Cable Supported Bridges E-Book

Niels J. Gimsing

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 885

Veröffentlichungsjahr: 2011

Beschreibung

Fourteen years on from its last edition, Cable Supported Bridges: Concept and Design, Third Edition, has been significantly updated with new material and brand new imagery throughout. Since the appearance of the second edition, the focus on the dynamic response of cable supported bridges has increased, and this development is recognised with two new chapters, covering bridge aerodynamics and other dynamic topics such as pedestrian-induced vibrations and bridge monitoring. This book concentrates on the synthesis of cable supported bridges, suspension as well as cable stayed, covering both design and construction aspects. The emphasis is on the conceptual design phase where the main features of the bridge will be determined. Based on comparative analyses with relatively simple mathematical expressions, the different structural forms are quantified and preliminary optimization demonstrated. This provides a first estimate on dimensions of the main load carrying elements to give in an initial input for mathematical computer models used in the detailed design phase. Key features: * Describes evolution and trends within the design and construction of cable supported bridges * Describes the response of structures to dynamic actions that have attracted growing attention in recent years * Highlights features of the different structural components and their interaction in the entire structural system * Presents simple mathematical expressions to give a first estimate on dimensions of the load carrying elements to be used in an initial computer input This comprehensive coverage of the design and construction of cable supported bridges provides an invaluable, tried and tested resource for academics and engineers.

Leseprobe

Contents

Cover

Title Page

Copyright

Preface to the Third Edition

Introduction

Chapter 1: Evolution of Cable Supported Bridges

Chapter 2: Cables

2.1 Basic Types of Cables

2.2 Corrosion Protection

2.3 Mechanical Properties

2.4 The Single Cable as a Structural Element

2.5 Static Analysis of Cables

2.6 Bending of Cables

2.7 Dynamic Behaviour of the Single Cable

Chapter 3: Cable System

3.1 Introduction

3.2 Suspension System

3.3 Fan System

3.4 Harp System

3.5 Hybrid Suspension and Cable Stayed System

3.6 Multi-Span Cable System

3.7 Cable Systems under Lateral Loading

3.8 Spatial Cable Systems

3.9 Oscillation of Cable Systems

Chapter 4: Deck (Stiffening Girder)

4.1 Action of the Deck

4.2 Supporting Conditions

4.3 Distribution of Dead Load Moments

4.4 Cross Section

4.5 Partial Earth Anchoring

Chapter 5: Pylons

5.1 Introduction

5.2 Structural Behaviour of the Pylon

5.3 Pylons Subjected Primarily to Vertical Forces from the Cable System

5.4 Pylons Subjected to Longitudinal Forces from the Cable System

5.5 Cross Section

Chapter 6: Cable Anchorage and Connection

6.1 Anchoring of the Single Strand

6.2 Connection between Cable and Deck

6.3 Connection between Main Cable and Hanger

6.4 Connection between Cable and Pylon

6.5 Connection between Cable and Anchor Block

Chapter 7: Erection

7.1 Introduction

7.2 Construction of Pylons

7.3 Erection of Suspension Bridge Main Cables

7.4 Erection of Stay Cables

7.5 Deck Erection - Earth Anchored Suspension Bridges

7.6 Deck Erection - Self Anchored Cable Stayed Bridges

Chapter 8: Aerodynamics

8.1 Historical Overview

8.2 The Bridge Deck and Pylon

8.3 Cables

Chapter 9: Particular Issues

9.1 Pedestrian-Induced Vibrations

9.2 Seismic Design

9.3 Structural Health Monitoring

9.4 Snow and Ice Removal and Prevention Systems

References

Index

This edition first published 2012© 2012, John Wiley & Sons, Ltd

First Edition published in 1983Second Edition published in 1997

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Library of Congress Cataloguing-in-Publication Data

Gimsing, Niels J.

Cable supported bridges: concept and design / Niels J. Gimsing, Christos T.

Georgakis. — 3rd ed.

p. cm.

Includes bibliographical references and index.

ISBN 978-0-470-66628-9 (cloth)

1. Cable-stayed bridges. 2. Suspension bridges. I. Georgakis, Christos T.

II. Title.

TG405.G55 2012

624.2′38—dc23

2011024092

A catalogue record for this book is available from the British Library.

