.T. Layout

134 A PPENDIX A Chapter 2 Supplementary Information

139 A PPENDIX B Chapter 4 Supporting Calculations

140 B.1 Girder Bridge Preliminary PT Design A - Mixed Tendons

144 B.2 Girder Bridge PT Design A - Detailed Model SLS Stress Checks

145 B.3 Girder Bridge PT Design A - Detailed Model ULS Moment Capacity Check

146 B 4 Girder Bridge Preliminary PT Design B Internal Tendons


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LIST OF FIGURES

1 1 W HAT M AKES A B RIDGE E XTRADOSED ?

1 1-1 Comparison between cantilever-constructed girder, extradosed, and cable-stayed bridge types.

2 1-2 Finback, cable-panel and extradosed bridge types.

4 1-3 Ganter Bridge (Vogel & Marti 1997)

5 1-5 Barton Creek Bridge (Gee 1991).

5 1-4 Arrt-Darr Viaduct (Mathivat 1988).

6 1-6 Odawara Blueway Bridge (Kasuga 2006).

7 1-7 Saint-Remy-de-Maurienne Bridge (photo by Jacques Mossot, Structurae).

7 1-8 Concept for Usses Viaduct (Virlogeux 2002b).

8 1-9 Santiago Calatravas concepts for crossing deep Alpine valleys. From left to right: Variant 1,

Variant 2 model, Variant 7 sketch and detail presented by Menn at the IABSE Symposium

in Zurich in 1979 (Calatrava 2004).

8 1-10 Response of cable-stiffened, girder-stiffened, and tower-stiffened cable-stayed bridge to live

load.

9 1-11 Poya Bridge, Switzerland: a) Menns 1989 proposal (Menn 1996) and b) cable-stayed design


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30 2-6 Average girder concrete thickness of cantilever-constructed girder, extradosed and cable-stayed

bridges.

30 2-7 Average girder concrete thickness of extradosed bridges.

31 2-8 Mass of steel in cantilever constructed girder bridges: a) longitudinal prestressing steel, and b)

reinforcing steel (plots are based on data from SETRA 2007, Lacaze 2002, DEAL 1999).

32 2-9 Moment of inertia of girder at midspan for extradosed and cable-stayed bridges (per 10 m

width).

33 2-10 Odawara Extradosed Bridge details of tower saddle and arrangement of prestressing bars in

tower from FEM analysis (Kasuga et al. 1994).33 2-11 Odawara Extradosed Bridge: a) strand supply system; b) saddle structure at the pier top, and

c) anchorage structure at the main girder. (Toniyama & Mikami 1994).

34 2-12 Ibi River Bridge Prestressing Tendon Layout in Cross-Section (Kutsuna et al. 1999).

35 2-13 Nonlinear Behaviour of the Ibi River Bridge up to ultimate load (Kutsuna et al. 2002).

35 2-14 Shin-Meisei Birdge construction of side spans (Iida et al. 2002).

36 2-15 Shin-Meisei Birdge a) photo of steel shell of tower; b) elevation of composite tower and c)

details of composite tower (drawings: Iida et al. 2002, photo and rendering: Kasuga 2006).

36 2-16 North Arm Birdge a) deck level extradosed cable anchorage; b) precast tower, and c) tower

anchor segment (from Griezic et al 2006)


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54 3-6 Comparison of span to depth ratio and effect of the roadway height above ground on the overall

proportions of 3 span cantilever, extradosed, and cable-stayed bridges.

55 3-7 Extradosed bridge geometry studied by Chio Cho (2000).

55 3-8 Girder and extradosed bridge proportions recommended by others.

56 3-9 Bridge proportions used for design in Chapter 4.

57 3-10 Effect of cable inclination on the force components in a cable for a) a constant total force and

b) a constant vertical force.

57 3-11 Quantity of cable steel as a function of relative height of towers - Comparison between fan and

harp cable configurations in a) 1970 (Leonhardt & Zellner 1970) and b) 1980 (Leonhardt& Zellner 1980).

58 3-12 Quantity of cable steel as a function of relative height of towers - comparison between semi-

fan and harp cable configurations for 140 m main span.

59 3-13 Influence of partial cable support (adapted from Tang 2007).

61 3-14 DSI Extradosed Anchorage Type XD-E (Dywidag 2006).

65 3-15 Ratio of equivalent to initial modulus of elasticity showing the influence of a cables sag on

its stiffness (plot adapted from Leonhardt & Zellner 1970).

66 3-16 Allowable stress in cable stays as a function of the stress range due to live load at SLS

70 3 17 Cable pre strain and ma im m moments for 25 iterations of the ero displacement method


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77 3-23 Kiso and Ibi River Bridges, Japan (completed 2001): 275 m maximum spans, span to depth

ratio 39 at piers and 69 at midspan, cantilever construction with precast segments lifted with

600 tonne barge mounted cranes, and central 95 to 105 m steel sections strand-lifted from

barges and made continuous (Casteleyn 1999, Kasuga 2006).

77 3-24 Shin-Meisei Bridge, Japan (completed 2004): 122.3 m main span, span to depth ratio 35, cast-

in-place cantilever construction (Kasuga 2006).

77 3-25 North Arm Bridge, Vancouver, Canada (completed 2008): 180 m main span, span to depth

ratio 53, cantilever construction with precast segments (Griezic et al. 2006).

77 3-26 Trois Bassins Viaduct, Reunion (completed 2008): three main spans of 126 - 104.4 - 75.6 m,

with cables overlapping through the middle span, effective span to depth ratio 30 at tallest

pier and 50 at midspan, cantilever construction of central box, and construction of deck

cantilevers and struts with mobile carriages (Frappart 2005).

78 3-27 Tsukuhara Bridge, Japan (completed 1997): main span of 180 m, span to depth ratio of 33 at

piers and 60 at midspan, cantilever construction in 6 m long segments, transverse tendons

in deck (Kasuga 2006).78 3-28 Himi Bridge, Japan (completed 2004): main span of 180 m, span to depth ratio of 45, cantilever

construction (Kasuga 2006).

78 3-29 Korror-Babeldoap (Japan-Palau Friendship) Bridge, Palau (completed 2002): main span of


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81 3-36 Saint-Rmy-de-Maurienne Bridge, France (completed 1996): spans of 52.4 and 48.5 m,

effective span to depth ratio of 35, cast-in-place on falsework (Grison & Tonello 1997).

81 3-37 Sunniberg Bridge, Switzerland (completed 1998): main spans 128, 140, and 134 m, span to

depth ratio of 127, cantilever construction in 6 m stages (Figi et al. 1997).

81 3-38 Third Bridge over Rio Branco, Brasil (completed 2006): main span of 90 m, span to depth ratio

of 36 at piers and 45 at midspan, cantilever construction (Ishii 2006).

82 3-39 Golden Ears Bridge, Canada (completion 2009): main span of 242 m, span to depth ratio of 54

at piers and 80 at midspan, cantilever construction with precast deck panels (Bergman et al.

2007).

83 3-40 Possible types of tendons in an Extradosed Bridge

85 3-41 Sunniberg Bridge form traveller (adapted from Figi et al. 1998).



88 4-1 Roadway cross-section.

92 4-2 Construction sequence.

93 4-3 Girder cross-section of cantilever constructed girder bridge.

95 4-4 Bending moment in cantilever girder bridge (SAP2000 diagrams at the same relative scale).


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LIST OF TABLES

15 2 R EVIEW OF E XISTING E XTRADOSED B RIDGES

16 2-1 Summary of Extradosed Bridges.

41 3-1 Load factors and load combinations (CSA 2006a).

41 3-2 Permanent loads - maximum and minimum values of load factors for ULS (CSA 2006a).

41 3 D ESIGN AND C ONSTRUCTION OF E XTRADOSED B RIDGES

44 3-3 Comparison of multiple lane load effects according to CHBDC (2006a) and ASCE (Buckland1981) for the same basic lane load.

48 3-4 Comparison between Sunniberg Bridge and North Arm Bridge response to live load.

49 3-5 Comparison between monolithic and released connnection at main piers of the North Arm

Bridge.

62 3-6 Minimum saddle radii for strand based cables to prevent fretting fatigue.



