Bridge aerodynamics

AERODYNAMICS OF LARGE BRIDGES

PROCEEDINGS OF THE FIRST INTERNATIONAL SYMPOSIUM ON AERODYNAMICS OF LARGE BRIDGES / COPENHAGEN / DENMARK/19 - 21 FEBRUARY 1992

Aerodyna Aerodynamics mics o f L La arge Bridges  Edited by

ALLAN LARSEN COWIconsult  Organized by

DANISH MARITIME MARITIME INSTITUTE

A. A. BALKEMA BALKEMA / ROTTERD ROTTERDAM AM / BROOKFIELD BROOKFIELD / 1992

The The texts of o f the the various papers in this volume volume were set set individually i ndividually by typists typists under under the supervision o off each each of the authors concerned.

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Published by A. A. Balkema, P.O.Box 1675,30 16 75,3000 00 BR Rotterdam, Rotterdam , Netherlands Nether lands A. A. Balkema Publishers, Publishe rs, Old Post Road, B rookfield, VT 05036, USA ISBN 13: 9789054100423 ©

1992 A. A. A. Balkema, Rotterdam

 Aerodynam  Aerodynamics ics of Large Large Bridges Bridges,, A. A. Larsen Larsen (ed.) (ed.) © 1992 Balkema, Rotterdam. ISBN 905410 042 7 

Table of contents

Preface

vn

1 Overview Bridge engineering and aerodynamics  Klaus H.Ostenfeld & Allan Larsen

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2 Wind  Aspects o f the natu natura rall wind o f relevance to large bridges  N.O.Jensen,  N.O.Jensen, J.Mann & LKris LK risten tense sen n

25

Wind criteria criteria for long lon g span bridges  Henrik Overgaar Over gaard d Madsen & Peter Ostenfeld-Rosenthal 

33

3  Aerodynamic aspects Wind dynamics dynamics of long-span bridges bridges  R.H.Scanlan

47

The improvement of aerodynamic performance  R.LWa  R.L Wardla rdlaw w

59

Wind engineering o f large bridges in Japan Japan  M.Ito

71

4 Tools Similitude and modelling in bridge aerodynamics  H.Tana  H.Tanaka ka

83

Section model tests  E.Hjorth-Hansen

95

Taut strip model tests  A.G.Davenport,  A.G.Davenp ort, J.P.C.King & G.LLa G.L Laro rose se

113

Full aeroelastic model tests  P.A  P.A.. Irwin

125

A new wide wid e boundary boundary layer wind tunnel at the Danish Danis h Maritime Institute  Lei  L eiff Wagner Smitt & Michael Michae l Brinch

137

5 Application!design The construction phase and its aerodynamic issues issu es Fabio Brancaleon B rancaleoni  i 

147

Recent British developments: Windshielding Windshiel ding o f bridges for traffic T.A.Wyatt 

159

Examples o f analytical analytical aerodynamic aerodynamic investigations of long-span bridges  Holger  Holg er S.Svensson & Imre Kovacs Kovac s

171

Wind design desig n and analysis for the Normandy Bridge  Michel Virlogeux 

183

Akashi Kaikyo Bridge: Bridge: Wind effects and full model wind tunn tunnel el tests Toshio Toshio Miyata Miyat a , Koichi Yokoyama Yokoyama,, Masahiko Yasuda Yasuda & Yuichi Yuichi Hikami 

217

The bi-stayed bridge bridge concept: concept: Overview o f wind engineering problems problems  J.  J. Muller  Mulle r 

237

Bel t experience experience 6 Great Belt The fixed link across the Gre Great at Belt Christian Tolstrup

249 24 9

Wind tunnel tests for the Gre Great at Belt link Timothy A. Reinhold, Micha el Brinch & Aage D ams gaard   ga ard 

255

Aerodynamic design o f the Gr Great eat Belt East Bridge  Allan Larsen & Arne S Jaco  Ja cobs bsen en

269

Simulation o f marine traffic traffic for assessment assess ment of bridge span  Jens Bay & Stig E. E. Sand 

285

1 The The future futu re Large bridges o f the futur futuree  Niels J.Gimsing 

295

Author Author index

305

VI

 Aerodynam  Aerodynamics ics of Large Large Bridges Bridges, A. Larsen Larsen (ed. (ed.)) © 1992 1992 Balkema Balkema, Rotterdam Rotterdam.. ISBN 905410 042 7 

Preface

As bridge b ridge spans get longer, lighter and more slender, aerodynamic aerodyn amic loads load s becom bec omee a matter matter for serious study. The very long spans currently under design and construction notably in Japan, France and Denmark have necessitated thorough investigations into the wind conditions at the bridge site and the aerodynamic performance of the bridge structures. Future bridges with ultra-long spans, partly built in new light weight materials, will further accentuate the need for a thorough aerodynamic understanding even at early planning and design stages. Bridge Aerodynamics fall into a ‘grey zone’ between established fields of work associated with Civil Engineering, Mechanical Engineering and Meteorology. Hence most of the literature on the aerodynamics aerodynamics o f bridges bridges is scattered scattered in periodicals and conference conferen ce proceedings proceed ings related to Structur Structural al Dynamics, Dynamics , Fluid Dynamics Dynam ics and Wind Engineering. The 1992 Internat Internation ional al Symposium on Aerodynamics Aerodynamics o f Large Large Bridges Bridges - ISALB’92 ISA LB’92 - is arran arranged ged at at the occasion of the t he extensive exten sive aerodynamic investigations investi gations carried carried out for the Great Great Belt East Bridge, a 1624 meter main span suspension bridge, currently under construction in Denmark. This very long span has warranted a wide range of analytical and experimental investigations, including testing o f a full aeroelastic bridge bridge model in a wide purpose built wind tunnel at the the Danish Maritime Maritime Institut Institute. e. The ISALB ’92 symposium sympos ium brings together tog ether internationally internationally recognized recogn ized experts in Bridge Building, Meteorology and Wind Engineering to present state-of-the-art contributions within a common framewor framework: k: The analysis and design o f long span bridges bridges for adequate aerodyna aerodyna mic performance. The proceedings contain specially invited papers presented at seven plenary sessions held in Copenhagen, Denmark, 19-21 February 1992. An additional paper on the design and performance of the new wide wind tunnel inaugurated at this occasion is included for completeness. The sequence of the papers in the proceedings is based on the division into sessions during the symposium. The proceedings are printed by direct offset from the individual authors’ original manuscripts. The editor is therefore not responsible for misprints or errors in the text. The opinions expressed are those of the author authorss and not necessarily those o f the editor editor.. The editor and the organizers extend warm and sincere thanks to all authors and co-authors for their valuable contributions. Als o the editor and organizers organizers convey conv ey appreciation appreciation to the COWIfoundation for ensuring financial suppor supportt which allows allow s wide wi de publication of o f the proceedings. Allan Larsen, Editor and Chairman of Technical Committee

Arne Hasle Nielsen, Chairman of Organizing Committee

SYMPOSIUM ORGANIZED BY: The Danish Maritime Institut Institutee (DMI) (DM I) under the auspices of: The Danish Group Group of o f the Internati International onal Association Associ ation for Bridge and Struc Structur tural al Engineering (IABSE) (IABS E) and and The Danish S ociety for Stru Structu ctural ral Science Scien ce and Engineering SYMPOSIUM SPONSORED BY: B.H0jlund Rasmussen, Consulting Engineers CMFSudS.p.A. Commission of the European Communities Danish Maritime Maritime Institute Institute Danish Technical Research Council Great Gre at Belt Bel t A. S. Kampihl PROCEEDINGS SPONSORED BY: COWIfoundation ORGANIZING COMMITTEE Arne Hasle N ielsen ielse n (Chairman), (Chairman), Director Director,, Danish Da nish Maritime Institute Institute Erik Kasper (Secretary), Danish Maritime Institute Mikael W. W. Brae Braestru strup, p, Danish Dan ish Society So ciety for Structur Structural al Scienc Sc iencee and Engineering Ole Damgaard Larsen, Danish Group of the International Association for Bridges and Structural Engineering (IABSE) TECHNICAL COMMITTEE COMMITTEE Allan Larsen (Editor and Chairman), COWIconsult Niels J.Gimsing, Professor, Technical University of Denmark  Timothy A. A . Reinhold, Danish Dan ish Maritime Institute Institute

VIII

1 Overview

 Aerodyna  Aerodynamics mics of Large Large Bridges Bridges,, A. A. Larsen Larsen (ed.) (ed.) © 1992 1992 Balkem Balkema, a, Rotter Rotterdam dam.. ISBN 905410 042 7 

Bridge engineering and aerodynamics Klaus H.Ostenfeld & Allan Larsen COWIconsult, Consulting Engineers and Planners A IS, Den  Denm mark  ark 

ABSTRACT: Aerodynamic performance of long span bridges is accentuated by the trends to span still wider straits and busy shipping lanes, safely and economically. The present paper outlines the salient aerodynamic features in present and future bridge design. The theoretical and experimental tools available to the designer are addressed. Research and development needs are identified in order to meet the aerodynamic challenges where costs, construction and maintenance will introduce new structural materials with improved strength/weight ratios. Such very light structures will be aerodynamically sensitive if special precautions are not taken. A computer controlled active stabilization system is outlined inspired by active control surface systems in advanced aircraft.

1 INTRO DUC TION

the 19th Century. James Finley built some 40 bridges in the first decade. They were quite daring, prone as they were to destruction by relatively light loads - and winds. For more than 150 years interaction between betwe en wind and structure was poorly under stood in suspension bridge design. Many sus pended spans were damaged or completely wrecked by storm winds. Notable examples recorded by eye witnesses are: are: Brighton Chain Pier (1836), Menai Straits (1839), Wheeling (1854) and Niagara-Clifton (1888) (ShirlySmith 1964, Plowden 1974). The awakening for aerodynamic investiga tions did not come until the very light and slender Tacoma Narrows Bridge was destroyed by a relatively low 20 m/s wind in 1940 (Farquahrson et. al. 1949). It was probably the problem of dynamic instability and structure/wind interaction that caused most of the earlier wind-induced fail ures of suspension bridges as well.

The oldest form of bridge used for spanning land or water is probably pure suspension bridges bridges.. The earliest examples had cables con con  sisting of jungle creepers or iron chains. This material was used in China already two hun dred years BC. The load was carried by the tension cables acting alone, and the flexible deck had to follow the curve of the cables although it did not always rest directly on them. The purpose of these bridges was to provide a pathway and it was not always a safe one. They were highly deformable as the pure tensional members had to deform from the catenary shape in order to carry imposed concentrated load. The much later introduced stiffening girder was an improvement. It stiff ens the bridge and distributes concentrated loads along the cable by shear and moments. The age of the fully developed suspended span with a horizontal traffic path began in

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3.1

2 DESIGN REQUIREMENTS AND WIND EFFECTS

Truss Girders

Historically most long span cable supported bridges have been built with truss girders in order to facilitate fabrication and erection, whereas little attention was paid to mainte nance and aerodynamic performance. A notable exception to the latter is the design philosophy proposed by Roebling who sug gested truss railings for stiffening the stormwrecked Wheeling span reconstructed in 1855 (Plowden 1974). Roebling also devised deep timber trusses for the two level Niagara rail and road suspension bridge (1855) which, unlike other suspended spans at the Niagara,

The challenges for the designer are to develop bridge concepts with sufficient structural relia bility and avoid e.g. excessive deformations, cracking, plastic deformation, and of course collapse. Long service life requires a structure with minimum deterioration and wear: durability. Likewise, the users require a high level of  comfort: serviceability. The society requires a low level of risk  associated with operation of the bridge struc tures: third party risk. The aerodynamic phenomena which must be considered with respect to the above cri teria can roughly be categorized as follows: - Aerodynamic Aerody namic instability - statical divergence diverg ence or flutter - which if allowed to develop, will destroy the bridge. - Buffeting, the forced movements caused by randomly randomly fluctuating wind loads (turbulent) present at all wind speeds. Buffeting should be limited in order to obtain sufficient reliability and adequate comfort. - Vortex shedding, including forced vibra vibra tions induced in non streamlined objects like buff deck sections. - Rain induced vibration vibration of cables, caused by by change of aerodynamic properties from water flow along the cables. - Traffic Traffic comfort requires requires low acceleration levels for the structures and limitation of  variations of lateral wind loads and wake turbulence on passing vehicles.