Preface to the Third Edition

The decision to prepare a manuscript for a book titled Cable Supported Bridges was taken by Niels J. Gimsing in 1980 following his three year affiliation as an adviser on bridge technology to Statsbroen Store Bœlt—the client organization established to design and construct a bridge across Storebælt (Great Belt) in Denmark. During the design period from 1976 to 1979, a large number of different designs for cable stayed bridges (with spans up to 850 m) and suspension bridges (with spans up to 1800 m) were thoroughly investigated and it was during that period the idea matured to write a book covering both cable stayed bridges and suspension bridges. The chance to prepare the manuscript came in 1979 when the Danish Government decided to postpone the construction of the Storebælt Bridge and to keep the design work at rest for a period of five years.

The manuscript for the First Edition was completed in 1982 and the book was published in 1983.

The decision to prepare a manuscript for a Second Edition was taken in 1994 when Niels J. Gimsing was involved in the design of both the 1624 m main span of the Storebælt East Suspension Bridge and the 490 m main span of the Øresund cable stayed bridge. Both bridges were under construction during the writing of the manuscript (from 1994–1996) and so useful information on construction issues could be collected.

The Second Edition was published in 1997; fourteen years after the First Edition appeared.

The Second Edition was sold out from the publisher after only 5 years on the market, so a Third Edition became desirable, and initially it was anticipated that this would be just a simple updating of the Second Edition. However, when digging deeper into the matter it became evident that a considerable evolution had taken place during the decennium following the publishing of the Second Edition. Very notable cable supported bridges had been constructed and a number of design issues related primarily to dynamic actions had gained in prominence.

It was, therefore, realized that the Third Edition had to be more than just a simple updating of the Second Edition. To emphasize the importance of issues pertaining to dynamic actions and health monitoring it was decided that two new chapters would be added. With his years of experience within the field, Christos T. Georgakis was entrusted with this task.

The Third Edition is published in 2011; fourteen years after the Second Edition appeared.

Besides revisions and additions in the text it was also decided to update the figures by preparing them in electronic versions that could be more easily edited to appear in a uniform manner throughout the publication. The financial support to cover the expenses for the figure updating came from the COWI Foundation. The figures were updated by Kristian Nikolaj Gimsing.

In the process of preparing the Third Edition, highly appreciated contributions came from Professor Yozo Fujino of the University of Tokyo, on matters relating to structural health monitoring and structural control, and from Professor Francesco Ricciardelli of the University of Reggio Calabria, on matters pertaining to bridge aerodynamics. PhD student Joan Hee Roldsgaard helped greatly with the preparation of elements of Chapters 8 and 9 and for the proof correcting of the book. Our great appreciation is also extended to all those who provided pictures, figures and copyright permissions. They are too many to mention here.

Niels J. Gimsing and Christos T. GeorgakisTechnical University of DenmarkJune 2011

Introduction

In the family of bridge systems the cable supported bridges are distinguished by their ability to overcome large spans. At present, cable supported bridges are enabled for spans in the range from 200 m to 2000 m (and beyond), thus covering approximately 90 per cent of the present span range.

For the vast majority of cable supported bridges, the structural system can be divided into four main components as indicated in Figure 0.1:

1. the deck (or stiffening girder);

2. the cable system supporting the deck;

3. the pylons (or towers) supporting the cable system;

4. the anchor blocks (or anchor piers) supporting the cable system vertically and horizontally, or only vertically, at the extreme ends.

Figure 0.1 Main components of a cable supported bridge

The different types of cable supported bridges are distinctively characterized by the configuration of the cable system.

The suspension system (Figure 0.2) comprises a parabolic main cable and vertical hanger cables connecting the deck to the main cable. The most common suspension bridge system has three spans: a large main span flanked by shorter side spans. The three-span bridge is in most cases symmetrical with side spans of equal size, but where special conditions apply, the side spans can have different lengths.

Figure 0.2 Suspension bridge systems with vertical hangers and cable support of three spans (top) or only the main span (bottom)

In cases where only one large span is needed, the suspension bridge may have only the main span cable supported. However, to transmit the horizontal component of the main cable pull acting at the pylon tops, the main cable will have to continue as free backstays to the anchor blocks.