89 4-1 Material Characteristics assumed for design.

d l f d h ( )


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1 WHAT MAKES A BRIDGE EXTRADOSED?1.1 Introduction

From 1994 to 2008, over fifty extradosed bridges have been constructed worldwide, and the preferred

proportions and cable arrangements have evolved. While there are many articles available on the design of

specific extradosed bridges, very little has been published on their design from a general perspective.

The intrados is defined as the interior curve of an arch, or in the case of cantilever-constructed girder

bridge, the soffit of the girder. Similarly, the extrados is defined as the uppermost surface of the arch. The

term extradosed was coined by Jacques Mathivat (1988) to appropriately describe an innovative cabling

concept he developed for the Arrt-Darr Viaduct (shown in Figure 1-4 ), in which external tendons were

placed above the deck instead of within the cross-section as would be the case in a girder bridge. To

differentiate these shallow external tendons, which define the uppermost surface of the bridge, from the

stay cables found in a cable-stayed bridge, Mathivat called them extradosed prestressing.

There is some debate over the boundary between cable-stayed and extradosed bridges. Visually,

extradosed bridges are most obviously distinguished from cable-stayed bridges by their tower height in

proportion to the main span, as shown in Figure 1-1 . Extradosed bridges typically have a tower height of

less than one eighth of the main span, corresponding to a cable inclination of 17 degrees, as observed from

the bridges considered in Section 2. In this thesis, the term extradosed bridge will be used to describe all

bridges that have a tower that is shorter than that of a conventional cable-stayed bridge, which is widely

accepted to be around a fifth of the span, as will be explained in Section 3.4.1 .


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The detailing and technology found in extradosed bridges is taken directly from externally prestressed

girder bridges and from modern cable-stayed bridges. Modern cable-stayed bridges have a fifty year

history and have been constructed with span lengths from 15 m to over 1000 m.

As compared with cable-stayed bridges, the advantages of extradosed bridges for spans less thanapproximately 200 m are numerous. Since the live load stress range is typically small (Mathivat 1988), the

cables can be deviated at the piers by means of a saddle, allowing for a more compact tower, especially in

the case of a fan cable arrangement. The stay cables can be anchored near the webs and the vertical

component of the stay cable force (which is small in comparison to a cable-stayed bridge) is transferred

directly to the girders without the need for a transverse diaphragm at the anchorage location. As with

external prestressing, extradosed bridges can use normal prestressing anchorages instead of the high stressrange type used for cable-stayed bridges. Given a stiff girder, the extradosed bridge can be constructed

without any need to adjust the tension in the cables (Chio Cho 2002).

The development of the extradosed bridge has evolved with and may have been influenced by othertypes of unconventional cantilevered bridges in which the top tendons rise above the deck level in the

negative moment regions, as shown in Figure 1-2 . The fin-back bridge has a wall containing the negative

moment tendons that is monolithic with the deck creating a single section, whereas a cable-panel bridge

Finback Bridge Cable-Panel Bridge Extradosed Bridge

Figure 1-2. Finback, cable-panel and extradosed bridge types.


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point for initial dimensioning of the overall structure and its components, and for estimates of material

quantities.

Chapter 3 discusses the primary factors that define the design of an extradosed bridge, from where it

fits into the realm of bridge types, to solutions for critical details that must be worked out in the finaldesign. Many of the issues discussed are of general applicability to any type of medium to long-span

bridge, as they represent important considerations in the conceptual design process, and are brought

together here in one document. The analysis and comparisons, however, are more specific in their

findings, and may be limited to the typical extradosed bridge problem assumed.

In Chapter 4, designs of a cantilever-constructed girder bridge, a stiff girder extradosed bridge, and a

stiff tower (slender girder) extradosed bridge are presented for a three span bridge, with a central span of140 m. in length. Variations in prestressing approach are also considered. A materials and cost

comparison is presented to highlight the main differences and overall cost-effectiveness of each design.

Finally, Chapter 5 concludes the thesis by summarizing the primary findings of the preceding chapters

and gives suggestions for future studies.

This thesis will provide enough detail on the designs undertaken to allow a practicing engineer to

understand the key design steps involved in designing an extradosed bridge, in accordance with theCanadian Highway Bridge Design Code (CHBDC - CSA 2006a) and other relevant codes.

1.3 Historical Context

Jacques Mathivat is most commonly credited for inventing the concept of extradosed prestressing, which


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concrete cable-stayed structures (around 200 m), which combined with temporary stays for cantilever

construction of constant depth girder bridges of medium span length (around 80 m), result in a hybrid form

where the temporary stays are made permanent.

Mathivat (1988) points out that cable-panel bridges and fin-back bridges may have been inspired bythe same desire to reduce the self-weight of cantilever constructed girder bridges. By locating the

prestressing cables in walls above the deck, the capacity of deck slab in compression can be utilised in

negative moment regions (over the piers) leading to a more efficient structure than a conventional

cantilever constructed box girder bridge. These structures bear some resemblance to extradosed bridges,

but they differ in appearance and in their stiffness, and the cables cannot be easily replaced since they are

encased in a concrete wall. Nevertheless, the proportions of this type of bridge had a significant impact onthe development of the extradosed bridge. The Ganter Bridge, completed in 1980, was the first bridge of

this type, is the most well-known, and inspired the concept for the Arrt-Darr Viaduct (Virlogeux 2002c).

The Ganter Bridge, located in Switzerland, is a cable-

panel bridge with a main span of 174 m that takes a roadway

over a deep valley at heights of up to 140 m above the valley

floor. The bridge is designed by Christian Menn, formerProfessor of Structural Engineering at the ETH in Zurich and

the designer of many elegant prestressed concrete bridges in

Switzerland. The roadway runs parallel to the valley on either


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The first application of extradosed prestressing was Mathivats proposal for the Arrt-Darr viaductwith precast box girder sections (Mathivat 1987), developed in 1982-1983. The extradosed prestressing

along with voided box girder webs resulted in a material savings of 30% compared with a conventional

cantilever constructed box girder bridge. Mathivats proposal substituted the internal tendons in the top

flange of a box girder for external cables above the running surface, deviated over the piers by stub

columns and anchored inside the box girder, which he called extradosed cables. The low eccentricity of

the cables over the piers allowed them to be stressed to the same level as traditional prestressing since thecables primary role was to provide horizontal prestress, and they were subject to a low fatigue stress.

Virlogeux explains (1999) that the concept was partially motivated by a distortion of code specifications

to use stay cables more efficiently, since an allowable stress of 0.65 f pu could be used for design of the

cables instead of the al e of 0 45 f t picall adopted for cable sta ed bridges Unfort natel the

Figure 1-4. Arrt-Darr Viaduct (Mathivat 1988)


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awarded based on an alternative design of a conventional box-girder bridge (Gee 1991). Tony Gee and

Partners, having been involved with previous fin-backed proposals, designed the Barton Creek Bridge with

constructibility as the most important objective. The cross-section consists of a single box girder below

the deck, with constant dimensions and no internal diaphragms (even over the piers) and webs that inclineinwards from the bottom slab to merge at the deck slab into a central fin that rises above the deck with

constant width. The segments were poured with the median barrier, which allowed the fin to be built up

progressively and off the critical path, as three segments could be cast before increasing the height of the

fin. The bridge was constructed with a form traveller supported laterally outside the webs and on the ribs,

and was completed in 1987 at a cost that was 20% above the original estimate (Gee 1991). The increase

was accounted for in additional items (lighting, approach railings) not included in the initial estimate. Interms of durability and maintenance, the fin-back bridge has the advantage over a conventional cantilev-

ered bridge that the main tendons are encased in the massive fin, away from the deck surface which is

exposed to traffic. As well, there is no decrease in longitudinal prestress in the deck under live load near

the piers, because the neutral axis of the section lies in the deck slab. Despite the success of the Barton

Creek Bridge, there have been very few fin-back bridges built since.

Virlogeux (1999) claims that the concrete walls in cable-panel and fin-back bridges have twodrawbacks: the tendons cannot be replaced and there is a cost to construct the concrete walls. The

designers of the Barton Creek Bridge took measures to reduce the cost of the single concrete wall and it is

conceivable that the additional cost of the protection system for stay cables would have exceeded the cost


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in profile. Kasuga (2006) states that practical experience has induced great admiration for the

incisiveness of Mathivats proposal.

