Journal of Wind Engineering and Industrial Aerodynamics, 41-44 (1992) 1405-1416 1405 Elsevier

W I N D E N G I N E E R I N G A S P E C T S OF T H E EAST B R I D G E T E N D E R P R O J E C T

Allan Larsen ° and Niels L ~3imsing b

Aerodynamicist Bridge Design, B.Sc., Ph.D., COWlconsult Consulting Engineers and Planners A/S, 45 Teknikerbyen, DK-2830 Virum, Denmark

b Technical Advisor, A/S Storeba~ltsforbindelsen, 10 Vester Segade, DK-1601 Copenhagen. Professor, Department of Structural Engineering, Technical University of Denmark

Abstract The Present paper presents a review of simple analytical models available in the literature for

assessment of structural dynamic and aerodynamic performance of suspension bridges. Analytical predictions are compared to results obtained from structural FEM-models and comprehensive wind tunnel tests carried out for a box girder suspension bridge of 1624 meter main span. Satisfactory correlation is obtained for basic natural frequencies and for flutter and buffeting predictions. A modification to the Selberg formula is suggested which accounts for the enhancement of aerodynamic stability through a windward shift of the section centre of gravity.

INTRODUCTION

Long span suspension bridges are susceptible to the action of storm winds. Wind engineering aspects of a proposed suspension bridge must thus be given due consideration at an early stage in the design process where major decisions relating to the principal dimensions of the bridge are takcn. Typical examples tire: choice of main span and side span lengths, tower height, capacity ot carriageway, and cable configuration. Advanced numerical and experimental techniques sire available for amdysis of structural and aerodynamic perlbrmance of suspension bridges, but prudent application require a certain level of detailing which rarely can he met at conceptual stages. Thus the designer must resort to l'airly simple analytical methods for assessment of the aerodynamic perlbrmance, much the same way as is done for early quantity estimates. Once a bridge concept is established on this basis, the designer can pursue detailed analysis by means of advanced computer models and extensive wind tunnel testing.

The present paper reviewcs selected analytical methods available in the literature and compares the analytical predictions to results obtained from Finite Element computations and wind tunnel testing conducted during development of the Great Belt East Bridge Tender Design. The experimental programme included wind tunnel tests of 1:80 scale section models in smooth and turbu- lent flow, and "taut strip" tests of a 1:300 scale model in simulated atmospheric boundary layer flows.

1. GREAT BELT EAST BRIDGE TENDER PROJECT

The fixed rail/road link across the 18 kilometre wide Great Belt strait, Denmark, comprises three major civil engineering structures:

0167-6105D2/$05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.

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East Tunnel, a twin bored railway tunnel. West Bridge, low level concrete box girder bridges for road and rail traffic. East Bridge, a high level suspension bridge with box girder approach spans for road traffic. The East Tunnel and West Bridge are currently under construction, and are scheduled to be

opened for rail traffic in 1994. The East Bridge, which will carry a four lane motorway and two emergency lanes across the international navigation channel of the Great Belt, is scheduled for opening in 1997.

Risk studies of the ship traffic en route to and from the Baltic region have identified a suspension bridge of 1624 meter main span with 535 meter side spans as a feasible structure for safe ship operation in the international navigation channel. The strategy for tendering of the East Bridge called for development of a detailed tender project for the bridge, a task undertaken by a Danish joint venture with COWlconsult as leading partner, B. Hojlund Rasmussen and Ramb¢ll & Hannemann. The design project involved elaborate risk analyses and comprehensive aerodynamic studies.

Main particulars and general arrangement of the East Bridge Tender Project are given in Figure 1. General arrangements like this are typical of the level of technical information available at early design stages. For further details on the tender design and special studies carried out, please refer to Tolstrup and Jacobsen [1 ].