A single-span suspension bridge will be a natural choice if the pylons are on land or close to the coasts/river banks so that the traffic lanes will continue on viaducts outside the pylons.

The cable-stayed system (Figure 0.3) contains straight cables connecting the deck to the pylons. In the fan system, all stay cables radiate from the pylon top, whereas parallel stay cables are used in the harp system.

Figure 0.3 Cable stayed bridge systems: (top) pure fan system; (centre) semi-fan system; (bottom) harp system

Besides the two basic cable stayed systems (the fan system and the harp system), intermediate systems are often found. In the semi-fan system, the cable anchorages at the pylon top are spread sufficiently to separate each cable anchorage and thereby simplify the detailing. With cable anchorages positioned at minimum distances at the pylon top, the behaviour of the semi-fan system will be very close to that of the pure fan system.

The stay cable anchorages at the deck will generally be spaced equidistantly so in cases where the side spans are shorter than half of the main span, the number of stay cables leading to the main span will be greater than the number of stay cables leading to the side span. In that case the anchor cable from the pylon tops to the anchor piers will often consist of several closely spaced individual cables (as shown for the semi-fan system).

In the harp system, the number of cables leading to the main span will have to be the same as in the side spans. With the anchor pier positioned at the end of the side span harp, the length of the side span will be very close to half of the main span length. That might prove inconvenient in relation to the overall stiffness of the system. It can then be advantageous to position the anchor pier inside the side span harp as indicated in Figure 0.3.

The position of the anchor pier closer to the pylon can also prove favourable in a fan system, if designed with fans of equal size in the main and side spans (Figure 0.4).

Figure 0.4 Semi-fan system with side span pier inside the fan

For the harp system the most efficient structural system will be achieved if a number of intermediate piers can be positioned under the side span harps (Figure 0.5). This will be the preferred solution if the side spans are on land or in shallow water.

Figure 0.5 Harp system with intermediate supports in the side spans

The most common type of cable supported bridge is the three-span bridge with a large main span flanked by two smaller side spans. However, especially within cable stayed bridges, there are also examples of a symmetrical arrangement with two main spans of equal size or an asymmetrical two-span arrangement with a long main span and a somewhat shorter side span (Figure 0.6). If the two spans are of equal size, it will be necessary to stabilize the pylon top with two anchor cables whereas the asymmetrical arrangement often can be made with only an anchor cable in the shorter span.

Figure 0.6 Two-span cable stayed bridges

The vast majority of cable supported bridges are built with three or two spans, but in a few cases this has not been sufficient. A straight forward solution that maintains the advantages of the three-span configuration is then to arrange two or more three-span bridges in sequence, as shown in Figure 0.7 (top). In appearance, the bridge will have every second opening between pylons without a central pier and the other openings with a central anchor pier (or anchor block).

Figure 0.7 Multi-span cable supported bridges

A true multi-span cable supported bridge will consist of a number of main spans back-to-back as shown in Figure 0.7 (bottom).

In many cases, a true multi-span cable stayed bridge (bottom) will be preferable to a series of three-span bridges (top) from the point of view of appearance and function. However, from a structural viewpoint, the true multi-span arrangement presents a number of problems.

Due to the lack of anchor cables leading from vertically fixed points at the deck level to the pylon tops, the pylon must possess a considerable flexural stiffness to be able to withstand (with acceptable horizontal displacement at the top) a loading condition with traffic load in only one of the two spans adjacent to the pylon. In such a loading condition, the cable pull from the loaded span will be larger than from the unloaded span so the pylon must be able to withstand the difference between the horizontal force from the cable system in the loaded span and in the unloaded span.

In the early cable stayed bridges built from the mid-1950.s to the mid-1970s, the distance between cable anchorages at deck level was generally chosen to be quite large and as a consequence each stay cable had to carry a considerable load. It was therefore necessary to compose each stay of several prefabricated strands joined together (Figure 0.8, left).

Figure 0.8 Cable stayed system with few multi-strand cables (left) and a multi-cable system (right)

It was necessary to let the multi-strand cable pass over the pylon on a saddle as the space available did not allow the splitting and individual anchoring of each strand, and at the deck the anchoring of the multi-strand cable made it absolutely necessary to split it into individual strands.