 I  -------------------------  -------------------------- - — ----------------------- J-

3 ELEMENT SHAPES AN D CONFIGURATIONS In long span cable supported bridges all the different structural elements contribute as an assembly to the overall aerodynamic perform ance. ance. The stiffening girder generates normally normally the major part of the wind loading. For very long span bridges the towers, cables and equipment also contribute considerably to the overall aerodynamic behaviour of the struc ture.

Fig. ig. 3.1 Drag Dra g coefficie coeff icient nt CDOfo r a truss section sect ion and a streamlined box section (Little Belt sus  pension  pensio n bridge) bridge)..

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3.2

survived the frequent storms at this location (Shirly-Smith 1964). Trusses can be designed to exhibit suffi cient torsional stiffness to safeguard the bridge against torsional flutter instability by introducing horizontal top and bottom windbracings and adopting a truss depth of 1:170 1:120 of the span length. The flutter resistance can be further enhanced by longitudinal open slots in the road deck, a well known feature from post World War II suspension bridges in North America and Japan. The open lattice truss structure structure perpendicu perpen dicu lar to the wind also prevents periodic forma tion and shedding of large vortices in the wake of the truss with associated risk of res onant oscillation. However, truss sections usually exhibit quite high wind forces (drag loading) which must be resisted by the bridge structure. This will have a relative effect on costs. As an example, figure 3.1 compares the drag coeffi cient Qdo  at zero incidence measured for a truss and box design for the Little Belt bridge (Ostenfeld et. al. 1970). It is noted that the drag of the truss section is more than 3 times that of the streamlined box. The Little Belt bridge was one of the two first suspension bridges adopting the modern box girder design. The high lateral wind loads for truss girders compared to streamlined box girders are usually only of relative minor importance for medium span classical suspension bridges. It is of fundamental importance in the design of  long span cable-stayed bridges, particularly during the cantilever erection, and in the case of very long span suspension bridges. Truss girders are commonly found to be 15% - 20% heavier than box girders designed for similar live load. Also maintenance is diffi cult, and costs are considerably higher. Nevertheless, the truss girder still remains an alternative for future long span bridges particularly from the point of view of aerody namic namic stabili stability. ty. Further developm de velopment ent would be useful to minimize structural dead load and drag loading. This may partly be accomplished by use of aerodynamically shaped (circular or - even better - elliptical) members.

Box Girders

The need for fast and efficient rebuilding of  approximately 8500 bridges in post-war Ger many called for the development of new design concepts and fabrication techniques. The box girder, originally introduced by Robert Stephenson in the 19th Century, was perfected into the thin-walled all-welded structural member commonly used today (Plowden 1974). Contrary to the traditional truss girder, the orthotropic steel deck in a contemporary box girder serves as an integral part of the structure. Substantial savings in weight are obtained, also in construction and maintenance costs, but aerodynamic problems problems persist. In particular during the erection phases when the girder lacks the final torsio nal stiffness, mass and continuity. Aerodynamically the box section concept holds a promise to reduce the lateral wind loading in comparison with the truss girder, as demonstrated in figure 3.1, while maintaining the structural stiffness in torsion. A drawback  is the tendency of the wind to form and shed vortices in the wake of the box because of  insufficiently aerodynamical shaping of the downstream edge of the girder. In many instances this leads to small amplitude oscilla tions at low wind speeds. Vortex induced oscillations may not have immediate cata strophic consequences consequ ences for the bridge structure structure itself, but are unacceptable to users, and may cause structural structural fatigue and wear in joints and bearings. Vortex shedding action can be reduced to an acceptable level by "streamlin ing" the box section, i.e. use of aerodynamic fairings - guide vanes - at the wind-ward and down-wind edges as used for the first time for the Little Belt bridge (Ostenfeld et. al. 1970). This method has also found its use as a retrofit measure i.e. in case of the Long’s Creek cable-stayed bridge (Wardlaw & Goettler 1968). In bridge design a set of conflicting requirements becomes apparent in case of the box girder. A slender airfoil shaped bridge girder would produce minimum drag and effi ciently prevent vortex shedding. Practical bridge decks with an upper surface suitable for traffic can only with difficulty be shaped

5

with a sufficiently low thickness ratio to obtain minimum drag. Ideally, low thickness ratio (depth/width) should be combined with soft curvatures of panels extended thin trail ing edge and rounded upstream nose (airfoil design). For real bridges the deck may be exposed to wind from both sides. Thus a box design, symmetrical about the vertical centre plane and featuring rounded off edges, is pre ferable. In this case, disadvantageous down stream flow may develop, but can be compen sated/improved by introduction of guide vanes. The aerodynamic instability of box girders is often found to be of the classical flutter type (2 Degree Of Freedom - 2 DOF - ben ding/torsion) also encountered encounter ed in aeronautical engineering for the wings of aircraft. Flutter often becomes a governing factor in the design of very long span bridges, and it is con ceivable to have catastrophic consequences for the bridge structure, if stability require ments are not observed as for the Tacoma bridge. The aerodynamic stability performance

of cross sections may conveniently be com pared to that of a flat plate section with iden tical width and dynamic properties. The criti cal wind speed Uf for the onset of flutter for a flat plate (which can be determined theo retically) becomes a suitable reference figure for evaluation of the flutter performance of  actual bridge bridge section designs. Figure 3.2 shows the critical wind speed relative to that of the flat plate, U/Uf, for three box section geometries investigated for the Little Belt suspension bridge (Ostenfeld et. al. 1970). It is observed that by gradually ’’streamlining" the rectangular box, i.e. by fitting of cantilevered decks or wedge shaped fairings suc cessively, it is possible to more than double the critical wind speed of the proposed box section. Further enhancement of the critical wind speed Uc can be obtained by longitudinal ventilated slots as known from traditional truss girders. Figure 3.3 shows the critical wind speed relative to that of the flat plate, U /U f for five girde girderr sections intended for suspension bridges with main spans in the range of 2000 m - 3000 m. Two box sections for road bridges are shown along with propo sals for two level combined box/truss sections designed for road and rail traffic. It is noted that longitudinal ventilated slots present a means to subdue aerodynamic instability of  bridge girder cross sections. The penalty is increased drag - and construction costs. Judging from figure 3.3 the slotted box section performs approximately 20% better (critical wind speed) than the conventional "streamlined" box. The actual increase in criti cal wind speed for a given bridge design is somewhat higher due to the increase of tor sional stiffness and mass of the slotted box over that of the conventional design. This is illustrated in figure 3.4 which compares criti cal wind speeds of conventional 3 span sus pension bridges with main span lengths from 2000 m - 5000 m based on the slotted and the conventional box girder concept. It is observed that the critical wind speeds obtained for the slotted box girder are enhanced by approximately 38%, but at the expense of a 36% increase in structural steel.

JH Uc / U f = 0.43 0.43 s

V

i  s

Uc /U f = 0.6 0.62 2

Uc / U f = 0.9 0.91 1

Uc / U f : Critica Criticall Wind Wind Speed Speed Relative to Flat Plate

Figu Figure re 3.2 Critical wind speeds for three three box   girder  girder concepts suggested suggested for fo r the Little Lit tle Belt sus s us  pension bridg bridge. e.

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Proposed Sections 2000m - 3000m Cable Supported Support ed Spans

Road/Rail

Uc /U f = 0.8 0.85

Uc /U f

= 0.98 0.98

Uc / U f = 1.22 .22

Figu Figure re 3.3 Flutter Flutter performance o f five girder sections propos pro posed ed for 2000 m - 3000 m main span suspension bridges.

The figure is based on smooth flow assump tion. Turbulent flow conditions will generally reduce flutter speeds.

Most box girders are built from flat trough stiffened panels in order to ensure adequate stiffness and minimize fabrication costs. Hence the cross sections will be polygonal straight lined trapezoids. Curved wind-ward and down-wind fairings fairings will will reduce the section drag (lateral wind loading), and the vortex shedding performance somewhat, but the critical wind speed is likely to remain virtually unaffected. This trend is demonstrated in figure 3.5 where drag coefficients at zero in ciden ce CD0 for basic sharp edged ed ged and rounded-off two dimensional shapes are com pared to drag coefficients obtained for the box sections proposed for the Normandie cable-stayed bridge under construction in France (Szechenyi 1989). This is an excellent example of application of the "streamlining” process as mentioned earlier in this section. The box girder possesses qualities which today makes it structurally and economically superior to the truss girder, but aerodynami cally the box girder may encounter stability problems if applied to the extreme spans of 

Critical Wind Speed Uc

Main Span Lenght (m)

Figu Figure re 3.4 Estimated Estim ated critical critical wind speeds for  3 span suspension bridges bridges based on conventional  and slotted box gird girders ers.. Side span/main span ratio = 1/3, cable sag ratio =  H9.  H9. Traf Traffic fic capac ity: 4 lanes of road traffic.

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flow separation and turbulent wake (similar (similar to an airfoil stall). Such devices may include guide vanes, winglets or various types of  wedge shaped or perforated edge fairings. Appendages may be applied as a retrofit measure in order to relieve adverse aerody namic effects unforseen at the design stage, or incorporated in the original design. An example of the latter approach is the guide vane developed for the Little Belt sus pension bridge. It is situated at the outer edge of the roadway, see figure 3.6, and has two aerodynamic functions: - To avoid or reduce the formation of coher ent large scale vortices in the wake of the girder due to the relatively abrupt change of surface angle, and thus eliminate vortex induced vibrations vibrations at low wind speeds. - To increase the aerodynamic damping damping in torsion and thus enhance the critical wind speed for onset of flutter. This guide vane was not found strictly necessary for the 600 m span of the Little Belt bridge, but was adopted as an extra and inex pensive safety precaution. The guide vane has later found its use on a number of bridge girders. In the St. Nazaire cable-stayed bridge in France which is designed with a consider ably more bluff box girder than the Little Belt bridge, the guide vanes were found necessary to improve flow conditions and reduce the

Basic Section Forms

■ t c

0.90

Proposed Sections, Normandie Bridge

do

  =

Drag Coeffi Coe fficie cient: nt: C D0 =

0 -4 -4 2

Drag Load/Unit Length 1 /2 p U h

Figure Figure 3.5 Influence o f edge configuration on drag coefficients for simple two dimensional  shapes shapes and box girder girder sections proposed propo sed for the  Normandie bridg bridge. e.

the future. Research and development activ ities should thus focus on box girder concepts which alleviate the aerodynamic problems. A closed box version of the twin deck girder (Richardson 1988) may constitute one way to achieve this goal without increasing mainten ance and fabrication costs dramatically. New active control systems may however be even more promising and economical as further presented in section 5.