254.1

Belt East Bridge, Tender Design Great

27,0 rn • ,r

E'. ,q'

310 m p , Box Gi~det Cross Section

Main Particulars: Main Span Length I m = 1624 m Side Span Lenolh I s = 535 m CablaSag a = 180m Cablo Spacing 2a = ;?70 m Cable Aroa ( o~o cable ) A ¢ '= 0 40 m 2 Gitdor Width B ,,, 31,0 m G~rdar Dop,~l b ,,, 4 4 m Gi~dcr torsional ConGtant K ~ 7 6 m 4 3 Girder Me~e ( incl, cable ) m ~ ~P,74 '~ 10 k g / m

Girder M o ~ Moment or Inertia I ~ P 41 * 106k0m~/m ( incl, cable )

I "It

i ....

Pylon

, 535.0 m , t624 m , 535,0 m ;

Elevation

Figure 1. Main Particulars and General Arrangement of the East Bridge Tender Project,

2. S'I'RUC'I'URAL DYNAMICS OF SUSPENSION BRIDGES

The structural dynamics of a suspension bridge, i.e. natural frequencies (in vacuo) and mode shapes, must be known with a certain accuracy in order to quantify the aerodynamic performance. Dynamic analyses are commonly made by means of iterative eigenvalue procedures applied to complex numerical space-frame Finite Element Models involving 600 - 1000 nodes typically.

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Establishment and checking of the numerical model is at best a tedious job, and parametric studies which involve systematic variations, say of main span length and cable sag, becomes quite time consuming.

An alternative to numerical FEM-models is the Rayleigh-Ritz cable/beam model described by Richardson [2]. As~aming mode shapes to be harmonic functions of the spanwise coordinate, and that the bridge is symmetrical with respect to the longitudinal centre-plane, the Rayleigh-Ritz method provides simple analytical expressions for determination of natural frequencies. Furthermore, the method offers physical insight, and identifies parameters which govern suspension bridge dynamics.

Basic parameters to the cable/beam model are the horizontal cable tension H and the cable stiffness parameters Pz, Pe for vertical and torsional modes:

mst~ " = Sd (1)

32d 2EA c P, = (2) HI.L

n% -- e , I 0- , ua2)6r (3)

where m is the section mass, S is the acceleration of gravity, i , is the main span length, d is the cable sag, a is half the spacing between cable planes, A c is the cable area (one main cable), E is the section torsional constant, and E , O are Youngs modulus of the main cable and the shear modulus of the cross section respectively. L is the length of the main cable which may be found from the following approximate formula:

L 3 t z.) j

Eigenvalues for symmetric modes which involve cable stretching are governed by a transcendental expression in the non.dimensional frequency parameter q,,0:

P~o = m(q,.,O.,.2tn,n(~,q.,O, t. I+2).

q~.0

Once q,.o is evaluated from (5), the in vacuo natural frequencies fz,/0 (Hz) in vertical bending and in torsion are obtained as follows:

q ' l fz -- ~ -~ (6)

(7) Comparison between natural frequencies for the basic symmetrical vertical and torsional modes

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Ritz cable/beam model outlined above is given in Figure 2. The agreement is surprisingly good taking into account that elastic and mass parameters vary somewhat along the span of the FEM-model, but are assumed to be constant along the span of the analytical cable/beam model.

The expressions given above apply to the fully-built bridge and assumes constant section properties along the entire span. The influence of pylon stiffness is also neglected. The method can be extended to cover the influence of pylon stiffness and aerodynamic coupling between vertical and torsional modes if desired. Some of the simplicity which makes the method attractive for conceptual studies will however be lost.

Great Belt East Bridge, Dynamic Analysis

Finite Element Model

fo = 0272 HZ

f t ~ 0099 HZ

Continuous Cable/Beam Model Cable Stretching Modes

log P

3,0 i

log Pz

Ioo F' e

0,0

I

I I I I I i r i

233 3,68 I v~- -q

4,0

fo = 0.281 HZ fz = 0,094 HZ

Figure 2. Comparison of basic mode natural frequencies for the East Bridge Tender Project obtained from FEM-analysis anti the Rayleigh-Ritz cable/beam model.

3. AEROI)YNAMIC STABILI'IN' AND WIND LOADING

Aerodynamic stability and wind loading on the stiffening girder are important parameters to be considered in the design or'suspension bridges. Both quantities depend on the choice of cross section type (box, plate or truss), and must be evaluated accordingly.