Several articles on extradosed bridges in Japan credit and praise Mathivat for inventing the extradosed

bridge (Ogawa and Kasuga 1998; Hirano et al. 1999; Kato et al. 2001; Kasuga 2006), but these bridges aremore similar in appearance and proportions to the Ganter Bridge than to the Arrt-Darr concept, with the

difference that they do not have cables encased in concrete walls. All extradosed bridges in Japan to date

have cables arranged in a semi-fan configuration, with the first cable offset about a fifth of the span from

the pier. Most of these bridges are cast in place and have variable depth girders that are 50% deeper at the

piers than in midspan. The Japan Highway Public Corporation, the owner of several extradosed bridges

including the Odawara, Tsukuhara, and Kiso and Ibi extradosed bridges, allows only external tendons to be used in their bridges (Chilstrom 2001). Mathivats bridge had six spans with a continuous girder

supported on bearings whereas the first extradosed bridges constructed in Japan were three span structures,

with monolithic connections at the piers that result in frame action. This distinction allowed the first

extradosed bridges to be more slender than Mathivat originally proposed.

In France, the first extradosed bridge was constructed on a much smaller scale than those in Japan, as a

means of spanning further with minimal structural depth available below the roadway. The Saint-Remy-de-Maurienne Bridge over the A43 highway, shown in Figure 1-7 , was tendered in 1993 and completed in

1996 and has a maximum span of only 54 m (Grison and Tonello 1997). On this small scale, it is difficult

to imagine that extradosed tendons could be more economical than constructing concrete walls up to a


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of the Usses viaduct was adopted for the viaduct over Trois-Bassins in Runion, completed in 2008 and

shown later in Figure 3-26 .

In Switzerland, the Ganter Bridge led to a different path for the extradosed bridge. Santiago Calatrava,while studying at the ETH in 1979, produced a series of sketches of alternatives of the Ganter Bridge, some

of which were presented by Menn at the IABSE Symposium in Zurich in 1979 (Tzonis and Donadei 2005).

All sketches show a slender deck, suspended by cables from a stiff pier. In some alternatives, the two sides

f h fl d f h d i d d h bl l d

Figure 1-9. Santiago Calatravas concepts for crossing deep Alpine valleys. From left to right: Variant 1, Variant 2model, Variant 7 sketch and detail presented by Menn at the IABSE Symposium in Zurich in 1979 (Calatrava 2004).


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under-deck cable-stayed configuration. His proposal was not accepted and a cable-stayed bridge is now

under construction after many years of public consultation. Both concepts are shown in Figure 1-11 .

In 1993, Menn proposed his extradosed concept for the Sunniberg

Bridge (Honnigmann and Billington 2003). Menn, again serving onthe jury for the design competition and not satisfied with the three

designs submitted, presented his concept to the highway departments

architectural consultant who endorsed it and helped convince the

department to accept it. The 526 m length of the bridge and 60 m

depth of the valley below the roadway favoured multiple piers with

spans of around 150 m. Menn favoured the proposal for the sameaesthetic reasons that he claimed for the Poya Bridge: if the towers

were designed with conventional proportions, they would rise 35 m

above the roadway, and would overpower the surrounding landscape

(Figi et al. 1997). A multiple span cable-stayed bridge with conventional proportions would still require

stiff towers, as illustrated by the conceptual drawings shown in Figure 1-12 for the towers of the Millau

Viaduct, an 8 span cable-stayed bridge (Virlogeux 2004). Cross cables between towers have been proposed as another means of stabilising them in the horizontal direction, but this solution has questionable

aesthetics and is difficult to construct (Walther et al. 1999) if not infeasible on a curved roadway. The

designs submitted for the design competition did not include a cable-stayed bridge but were of a more

Figure 1-12. Millau Viaduct toweroptions (Virlogeux 2004). Drawn by Sir

Norman Foster after discussions with Virlogeux.

Alternatives to provide adequate rigiditybetween pier, tower, and deck

Pier options to accommodatelongitudinal deformations


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effects of concrete hardening, but are also more accommodating of field adjustments to their final

geometry since the deck profile can be readjusted after completion without introducing considerable

igure 1-13. Sunniberg Bridge, Switzerland.


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Extradosed bridges are becoming increasingly popular for spans from 50 m to 250 metres. Over 25

extradosed bridges have been completed in Japan and 15 are underway in South Korea (Bd & e 2006).

Many extradosed bridges constructed to date cross waterways where there is a navigational clearance

requirement as well as interest in minimizing the roadway grade raise at the approaches. This favours anextradosed bridge over a cantilever-constructed girder bridge, which would have a girder depth at the

supports of two to three times that of the extradosed bridge of equivalent span. While a cable-stayed

bridge is sometimes a feasible option, an extradosed bridge has been selected in many cases because of

overhead glidepath clearance requirements imposed by nearby airports (Stroh 2003; Griezic et al. 2006).

In 2001, the Ibi and Kiso Bridges set the record for longest extradosed viaducts with total lengths of

1145 and 1400 m respectively, and extradosed spans of up to 275 m. This was achieved with a hybrid

girder arrangement: a variable depth concrete girder was supported by extradosed cables from the piers and

100 m central steel box girder was connected to the concrete girder to transfer moment and shear but allow

longitudinal expansion. In 2002, the Japan-Palau Friendship Bridge was completed with the same hybrid

Figure 1-15. Golden Ears Hybrid Extradosed Bridge, Vancouver (Bergman 2007).


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some of which are sculptural but structurally inefficient and would be unable to support the tension forces

from the stay cables if the girder did not share some of the load.

SETRA (2001) published recommended allowable stress limits that cover the full range of external

cables. In that document, external prestressing tendons are defined as being subjected to a stress range of

up to 15 MPa under live load while stays for cable-stayed bridges are subjected to a stress range of around

100 MPa and above. Extradosed cables are characterised as being subjected to a live load stress range between 30 MPa and 100 MPa and are not sensitive to wind vibrations. These specifications resulted from

a need for design recommendations for bridges that do not fall into distinct categories, and they propose

design limits and approximations based on rational principles. These recommendations were used for the

design of the North Arm Bridge in Canada (Griezic et al 2006) and they influenced the allowable stress

Figure 1-16. North Arm Bridge, Canada Line LRT,Vancouver (photo courtesy of Stephen Rees)

igure 1-17. Pearl Harbor Memorial Bridge in Newaven, Connecticut (Stroh et al. 2003)
http://www.tiefbauamt.gr.ch/projekte/pdf_klosters.htmhttp://www.tiefbauamt.gr.ch/projekte/pdf_klosters.htmhttp://www.tiefbauamt.gr.ch/projekte/pdf_klosters.htm


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4. Extradosed cable can use conventional anchorages instead of the expensive anchorages with a high

fatigue strength as used for cable-stayed bridges. Extradosed cables are less sensitive to vibration, and

they do not need to be restressed during construction. On this basis, Komiya concludes that extradosed

cables are more economical than conventional stay cables and lead to better constructibility;5. Extradosed bridges are less costly than cable-stayed bridges but more costly than cantilever con-

structed girder bridges, based on materials consumption. Extradosed bridges could be more economi-

cal than girder bridges in the case where girder depth is limited by traffic or navigational constraints, or

in the case where poor soil conditions provide an incentive to reduce the structures self-weight.

Chio Cho (2000) carried out a parametric study on an extradosed bridge with similar characteristics to the

Odawara Blueway Bridge, with span lengths of 74 - 122 - 74 m. The results of his study on the structural behaviour of extradosed prestressing during construction and in service lead to a few important design

recommendations (Chio Cho 2002). The first cable should be anchored between 0.18 and 0.25 of the main

span from the tower as the cables closest to the tower are ineffective. The deck should be proportioned

with a span to depth ratio of 35 at the piers and 45 at midspan to keep all live load stress range in the cables

below 80 MPa, the limit for conventional prestressing anchorages. A compensation of all permanent

loads, with the cables stressed as the bridge is constructed in balanced cantilever, results in high tensileforces in the bottom fibre of the deck, making a single stressing operation impractical. A compensation of

80% of the permanent load is preferred in order to control the stresses during construction and avoid

restressing after the final structural configuration is acheived. Since it is not possible to completely


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Table 2-1. Summary of Extradosed Bridges

Opera-tionalDate

Name andLocation

-Deck Depth x Width-Span Lengths-Deck Description

Picture Detailed Drawing

1980Ganter Bridge,Switzerland

2.5 - 5 x 10

Wide single cell concrete box girder, cable-panel stayed.