Railing Guide vane

3.3 Aerodynamic Appendages The aerodynamic performance of trapezoidal bridge girders - often called "streamlined", but not really streamlined in a true aerodynamic sense - may be enhanced through application of various types of appendages which reduce

St. Nazaire Bridge

Figure Figure 3.6 Guide vanes as incorporate incor porated d in the  Little Belt and St. St. Nazaire girder design designs. s.

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vortex shedding oscillations to acceptable levels (Wardlaw 1971). Guide vanes are also reported to be incorporated in the design of  the future Tsing Ma suspension bridge in Hong Kong (Simpson et. al. 1991).

3.4

Wind Screens

Wind screens might be necessary for bridges at certain locations to protect light traffic from strong cross-winds. They may be designed as porous fences with a height simi lar to tall vehicles. Typical designs constitute shields shields composed of longitudinal or horizontal equispaced bars or of perforated plates with holes, see figure 3.7. Wind tunnel tests indi cate that the shape of the openings is of  minor importance for the efficiency of the screen. The porosity however, i.e. the ratio of  openings to the total screen area, is of signifi cant importance to the shelter provided and to the drag loading generated by the screens on the bridge. Wind screens of small porosity, say 0.1 0.2, provide very effective shelters character ized by mean wind speeds as low as 10% 25% of the onset wind speed. The penalty paid for low porosity screens is a very high drag loading which may amount to twice that of the bridge girder itself. Also low porosity will create separating turbulent flow behind the screen which will will cause unfavourable u nfavourable fluc tuating wind loads on vehicles travelling at a certain distance from the screen outside the Figuree 3.7 Wind screens of bar and perforated  directly sheltered zone. Wind screens of  Figur  pla te design design suggested for a 1624 m main span porosity 0.4 - 0.5 are more suitable for bridge  plate design, because they offer a reasonable com suspension bridge. promise between shelter efficiency (reduction in onset wind speed) in the range of 50% 75%, and the drag loading will equal that of  3.5 Cables a well designed box girder. Wind tunnel tests Wire cables constitute an important load have shown that wind screens of 0.5 porosity carrying element in both suspension and can be arranged on "streamli " streamlined” ned” box girders girders cable-stayed long span bridges. with little if any penalty to the aerodynamic Main cables in suspension bridges have stability. An appropriate air-gap must however be allowed for between the bottom member of  never been reported to cause aerodynamic problems for the bridge in service, but their the screen screen and the deck to ensure undisturbed drag loading must be assessed during design flow (Ostenfeld 1989). and incorporated in the overall wind loading on the th e bridge. bridge. Dynamic Dynam ic actions, such as vortex

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shedding oscillations or galloping under icedup conditions, are not possible due to the fixation of the cable by the stiffening girder via the multiple hangers. During erection of main cables using the air-spinning method, thin steel wires are pulled across the span from anchorage to anchorage via the tower tops. This procedure is sensitive to wind conditions, and on windy days work has to be stopped. The use of prefabricated parallel wire strands, e.g. hexagonal bundles of 127 single wires as the building block of main cables, decreases the wind sensitivity of the cable erection process, but current cable technology only allows this method to be used in suspen sion bridges bridges of o f main spans up to approximate ly 2000 m (Akashi bridge, Japan). Long hangers are slender and relatively light and often characterized by very low structural damping. The mechanical properties in connection with the circular or hexagonal cross sections promote vortex shedding oscil lations which are self-limiting in nature, but may be objectionable from a psychological point of view. Vibration phenomena in stay cables and hangers hangers are often remedied by interconnecting the individual stay- or hanger cables by auxili ary ropes of wires at non-equidistant points thereby efficiently preventing higher mode vibrations. This strategy has been adopted for the Far0 cable-stayed bridge in Denmark  (Langs0 & Larsen 1987) and also for the 856 m main span world record Normandie cablestayed bridge under construction in France (Virlogeux 1991). Other possibilities are the introduction of dashpot dampers (shock  absorbers) between elements with relative movements, or fitting of Stockbridge units (tuned mass dampers) to the cables, see figure 3.8. Dashpot damping elements between deck  and stay cables were provided on the Brotonne bridge and later on the Sunshine Skyway Bridge in Florida. Stockbridge dampers are mounted on the long hangers of the Humber suspension bridge. Long cables of circular or nearly circular cross sections are not prone to galloping oscil lations, but if the external form is altered e.g.

Figure Figure 3.8 Design measures for fo r suppression o f  cable vibrations.

by ice accumulation or water adhering to the surface, galloping becomes a risk. Galloping grows grows without limits at increasing wind spee ds until failure or violent motions are counter acted by nonlinear energy absorbing effects. The large amplitude oscillations thus pro duced may be harmful to the bridge structure and are certainly certainly objectionable objectiona ble from a psycho logical point of view. Again dampers and auxiliary ropes may be of use, but more effec tive means are to remove the cause of the evil, i.e. prevent building of ice and formation of rain water rivulets on the cables. Recent research in Japan has identified various cable surface appendages as possible means to suppress cable galloping due to formation of rain water rivulets (Matsumoto 1989). Axial grooves, helical strakes and semi circular fins, see figure 3.9, are reported to accomplish the task with various degrees of  success. However, they increase the risk of ice

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accumulation and add to the aerodynamic drag loading to be resisted by the bridge structure. Reduction of the adhesion between water or ice and the cable surface is another method which is attractive from a designer’s point of view.

 Axi  Axial al Gro Groov oves es

Helical Strakes

Cable Fins

Figu Figure re 3.9 Design measures for fo r elimination o f  the formation of rain rivulets on cable stays.

3.6

tural weight is limited. By contrast, concrete towers are commonly built as thick-walled reinforced structures leading to structural weights of approximately 6-7 times that of  steel towers. The weight combined with increased damping relative to steel alleviates potential aerodynamic instability problems and greatly reduces the need for temporary measures. measures. This effec t is demonstrated in prin prin ciple in the aerodynamic stability diagram, figure 3.10, which identifies typical values of  the structural mass/damping parameter 2/7?8s/pd,2for steel and concrete towers rela tive to the stability boundaries for vortex shedding excitation excitation and galloping of rectangu lar sections. Galloping of concrete towers could theoretically occur at high wind speeds, but the galloping wind speeds are consider ably lower for steel towers. Important practi cal examples of aerodynamic instabilities of  steel towers are the vortex shedding oscilla tions encountered in the free standing towers of the Firth of Forth suspension bridge (Walshe 1972) and the destruction by gallop ing of a hexagonal cross section pylon of the cable-stayed Lodemann Briicke (Mahrenholtz & Bardowicks 1979). Steel towers are often resorted to in earth quake regions and/or in cases where speedy erection justify an additional cost of approxi mately 30%-50% above concrete towers. The designer of slender steel structures must be

Towers

Most towers for long span bridges are slender and flexible structures. They remain relatively insensitive to wind vibrations, when elastically supported by the main- or stay cables at saddle levels. During construction, however, it is necessary to consider the aerodynamic per formance of the completed tower in a free standing or pulled back position. The aerodynamic performance of bridge towers is influenced by the structural prop erties and external shape. Steel towers are often built as mono- or multi-cellular thinwalled boxes in order to achieve high strength and rigidity at a minimum cost. Thus struc

2mds d2

p

Figur Figuree 3.10 Aerodyn Aer odynamic amic stability stabili ty diagram diagram for  square sections identifying typical relative values of the mass/damping parameter for steel and  concrete towers.

11

prepared to specify temporary measures such as friction-, tuned mass, or sloshing dampers. Corner cuts, chamfers, rounded edges or guide vanes may also be introduced to the rectangular cross sections of the tower legs in order to reduce vortex shedding excitation. Such measures are a complication and could be in conflict with aesthetic requirements.

4 STRUCTURAL SYSTEMS The key structural parameters affecting the aerodynamic performance of long span cable supported bridges are mass and stiffness prop erties, and to some extent, the structural damping of the bridge. Basic considerations reveal that buffeting response to turbulent wind and vortex shedd ing excitation respon se decreases decre ases with increas ing structural mass density, and the critical wind speed for onset of flutter increases. Very heavy bridge structures, such as the George Washington and Verrazano Narrows suspen sion bridges are rarely plagued by aerodynam ic problems, but control of the aerodynamic performance by means of mass is hardly ac ceptable from an economic point of view. The designer’s challenge is to save material (struc tural weight) and still maintain a suitably stiff  structural structural system system that will keep buffeting- and vortex shedding response within acceptable limits and ensure a sufficiently high critical wind speed. New lighter materials will accen tuate this need.

4.1

Girders

The torsional stiffness of a classical suspen sion bridge derives from the cable system and the stiffening girder. girder. For bridges bridges accommodat accom modat ing 4-6 lanes of vehicle traffic and spanning up to about 1000 m, shallow box girders are usually found to possess adequate torsional stiffness to comply with common requirements for aerodynamic stability. In case of spans in the range of 1000 m - 2000 m, it may be necessary to consider special measures to obtain sufficient torsional girder stiffness.

If the girder width is fixed, the torsional stiffness may be enhanced enhanc ed either eith er by increasing increasing the thickness of the shell plating, or more effectively, by increasing the depth of the box. The first possibility leads to a higher steel quality which makes the second solution pre ferable from an economical point of view. However, this design philosophy produces bluff sections which may suffer degradation of  the aerodynamic performance relative to a shallow "streamlined" design. In particular, attention must be given to vortex induced oscillations at low wind speeds. In this context it is interesting to note that an increase of the depth of the girder was proposed as a measure for enhancing the aerodynamic sta bility bility of the box girder alternative alternative for th e 1990 m main span Akashi suspension bridge in Japan. Wind tunnel tests reveal that satisfac tory aerodynamic stability is ensured (Fujino et. al. 1988), but the vortex shedd ing perform ance at low wind speeds is not reported. By way of comparison truss girders can be designed to any particular depth and thus torsional stiffness without encountering encounter ing vortex shedding problems, as demonstrated in the Mackinac bridge. The penalty is an increase of the lateral wind loading on the bridge and possibly in addition an unacceptable raise in maintenance costs.