Experience gained from Danish bridges reveals that construction and maintenance costs are considerably lower [br box girders than R~r plate or truss girders. Adequate torsional stiffness can be built into shallow box girders which furthermore may be designed ['or desirable aerodynamic perlbrmanc¢ by introduction of wedge shaped edge fairings, in conclusion, the "streamlined" box section appeared to be the logical choice tbr the East Bridge Tender Project.

Methods tbr prediction of t he aerodynamic stability of"streamlined" box sections have been treated e.g. by Frandsen [3] and by Selberg [4]. Frandsen applied the classical Thoedorsen flutter theory in

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order to establish the range of validity of Selberg's empirical formula for the onset wind speed U= of divergent (catastrophic) oscillations. In non-dimensional form the Selberg formula reads:

J u: = ~ (8)

where p is air density and a is over all deck width. In case of the stiffness and mass parameters valid for the East Bridge Tender Project, critical wind

speeds calculated by the two methods differ less than 1%, if the slightly favourable effect of structural damping is neglected.

During development of the East Bridge Tender Project, 16 different box section configurations were designed and subjected to wind tunnel tests in smooth flow and turbulent flow of 7.5% intensity in the along-wind direction. The tests were conducted at the Danish Maritime Institute using 1:80 scale section models of aspect ratio 6.6 [5]. Figure 3 compares measured critical wind speeds t]=, as fraction of the theoretical value obtained from eqn. (8), for 10 selected cross section configurations. Figure 3 reveals that all sections meet the theoretical U= value with narrow margins, despite the dif- ferences in section geometry. Turbulence has a slight destabilizing effect on the aerodynamic stability, an effect which may be linked to the vertical force perturbations caused by turbulent eddies passing the section.

Desig- nation

H1,1

H1,2

H3.1

Critical Wind Speeds U= for onset of Flutter

U'o measl Flow U¢ mess Flow Desig- Cross Section ~ Condition Cross Section Uct~e-o- Condition nation

,L" 6.0 I 9.0 i ( 0.994 ) .... 0.934 Turbulenl

I i ,04 smooth 1,028 Smooth H6.1 ~ 0,940 Turbulent

I 6.0 i IO.S ,, (0,9S3) l 9.65 (0.899)

..> , lo8 ooo,h ,03, s oo,h ,~ 0.964 Turbulent H7.1 0,952 Turbulent

[ 7.3 ,L 7.7 c0.932) ~ t30 ~ _ ~.0 C0.911)

, 000 H4.1 0.952 Turbulent H9'1 ' 0,944 Turbulent

f 9,0 ~ 50, c09.1 ~s L6;o . c09031 ~. R=2.5 ~.

H'~.2 [ 0.975 Turbulent Wind 0,942 Turbulent ~, 6 . 0 5 9 . 0 ~ ( 0,933 ) ScreenAdded ~ 9.5 L_6.0_ ' ( 0.901 ) I

Figure 3. Critical wind speeds for the tested cross section configurations given as fraction of the theoretical value obtained from the Selberg formula. Valises in parenthesis correspond to [/~ predictions using natural frequencies obtained from the Rayleigh-Ritz cable/beam model.

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2.4 meter high wind screens of 50% perforation, lifted 0.6 meter above the crown of the roadway, were fitted to selected section models. Tests revealed that this type of wind screen can be arranged with virtually no influence on the critical wind speed as indicated by comparison of results for sections H9.1 and H9.2. Obstruction of the free airflow over the top slab, i.e. by snow accumulation along the guard rail, caused a 50% drop in t./,, while changing the mode of motion from classical 2 DOF flutter to 1 DOF torsional flutter. For the H9.1 section, actually chosen for the East Bridge Tender Design, Figure 3 yield a prototype critical wind speed O, = 71 m/s which meets the design criterion ot"60 mls with a comfortable margin. This magnitude of the critical wind speed was confirmed through "taut strip" tests with a 1:300 scale model conducted at the University of Western Ontario, Canada [9 i.