1127.0 + 174.0 + 127.0

Vogel & Marti 1997, Kasuga 2006

ProposedArrt-DarrViaduct, France

3.75 x 20.5

Single cell concrete box girder with voidedwebs and struts supporting deck cantilevers.

260.0 + 100.0 + 100.0 + 100.0 + 100.0 + 52.0

Photo from Virlogeux 1999Mathivat 1986, Mathivat 1988, Virlogeux 2002a

1987Barton CreekBridge, Austin,USA

3.7 - 10.7 x 17.7

Single cell concrete box girder with websinclined inwards into a central fin above thedeck level, and transverse struts supporting thedeck slab.

347.6 + 103.6 + 57.9

Photo from Gee 1999Gee 1990

1993SocorridosBridge, Madeira,

l

3.5 x 20

Single cell concrete box girder cable panel

454.0 + 85.0 + 106.0 + 86.0

16


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Opera-tionalDate

Name andLocation



Table 2-1. Summary of Extradosed Bridges (continued)

1998Kanisawa Bridge, Japan

3.3 - 5.6 x 17.5

Concrete box girder.

899.3 + 180.0 + 99.3

Photo from Cho 2002Kasuga 2006

1998Shin-KaratoBridge, Kobe,

Japan

2.5 - 3.5 x 11.5

Two and three cell concrete box girder.

974.1 + 140.0 + 69.1

Photo from Tomita et al. 1999Tomita et al. 1999

1998Sunniberg Bridge,Switzerland

1.1 x 12.375

Concrete slab with edge stiffening beams.

1059.0 + 128.0 + 140.0 + 134.0 + 65.0

Photo by author Figi et al. 1997, Figi et al. 1998, Menn 1998, Baumann & Dniker 1999,Honigmann & Billington 2003

1999Santanigawa(Mitanigawa)Bridge, Japan

2.5 - 6.5 x 20.4

Double cell concrete box girder.

1157.9 + 92.9

17


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Opera-tionalDate

Name andLocation




2000Shikari Bridge, Japan

3 - 6 x 23


1694.0 + 140.0 + 140.0 + 140.0 + 94.0

Photo from www.jsce.or.jp/committee/tanaka-sho/jyushouStroh et al. 2003

2000SurikamigawaBridge, Japan

2.8 - 5 x 9.21784.82

Kasuga 2006

2000Wuhu YangtzeRiver Bridge,Wuhan, China

15 x 23.4

Double-decker steel truss with composite deckslab on top roadway, two rail lines on bottomlevel.

18180.0 + 312.0 + 180.0

Photo from Fang 2004Fang 2004

2000Yukisawa-OhashiBridge, Japan

2 - 3.5 x 15.8

Two cell concrete box girder with widesidewalks on deck cantilever overhangs outside

1970.3 + 71.0 + 34.4

18


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Opera-tionalDate

Name andLocation




2001MiyakodagawaBridge, Japan

4 - 6.5 x 19.9

Parallel double cell box concrete box girders.

23134.0 + 134.0

Photo from www.jsce.or.jp/committee/tanaka-sho/jyushouKato et al. 2001, Terada et al. 2002

2001Nakanoike Bridge, Japan

2.5 - 4 x 21.42460.6 + 60.6

Kasuga 2006

2002Fukaura Bridge, Japan

2.5 - 3 x 13.72562.1 + 90.0 + 66 + 45.0 + 29.1

Kasuga 2006

2002Korror BabeldoapBridge, Palau

3.5 - 7 x 11.6

Hybrid cross section: wide single concrete boxgirder near piers and steel box girder in central82

2682.0 + 247.0 + 82.0

19


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Opera-tionalDate

Name andLocation




2004Korong Bridge,Budapest, Hungary

2.5 x 15.85

Three cell concrete box girder stiffened withtransverse ribs.

3152.26 + 61.98

Photo from Becze & Barta 2006Becze & Barta 2006

2004Shin-MeiseiBridge, Japan

3.5 x 19

Three cell concrete trapezoidal box girder.

3289.6 + 122.3 + 82.4

Photo from Mutsuyoshi et al. 2004Iida et al. 2002, Kasuga 2006

2004Tatekoshi Bridge, Japan

1.8 - 2.9 x 19.143356.3 + 55.3

Kasuga 2006

2005Sannohe-BoukyoBridge, Aomori,

Japan

3.5 - 6.5 x 13.45


3499.9 + 200.0 + 99.9

20


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Opera-tionalDate

Name andLocation




2006Tagami Bridge, Japan

3 - 4.5 x 17.83980.2 + 80.2

Kasuga 2006

2006Third Bridge overRio Branco, Brasil

2 - 2.5 x 17.4

Deck slab with L shaped edge beams (appearsas single box girder with incomplete bottomslab) that taper to I beams at midspan.

4054 + 90 + 54

Photo from Ishii 2006Ishii 2006

2006Tokuyama Bridge, Japan

4 - 6.5 x 17.441139.7 + 220.0 + 139.7

Stroh et al. 2003

2006Yanagawa Bridge, Japan

4 - 6.5 x 17.442130.7 + 130.7

21


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Opera-tionalDate

Name andLocation




2008Cho-Rack Bridge,Dangjin, SouthKorea

- x 14

Multiple cell concrete box girder.

4770.0 + 130.0 + 130.0 + 130.0 + 70.0

Structurae

2008North ArmBridge (CanadaLine ExtradosedTransit Bridge),Canada

3.4 x 10.31

Single cell concrete box girder for LRT.

48139.0 + 180.0 + 139.0

Photo from bd&e 2004Griezic 2006

2008Trois BassinsViaduct, Reunion,France

4 - 7 x 22

Single cell concrete box girder with steel strutssupporting long deck cantilevers.

4918.6 - 126.0 - 104.4 - 75.6 - 43.2

Photo from Frappart 2005Frappart 2005, Boudot et al. 2007

2009Golden EarsBridge, Canada

2.7 - 4.5 x 31.5

Steel box girders at edge of deck withtransverse floor beams composite with precast

t d k

50121.0 + 242.0 + 242.0 + 242.0 + 121.0

22


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24


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25


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26

27


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27

Tied arches and extradosed spans are two good options for urban environments. Girder bridges are not

visible to the driver and as stated by Menn (1991): the general public was never captivated by modern

bridge construction. Beam bridges were largely perceived as boring. For a signature bridge, girder

bridges do not have the visual elegance that is desired by governing authorities and designers alike.

The choice between a tied arch and an extradosed structure might be guided by the span configuration.

If only one long span is required, a tied arch may prove to be economical, but in other cases a cable-

supported bridge will be a clear choice due to the potential for cantilevered construction, which has a

relatively low impact on the terrain below. As the cost of concrete increases and the incremental cost

premium for higher strength decreases, there is more incentive to use materials efficiently. The extradosed

bridge presents a way to make use of the compressive capacity of the concrete, while maintainingconventional girder cross-sections and common construction methods. \

Extradosed bridges allow for unequal span lengths, unsymmetrical span arrangements, multiple stayed

spans and approach spans with the same cross section as the main spans. Of the extradosed bridges in this

study, 41 of 51 have main spans between 75 and 200 m; 11 have two extradosed spans (one tower), 30

have three extradosed spans (2 towers), and 10 have more than three extradosed spans. From Figure 2-4 b,

it is observed that multiple span bridges are viable for all span lengths.Mathivats concept for a span to depth ratio of between 30 and 35 at the piers has been followed for 22

of the extradosed bridges, but the span to depth ratio at midspan has been increased to over 50 in 23

bridges, as observed from Figure 2-2 . There are 13 extradosed bridges with a constant depth cross-section,

28


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28

Variable depth girders are more frequently used at longer span lengths, as shown in Figure 2-4 a. A

variable depth cross-section, with the depth at the pier more than 1.5 times the depth at midspan, is used in

26 extradosed girders. As the span length increases, the degree of haunching, or pier to midspan depth

ratio, also increases as observed from Figure 2-4 b.

0

20

40

60

80

100

120

140

50 100 150 200 250

Longest Span, m

275

S p a n : D e p t h

Variable Depth Simple Supports

Constant Depth Simple SupportsConstant Depth Embedded

Variable Depth Embedded

1:55

1:30

66

at m idspanat pie r

Figure 2-3. Span to depth ratios of extradosed bridges at midspan and pier.