4.2

Suspension Systems - Cables and Towers

The stiffness of the main cable system in clas sical suspension bridges can be enhanced in a number of ways leading to higher torsional stiffness and improved aerodynamic perform ance (Astiz & Andersen 1990). Probably the oldest modification is the introduction of auxiliary stay cables radiating from the tower tops as devised by Roebling for the Brooklyn bridge. Aerodynamic perfor mance was not of primary concern in that case, but Roebling’s idea was adopted in the Bronx-Whitestone suspension bridge when fitted with auxiliary cable stays upon comple tion. The objective was to suppress annoying vortex shedding oscillations developing in moderate to high winds (Plowden 1974). The

12

Figu Figure re 4.1 Alternative suspension systems for fo r very very long span bridges and their relative aerodynamic stability performance. system is an efficient torsional stiffening device if applied to bridges with rigid tower structures or alternatively, if the cables are anchored near the centre line in case of  bridges with flexible towers. Incompatibility between behaviour and deformation of sus pension and cable stay systems can also cause problems. Another system devised for enhancement of  aerodynamic performance is the lateral-stay or ’’crossed hanger" system applied as a retrofit measure e.g. in the Deer-Isle suspension bridge bridge (Bosch 1987). Crossed hangers increase the torsional torsional stiffness o f suspension bridges as they counteract "in-phase" movement of main cables and girder edges at the cable planes. Crossed hangers require that the main cables are mutually fixed in the lateral direction, i.e. by introduction of compression members be tween the main cables. In the above mentioned systems the main cables are situated at the outer edges of the girder and thus contribute significantly to the

torsional inertia of the total system. By mov ing the main cables to the centre line of the bridge, torsional inertia is decreased and higher dynamic stiffness is a result. The mono-duo cable concept, where main cables are close together near the pylons and separate towards girder edges at 1/3 or 1/4 span points, allows for a combination of low torsional inertia with desirable deflection characteristics. The aerodynamic stability of a long span mono-duo cable bridge is thus simi lar to that of a classical suspension bridge of  considerably shorter main span. Classical 3 span suspension bridges are, for economical reasons, often built with flexible towers which results in substantial dynamic interaction between main span and side spans. spans. This interaction may be reduced considerably considerably by torsionally stiff A-frame towers which approach the aerodynamic performance of the 3 span bridge to that of a 1 span suspension bridge of equal main span length. The different suspension systems outlined

13

above and their aerodynamic stability per formance relative to that of a classical 3 span suspension bridge with side span/main span ratio of 1/3 are illustrated in figure 4.1.

4.3 A Desigti Example Ultra-long span suspension bridges must be designed to possess adequate aerodynamic stability, and further, the horizontal wind loading should be minimized in order to avoid large horizontal deflections of the bridge girder. A possible solution that combines these features is outlined below. The discussion of cable systems given above has emphasized that the mono-duo cable concept in combination with stiff A-frame towers enhances the flutter speed significant ly. Taking this concept to its extreme by allow ing the main cables to be positioned close

together along the entire span, i.e. 1-2 cable diameters apart, ensures a cable system with high torsional stiffness but relatively little tor sional inertia. A combination of this cable system with a closed elliptical steel sandwich deck as proposed for the Gibraltar crossing (Astiz & Andersen 1990), will lead to a high torsional stiffness of the bridge ensuring to high flutter wind speeds. The closed elliptical cross section has also the advantage that the drag loading may be reduced to approximately 30% of the drag loading of a conventional ’’streamlined” deck section of equal equa l width. In addition, traffic will be completely sheltered to high winds. The closely spaced main cables will exert relatively small twisting force couples on the tower tops as compared to a classical suspen sion bridge. bridge. The configuration thus eliminates strong dynamic torsional coupling between main span and side span girders. The particu lar bridge configuration, which is envisaged for main spans in the 3500 - 5000 m range is illustrated in figures 4.2 and 4.3.

5 SYSTEM CONTROL Under extreme conditions and for very long spans it may be necessary to provide special facilities or to prescribe specific operational procedures in order to ensure satisfactory performance of the bridge under all conceiv able weather conditions.

5.1

Figu Figure re 4.2 Elliptical Elliptic al cross cross section and cable configu configuratio ration n envisaged for ultra-long ultra-long span sus  pension brid bridge ge..

Damping 

If properly arranged, damping will reduce the amplitudes of the wind response due to buffe ting and vortex shedding and furthermore enhance the critical wind speed for onset of  aerodynamic instability. Application of structural materials with a high internal structural damping is the most direct way to introduce damping, but not pra ctical. Discrete damping elements can also be used. Dashpots and damping elements based on friction or viscoelastic materials may be arranged between elements with relative mutual displacements, or between the struc-

14

Suspension  Attachm  Attachment: ent:

Edges

| centerj ,

Edges

3500m

Figu igure 4.3 Elevation o f ultra-long ultra-long span suspension bridge bridge indicating areas of central and edge attachment of hangers.

ture and fixed points at ground level. Viscoelastic damping elements are, to our knowledge, not yet applied in bridges, but have been built into several high rise buildings buildings e.g. in a large quantity in the World Trade Centre to increase the structural damping (Mahmoodi et. al. 1987). Tuned mass dampers are widely used in girders and towers for damping of global vi brations. brations. Tuning to critical critical oscillation frequ frequen en cies is effectuated by proper combination of  masses, spring elements and dashpots (Malhorta & Wieland 1987). Liquid column dampers have been proposed for damping of  steel towers during construction, but this damper type may also have a potential for application in permanent bridge structures (Sakai et. al. 1991).

hancement of the aerodynamic stability of  suspension bridges under construction. If placed inside bridge girders girders and movable in transverse direction, eccentric masses con stitute a possible means of improving the aerodynamic stability of very long span bridges bridges in service. This This cconcep onceptt requires auto matic systems to monitor wind conditions and to initiate positioning positioning of the masses to prede termined positions in due time. A devise com bining the eccentric mass concept conc ept and a liquid column damper could be b e envisaged being

Critical Wind Speed  Act  Activ ive e Co Contro trol

5.2 Deployment o f Eccentric Eccentric Mass Additional masses placed eccentrically wind ward of the centre-line inside or on the bridge girder, will increase the critical wind speed for onset o f flutter. flutter. The principle is well lmown in aeronautical engineering and is used for sta bilization of control surfaces of aircraft. Basic considerations reveal that eccentric mass de ployment is most effective for systems where the natural frequencies for vertical- and tor sional oscillations are relatively close. Hence this method is particularl particularly y suitable for en en 

Figu Figure re 5.1 Potential enhancement enhancement o f aerody namic stability through actively controlled  control contro l surface surfaces. s.

15

somewhat similar to roll-damping tanks found in ships.

5.3 Active Act ive Control Systems The damping concepts presented above have the common characteristic with exception of  the moving mass that they are passive and rely on relatively simple mechanical concepts. Hence the performance can be made so reli able that not only the comfort may be en hanced by the damping effect, but even the structural reliability may rely on some of the concepts e.g. stationary winglets (Ragget 1987). In high rise buildings tuned mass dampers are applied to control wind induced oscilla-

Suspenslon System

 j Suspensio Suspension n Syst System em

IL 'V ''

!,5°

^ W /l

. . .

Hydraulic Hydraulic Cylinder   Actuator   Actuator 

— BulWiea BulWiead d ( Torsion Box )

Figu Figure re 5.2 Suggestions Suggestions for fo r implimentation of   Active  Act ive Control Surface Surface Systems in streamlined  bridgegirders.

tions and to assure the comfort of the occu pants. Contemporary systems do not entirely rely on passive elements, but also comprise computer controlled contro lled servo-hydraulic servo-hydraulic actuators to emulate a Den-Hartog tuned damper. Ho wever, only serviceability aspects are enhanced by these elements. The structural reliability of the system depends solely on the structure itself. Research is dealing with actively actively controlled tendons aiming to reduce e.g. bridge deflec tions or sway motion of high rise buildings. Active control is applied in advanced aircraft for suppression of aerodynamic instability. The mechanism involves actively controlled surfaces acting with a prescribed amplitude and phase-lag relative to the main surfaces (wings, flaps or ailerons) on which they exert control. Such control surfaces are operated via hydraulics governed by a computerized feed-back loop which responds to sensors attached to the main surfaces. A preliminary theoretical study conducted by COWIconsult has explored the potential of  actively controlled surfaces for enhancement of the flutter instability of long span cable supported bridges. bridges. The system is based on the idea of constantly monitoring movements of  the deck and use of control surface move ments to generate stabilizing aerodynamic stabilizing forces (lift) counteracting any ten dency to movement. An excerpt of the study is presented in figure 5.1, which displays the potential increase in critical wind speed to be obtained by fitting actively controlled sur faces to a "streamlined" box section. The cordlength of the control surfaces corresponds to 10% of the deck section width. The control surfaces are assumed to be situated up-stream and down-stream of the deck, and the pitch of  the leading and trailing control surfaces is controlled to be of opposite phase. It is observed that the critical wind speed may be enhanced by 50% or more, relative to that of  the flat plate UJUp   provided the actuator function amplitude and phase of the control surface pitch is appropriately chosen. An active control system has been con ceived by the authors to be applied for very long span bridges, where adequate flutter

16

stability or possibly static divergence stability is difficult to attain. The concept is based on application of  actively governed control surfaces installed in front and behind the leading/trailing edges of  an aerodynamically smooth girder. It is of  course necessary that the control surfaces are located outside the turbulent boundary layer and as far away from the local flow pattern around the bridge girder as practical to be effective. Therefore it is also essential that the girder does not create wake turbulence/vortices which will decrease the efficiency of the trailing edge control surface. The principle is attractive because the aero dynamic forces acting on the control surfaces will increase proportionally to the wind speed squared, and thus proportional to forces act ing on the box girder. A location in front/behind the girder edges and below the bottom cord is preferred in cases with undisturbed flow along the smooth bottom of the girder, see figure 5.2. Standardized control surfaces fabricated as symmetrical airfoils of a simple polyurethane foamed stainless steel sheeted sandwich can be supported at 5-10 m distances by aerodynamically shaped pylons. Control rods located inside the pylons and activated by hydraulic cylinders with short sh ort rise time will govern the control surfaces. The hydraulic cylinders are activated by means of computer controlled servo pumps. The computer operates on the basis of signals from accelerometers located in the box. The computer operates th e servo in accord accord ance with a service function developed on the basis of mathematical modelling and wind tunnel tests. Adequate system reliability will - as in air craft - be accomplished by sectionizing and duplication duplication or triplication triplication o f parallel indepen  dent systems with independent power sup plies. All members of the box/control surface assembly are shaped for minimum drag loads thereby minimizing lateral displacement of the girder and overall wind resistance on the bridge.

The control surfaces, which most of all resemble so-called all-flying elevators on air craft, will be efficient for both torsion and bending (vertical) movements with their very efficient long moment arm relative to the centre line. The computer will guide relative movements of leading and trailing edge con trol surfaces as well as the various control surfaces along any edge in an out of phase motion in order to efficiently counteract (sta bilize) any relevant movement of the girder. The system, which is patent pending, will be Classical Classical Flutter (2DOF) (2DOF)

U

t

V  4 Chord Open Guard Rail U% f

=0 =0 ..9 98

Torsional Torsi onal Flutter Flutt er (1DO (1DOF)

V 2  2  Chord

Snow Blocked Guard Rail U5f if

= 0.4 0.44

Figure Figure 5.3 Flutter behaviour behavi our o f bridge girder  with open railings and railings blocked by snow accumulation.

17

further developed and tested for practical application. Actively controlled systems are envisaged in the future as common elements in wind sensi tive bridges to enhance the comfort of the users and to reduce fatigue damage.