Steady-state wind load coefficients and their slopes with angle of attack are important parameters for evaluation of the wind load on the bridge structure, and the buffeting response of the bridge deck to turbulent wind. Figure 4 compares wind load coefficients obtained from wind tunnel tests of the 1:80 scale models of the H9.1, H9.2 sections to similar results for a 1:300 scale model of the H9,1 section. Wind load coefficients for a model of the cross section adopted for the Humber Bridge [6] are included for comparison. Lift and Moment slopes deride, deatd= are quite similar tbr the shown section configurations and indicate that the presence of wind screens ( or cantilevered footways for that matter ) has little influence on the vertical and torsional buffeting forces exerted on bridge structures with "streamlined" box sections. Addition of the above mentioned wind screens to the H9.1 section leads to a doubUng of the section drag coefficient Coo, a factor which must be taken into account in the design of cable saddles, pylons and girder bearings.

Dosig- Cress Section nation

H9,1

Hg,1

Steady - State Wind Load Coefficients

; 0 0 ; 0 0 I

Lilt CLO

Lift Slope aCLld,~

Moment CM0

Morn. Slope dCM/d~

Drag C00

Comments:

H,2 T ¸r

T _.>-- ; 36.L 7.4 ,3,0~

0,067

- 0050

4 37

4,41

0,028

0,013

1.17

0.93

0,57

0.59

- 0.18

- 0,18

435

4.20

- 0 O12

0.018

1,17

1,40 0.45

Turbulent Flow 1:60 Scale

Turbulent Flow

1:300 Scare

Turbulent Flow 1,21 1:80 Scale

Wind Screens

Turbulent Flow Humber Bridge Ref, ( 6 )

Figure 4. Steady-state wind lt~ad coefficients measured for the East Bridge Tender Project and the ]tumbcr Bridge,

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4. BUFFETING RESPONSE

The action of turbulent winds on suspension bridges gives rise to time dependent motions of the stiffening girder mainly in twist, cross-wind vertical and along-wind directions. Knowledge of these motions, i.e. the buffeting response, is important for evaluation of the bridge performance against comfort criteria, and for assessment of equivalent static wind loading, e.g. by the method suggested by Davenport and King [7]. The torsional response of a suspension bridge is often considered to be the most important (critical) of the three buffeting components due to the relatively low aerodynamic damping which is often encountered in this mode of motion. The present discussion will thus focus on torsional buffeting.

In a recent survey of bridge aerodynamics, Scanlan [8] gives expressions for calculation of the response of bridge decks subjected to turbulent winds. Assuming C~0 < dC~/d= for the cross section

in question and introducing the aerodynamic admittance function x=($), the Mean Square response o~ at midspan of 1. torsional mode may be approximated as follows:

, , % -" - - ~c+(A ) 2

+zeg, t J k z ) L + d=) 4(c,+c,,, o,, J (9)

where:

X=( & ) = l a Sears Function approximation (10)

C = = & / r./ ' a : exponential decay factor for lateral coherence ranging between 7 and 15 (11)

+__:,+o/+;-] TorAet I

+~!??to-#oj?'J

Power Spectral Density

. . . . . . . . +-+i . . -+,-+-.+.i~

~ -+ . lq+ - . l . - t ~ , p t , I l,tceff i i i (+°L~,~t.H+

.4,4-t+14.11

O,OI 0,1 I

reduced Frequency IB/U

0,3 006 1

0,=~ !°°+ 1 oo+ I

o,2 o032 o,t+, q~ oo~ : 0.1 ~ 0 0 1 ,

O,Ob O '

I)QI

RMS Torsional Response Section Model

. . . . . . . . . . . . . . . . . 14

- - ~ F~qrl(!)l Exe] kdlTtlll . . . . . . . . . . . 1

+ . - - - o - - - t'.qtl(9) lm'l Adrmtt I . . . . . . . . . . . . . . . 0 5 _ ~ . =

. . . . . . . . . . . . . . . . . + . . . . . , o .

Measurement J

i - . . . . . ~ .b - l _ _ ~_ .~- I (1

0 I 2 3 4 5

Red.cad Vcloc=ty U / I l l

Aerodynamic Damping in Torsion

~U&$I ~tntlunnry

• - " ( ~ ' - 8edlon Model

'l'heodorgen

I a 3 4 5 6 7

r e d u c e d Ve loc i ty U / I B

RMS Torsional Response "Taut Strip" Model

0 6 . . . . . . . . . . - - - , . . . . . . . " . . . . . . . . .