10

15

e s

>1.5

1-1.5

=1 2

3

t h a t

M i d s p a n

29


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29

2.3 Characteristics of Extradosed Bridges

2.3.1 Materials Usage

The average girder thickness, the volume of concrete in the girder divided by the deck surface area, can be

used to compare the material usage of different bridge types. In Figure 2-6 , the average girder thickness ofextradosed bridges and a selection of cantilever-constructed girder bridges and cable-stayed bridges, is

plotted against the longest span. Information on the girder and cable-stayed bridges considered in this

section is included in Appendix A. Also shown in Figure 2-6 are estimates of average girder thickness t g

Variable Depth Simple Supports

Constant Depth Simple SupportsConstant Depth Embedded

Variable Depth Embedded0

2

4

6

8

10

12

14

S p a n : H e

i g h t o

f T o w e r

5Cable-Stayed

Typical

Mathivat (1988)15

8

50 100 150 200 250Longest Span, m

27566

igure 2-5. Span to tower height ratio of extradosed bridges.

30


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30

0.3

0.34

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

0 100 200 300 400 500Longest Span, m

A v e r a g e

d e p t h o

f c o n c r e t e

, m 3 / m

2

ExtradosedCantilever Constructed Girder

Cable-Stayed

Menn (1990) Estimate

SETRA (2007) Estimate

Extradosed Regression

Cantilevered Regression

Cable-StayedRegression

1.17

530

Figure 2-6. Average girder concrete thickness of cantilever-constructed girder, extradosed and cable-stayed bridges.

0 90.91


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32


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the variation in span to depth ratio at midspan observed in Figure 2-3 . At the upper end, the moment of

inertia of some extradosed bridges is higher than that of cantilver constructed girder bridge of equal span,

while on the lower end, it is barely higher than that of a cable-stayed bridge of equal span, as seen in

Figure 2-9 . There is however one extradosed bridge, the Sunniberg Bridge, which has a girder that is

considerably more flexible (lower moment of inertia) than most extradosed bridges. Its structural

behaviour appears to be more like a cable-stayed bridge, despite having a cable inclination of an

extradosed bridge.

It can also be observed that there is a distinct difference between the moment of inertia of cable-stayed

bridges that have box-girders and those that have slabs stiffened by edge beams. In this small sample of

cable-stayed bridges, all box girders are centrally suspended, while all slab or stiffened slab bridges are

laterally supported.

15

20

25

e r 1 0 m

w i d t h

, m 4

ExtradosedCable-Stayed Typical CantileverConstructed Box Girder

Span/40 Span/50

33


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they curve inwards to provide the necessary clearance for jacking them from within the box girder. This is

a unique solution to conceal the cable anchorages from view above or beneath the bridge. The sheaths are

installed in steel recess tubes both over the towers and through the girder to allow for future replacement of

the complete cable (Taniyama & Mikami 1994). Details of the cable anchorages and installation are

shown in Figure 2-11 . The strands are epoxy coated and grouted inside an FRP sheath. High damping

rubber dampers are installed at the stay anchorages to decrease rain and wind vibrations.

Figure 2-10. Odawara Extradosed Bridge details of tower saddle and arrangement of prestressing bars in tower fromFEM analysis (Kasuga et al. 1994).

Section through top of pylon

a) b)

34


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The deck slab spans 9 m between webs and is post-tensioned with 28.6 mm dia monostrand tendons with

an after-bond pregrouted epoxy that does not require conventional grouting.

There are 2 lateral planes of 8 extradosed 27-15 mm dia strand tendons per half span. The maximum

stress range in the extradosed cables due to live load is 37 MPa (Ogawa et al. 1998). The strands are

individually sheathed with polyethylene, bundled and encased in an HDPE pipe which is filled with a

polyethylene filler (Chilstrom 2001). There are 12 external 19-15 mm dia strand tendons inside the box

girder across the main span to resist positive bending moments, and internal 12-13 mm dia strand tendons

that are mainly used for cantilevering of 7 m segments (Ogawa et al. 1998).

The Tsukuhara Bridge has a span to depth ratio of 60 at midspan, which is very shallow compared with

others studied in this chapter. Despite this fact, the live load stress range in the cables is very low.

2.4.3 Ibi and Kiso River Bridges, Japan

The Ibi and Kiso River Bridges are 5 and 6 span continuous structures that have total lengths of 1397 and

1145 m respectively, with maximum spans of 271.5 and 275 m. The towers are integral with the deck and

the superstructure rests on force distributing rubber bearings on the piers (Chilstrom 2001). The

superstructure has a hybrid construction, with each span consisting of cable-supported precast concrete

segments for the first 90 m from the piers, and a central steel box girder which is continuous with theconcrete sections. The continuity is achieved with shear studs, internal prestressing, and external

prestessing which is installed across the concrete segments, deviated at the piers and in span, and anchored

at the ends of the steel girders (Hirano et al. 1999).


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36


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joint down the centre of the tower, shown in Figure 2-15 , alleviates any cracking that would occur from the

elastic strain across the tower as the cables are installed.

2.4.5 North Arm Bridge, Canada

The North Arm Bridge is an extradosed bridge carrying the Canada Line LRT from the Vancouver Airport

into the City across the Fraser River North Arm. The extradosed bridge type was chosen to keep the track

profile as low as possible to cross the navigational clearance envelope, while keeping the towers below the

glidepath clearance envelope (Griezic et al. 2006). The main span is constructed from precast segments of

2 8 m maximum length with a maximum weight of 70 tonnes for transportation and lifting A deck level

Figure 2-15. Shin-Meisei Birdge a) photo of steel shell of tower; b) elevation of composite tower and c) details ofcomposite tower (drawings: Iida et al. 2002, photo and rendering: Kasuga 2006).

a) b) c)

37


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The designers of this bridge made two important decisions based on economy. A detailed comparison

was made and anchorages were chosen over saddles in the towers. Secondly, a constant depth girder was

chosen over a variable depth girder at the piers.

2.4.6 Pont de Saint-Rmy-de-Maurienne, FranceThe bridge crosses over the A43 highway and a river on a curve, at a location with tight geometry where a

very shallow clearance was required, since the roadway surface is only 0.9 m above the highway clearance

envelope. The bridge has two spans of 52.5 and 48.5 m, and is cast-in-place on falsework and post-

tensioned. The bridge cross-section is U shaped and consists of edge girders with transverse cross-beams

at 2.27 m spacing supporting a 220 mm thick concrete deck.

There are 6 34-15 mm dia strand tendons in each girder, which are internal through most of the spanand rise above the girder only around the deviators to become extradosed cables (Grison & Tonello 1997).

With an average girder thickness of 0.65 m, the Saint-Rmy Bridge has a longitudinal prestressing mass

per unit volume of concrete of 52 kg/m 3 and a mass per unit area of deck surface of 30 kg/m 2. This is

comparable to another short extradosed bridge, the Korong Bridge (Becze & Barta 2006), which has two

spans of 62 and 52 m, an average girder thickness of 0.785 m and a longitudinal prestressing mass of 43

kg/m 3 and 33 kg/m 2. However, this is quite alot more prestressing than in a conventional box girder bridgeof equivalent spans, which would be expected to have a similar average girder thickness of around 0.6 m

but a longitudinal prestressing mass of only 20 to 30 kg/m 3, based on Section 2.3.1 .

Compared with other channel bridges, the material quantities in the Saint-Rmy Bridge seem more

38


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2.4.7 Viaduc de la ravine des Trois Bassins, Runion

The extradosed bridge form was found to be a good solution for the ravine both

in terms of technological and architectural considerations, and was thought to

integrate harmoniously into the environment (Frappart 2005). A concrete bridge

was favoured due to the local availability of the material and a labour force that

was not familiar with structural steel. The bridge has spans of 126 - 104.4 - 75.6

- 43.2 m with a counterweighted span of 18.6 m adjacent the longest span to

stabilise the bridge transversely against cyclone winds of up to 49 m/s. The

unusual span arrangement was chosen partly because access was restricted to one

side of the ravine only. The bridge was cast-in-place with 60 MPa concrete in

segments of 3.6 m length. For each segment, the form traveler was used to cast

the main box section, while two smaller mobile formwork travelers were used to

install the struts and cast the deck overhang cantilevers in 7.2 m segments, off the

critical path. The bridge was constructed starting with the short spans and ending with the closure of the

longest span.