In modern cable stayed bridges, the number of stay cables is generally chosen to be so high that each stay can be made as a mono-strand. This will ease installation, and particularly replacement, and it will render a more continuous support to the deck (Figure 0.8, right).

With the multi-cable system it will be possible to replace the stays one by one if the deck is designed for it, which will often be required in the Design Specifications. The advantages gained in relation to erection, maintenance and replacement have to some extent been set against an increased tendency for the stays in a multi-cable system to suffer from wind-induced vibrations.

Besides the configuration of the cables, cable supported bridges can also be distinguished by the way the cable system is anchored at the end supports. In the self-anchored system, the horizontal component of the cable force in the anchor cable is transferred as compression in the deck, whereas the vertical component is taken by the anchor pier (Figure 0.9, left). In the earth anchored systems, both the vertical and the horizontal components of the cable force are transferred to the anchor block (Figure 0.9, right).

Figure 0.9 Connection between the side span cable and the anchor pier/block in a self-anchored system (left), and in an earth-anchored system (right)

In principle, both earth anchoring and self-anchoring can be applied in suspension bridges as well as in cable stayed bridges. However, in actual practice, earth anchoring is primarily used for suspension bridges and self-anchoring for cable-stayed bridges.

For the suspension bridges, self-anchoring is especially unfavourable in relation to structural efficiency and constructability. In modern practice, self-anchored suspension bridges are therefore only seen when the decision to use the system is taken by people without structural competence and who are not concerned about construction costs.

In the transverse direction of the bridge, a number of different solutions for the arrangement of the cable systems can be found. The arrangement used traditionally in suspension bridges comprises two vertical cable planes supporting the deck along the edges of the bridge deck (Figure 0.10). In this arrangement (which is also seen in many cable stayed bridges), the deck is supported by the cable systems both vertically and torsionally.

Figure 0.10 System with two vertical cable planes attached along the edges of the bridge deck

In cases where the bridge deck is divided into three separate traffic areas, e.g. a central railway or tramway area flanked by roadway areas on either side, the two vertical cable planes might be positioned between the central area and the outer areas (Figure 0.11, left). This arrangement is especially attractive if the central area is subjected to heavy loads that would induce large sagging moments in the transverse girders if the cable planes were attached along the edges of the bridge deck. On the other hand, with the cable planes moved in from the edges towards the centre of the deck, the torsional support offered by the cable system will be drastically reduced. A more moderate displacement of the cable planes from the edges of the deck is found in bridges with cantilevered lanes for pedestrians and bicycles (Figure 0.11, right).

Figure 0.11 Systems with two vertical cable planes positioned between three separate traffic lanes

The application of more than two vertical cable planes (Figure 0.12) was seen in some of the large American suspension bridges from the end of the nineteenth century and the beginning of the twentieth century. In bridges with a wide bridge deck, more than two cable planes could still be considered, as the moments in the transverse girders will be significantly reduced.

Figure 0.12 System with four vertical cable planes positioned outside and between three separate traffic lanes

Only one vertical cable plane (Figure 0.13) has been widely used in cable stayed bridges. In this arrangement, the deck is only supported vertically by the cable system, and torsional moments must therefore be transmitted by the deck. Consequently, the deck must be designed with a box-shaped cross-section.

Figure 0.13 System with one central cable plane

Inclined cable planes (Figure 0.14) attached at the edges of the bridge deck and converging at the top are found in cable stayed bridges with A-shaped pylons. In this arrangement the deck is supported both vertically and torsionally by the cable system.

Figure 0.14 System with two inclined cable planes

Two inclined cable planes converging at the top can also be supported on a single vertical pylon penetrating the deck in the central reserve or in the gap between two individual box girders.

Chapter 1

Evolution of Cable Supported Bridges

The principle of carrying loads by suspending a rope, chain or cable across an obstacle has been known since ancient times. However, it was not until 1823 that the first permanent bridge supported by cables composed of drawn iron wires was built in Geneva by the Frenchman Marc Seguin, one of five brothers who, in the following two decades, built hundreds of suspension bridges around Europe. All of these bridges were of modest size but they marked an important step on the way to the more impressive structures that followed.