0 ~ ] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v?t,2712~,!?!,/,~. L, _. ~ ;

~ 0 4 . . . . . . . . . . . . + . . . . . . . . . . + . . . . . . ~ - . . . . . . ' . . . . . . . ~ - ~ - - 4 .~ , ,C, - - - Eqrl(9) Exd kdn111i

0 1

O. I 2 3 4 5 6

reduced Vdoeity U/fB

Figure 5. PSD of vertical turbulence, aerodynamic damping and comparison of estimated and measured RMS torsional response from section model tests and "Taut Strip" tests.

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The fashion in which the aerodynamic admittance is introduced in equation (9) is not formally correct, reference is made to Davenport and King [7]. The error involved will, however, be of minor importance for lightly damped structures for which resonant excitation dominates the response.

Prediction of Root Mean Square torsional response % is now possible, once all quantities in eqs. (9), (10) and (11) have been established. Moment slope dC~ld~, is usually obtained from steady-state testing of section models. Aerodynamic damping ~o may be obtained from theoretical considerations, i.e. from quasi stationary theory, Theodorsen theory or alternatively through model tests. Data on the flow field such as vertical turbulence intensity lw, decay factor a, and power spectral density

f S~,( / )/a~ of vertical turbulence are meteorological parameters to be obtained for a particular bridge site. The structural damping C, is a difficult quantity to estimate for a new bridge design, but estimates derived from lull scale measurements are available in the literature.

For the East Bridge Tender Design, most of the above mentioned quantities are available either from 1:80 scale section model tests [5] (mode factor J = 1), or from "Taut Strip" model tests with a 1:300 scale model of the main span [9] (mode factor J = 0.5). For these cases Figure 5 offers a comparison between measured torsional RMS responses and predictions made by means ofeqs. (9) - (11). Figure 5 also gives normalized power spectral densities of vertical turbulence measured as part

of the section model and "taut strip" tests. The decay factor a for lateral coherence of vertical turbulence was estimated to range between 7 and 9 for the section model tests and was assumed to take the same valt~es for the "taut strip" tests, but no experimental proof is available at present.

Aerodynamic damping in torsion obtained from free oscillation tests with the 1:80 scale section model yields considerably lower values than expected from quasi stationary considerations or Theodorsen theory. For the present comparison between theory and experiment, the aerodynamic damping was approximated by the following expression:

~a :B tl 02)

The general impression from Figure 5 is that bufl'cting response is quite well predicted by eqs. (9) - (1 l) for "streamlined" be× sections, provided intbrmation on the turbulent flow field can be obtained

with satisfactory ac~:uracy. Introduction of the Sears Function expression in eqn. (9) leads to a 56% reductkm of the torsional response at the design wind speed, as compared to the case where the aerodynamic admittance is neglected, i.e. Z~( f ) -- 1. Measured torsional responses are seen to be bracketed by predictions including and excluding the aerodynamic admittance, of more bluff shape.

Analytical expressions, similar to eqs. ( 9 ) - (11), are available ['or the vertical and lateral components of the buffeting response [8].

$. VORTEX SHEDI)ING RESPONSE

Box and plate girders arc known to be susceptible to the action of rhythmic vortex shedding. Vortices shed of the leading edge of the cross section tend to "lock-in" with structural motions at the natural frequencies of the bridge. This action leads to resonant excitation of the girder at certain discrete vek~city intervals. Assessment of the wind speeds at which "lock-in" occurs and estimation of the response magnitude of the structure is important for evaluation of the aerodynamic performance against comtbrt criteria and possibly for estimation of weber in bearings and joints, Vorte:~ shedding may induce vertical as well as torsional motions of the bridge girder, but vertical response is often found to be dominant in most cases reported in the literature.