The webs are inclined outwards to achieve the necessary torsional resistance of the section without

increasing the web thickness, and concurrently limiting the offset between the extradosed anchorages and

the webs (Frappart 2005).

There are double planes of 7 extradosed 37-16 mm dia strand cables across the main tower, as shown

Figure 2-17. TroisBassins Viaduct main pier(Frappart 2005).

39


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below during construction (Figi et al. 1997). The deck cross-section consists of a solid slab with

longitudinal edge beams, with a 7% roadway superelevation.

The bridge is curved in plan and connected monolithically at the abutments, which provides fulllongitudinal restraint and allows the bridge to deform as a horizontal arch under deformation due to

temperature range. The abutments were designed as earth filled containers to anchor the horizontal

reaction forces (Baumann and Dniker 1999). The pier columns have a parabolic variation in depth, and

flare outwards from the base so that the towers are leaning outwards in order to provide the required

clearance for the cables.

There are two planes of 8 to 10 stay cables per half span. Each cable consistsof 125 to 160 galvanised 7 mm dia wires, prefabricated to length and anchored

by means of button heads in BBR DINA bonded anchorages, for a high fatigue

resistance. The cables have an ultimate tensile strength of 1600 MPa and were

4o22 5 o 26 o 14 e=20 o14/o16 e=15

o 30 e15/12.5Longitudinalprestressing4o224o22

3 .5 m3 .5 m 1 m

1 . 9

m

m4.0

1 m

1.15m

Staycable

Cable anchorage

Figure 2-18. Snniberg Bridge a) deck cross-section and b) prestressing and reinforcement (adapted from Tief- bauamt Graubnden 2001).

a) b)

Stay cables with 125

Steel construction

40


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volume of concrete in the deck is 100 kg/m 3 and the mass per unit area of deck is 97 kg/m 2. These values

are higher than are typically found in extradosed bridges, such as the viaduc de la ravine des Trois Bassins

Live load

Form traveler advanced to Stage 5

Displacement

Displacement

PermanentVariable

PermanentVariable

Midspan Tower CL

Axial force from Stay Cables

Axial force from Internal Prestressing

Displacement

Deck poured

Stay Cables installed and stressed

Moments in inner edge beam

Displacements due to live load

Concrete

Figure 2-20. Sunniberg Bridge a) bending moments and deflections of the edge beam through one stage of construc-tion, and b) forces and deflections of the main span inner edge beam of the final structure due to permanent and liveloads (adapted from Figi et al. 1998).


55/176

42


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superimposed with a uniformly distributed load of 9 kN/m. Under serviceability limit state (SLS) and

ultimate limit state (ULS), the CL-625 Truck load effect is increased by the addition of a dynamic load

amplification (DLA) factor to account for impact, which varies depending on how many axles are loading

the component under consideration as shown in Figure 3-1 . For all axles acting on the bridge, the DLA is

25%. A DLA is not applied to the CL-625 Lane load, as this maximum load condition is assumed to occur

with stationary vehicles on the bridge (CSA 2006b). The CL-625 live load is shown in Figure 3-1 .

For spans up to approximately 50 m, the CL-625 Truck will govern the loading, but at spans beyond

approximately 90 m, the CL-625 Lane load will govern. In between these span lengths, the Truck willgovern in positive moment regions, while the Lane load will govern in negative moment regions. At

SLS1, the live load is reduced to 0.9 of the value of the CL-625 Live load.

CL-625 Truck

CL-625 Lane Load

Clearance Envelope

CL-625 Truck Dynamic Load

Allowance Modi cation factor for

multiple lane loading

Figure 3-1. CL-625 Live Loading: Maximum of CL-625 Truck (including DLA) or CL-625 Lane Load.

Fractions of Basic Lane Load

43

k d l d b h b d f k


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trucks, and was selected by the CHBDC Subcommittee on Loads to account for an increase in truck

weights in the last 25 years and to allow for future growth in truck traffic (CSA 2006b).

The loading of multiple lanes is not a simple matter, but it is important because it has a significant

effect on the stress range of the cables due to live loading. Buckland (1991) presents a comparison of live

loading between British Standards (BD 37/88, BS 5400 1978) and North American Standards (ASCE,

AASHTO 1983, CAN/CSA-S6-88 1988) with a section on multiple lane loading. While the current

CHBDC CL-625 Lane load is based on the ASCE 30% heavy vehicle curves, the multi-lane factors do not

follow the ASCE recommendations.

The multi-lane loading factors in the CHBDC follow the North American practice of reducing the lane

loads uniformly across all lanes. The multi-lane loading takes into account the reduced probability of more

than one lane being loaded simultaneously, due to actions such as traffic distribution, traffic volume, traffic

speed, accident situations, and decrease of dynamic loads since it is unlikely that vehicles in multiple lanes

vibrate in harmony (CSA 2006b). The CHBDC positions the vehicles biased towards one side of the

design lane to produce the maximum load effect. In contrast, the ASCE loading positions the vehicles

centrally in the design lanes, based on the assumption that over a long span, vehicles will be randomly

spaced with the average position close to the centre of the lane (Buckland 1981).

European practice has been to keep one or two lanes fully loaded while reducing the load on all others.

As noted by Buckland, there is merit to this idea as there is no reason to suppose the most heavily loaded

lane will be less loaded simply because other lanes are open and he emphasizes the importance of

44


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Table 3-3. Comparison of multiple lane load effects according to CHBDC (2006a) and ASCE (Buckland 1981) forthe same basic lane load.

Comparison 2 Lanes 3 Lanes 4 Lanes 5 Lanes 6 Lanes 7 Lanes 8 LanesCHBDC/ASCETotal Load on single cable plane

1.06 1.14 1.12 1.03 1.00 1.04 1.07

CHBDC/ASCETotal Load on two planes of cables

1.08 1.04 1.03 0.99 0.96 0.92 0.94

CHBDC - Ratio of total load of two planes to 1.10 1.07 1.10 1.14 1.14 1.04 1.02

2 lanes 3 lanes 6 lanes4 lanes 5 lanes 8 lanes7 lanes

CHBDC 2006

ASCE 1981

Central Suspension

Lateral Suspension

0

1

2

3

4

5

Wc, m

M u

l t i p l e o

f B a s

i c L a n e L o a d

CHBDC Central

CHBDC Lateral

ASCE Central

ASCE Lateral

0

1

2

3

4

5

10.0 13.56.0 17.0 27.520.5 24.0 31.0

Figure 3-3. multiple lane loading effect by deck width according to CHBDC 2006 and ASCE 1981, for two planes ofcables and for single plane central cable suspension.

45

gradient in the girder temperat re differential bet een the cables and girder and a niform temperat re


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gradient in the girder, temperature differential between the cables and girder, and a uniform temperature

range applied to the entire structure. The effects of temperature gradient and temperature differential on

the extradosed bridge become more significant as the stiffness of girder increased and must be considered

and will be discussed in greater detail, while a temperature range mainly affects the piers.

Temperature Gradient in Girder

The CHBDC (CSA 2006a) specifies a linear temperature gradient which is a function of the section

depth. This may provide a reasonable approximation of the curvature induced by the sun shining on the

surface of a bridge deck for short spans, but is overly conservative for deeper cross-sections where

corresponding curvature is primarily due to the strain in the deck slab and its distance to the centroid of the

girder cross-section.

One of the earlier rational models for temperature gradient was proposed by Priestley (1978) based on

experimental and analytical research conducted in the early 1970s. A design gradient was proposed that

would accurately predict the critical conditions for seven bridge sections investigated and was adopted for

all major concrete bridge design in New Zealand (Priestley 1978). This design gradient is specified by a

fifth-order curve with the point of zero temperature difference at 1200 mm below the deck surface.

0

0.4

0 8

0.0 10.0 20.0 30.0T, deg C

m

d e c k a b o v e v

o i d s we bs, can t i le v

e rs

( )5T = 32 - 0.2h

Zone1

T130

T27.8


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47

resulted in a bridge with a span to depth ratio of 31 at the piers and 45 elsewhere For a 5 lane bridge of


61/176

resulted in a bridge with a span to depth ratio of 31 at the piers and 45 elsewhere. For a 5 lane bridge of

157 m main span, the cable mass required to support half of the main span was 41 tonnes, a mass of 18 kg/

m of the deck surface.