5.4

Winter Winter Conditions

Accumulation of ice on cables can modify their aerodynamic shape to such a degree that oscillations from wind may occur as elabor ated in section 3.5. Furthermore, falling ice sheets constitute a risk to users. To our know ledge, deicing systems, common to aircraft, have not yet been used on a bridge. Future suspension bridges in areas where ice ic e accumu lation is common may be envisaged with simi lar systems. This is partly necessary for lead ing edges and in case of active control sys tems. If snow ploughs leave barriers along the railings it will disturb a smooth air flow past the railing elements and girder edges. A severe reduction of the aerodynamic stability properties of bridge girders has been docu mented in wind tunnel tests with section models (Damsgaard et. al. 1990) as demon strated in figure 5.2. Although snow removal is not normally a remedy to be included in the structural design, it can be an absolutely necessary precaution in order to obtain a reliable structure under all circumstances. If sloping areas on bridge girders girders are prone to snow accumulation, special surface treat ments or installation of deicing heating elements may relieve the snow accumulation problem.

been made, and today wires with a tensile strength of 1800 Mpa have been adopted for the Akashi bridge in Japan. As span lengths for suspension bridges are increasing, increasing, new materials with improved sp eci fic strength (ratio between strength and den sity) for cables become of interest. Composite materials from carbon fibres embedded in a plastic matrix hold promise for the future - in particular particular if mass production can lower low er prices. In the aerospace industry these new materials materials are widely used for structure com po nents, but also bridge engineers have recognised the perspectives in relation to suspension bridge cables. The three most interesting and relevant types of fibres are carbon and aramid. Fibres may either be laid out continuous in the direction of principal stress, or chopped into short lengths and laid in a random fashion, depending on the need for isotropic or anisotropic behaviour. In the manufactur ing process, fibres can be placed as either continuous rovings or in mat form where lay ers of rovings can be built up in different directions, either stitched of woven together. Three-dimensional reinforcement is available as well, giving assured assured through-thickness through -thickness prop erties.

6.1

Design Examples Exampl es

The outer diameter of cable stays may be reduced through new materials. As an example, Carbon Fibre Reinforced Polyester, CFRP, with tensile strength of 3300 MPa and density of 1.56 1.56 kg/m (Meier 1991), may reduce the external diameter by theoretically 35% compared to steel cables, and still maintain the vertical load carrying capacity. For a large cable-stayed bridge it will typically lead to a 15%-20% reduction in the lateral wind load ing. Lateral wind loading and structural weight decrease. The susceptibility of cables to vortex shedding oscillations increases con siderably as shown in the stability diagram, figure 6.1. It is observed that the mass/damping mass/damping parameter 2mbs/p d 2 for CFRP cables is only about 20% of that of steel cables.

6. MATERIAL SELECTION During the 20th Century, the main cables for suspension bridges have been steel wires with a tensile strength higher than 1450 Mpa. The first first bridge with cables of such a high strength was the Williamsburg bridge (1903). Already in 1909 the tensile strength was improved to 1500 Mpa for the Manhattan bridge. Since then, only small increases have

18

2m5S  fl  fld*~

Figu Figure re 6.1 Stability diagram for fo r vortex  shedding excitation of circular cylinders indicat ing typical mass/damping parameters for steel  and CFRP cables.

According to figure 6.2 suppression of vor tex shedding oscillations in steel cables may be effectuated by a modest increase in the logarithmic decrement of structural damping. This may be accomplished by external dampers mounted at the cable base. CFRP cables will, in contrast, require substantially more external damping in order to eliminate the risk for vortex shedding oscillations. CFRP is attractive for main cables in very long span span suspension bridges because beca use th e high tensile strength to weight ratio allows con siderably higher payload/unit mass of cable than steel does. Designing for maximum allowable stresses in main cables (1700/2.2 MPa for steel and 3300/2.8 MPa for CFRP) leads to lighter and more flexible superstruc tures. Assuming a classical 3 span suspension bridge with CFRP main cables, the critical wind speed for onset of flutter decreases about 10% relative to that of the all steel superstructure. If CFRP main cables are designed design ed for maxi mum allowable stress it would probably lead to suspended structures with unacceptably high flexibility due to the decrease in main cable area and further, because the Emodulus for CFRP is slightly lower than that of cable steel (165000 Mpa for CFRP versus 205000 Mpa for steel). Large deflections can be controlled by increasing the cable area.

Adopting as design criterion that deflections must remain unchanged, leads to a 50% increase of the cable area of the CFRP design over the steel design, but this would of cause not be economical. As a result critical wind speeds for onset of flutter are enhanced by 10%-15% over the all steel design, depending on the main span length. Figure 6.2 displays the critical wind speed estimated for a classi cal 3 span suspension bridge as function of  main span length. The steel cables and the CFRP cables are designed for the maximum allowable stress and the unchanged deflection criterion. criterion. A conventional conv entional ’’ ’’streamlined” box girder section as shown in figure 3.3 is assumed. Critical Wind Speed Uc

Main Span Lenght (m)

Figu Figure re 6.2 Estim ated critical critical wind speeds for  classical 3 span suspension bridges equipped  with steel and CFRP main cables. Conventional  box section accommodating 4 lanes for road  traffic. The buffeting response in torsion of the steel and CFRP designs remains almost of the same magnitude with a slight tendency to decrease for the CFRP cable design. An effect attributed to the fact that lower structural masses in the CFRP designs are almost bal anced by an increase in the natural frequenci es of the system. For vertical motions the buffeting response is almost doubled for the CFRP design relative to the all steel suspen sion bridge. The current cost ratio of material cost/unit weight of approximately 36 for CFRP com 19

pared to steel cables (Meier 1991) indicates a break-even point beyond the 5000 m main span length for the present example, provided the maximum allowable stress design philos ophy applies. Also more fundamental structural and aerodynamic problems have to be solved in order to achieve the necessary level of safety, before CFRP cables are used in classical suspensio n bridges for road traffic. traffic.

7 PROBABILISTIC METHODS Stochastic models of the wind field have now been applied for decades in wind engineering to estimate the wind response of structures. But the uncertainty of other important para meters, meters, e.g. damping and masses, has no t been treated with a similar stringency. Contemporary probabilistic reliability methods provide the necessary tools to include such uncertainties in complete analy ses of the probability of limit state exceedance - serviceability, ultimate or others. The methods have been used to establish design criteri criteria a for aerodynamic stability of suspension su spension bridges on a rational basis (Ostenfeld-Rosentahl et. al, 1991). Reliability of towers against failure due to buffeting loads has also been treated by the methods, and it is expected that other wind phenomena will be analyzed routinely in the future. At a first glance it may seem to be of minor importance to apply probabilistic methods, but as the methods provide the designer with quantified assessments of the reliability against failure, it is possible to compare the threat to the structure structure from the various causes of failure due to wind. Similar analyses of  other failure mechanisms finally enable the designer to make a rational assignment of risk  to the various failure mechanisms - depending on the consequences - and make a backward calculation to establish design criteria. In this process even accidental events may be included. In future wind engineering analyses it is envisaged that stochastic models of structural parameters will be necessary. This develop ment is expected to influence the experimen

tal approaches used in wind engineering lab oratories.

8 TOOLS IN AERODYNAMIC DESIGN OF LONG SPAN BRIDGES. The development of tools for aerodynamic design of long span bridges started with the investigation into the collapse of the first Tacoma Narrows suspension bridge and the efforts to design an aerodynamically stable replacement bridge. The now classical experi mental investigations, headed by Farquharson at the University of Washington (Farquharson 1949-1954), began with the development of  procedures for wind tunnel testing of full aeroelastic bridge models. Later Farquharson’s investigations lead to the section model concept, the work-horse in most aerodynamic bridge design to this day. The basic goal of  section model testing remains unchanged, i.e. identification of aerodynamic stability, vortex shedding performance and measurement of  steady-state wind load coefficients for candi date girder configurations. The methods have changed with the advent of computer based data acquisition and analysis. Today’s section model tests are commonly supplemented by buffeting measurements in simulated turbu lent flows and extraction of aerodynamic deri vatives. Altogether highly useful studies to be used in conjunction with analytical assessment of equivalent static buffeting loads and aero dynamic stability during different mass- and stiffness conditions to be encountered during erection. Wind tunnel testing of full aeroelastic bridge models has seen a revival with the number of record breaking spans currently under design and construction. In contrast to Farquharson’s pioneering tests, which were conducted in smooth flow and beam winds, contemporary tests are performed in simu lated atmospheric a tmospheric boundary boundary layer flows, flows, and if  required, under skew winds. Testing of full aeroelasic bridge models mode ls is expensive and time consuming, hence this method is mainly resorted to as a means of verifying extrapola tions of proven designs.

20

wind tunnel for verification. This strategy is currently adapted in the aerospace industry, i.e. for evaluation of air intakes and high lift devices such as multi-element slats and flaps. In the automotive industry computational fluid dynamics are applied in the aerodynamic design of car bodies, and for evaluation of  internal flow and heat transfer in reciprocat ing engines. A quotation by David B. Steinmann, the legendary American bridge designer, states that ”The modem bridge engineer has to be an artist and a poet as well as a mathematician, scientist, financier and contractor" -  an appro priate summary of the present journey through elements of past and present engin eering of long span bridges. With the chal lenge to accomplish clear spans of 3000 m and beyond, we may include yet another pro fession - that of the aerodynamicist.

Development of analytical tools for analysis of the aerodynamic performance of long span bridges was also sparked of by the Tacoma Narrows incident and proceeded in parallel with the experimental investigations. Bleich advanced second order linearized deflection theory theory for calculation of vibration characteris ch aracteris tics of suspension bridges and adapted Theodorsen’s unsteady thin airfoil theory to the calculation of critical wind speeds of sus pended bridge decks (Farquharson 19491954). The Theodorsen theory is still proving useful as a first estimate for the critical wind speed of "streamline "streamlined” d” box sections, although computer based routines are preferred to look-up tables or graphical methods. Later developments of analytical methods involved the adaptation of linear stochastic response methods used in the aerospace in dustry for calculation of buffeting response of  bridges to turbulent winds. These methods, often referred to as linear buffeting theory, are now used on a routine basis for analytical assessment of equivalent static buffeting loads and responses in connection with verification of structural adequacy. More recently com puter simulation of turbulent wind loads has found applications in bridge design and is used in connection with response analysis of  non-linear bridge configurations in the time domain. Analysis of bridge structures saw major developments with the advent of Finite Element Methods. The need for structural dynamic model testing is now almost entirely eliminated, eliminated, and "hand hand turned” analytical analytical methods are only used in very preliminary design studies. Similar developments are dawning for the analysis of the aerodynamic performance of bridge elements. Comprehen sive fluid dynamic codes based on Finite Vol ume or Finite Element formulations of the Navier-Stokes equations are commercially available, and bluff body aerodynamics are receiving attention by researchers in the field of computational fluid dynamics. These trends promise a new area in bridge aerodynamics, where the designer is allowed to run "numerical" experiments and weed out inefficient configurations before turning to the