The application of thin wires in the main load-carrying elements gave rise to a number of problems especially in relation to durability, as an efficient method for corrosion protection had not been found at that time. Therefore, some of the leading engineers preferred to construct suspension bridges with the main load-carrying elements, the catenaries, composed of pin-connected eye-bars forming huge chains.

This principle was applied by the British engineer Thomas Telford in the world's first bridge to cross a strait used by ocean-going vessels, the Menai Bridge between the British mainland and the Isle of Anglesey (Figure 1.1). Opened to traffic in 1826, this bridge had its 176 m long main span supported by chains assembled from wrought iron eye-bars, each with a length of 2.9 m.

Figure 1.1 The suspension bridge across the Menai Strait (UK)

The chain support was generally preferred by the British engineers of the nineteenth century and a number of notable bridges were built, among these the famous Clifton Suspension Bridge, initially designed by Isambard Kingdom Brunel, but not actually constructed until after his death. The bridge was opened to traffic in 1864 and it comprised a main span of 214 m – an impressive span, considering that the strength-to-density ratio of the wrought steel in the chains was less than one-fifth of the ratio of modern cable steel (Figure 1.2).

Figure 1.2 Clifton Suspension Bridge (UK)

To erect the eye-bar chains, a temporary footway had to be established between the supporting points on the pylon tops and at the anchor blocks. In the case of the Clifton Suspension Bridge, this temporary footway was supported by wire ropes, so the principle of cable support was actually applied, although only in the construction phase.

A most unusual bridge based on application of eye-bar chains is the Albert Bridge across the Thames in London (Figure 1.3). The bridge was built from 1871 to 1873 and it is characterized by combining the cable stayed and the suspension system. A part of the deck load is transferred to the strong top chain through hangers and the rest is carried by a number of straight chains radiating from the pylon tops. The system is statically indeterminate to such a degree that it was impossible with the available tools to calculate forces and moments to get even close to the exact values. Nevertheless the bridge with its 122 m-long main span is still in service although there are restrictions on the traffic allowed to pass over it (Figure 1.4).

Figure 1.3 Albert Bridge across the Thames (UK)

Figure 1.4 Traffic restrictions on the Albert Bridge (UK)

Chain support was also applied in a number of bridges on the European continent, but here it was to a larger extent in competition with cable supported suspension bridges. Thus the longest free span in Europe was for several decades found in the wire supported Grand Pont Suspendu across the Sarine Valley at Fribourg in Switzerland. The bridge was completed in 1834 and it had a main span of 273 m. In the Grand Pont Suspendu, each of the four main cables was composed of over 1000 wires, grouped in 20 strands, each assembled on the ground and lifted individually into position. The bridge was in service for almost a century until it was finally demolished in 1923.

On a global level, the Swiss span record was beaten in 1849 by the completion of the Wheeling Suspension Bridge across the Ohio River in the USA. This bridge had a main span of 308 m, carried by a total of 12 parallel-wire cables, six on either side of the roadway.

The Wheeling Bridge is still in existence, although not in its original version. Five years after its completion, in 1854, a violent gale blew the bridge down. Subsequently it was reconstructed and later, in 1872, further strengthened by a fan-shaped system of stays. The principle of strengthening the suspension system with stays was originally introduced during the construction of the suspension bridge across the Niagara Gorge. This bridge was designed by the famous bridge designer John A. Roebling, who was born in Germany but emigrated to the United States of America at the age of 25. The Niagara Bridge was constructed in the period from 1851 to 1855 and it was the first major suspension bridge to have air-spun wire cables, a system invented by Roebling.

The span of the Niagara Bridge was not quite as long as for the largest suspension bridges of that time but, due to the fact that the bridge carried both a railroad track and a roadway, its span of 250 m was still a very impressive achievement. As a most unusual feature the truss of the Niagara Bridge had the railroad track on the upper deck and the roadway on the lower, inside the two trusses.

Another unusual feature of the Niagara Bridge was the use of wood in the truss. This might today seem to be an awkward combination of structural materials but it must be remembered that in the early days of railroad building in North America, wood was the preferred material for bridges across rivers and gorges. For the Niagara Bridge, the application of a wooden truss resulted in a relatively short lifespan as the bridge had to be replaced in 1897 after 42 years of service.