For the design of the Sunniberg Bridge (10 in Table 2-1) (Honigmann & Billington 2003), Menn has

used the same approach as for the design of a cable-stayed bridge: a cable arrangement is selected, cables

are sized according to maximum load for the allowable cable stress, and the girder is designed to resist the

bending moment between cables under dead load, and compatibility moments under live load, caused by

the distribution of axles loads to several adjacent cables. Finally, the cross section was checked for

buckling at the pier under combined bending and axial compression in the deck. This process resulted in a

bridge that has a span to depth ratio of 127. For a 2 lane bridge of 140 m main span, the cable mass

required to support half of the 140 m main span was 43 tonnes, a mass of 49 kg/m of the deck surface,

more than double that of the Pearl Harbour Memorial Bridge.

Most extradosed bridges built to date lie somewhere between these two examples, as is the case for the

North Arm Bridge (48 in Table 2-1), a 562 m long, five span LRT bridge with a 180 m extradosed main

span, recently completed in Vancouver (Griezic et al. 2006). A precast concrete segmental box girder

cross-section was being used on other parts of the project and was a logical choice for the extradosed span.

In addition, the approach spans could be cantilever constructed by varying the depth of the box girder. In

the main span, extradosed tendons were added to extend the useable span of the box girder while meeting

navigational and glidepath clearance requirements above and below the bridge. These constraints resulted

48

North Arm Bridge in Table 3-4 each subjected to point load uniform load and CL-625 live load The


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North Arm Bridge in Table 3 4 , each subjected to point load, uniform load, and CL 625 live load. The

ratios are higher for the Sunniberg Bridge than for the North Arm Bridge, and the ratio for point load at

midspan is higher than for a uniform load in each bridge.

Table 3-4. Comparison between Sunniberg Bridge and North Arm Bridge response to live load.

Sunniberg Bridge, 140 m main span North Arm Bridge, 180 m main spanAxial force and bending moment due to 9 kN/m uniform load across main span

Axial force and bending moment due to 625 kN point load applied at midspan

Axial force and bending moment envelopes due CL-625 live loading

= 0.72

Mmax = 670 kNm

= 0.23

Mmax = 9140 kNm

= 1.00

Mmax = 3570 kNm

= 0.43

Mmax = 11700 kNm

49

causes a downwards displacement in the loaded span and an upwards displacement in the adjacent span(s).


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causes a downwards displacement in the loaded span and an upwards displacement in the adjacent span(s).

To resist the bending moment in the girder and control displacements, the girder alone must have adequate

bending resistance and stiffness. For these two conditions to be jointly met, a certain section depth is

required to provide stiffness to the system, since the cables simply transfer the load in one span to the

adjacent span(s). A tensile force in a cable due to a point load in one span is distributed through the tower

to multiple cables in the adjacent span.

In the case of a superstructure embedded at the piers, any rotation of the superstructure at each pier will

be partially restrained by the substructure. This will decrease the bending moment in the girder due to live

load, since some of the moment is resisted by the pier. The corresponding displacements are also reduced.

If the girder is flexible, the substructure must provide enough stiffness to control deflections of the girder

due to live load.

Table 3-5. Comparison between monolithic and released connnection at main piers of the North Arm Bridge.

Bending moment due to 625 kN point load on main span

Bending moment due to 9 kN/m uniform load across main span

Mmin = -8290 kNm

Mmax = 11700 kNm

Monolithic

Mmin = -5500 kNm

Mmax = 14100 kNm

Mmin = -4760 kNm

Mmax = 6550 kNm

Released

50

Table 3-5. Comparison between monolithic and released connnection at main piers of the North Arm Bridge.


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Table 3-5 shows the forces and displacements in the North Arm Bridge resulting from live load across

the main span, for both the superstructure embedded on the piers (monolithic as it was constructed) and thesuperstructure simply supported (released against rotation) at the piers. The monolitic connection causes a

shift in the moment diagram from positive to negative moment regions, and virtually eliminates any

bending in the back spans. In the released condition, the live load in the main span is reflected in the back

spans, the effect of which is pronounced since the side spans are very long in this bridge.

3.2.3 Prestressing Methodology

From the previous two sections, we observe that there are two separate factors which influence the

magnitude of the bending moments in the girder due to live load. Firstly, the relative stiffness of the cables

and girder which affects the distribution of forces between these two systems, and secondly the connection

b h d h b h h ff h d b b h

Deflected shape envelope due CL-625 live loading* on main span

* Values given are for 2 lanes loaded including multilane reduction and service load factors.

p p g

d = -155 mm

d = 20 mmMonolithic

d = -300 mm

Released d = 67 mm

51

construction loads, then restressing the cables to balance the permanent loads, after the superimposed load


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, g p , p p

is applied to the continuous structure. This is efficient in terms of limiting the bending moment in the deck

at all stages but it requires a laborious restressing operation.

The aforementioned factors lead to the following prestressing methodology for cable-stayed bridges.

The cables are dimensioned to resist all permanent loads, all uniform live load, and concentrated live loads

reduced to account for some distribution into adjacent cables. The cables are first pretensioned to balance

construction loads during construction in balanced cantilever, then they are retensioned to balance all

permanent loads after construction of barriers and asphalt paving. Internal prestressing tendons are

straight and centred to limit creep effects, geometrical nonlinear effects, and uncertainties in the magnitude

of bending moments. Partial prestressing is used in the girder to limit crack widths at SLS (Hansvold

1994; Jordet & Svensson 1994; Wheeler et al. 1994), typically to 0.2 mm. Additional bending capacity at

ULS is provided by reinforcing steel. Full prestressing to keep the girder uncracked at SLS, especially at

midspan where there is no axial force induced in the girder from the cables, would require a prohibitively

high quantity of prestressing. Sometimes, the span is required to remain fully prestressed for a typical

truck, and only partially prestressed for full SLS loads (Bergermann & Stathopoulos 1988).

The challenge of designing an extradosed bridge with stiff girder lies in proportioning the girder,

cables and substructure to control the stress range in the cables due to live load, in order to take advantage

of a higher allowable stress for the extradosed cables. Since the girder is stiff, axial shortening of the

girder due to creep and shrinkage causes long term bending moments of similar magnitude to those due to

52

3.3 Conceptual Design


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p g

3.3.1 Fixity of the Girder to the Piers

Fixity of the girder, both at the side span supports and on the main piers, has a significant effect on both the

bending moment in the deck and on the stress range in the cables due to live load. Fixing the girder at the

piers allows the bridge to resist live load as a frame, causing a shift in bending moment in the loaded span

from positive to negative moment regions, where the moment is distributed into the piers. Fixing the

girder decreases the total bending moment in the deck and decreases the displacements, especially in the

spans adjacent to the applied load. Of the extradosed bridges in the Chapter 2 study, 26 out of 50 have

girders that are embedded on the piers.

Figure 3-5 shows the moment envelopes due to the CHBDC (CSA 2006a) CL-625 Live load for a

three span girder bridge of constant cross-section, with a main span of 100 m and side spans of different

length. The envelopes on the left side of the figure are for a case where the girder is fully restrained at the

inside piers, whereas those on the right side are for a girder on simple supports at the interior piers. For the

fixed condition, the moment range at the section of maximum moment in the side spans (difference

between maximum and minimum moment) is 55% of the value for the simply supported condition. When

the girder is embedded on the piers, the moment envelope will be somewhere between the two extremes

shown in Figure 3-5 .-25

-20

Moment, MNm

Girder fixed at interior supports Girder on simple supports

53

The height and configuration of the piers will influence the bending moment at the level of the


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foundations, especially due to resp. Piers that are fixed at their base deform in double bending, and thus

the moment at the base will be similar to that at the girder, unless there is a variation in the piers cross-

section. The piers can be proportioned to resist the bending moment due to live load without significant

reinforcement. The lever arm of the pier can be increased more easily than the deck, through a wider pier

or twin pier legs, without detriment to the aesthetics of the bridge. If footing dimensions are constrained, a

simply supported deck will be preferred to eliminate bending at the foundation level due to live load on the

superstructure.

The proportioning of the girder and piers are interrelated and cannot be treated independently. The

decision of whether to fix the girder to the piers in rotation or not should be made early on in the design

process as this significantly affects the forces in the bridge under live load. Both scenarios present no

difficulties in construction, and it appears preferable keep the girder embedded on the piers.