9 REFERENCES Shirly-Smith, H. 1964. The Worlds Great   Bridges.  Bridges.  London: Phoenix House. Plowden, D. 1974. The Spans of North  America.  New York: W.W. Norton & Company. Farquaharson, F.B. (Ed.) 1949-1954. Aerody  Aer ody namic Stability of Suspension Bridges.  Uni versity of Washington Engineering Station, Bull. No. 16: Parts I - V. Ostenfeld, C., Frandsen, A.G. & Haas, G. 1970. Motorway Bridge Bridge across across Lille Lillebce bcelt, lt, Publ. Publ.  X, aerodynamic Investigations Investigations for the Super structure. Bygningsstatiske Medd elelser Vol. 41, No. 2. Wardlaw, R.L. & Goettl Goe ttler, er, L.L. 1968. >1 Wind  Tunnel Tunnel Study of o f Modifications to Improve the  Aerodynamic  Aerodyn amic Stability o f the Lo ng’ ng ’s Creek   Brid  Bridge ge..  Report No. LTR-LA-8, NAE, Na tional Research Council, Ottawa, Canada. Szechenyi, E. 1989. Etude  Etud e de componentes dans le vent du du tablier dejinitifdu dejinitifdu pon t de Norman die.  Rapport Technique No. 15/3588 RY 091R-391G. Office National d’Etudes et de Recherches Aerospatiales. Aerospatiales. Wardlaw, R.L. 1971.  Some Approa A pproaches ches forlmfor lm proving the Aerodynamic Aerodyn amic Performance o f 

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 Bridge  Bridge Road Roa d Decks. Deck s.  3rd. Int. Conf. on Wind Effects on Buildings and Structures. Tokyo. Tokyo. Simpson, A., Beard. A. & Young, J. 1991.  Design Evolution o f the Tsing Tsing Ma Brid Bridge. ge. IABSE Symposium: 461-466. Leningrad. Ostenfeld, K.H. 1989.  Denmarlcs  Denmarlcs Great Belt   Link.  The 1989 ASCE Annual Civil Engin eering Convention. New Orleans. Richardson, J.R. 1988. Radical  Radic al deck Designs for  Ultra-long Span Bridges.  13th IABSE Congres Report: 901-904. Helsinki. Langs0, H.E. & Larsen. O.D. 1987. Generating   Mechanism for fo r Cable Stay Oscillations at the Far0 Bridge.  Int. Conf. on Cable-Stayed Bridges. Bangkok  o f  Virlogeux, M. 1991. Design and Construction of  the Normandie Bridge.  Innovation in CableStayed Bridges, H. Otsuka (ed.): 23-40. Fukuoka: Maruzen Matsumoto, M., Knisely, CM, et. al. 1989.  Inclined Cable Aerodynamics. Aerodyna mics.  ASCE Struc tures Congerss: 81-90. San Francisco. Walshe, D.E.J. 1972. Wind Excited Oscillations Oscillations of Structures.  Publication of Her Majesty’s Stationary Office. London. Mahrenholtz O., & Bardowicks, H. 1979.  Aeroelastic Problems Pro blems at a t Masts and Chimney Chimneys. s. 3rd Colloquium on Industrial Aerodynam ics: 261-272. Aachen: Elsevier Fujino, Y., Ito, M. et. al. 1988. Wind Tunnel   Study of o f Long-Span Long-Spa n Suspension Bridge Bridge under   Smooth and Turbulent Turbulent Flow. Flow.  International Colloquium on Bluff Body Aerodynamics and its Applications, M. Ito (ed.): 313-322. Kyoto: Elsevier Astiz, M.A. & Andersen, E.Y. 1990. On Wind   Stability o f very very long Spans in Connection with a Bridge across the Strait of Gibraltar. Strait Crossings, J. Krokeborg (ed.): 257264. Rotterdam: Balkema Bosch, H. 1987. A Wind Tunnel Investigation Investigation of  o f  the Deer Isle - Sedgewick Bridge (Phase 1). Federal Highway Administration Report No. FHWA/RD-87/027. McLean, Virginia. Mahmoodi, P., Robertson, L.E. et al. 1987.  Performance o f Viscoelastic Dampers Damp ers in World Trade Center Towers.  Dynamics of  Structures Proc. of 6th Structures congress of ASCE: 632-644. Orlando, Florida.

Malhorta, P.K. & Wieland, P. 1987. Tuned   Mass damper damp er for Supressing Supressing Wind Effects in a Cable-Stayed Bridge.  Int. Conf. on Cable-Stayed Bridges: 557-568. Bangkok  Sakai, F., Takaeda, S. & Tamaki, T. 1991. Tuned Liquid Colum Dampers for Cable  Stayed Bridges. Bridges.  Innovation in Cable-Stayed Bridges, H. Otsuka (ed.): 197-205. Fukuoka: Maruzen Ragget, J.D. 1987.  Stabilizing Pair Pa ir o f Wingle Winglets ts  for Slender Bridge Decks. Bridges and Trans mission Line Structures, Proc. of 6th Struc tures congress of ASCE: 292-302. Orlando, Florida Damsgaard, A., Jensen A.G., et. al. 1990. The Use of Section Model Wind Tunnel Tests in the Design of the Storebcelt East Bridge in  Denmark.  Strait Crossings, J. Krokeborg (ed.): 281-287. Rotterdam: Balkema Meier, U. 1991.  Modem  Mo dem Materials in Bridge  Engin  Engineer eering ing..  IABSE Symposium: 311-323. Leningrad. Ostenfeld-Rosentahl, P., Madsen, H. & Larsen, A. 1991. Probabilistic Flutter Criteri Criteria a  for Long Lon g Span Bridge Bridges. s.  8th Int. Conf. on Wind Engineering, A. Davenport (ed.): London, Canada.

22

Shirly-Smith, H. 1964. The Worlds Great Bridges. London: Phoenix House. Plowden, D. 1974. The Spans of North America. New York: W.W. Norton & Company. Farquaharson, F.B. (Ed.) 1949   1954. Aerodynamic Stability of Suspension Bridges. University of Washington 1954. Engineering Station, Bull. No. 16: Parts I    V. Ostenfeld, C. , Frandsen, A.G. & Haas, G. 1970. Motorway Bridge across Lilleb  lt, Publ. X, aerodynamic lt, Investigations for the Superstructure. Bygningsstatiske Bygningsstatiske Meddelelser Vol. 41, No. 2. Wardlaw, R.L. & Goettler, L.L. 1968. A Wind Tunnel Study of Modifications to Improve the Aerodynamic Stability of the Long   s Creek Bridge. Report No. LTR-LA-8, NAE, National Research Council, Ottawa, Canada. Sz ch  ch  nyi, E. 1989. Etude de componentes dans le vent du tablier d nyi,  finitif du pont de Normandie. Rapport finitif Technique No. 15/3588 RY 091R-391G. Office National d   Etudes et de Recherches A Etudes rospatiales.  rospatiales. Wardlaw, R.L. 1971. Some Approaches forImproving the Aerodynamic Performance of Bridge Road Decks. 3rd. Int. Conf. on Wind Effects on Buildings and Structures. Tokyo. 22 Simpson, A. , Beard. A. & Young, J. 1991. Design Evolution of the Tsing Ma Bridge. IABSE Symposium: 461 466.   466. Leningrad. Ostenfeld, K.H. 1989. Denmarks Great Belt Link. The 1989 ASCE Annual Civil Engineering Convention. New Orleans. Richardson, J.R. 1988. Radical deck Designs for Ultra-long Span Bridges. 13th IABSE Congres Report: 901 904.   904. Helsinki. Langs  , H.E. & Larsen. O.D. 1987. Generating Mechanism for Cable Stay Oscillations at the Far  Brid Br idge ge.. Int. In t. Conf. on Cable-Stayed Bridges. Bangkok Virlogeux, M. 1991. Design and Construction of the Normandie Bridge. Innovation in Cable-Stayed Bridges, H. Otsuka (ed.): 23   40. Fukuoka: Maruzen 40. Matsumoto, M. , Knisely, C.M. , et. al. 1989. Inclined Cable Aerodynamics. ASCE Structures Congerss: 81 90.   90. San Francisco. Walshe, D.E.J. 1972. Wind Excited Oscillations of Structures. Publication of Her Majesty s  Stationary Office. London. Mahrenholtz O. , & Bardowicks, H. 1979. Aeroelastic Problems at Masts and Chimneys. 3rd Colloquium on Industrial Aerodynamics: 261   272. Aachen: Elsevier 272. Fujino, Y. , Ito, M. et. al. 1988. Wind Tunnel Study of Long-Span Suspension Bridge under Smooth and Turbulent Flow. International Colloquium on Bluff Body Aerodynamics and its Applications, M. Ito (ed.): 313 322.   322. Kyoto: Elsevier Astiz, M.A. & Andersen, E.Y. 1990. On Wind Stability of very long Spans in Connection with a Bridge across the Strait of Gibraltar. Strait Crossings, J. Krokeborg (ed.): 257   264. Rotterdam: Balkema 264. Bosch, H. 1987. A Wind Tunnel Investigation of the Deer Isle    Sedgewick Bridge (Phase 1). Federal F ederal Highway Administration Report No. FHWA/RD-87/027. FHWA/RD-87/027. McLean, Virginia. Mahmoodi, P. , Robertson, L.E. et al. 1987. Performance of Viscoelastic Dampers in World Trade Center Towers. Dynamics of Structures Proc. of 6th Structures congress of ASCE: 632   644. Orlando, Florida. 644. Malhorta, P.K. & Wieland, P. 1987. Tuned Mass damper for Supressing Wind Effects in a Cable-Stayed Bridge. Int. Conf. on Cable-Stayed Bridges: 557 568.   568. Bangkok Sakai, F. , Takaeda, S. & Tamaki, T. 1991. Tuned Liquid Colum Dampers for Cable Stayed Bridges. Innovation in Cable-Stayed Bridges, H. Otsuka (ed.): 197   205. Fukuoka: Maruzen 205. Ragget, J.D. 1987. Stabilizing Pair of Winglets for Slender Bridge Decks. Bridges and Transmission Line Structures, Proc. of 6th Structures congress of ASCE: 292   302. Orlando, Florida 302. Damsgaard, A. , Jensen A.G. , et. al. 1990. The Use of Section Model Wind Tunnel Tests in the Design of the Storeb  lt East Bridge in Denmark. Strait Crossings, J. Krokeborg (ed.): 281 lt   287. Rotterdam: Balkema 287. Meier, U. 1991. Modern Materials in Bridge Engineering. IABSE Symposium: 311 323.   323. Leningrad. Ostenfeld-Rosentahl, Ostenfeld-Rosentahl, P. , Madsen, H. & Larsen, A. 1991. Probabilistic Flutter Criteria for Long Span Bridges. 8th Int. Conf. on Wind Engineering, A. Davenport (ed.): London, Canada.

Shirly-Smith, H. 1964. The Worlds Great Bridges. London: Phoenix House. Plowden, D. 1974. The Spans of North America. New York: W.W. Norton & Company. Farquaharson, F.B. (Ed.) 1949   1954. Aerodynamic Stability of Suspension Bridges. University of Washington 1954. Engineering Station, Bull. No. 16: Parts I    V. Ostenfeld, C. , Frandsen, A.G. & Haas, G. 1970. Motorway Bridge across Lilleb  lt, Publ. X, aerodynamic lt, Investigations for the Superstructure. Bygningsstatiske Bygningsstatiske Meddelelser Vol. 41, No. 2. Wardlaw, R.L. & Goettler, L.L. 1968. A Wind Tunnel Study of Modifications to Improve the Aerodynamic Stability of the Long   s Creek Bridge. Report No. LTR-LA-8, NAE, National Research Council, Ottawa, Canada. Sz ch  ch  nyi, E. 1989. Etude de componentes dans le vent du tablier d nyi,  finitif du pont de Normandie. Rapport finitif Technique No. 15/3588 RY 091R-391G. Office National d   Etudes et de Recherches A Etudes rospatiales.  rospatiales. Wardlaw, R.L. 1971. Some Approaches forImproving the Aerodynamic Performance of Bridge Road Decks. 3rd. Int. Conf. on Wind Effects on Buildings and Structures. Tokyo.