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found to be dominant in most cases reported in the literature. The relation between wind speed and the frequency of vortex shedding is linked to the section

Strouhal Number ,~ based on the maximum cross-wind depth D of the section. The Proposed British Design Rules [6], gives the following expression for the Strouhal Number of bluffcross sections:

a - - f o _ (13) U (1.1BID + 1)

The non-dimensional wind speed///f~B for"loek-in" between vortex shedding and structural vibration is obtained as:

U 1 D - ( 1 4 ) foa st n

The ratio of the RMS response at "lock-in" to the cross-wind section depth for vertical vortex excitation is obtained from the following empirical expression:

o__~ = 1 pBlrZD v~ (15) D ~ 8~m~

whic, is derived from model experiments with a number of different cross sections. Table 1 compares predictions using cqs. (13) - (15) to results for vertical vortex shedding response

obtained from section model tests with the H9.1 section. It is observed that the wind speed for "lock- in" between vortex shedding and structural frequency is quite well predicted by eqs. (13) and (14). The girder response to vortex shedding is also quite well predicted for smooth flow cases, but overestimated by a factor 2 for the turbulent flow case.

Table 1 Vertical vortex shedding response, predicted and measured

Quantity Predict. Predict. See. Mod. Sec.Mod. See. Mod. ~a % 0.16% 0.48% 0.16% 0.48% 0.48% Flow Smooth Smooth Turbulent

U 1.24 1.24 1.22 1.13 1.07

°--~ z .049 .016 .034 .015 .007 D

6. AERODYNAMIC STABILITY DURING ERECTION

The erection of suspension bridges presents particular aerodynamic stability problems due to temporary lack of torsional continuity of the girder and stiffness of the main cables. For truss stiffened bridges the problem may be solved by erecting the open truss in one pass, leaving the full deck to be installed after the bridge girder has assumed full torsional stiffness. This strategy is not applicable to box girder bridges where the shell plating constitutes an integral part of the box sections. In this ease

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the partially built bridge will be fully exposed to the action of the wind through all phases of erection. When deck erection proceeds symmetrically from midspan, the natural frequency in torsion is

significantly lower than for the fully-built bridge, leading to low critical wind speeds according to eqn. (8). Critical wind speeds during erection may be enhanced through an alternative construction scheme where erection proceeds simultaneously from pylons and midspan, leading to increased stiffness of the main cables for a given number of sections erected at midspan.

Critical wind speeds during erection may further be enhanced by provision of eccentric ballast along the windward cable plane. By doing so, the section centre of gravity is shifted windward of the elastic centre of the bridge which remains at the centre line. This action promotes desirable structural coupling between torsional and vertical modes.

Classical Theodorsen flutter theory may easily be expanded to incorporate the effect of a shift of the section centre of gravity away from the elastic centre. This is effectuated by introducing the first order moment of the shifted section mass in the structural (left hand side) equations. Structural coupling of torsion and vertical motion is now present which will either magnify or counteract coupling by aerodynamic forces.

Classical Theodorsen theory does not allow closed analytical expressions for the critical flutter wind speed. Solutions must be obtained either by iterative procedures or by graphical methods as presented by Frandsen [3]. An approximate analytical expression, akin to the Selberg formula, may be obtained by modifying the divergence speed by a (1-( ~ Ife )2) factor yielding:

pn2( 4$*B ) tf0)] (16)

where s is the distance l'rom the centre of gravity to the elastic centre of the section. S is negative for windward locations of the centre of gravity in keeping with the sign convention adopted in 131. The factor in front of the first square root may be calibrated through comparison with Theodorsen flutter theory lbr the particular set of vertical and torsional frequencies in question. For the present ease a factor of 3.75 was found to be appropriate,

Figure 6 compares non-dimensional critical wind speeds as I'unction of/~/8, determined by Theodorsen theory, by eqn. (16) and through section model tests with the H9.1 cross section. The dynamic properties of the partially-built bridge are representative of an erection phase where 2()% of the main span deck structure is erected at midspan and 16% at each of the pylons. In the side spans 41% of the deck structure is erected from the pylons in order to balance the main span loading.

Windward Shift cJf (?entre of Gravity

I I

I

01tl Illl,~ r)l l l I)(11 O(bTI ~}Ot~ 11(17 IHI~I

,~/l l

' ~ Ml~|lt*c} ,%lh,r~ i i

Figure 6. Comparison of critical wind speeds versus windward shift of centre of gravity for the partially-built bridge.. Results from theoretical considerations and section model tests.