3.3.2 Side Span Length

When the girder is stiff, side spans should be proportioned similar to ordinary girder bridges (Kasuga

2006), generally between 0.6 and 0.8 of the main span, to balance the maximum moments in the side spans

and main span.Chio Cho (2000) found that side spans of less than half of the main span decrease the bending moment

in the main span, but recommends the use of side spans longer than 0.60 of the main span to produce a

positive bending moment in the side span due to live load that is similar in magnitude to that of the main

54

continuous spans simply-supported on the piers, and 40 to 45 for continuous spans embedded (fixed in


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rotation) at the piers. As a point of comparison, for cantilever bridges with internal tendons, Menn (1990)

suggests a span to depth ratio of 50 at midspan and 17 at the piers, based on aesthetic and economic

considerations.

The fib (2000) guide also suggests that the pier depth to midspan depth ratio of 3 is aesthetically

pleasing for bridges that are low to the ground but should be closer to 2 for tall structures. There is merit to

this recommendation; tall bridges with large variation in girder depth can look weak at midspan and out of

proportion with their wide piers, as shown in Figure 3-6 . However, this awkwardness can be diffused with

twin piers columns.

Cantilever Bridge

Span to Depth:17:1at piers

50:1 at midspan

Cantilever Bridge

Span to Depth:17.5:1at piers

35:1 at midspan

Extradosed Bridge

10:1 Span to Tower Height50:1 Span to Depth

Cable-Stayed Bridge

4 5:1 Span to Tower Height

Satisfactoryappearance

Goodappearance

Good Satisfactory

GoodGood

GoodTowers

55

Chio Cho (2000) recommends that towers not exceed a span to tower height ratio of 10, in order to


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limit the stress range due to live load in the extradosed cables to 80 MPa. Chio Cho claims that the purpose

of a variable depth cross-section is to reduce the cost of the bridge by reducing the girders self-weight,

without reducing the height at the supports. Haunching the deck at the piers reduces the quantity of both

internal and extradosed prestressing. Chio Cho suggests a span to depth ratio of 30 at the piers and 45 at

midspan for girders simply supported at the piers, with the transition occurring over a distance of 0.18 of

the span from the pier, as shown in Figure 3-7 b. Increasing the girder depth at the pier reduces the stress

range in the extradosed cables, and increases the bending moment at the supports with a small reduction in

moment at midspan. A larger girder depth at pier to depth at midspan ratio, as shown in Figure 3-7 c,allows

the first set of extradosed cables to be anchored farther away from the pier.

The aforementioned recommended proportions for span to tower height and span to girder depth ratios

are drawn in Figure 3-8 for the Chapter 4 bridge crossing, with a main span of 140 m. When compared to

the cantilever constructed girder bridges, the girder of the extradosed bridge dimensioned with Mathivats

proportions appears heavy at midspan, but the visual effect of the cables is subtle and unobtrusive. The

haunching at the piers recommended by Chio Cho and Komiya, combined with the fan cable configuration

Constant Depth Variable Depthhpier : hmid = 1.5

Variable Depthhpier : hmid = 2.0

Figure 3-7. Extradosed bridge geometry studied by Chio Cho (2000).

a) b) c)

56

rules, since they are based primarily on limits imposed on the maximum live load stress range in the cables


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of the bridges studied by those individuals. The variety in proportions of the bridges in Figure 2-1 should

be drawn upon for inspiration and to assess the feasibility in developing concepts for an extradosed bridge.

It seems necessary and rational to develop a computer model at an early stage in the design to account for

the interaction between tower, girder, substructure and cables to determine whether a given system

stiffness is adequate to limit the live load stress range in the cables to the desired level. This was the

approach taken in Chapter 4 which resulted in the bridges shown in Figure 3-9 .

In the Chapter 4 designs, a constant depth girder and harp cable configuration were chosen forconstructability and appearance. The constant depth girder provides the greatest continuity across the

entire bridge, while the parallel cables and simple tower shapes give the bridge a uniform texture.

Repetition and consistency of local components, such as ribs and anchorages, give the bridge an orderly

Extradosed Bridge with Stiff Girder- Chapter 4Span to tower height: 10:1

Span to depth ratio: 50:1

Extradosed Bridge with Stiff Tower - Chapter 4

Span to tower height: 10:1Span to depth ratio: 140:1

Figure 3-9. Bridge proportions used for design in Chapter 4.

Cantilever Constructed Girder Bridge - Chapter 4

Span to depth ratios: 17.5:1 at piers, 44:1 midspan

57

Tower Height h / Span Length l Tower Height h / Span Length lb)a)


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point, and thus the cables are often anchored at a constant offset down the tower in a semi-fan

configuration. The semi-fan cable configuration is more effective than a harp configuration in providing a

vertical component of resistance to the deck, but each cable anchorage at the deck level will be at a slightlydifferent angle and must be detailed separately. With a harp configuration, more cable steel is required,

but the cable anchorages have a common design which is advantageous, since the formwork and

reinforcement are consistent for all anchorage segments For shorter cables such as found in extradosed

Figure 3-10. Effect of cable inclination on the force components in a cable for a) a constant total force and b) aconstant vertical force.

0

0.2

0.4

0.6

0.8

1

Angle, deg

F o r c e Vertical

Horizontal

Total

Angle, deg

F o r c e

VerticalHorizontal

Total

16 302595 45 16 302595 450

2

4

6

8

10

120.13 0.250.200.07

Extradosed Typical Cable-Stayed Typical Extradosed Typical Cable-Stayed Typical

0.13 0.250.200.07

58

Leonhardt and Zellner (1970) published a chart comparing the stay cable steel consumption of harp


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and fan (radiating) cable configurations. From this chart, shown in Figure 3-11 a, it can be seen that the

optimum ratio of tower height to main span is around 0.30 considering stay cable steel consumption alone.

In 1970, the optimum height considering the cost of a tower was suggested to be between 0.16 l and 0.22 l

where l is the main span length, while in a similar chart published in 1980 (Leonhardt & Zellner 1980),

shown in Figure 3-11 b, the optimum height was 0.20 l to 0.25 l. This difference is attributed to the changes

in material preference and relative material costs. In the 1970 article, the tower is assumed to be steel,

whereas by 1980, concrete had become the economical material of choice. For the Brotonne Bridge,

completed in 1977, the cost of stay cable system was 29% of the total cost of the bridge, while the cost of

the tower was only 4% (Mathivat 1983).

A simple model was used to investigate the effect of tower height on steel consumption in stay cables

for a 140 m main span, the results of which are shown in Figure 3-12 . There are 10 cables in a half-span

spaced at 6 m, with the first cable 13 m from the pier, and each cable is assumed to resist an equal vertical

load of 0.05 units, for a total of 1 unit of load per span. For the semi-fan configuration, the cable

anchorages are spaced 0.3 m vertically on the tower. The graph bears a close resemblance to those of

Leonhardt and Zellner in Figure 3-11 . It is apparent that the harp configuration leads to a larger total cable

force, especially for a tower height below 0.1L.

8 n s p a n

)

10

59

increases the moment resistance of the girder, and the short towers can be easily proportioned to resist the


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increased bending.

Based on estimates from the aforementioned model, a harp cable configuration with a tower height of

L/8 requires a similar cable quantity to a semi-fan configuration with a tower height of L/12. For tower

heights of L/8 and L/12, the theoretical cable steel consumption will be 41 and 46 % more for the harp

configuration than the semi-fan while the maximum compression force in the deck will be 58 and 54%

higher.

Since the extradosed bridge has two load carrying systems, it is possible to provide cable support to

only a portion of the span. Figure 3-13 illustrates the effectiveness of providing partial cable support to the

deck, by plotting the ratio of fixed end moments of a partially loaded span to a fully loaded span (Tang

2007). For a section with constant weight and stiffness, it is most efficient to provide the cable support

closest to the midspan, as indicated by the upper line in Figure 3-13 . Many of the extradosed bridges

studied in Chapter 2 have cables distributed across 60% of the span. It can be determined from the upper

line Figure 3-13 that cables across 60% of the span will offset 80% of the moment of cables supporting

100% of the span.

0 6

0.8

1.0

, M

p a r t i a l

/ M f u l l

Mfull

60

3.4.2 Stay Cable Protection


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There are many systems for prot

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