22 Simpson, A. , Beard. A. & Young, J. 1991. Design Evolution of the Tsing Ma Bridge. IABSE Symposium: 461 466.   466. Leningrad. Ostenfeld, K.H. 1989. Denmarks Great Belt Link. The 1989 ASCE Annual Civil Engineering Convention. New Orleans. Richardson, J.R. 1988. Radical deck Designs for Ultra-long Span Bridges. 13th IABSE Congres Report: 901 904.   904. Helsinki. Langs  , H.E. & Larsen. O.D. 1987. Generating Mechanism for Cable Stay Oscillations at the Far  Brid Br idge ge.. Int. In t. Conf. on Cable-Stayed Bridges. Bangkok Virlogeux, M. 1991. Design and Construction of the Normandie Bridge. Innovation in Cable-Stayed Bridges, H. Otsuka (ed.): 23   40. Fukuoka: Maruzen 40. Matsumoto, M. , Knisely, C.M. , et. al. 1989. Inclined Cable Aerodynamics. ASCE Structures Congerss: 81 90.   90. San Francisco. Walshe, D.E.J. 1972. Wind Excited Oscillations of Structures. Publication of Her Majesty s  Stationary Office. London. Mahrenholtz O. , & Bardowicks, H. 1979. Aeroelastic Problems at Masts and Chimneys. 3rd Colloquium on Industrial Aerodynamics: 261   272. Aachen: Elsevier 272. Fujino, Y. , Ito, M. et. al. 1988. Wind Tunnel Study of Long-Span Suspension Bridge under Smooth and Turbulent Flow. International Colloquium on Bluff Body Aerodynamics and its Applications, M. Ito (ed.): 313 322.   322. Kyoto: Elsevier Astiz, M.A. & Andersen, E.Y. 1990. On Wind Stability of very long Spans in Connection with a Bridge across the Strait of Gibraltar. Strait Crossings, J. Krokeborg (ed.): 257   264. Rotterdam: Balkema 264. Bosch, H. 1987. A Wind Tunnel Investigation of the Deer Isle    Sedgewick Bridge (Phase 1). Federal F ederal Highway Administration Report No. FHWA/RD-87/027. FHWA/RD-87/027. McLean, Virginia. Mahmoodi, P. , Robertson, L.E. et al. 1987. Performance of Viscoelastic Dampers in World Trade Center Towers. Dynamics of Structures Proc. of 6th Structures congress of ASCE: 632   644. Orlando, Florida. 644. Malhorta, P.K. & Wieland, P. 1987. Tuned Mass damper for Supressing Wind Effects in a Cable-Stayed Bridge. Int. Conf. on Cable-Stayed Bridges: 557 568.   568. Bangkok Sakai, F. , Takaeda, S. & Tamaki, T. 1991. Tuned Liquid Colum Dampers for Cable Stayed Bridges. Innovation in Cable-Stayed Bridges, H. Otsuka (ed.): 197   205. Fukuoka: Maruzen 205. Ragget, J.D. 1987. Stabilizing Pair of Winglets for Slender Bridge Decks. Bridges and Transmission Line Structures, Proc. of 6th Structures congress of ASCE: 292   302. Orlando, Florida 302. Damsgaard, A. , Jensen A.G. , et. al. 1990. The Use of Section Model Wind Tunnel Tests in the Design of the Storeb  lt East Bridge in Denmark. Strait Crossings, J. Krokeborg (ed.): 281 lt   287. Rotterdam: Balkema 287. Meier, U. 1991. Modern Materials in Bridge Engineering. IABSE Symposium: 311 323.   323. Leningrad. Ostenfeld-Rosentahl, Ostenfeld-Rosentahl, P. , Madsen, H. & Larsen, A. 1991. Probabilistic Flutter Criteria for Long Span Bridges. 8th Int. Conf. on Wind Engineering, A. Davenport (ed.): London, Canada.

Abild, J. and B. Nielsen 1991. Extreme values of wind speeds in Denmark. Ris    M  M2842,107   2 842,107 pp. Choi, E.C.C. 1983. Gradient height and velocity profile during typhoons, J. Wind Eng. and Industr. Aerodyn., 13, 31 41.   41. Cook, N.J. 1985. The designer s  guide to wind loading on building structures. Buttersworth, London, 371 pp. Georgiou, P.N. , A.G. Davenport and B.J. Vickery 1983. Design wind speeds in regions dominated by tropical cyclones. J. Wind Eng. and Industr. Aerodyn., 13: 139 152.   152. Jensen, N.O. 1978. Change of surface roughness and the planetary boundary layer. Quart. J. Roy. Met. Soc., 15: 95 108.   108. Jensen, N.O. , E.L. Petersen and I. Troen 1984. Extrapolation of mean wind statistics with special regard to  wind energy applications. applications. WMO, WMO, World Climate Climate Programme, Report No. WCP-86, WCP-86, 85 pp. Jensen, N.O. , M. Nielsen and B. Nielsen 1988. Climatic overview of the Great Belt region. Ris    M  M2842,   2 842, 37 pp. Jensen, N.O. and B. Nielsen 1989. Extreme values of wind speeds over the Great Belt region. Ris -M-2842,  -M-2842, 25 pp. Kristensen, L. and N.O. Jensen 1979. Lateral coherence in isotropic turbulence and in the natural wind. Boundary-Layer Meteorol., 17, 353 373.   373. Kristensen, L. M. Casanova, M.S. Courtney and I. Troen 1991. In search of a gust definition. Boundary-Layer Meteorol., 55, 91 107.   107. Kristensen, L. and K. Frydendahl 1991. Denmark   s wind climate from 1870 until now (in Danish). Havforskning, Havforskning, nr. 2, Milj  styrelsen, Strandgade 29, DK-1401 Copenhagen, 57 pp. styrelsen, Mann, J. , L. Kristensen and M.C. Courtney 1991. The Great Belt Coherence Experiment. A study of atmospheric turbulence over water. Ris    R  R596,   5 96, 51 pp. Nielsen, N.W. 1991. An exposive storm development at the Faroes in September 1990 (in Danish). Vejret, nr. 3, 13: 3 19.   19. Sanders, F. and J.G. Gyakum 1980. Synoptic-Dynamic climatology climatology of the  bomb   bomb   . Mon. Wea. Rev., 108: 1589 1606.   1606. Sempreviva , Anna Maria , S.E. Larsen , N.G. Mortensen and I. Troen 1990. Response of neutral boundary layers to changes of roughness. Boundary-Layer Meteor., 50, 205 225.   225.

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Irwin, H.P.A.H. : Wind Tunnel and Analytical Investigations of the Response of Lions   Gate Bridge Brid ge to a Trubule Tru bulent nt Wind. National Research Council of Canada, NAE-LTR-LA-210, June 1977. Zan, S.J. : Analytical Prediction of the Erection Phase Response of the St. Johns River Cable-Stayed Bridge to a Turbulent Wind. National Research Council of Canada, NAE-LTR-LA-303, September 1987. Scanlan, R.H. : On Flutter and Buffeting Mechanisms in Longspan Bridges. Probabilistic Engineering Mechanics, 1988. Kovacs, I. , Svensson, H.S. and Jordet, E. : Analytical Aerodynamic Investigation of the Cable-Stayed Helgeland Bridge. ASCE, Journal of Structural Engineering, Jan., 1992. Engineering Sciences Data Unit (ESDU) No. 74031 (1974). Characteristic of Atmospheric Turbulence near the Ground. Single Point Data for Strong Winds. London, 1974. Engineering Sciences Data Unit (ESDU) No. 86010 (1986). Characteristic of Atmospheric Turbulence near the Ground. 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Baker, C.J. 1991. Ground vehicles in high crosswinds (3 parts). J. Fluids and Structures, 5, pp 69 90,   90, 91 111,   111, 221 241.   241. Baker, C.J. & Reynolds, S. pub.pending 1991. Wind induced accidents of road vehicles, Accident analysis and prevention. British Standard BS 5400, 1978. Steel, concrete and composite bridges: Part 2, Specification for Loads. BSI, London. British Standard BS 8100, 1986. Lattice towers and masts: Part 1, Loading. BSI, London. Brown, C.D. , Christensen, O. , Hay, J.S. , Simpson, A.G. , & Wyatt, T.A. 1981 Discussion of Session 2, Bridge Aerodynamics, TTL, London, 97 98.   98. Coleman, S.A. & Baker, C.J. pub.pending 1991. The reduction of accident risk for high sided road vehicles in cross winds, 8th Int. Conf. Wind Engineering, JWEIA. Cowdrey, C.F. 1971,1972. Time average aerodynamic forces on bridges. NPL Reports, Aero 1327 (1971) and Mar.Sci. 1 72.   72. Cowdrey, C.F. & Whitbread, R.E. 1976. Reduction of wind forces on high-sided vehicles on motorway bridges using barriers of uniform density. NPL Report Mar.Sci.R.149 Department of Transport; 1979. Papers of the Aerodynamics Research Panel (unpublished), letters from Avon County Police and the Forth Road Bridge Joint Board. Department of Transport; 1981. Proposed Design Rules, Bridge Aerodynamics, pub. as preface Bridge Aerodynamics, TTL, 3 20.   20. Department of Transport consultants report 1986. Study of Second Severn Crossing: final report. HMSO London. Flint, A.R. & Smith, B.W. 1992. The Severn Bridge strengthening; background research and development, Proc. Inst. Civil Engrs. (Structures & Building) I. 1. Head, P.R. & Churchman, A.E. 1989. Design specification and manufacture of a pultruded composite flooring system. Proc. Symp. Mass Production Composites, London, Imperial College. Head, P.R. 1991 (Sept.) The performance of bridge systems; the next frontier for design and assessment. The Structural Engineer, 69, 17. House of Commons, 1987. Special Report of the Select Committee on the Dartford-Thurrock Crossing Bill, (espec. Vol I p 37 40)   40) HMSO London. Irwin, P.A. & Stone, G.K. 1989. Aerodynamic improvements for plate-girder bridges. Proc. ASCE Structures Congress (San Francisco). New Civil Engineer, 1988, Editorial news item, London 18 February. Pritchard, R. 1985. Wind effects on high-sided vehicles, Highways & Transportation, 32, 4. 22 25.   25. Richardson, J.R. 1981. The development of the concept of the twin suspension bridge. NMI (UK) Report R.125. Rose, M.J. 1973. The MIRA crosswind generator, Proc. I.Mech.E. Auto. Divn. 187. Rose, M.J. & Bevan, B.G. 1989. Roadside windshielding to reduce vehicle overturning accidents in crosswinds. Proc. Autotech 1989, paper C.399/2, Inst.Mech.E. Simpson, A.C. , Curtis, D.J. & Choi, Y.-C. 1981.    Aeroelastic aspects of the Lan Tau fixed crossing Aeroelastic . Bridge Aerodynamics. TTL, London. 109 114.   114. Smith, B.W. & Wyatt, T.A. 1981. Development of the draft rules for aerodynamic stability. Bridge Aerodynamics, TTL 33 48.   48. Walshe, D.E. , Whitbread, R.E. & Elliott A.M.    Aerodynamic stability measurements Aerodynamic measurements on sectional models of some representative box girder bridges   . NPL Reports Mar. Sci. R127 (1975), Mar. Sci. R146 (1976), also two further reports of the National Maritime Institute 1976, unpublished. Walshe, D.E. 1981. Some effects of turbulence on fluctuating and time-average forces on sectional models of box girder bridges. Bridge Aerodynamics. TTL, 61 72.   72. Whitbread, R.E. 1968. On the introduction of turbulence into wind-tunnel investigations for the determination of  wind-induced amplitudes amplitudes of oscillation. oscillation. Proc. Simp. Wind Effects Effects on Buildings Buildings and Structures, Structures, Loughborough. Loughborough. Wyatt, T.A. & Scruton, C. 1981. A brief survey of the aerodynamic stability problems of bridges, Bridge Aerodynamics TTL, London 21 32.   32. Wyatt, T.A. 1991.    The dynamic behaviour of cable-stayed bridges: fundamentals and parametric studies The  . Cable-stayed bridges    recent developments developme nts and their future. f uture. Elsevier.