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Agreement between theory and experiment is fair and indicates that eqn. (16) may be used for a rough estimate of the enhancement of aerodynamic stability gained through a windward shift of the centre of gravity. Shift of the section centre of gravity may be effectuated by provision of eccentric mass loading at the windward cable plane.

7. POSTSCRIPT

The East Bridge Project was submitted for tender in the summer of 1990. Bids and construction proposals have now been received and evaluated. Detailed Design of the East Bridge is scheduled to start mid 1991 and will proceed for a period of one and a half year parallel to construction. Wind engineering studies will continue throughout the Detailed Design period and will include aeroelastic tests of a 1:200 scale model of the full bridge. The main objectives of these tests are to quantify three dimensional effects such as bridge response to wind flow yawed relative to the bridge axis, changes of girder cross section from side spans to main span and aerodynamic effects of multi mode interaction excited by turbulence.

8. NOTATION

a

d / S

m

q Ac B C D £

G /./

I 1,.. J g

L P S

U

Decay factor, Half cable Spacing Cable sag

Frequency in Hz Gravitational constant

Length, main span, side span Section mass

Non-dimensional frequency Area of one main cable

Cross section width Coherence parameter of turbulence

Cross section depth Youngs modulus of elasticity

Shear modulus Horizontal cable tension

Section mass moment of inertia Turbulence intensities

Modal fa~tor Torsional constant, cross section

Length, main cable Cable stiffness parameter Shift of centre of gravity

Mean wind speed

Ct ° -_. aerodyn vertical force Lift Coef. ,~pU2B

Cu ° = aerodyn tw/sgng moment Morn. Coef .

l12p ff2B2 C ~ = aerodyn horizontal force Drag Coef.

Vap O2 D

Is(f) 0 ")

d Id~

P O

X 2

Normalized PSD of turbulence

Slope with angle of attack Damping relative to critical

Ratio, sidespan mainspan length Air density

Standard deviation (RMS-value) Aerodynamic admittance

indices:

$

Z

0

!0

Aerodynamic Structural

Vertical Torsional

Along-wind Cross.wind vertical

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9. REFERENCES

1 C. Tolstrup and A.S. Jacobsen: "Suspension Bridge over the Eastern Channel of the Great Belt", IABSE Symposium on Bridges, Leningrad, USSR, September 1991.

2 J. R. Richardson: "Advances in Techniques for Determining the Aeroelastic Characteristics of Suspension Bridges". 4th International Conference on Wind Effects on Buildings and Structures, Heathrow, England, 1975.

3 A.G. Frandsen: "Wind Stability of Suspension Bridges". International Symposium on Suspension Bridges, Lisabon, Portugal, 1966.

4 A. Selberg and E. Hjort-Hansen:"The Fate of Flat Plate Aerodynamics in the World of Bridge Decks". The Theodorsen Colloquium 1976, Oslo, Norway, 1976.

5 Aa. Damsg~rd, A.G. Jensen, E. Hjort-Hansen and N.J. Gimsing: "The use of Section Model Wind Tunnel Tests in the Design of the Storebaelt East Bridge in Denmark". 2nd Symposium on Strait Crossings, Jon Krokeborg (ed.), Trondheim, Norway, 1990.

6 T. A. Wyatt (ed). "Bridge Aerodynamics", Symposium held at the Institution of Civil Engineers, London, England, 1981.

7 A.G. Davenport and J.P.C. King: "Dynamic Wind Forces on Long Span Bridges Using Equivalent Static Loads, IABSE Symposium, Vancouver B.C., Canada, 1984.

8 R.H. Seanlan: "State-of-the-art Methods for Calculating Flutter, Vortex-lnduced, and Buffeting Response of Bridge Structures". Federal Highway Administration Report No. FHWA/RD-80/050, 1981.

9 J.P.C King, G.L. Larose and A.G, Davenport: "A study of Wind Effects for the Storeb~elt Bridge Tende~' Design, Denmark". BLWT-IR-S67-1, 1990. (Draft Version).