Kl  PPEL, K. and Thiele, F. : Wind Tunnel Model Tests for the Sizing of Bridges against Wind Excited PPEL, Oscillations. Der Stahlbau 36, Volume 12, p. 353 to (in German) Starossek, U. : On the Load-bearing Behavior of Cable-Stayed Bridges under Dynamic Wind Loads. Dissertation at University of Stuttgart, 1991. (in German) Simiu, E. and SCanlan, R.H. : Wind Effects on Structures. John Wiley Sons, New York, 1986. Leonhardt, Andra und Partner , Kovacs, I. : Structural Dynamics. Stuttgart, Stuttgart, 1989. Leonhardt, F. and Zellner, W. : Past, Present and Future of Cable-Stayed Bridges. ASCE, Journal of Structural Engineering, 1992. Davenport, A.G. and King, J.P.C. : Dynamic Wind Forces of Long-Span Bridges. Final Report, 12th Congress, International Association for Bridge and Structural Engineering, Vancouver, BC, September 1984,705 712.   712. Irwin, H.P.A.H. : Wind Tunnel and Analytical Investigations of the Response of Lions   Gate Bridge Brid ge to a Trubule Tru bulent nt Wind. National Research Council of Canada, NAE-LTR-LA-210, June 1977. Zan, S.J. : Analytical Prediction of the Erection Phase Response of the St. Johns River Cable-Stayed Bridge to a Turbulent Wind. National Research Council of Canada, NAE-LTR-LA-303, September 1987. Scanlan, R.H. : On Flutter and Buffeting Mechanisms in Longspan Bridges. Probabilistic Engineering Mechanics, 1988. Kovacs, I. , Svensson, H.S. and Jordet, E. : Analytical Aerodynamic Investigation of the Cable-Stayed Helgeland Bridge. ASCE, Journal of Structural Engineering, Jan., 1992. Engineering Sciences Data Unit (ESDU) No. 74031 (1974). Characteristic of Atmospheric Turbulence near the Ground. Single Point Data for Strong Winds. London, 1974. Engineering Sciences Data Unit (ESDU) No. 86010 (1986). Characteristic of Atmospheric Turbulence near the Ground. Variations in Space and Time for Strong Winds. London, 1986.

Virlogeux, M. , J.-C. Foucriat & B. Deroubaix . Design of the Normandie cable-stayed Bridge near Honfleur. Proc. of the Int. Conf. on Cable-stayed bridges. Bangkok, November 1987. Deroubaix, B. , A. Demare & R. Lavou  . Le Pont Po nt de Normandie.Tr No rmandie.Travaux, avaux, April, Ap ril, 1989 19 89 & July, Ju ly, 1990. Virlogeux, M. Design and Construction of the Normandie Bridge. Innovation in cable-stayed bridges. Proc. of the Int. Conf. Fukuoka, April 1991.

T. Miyata , I. Okauchi , N. Shiraishi , N. Narita and T. Narahira , Preliminary design considerations for wind effects on a very long-span suspension bridge, Proc. 7th Int. Conf. Wind Eng.(Aachen), 1987. M. Ohashi , T. Miyata , I. Okauchi , N. Shiraishi and N. Narita , Considerations for wind effects on a l,990mmain span suspension bridge, Prerept. 13 th Congress IABSE (Helsinki), 1988. T. Miyata , H. Yamada and H. Akiyama , Codification of wind effects for a long span suspension bridge, Rep. Structural Design, Analysis & Testing, Proc. Structures Cong.  89,   89, ASCE (San Francisco), 1989. T. Miyata and H. Yamada , Coupled flutter estimate of a suspension bridge, J. Wind Eng. & Ind. Aero., 33, 1990. T. Miyata , H. Matsumoto and M. Yasuda , Circumstances of wind resistant design examination for very long suspension bridge, Proc. 8th Int. Conf. Wind Eng.(London, Ont.), 1991. T. Miyata , H. Yamada , K. Yokoyama , T. Kanazaki , T. Iijima and M. Tatsumi , Construction of boundary layer  wind tunnel for long-span bridges, Proc. 8th Int. Int. Conf. Wind Wind Eng.(London, Ont.), Ont.), 1991. Honshu-Shikoku Bridge Authority, Wind resistant design code for Honshu-Shikoku bridges(1976). Honshu-Shikoku Bridge Authority, Wind tunnel testing manual for Honshu-Shikoku bridges(1980). Honshu-Shikoku Bridge Authority, Wind resistant design code for Akashi Kaikyo Bridge(1990). G. Diana , M. Falco , M. Gasparetto , A. Curami , B. Pizzigoni and F. Cheli , Wind effects on the dynamic behaviour of a suspension bridge, Politec. of Milan, Dept. of Mechanics, Jan. 1986. N.J. Gimsing , Extreme span suspension bridges    structural systems, Final Rept. 12th Cong. IABSE(Vancouver), IABSE(Vancouver), 1984. J.R. Richardson , Influence of aerodynamic stability on the design of bridges, Final Rept. 12th Cong. IABSE(Vancouver), IABSE(Vancouver), 1984; The development of the concept of the twin suspension bridge, NMI Rept.125, 1981. A.G. Simpson , D.J. Curtis and Y.-L. Choi , Aeroelastic aspects of the Lantau Fixed Crossing / Discussion in Session 3-Design, Bridge Aerodynamics, TTL London, 1981.

ECCS 1987 (European Conventional for Constructional Steelwork). Steelwork). Recommendations for calculating the effects of wind on constructions. (Design Code Recommendations) Recommendations) British Design Rules for Bridge Aerodynamics. (Design Code Recommendations). Recommendations).

Larsen, S.E. , M.S. Courtney , F. Aa . Hansen, J. H  jstrup  and N.O. N.O. Jensen . Power spectra and turbulence intensity 70 metres above the water surface of the Great Belt. RIS0 National Laboratory, Roskilde, Denmark, RIS0-M-2898, January 1991 (draft). ESDU 86010: Characteristics of atmospheric turbulence near the ground, part III: Variations in space and time for strong winds (neutral atmosphere). Engineering Sciences Data Unit, London, England, 1986. Scanlan, R.H. State-of-the-art methods for calculating flutter, vortex-induced and buffeting response of bridge structures. Federal Highway Administration Report FHWA/RD-80/050, Washington, D.C., April, 1981. Poulsen, N.K. , Aa. Damsgaard and T.A. Rein-hold . Determination of flutter derivatives for the Great Belt Bridge. Paper for Int. Conference in London Ontario. King, J.P.C. , Larose G.L. and A.G. Davenport . A study of wind effects for the Storeb  lt Bridge Tender Design, lt Denmark. The University of Western Ontario, London, Canada, BLWT-IR-S67-1, December 1990 (draft). Reinhold, T.A. , A. Larsen , Aa. Damsgaard and E. Svensson . Integrated physical and analytical model studies for predicting the stability and dynamic response of suspension bridges in strong winds. Proceedings of International Workshop on Technology for Hong Kong   s Infrastructure Development, Hong Kong University of Science and Technology, Hong Kong, December, 1991. Brancaleoni, F. 1992. The Construction Phase and its Aerodynamic Issues. Proc. Int. Symp. on Aerodynamics of Large Bridges. Balkena: Rotterdam. Davenport, A.G. 1967. Gust Loading Factors. Journ. Struct. Div. ASCE, Vol. 93: 11   34 34 Davenport, A.G. & King, J.C. P. 1984. Dynamic Wind Forces on Long Span Bridges Using Equivalent Static Loads. IABSE Symposium Vancouver B.C., Canada. Davenport, A.G. , King, J.P.C. & Larose, G.L. 1992. Taut Strip Model Tests. Proc. Int. Symp. on Aerodynamics of Large Bridges. Balkena: Rotterdam. Holmes, J.D. 1978. Monte Carlo Simulation of the Wind Induced Response of a Cable-Stayed Bridge. Wind Engineering Report 2/78. James Cook Univ. North Queensland, Australia. Jensen, M. & Franck N. 1970. The Climate of Strong Winds in Denmark. Teknisk Forlag, K benhavn.  benhavn. Jensen, N.O. , Mann, J. & Kristensen, L. 1992. Aspects of the Natural Wind of relevance to Large Bridges. Proc. Int. Symp. on Aerodynamics of Large Bridges. Balkena: Rotterdam. Madsen, H.O. 1992. Wind Criteria for Long Span Bridges. ibid. Miyata, T. , Yokoyama, K. , Yasuda, M. & Hikami, Y. 1992. Wind Effects and Full Model Wind Tunnel Tests. ibid. Reinhold, T.A. , Brinch, M. & Damsgaard, Aa. 1992. Wind Tunnel tests for the Great Belt Link. ibid. Scanlan, R. H. , 1992. Wind Dynamics of Long-Span Bridges. ibid. Selberg, A. Hjort-Hansen, E. 1976. The Fate of Flat Plate Aerodynamics in the World of Bridge Decks. The Theodorsen Colloquium: 101 113.   113. Oslo, Norway. Svensson, H. & Kovacs, I. 1992. Examples of Analytical Aerodynamic Investigations of Long-Span Bridges. Proc. Int. Symp. on Aerodynamics of Large Bridges. Balkena: Rotterdam. Tilly, G.P. 1977. Dynamic Response of Bridges. Symp. on Dynamic Behaviour of Bridges. TRRL Supp. Report 275, Berkshire. Wagner Smitt, L. & Brinch, M. 1992. The New Wide Boundary Layer Wind Tunnel at DMI. Proc. Int. Symp. on Aerodynamics of Large Bridges. Balkena: Rotterdam. J. Bay , S. Spangenberg , N.H. Olsen and P.T. Pedersen (1991).    Ship simulations as an integrated part of the Ship design process for bridges crossing waterways   , Proc. Intern. Conf. PIANC, Oslo Danish Maritime Institute (1991)    Manoeuvring simulations, resund Manoeuvring  resund KM 4.2    Evaluati Eval uation on repor r eportt No. No . 1   (in (i n Dani Da nish sh), ), for DSB, Dept. of Transport and Great Belt Link Ltd. (Confidential).

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