Journal of Wind Engineer:.ng and Industrial Aerodynamics, 41-44 (1992) 1191-1202 1 191 Elsevier

Wind Effects on Long Span Bridges: Consistency of Wind Tunnel Results G. L. LAROSE ~, A. G. DAVENPORT b, and J. P. C. KING c

"Research Engineer, b Director, "Research Associate The Boundary Layer Wind ~nnel Laboratory, The University of Western Ontario, London, Ontario, CANADA, N6A 5B9

Abstrac t

This paper compares measurements made on full-scale bridges with some of the various models, experimental and theoretical, that are used for the prediction of the response of Ion s span bridges in turbulent wind. These models include full-bridge aeroe- ]astlc models, extended section models and a theoretical model which has come to be known as the quasi-steady aerodynamic approach. The comparisons are made for both suspension and cable-stayed bridges.

The conclusion resulting of these comparisons is that there ~s a very satisfactory degree of consistency between all three methods. The quasi-steady aerodynamic ap proach is defined and four case studies are presented, including the Humber Bridge, the F~r¢ Bridge and the Sunshine Skyway Bridge.

1 Introduct ion

The accuracy of the analytical and experimental methods used for predicting full scale bridge performance is of fundamental importance in assessing bridge safety. The purpose of this paper is to compare measurements made on real bridges with some of the various theoretical and experimental models used for the prediction of the response of long span bridges in turbulent wind.

~ ] I ~cale Measurements

Full scale measurements of the response of long span bridges are the key to solving many outstanding issues in bridge aerodynamics. Although still limited, the number of fun scale investigations has increased considerably in the past years. Here, previ- ously published results of fun scale measurements on the Humber Bridge [1] and the

0167-6105/92/$05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.

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Fare Bridge during construction [2] are reanalyzed and compared with prediction from full bridge aerodastic model tests and the theoretical approach based on the quasi-steady aerodynamics.

Wind Tunnel Results

The Boundary Layer Wind Tunnel Laboratory (BLWTL) has recently been in- volved in comparative studies of the behaviour of two-dimensional section model and three-dlmensional full bridge aeroelastic models in turbulent boundary layer flow and the consistency of experimental results was verified and compared with theoretical pre- diction using the quasi-steady aerodynamic approach.

The wind tunnel studies reported here were primarily carried out to evaluate the action of wind on cable-stayed superstructures and to provide information for structural design. They were typically comprised of an experimental investigation involving two wind tunnel models: an extended section model constructed at a large geometric scale (e.g. 1:100) and a smaUer scale full bridge aeroelastic model (e.g. 1:175). Data from the section model study were used for the analytical determination of the Equivalent Static LoeSs acting on the prototype bridge. The full bridge model tests were used to predict the three-dimensicnal responses of the prototype in turbulent wind.

2 Background

2.1 The Quasi-Steady Aerodynamic Approach

A simple approach to the action of wind on a flexible bridge deck has been for- mul~ted on the basis of a so-called quasi-steady aerodynamic assumption. In this, the instantaneous forces on the deck are taken equal to the steady forces induced by a steady wind having tile same relative velocity and direction as the instantaneous wind. The steady force coefficients of the deck cross-sectlon and their variations with angle of at- tack are then considered sufficient to solve the equations of motion of the deck in turbulent wind.

This approach has been shown to be valid in several occasions but with certain limitations. It is most valid for small reduced frequency f" - ~ (or large reduced velocity) where the time taken for the flow to traverse the bridge deck is very short compared to the oscillation time or otherwise that the effects of the motion of the deck are communicate rapidly to the flow region surrounding it. In another sense, it is valid when disturbance~ in the flow have appreciably larger dimensions than the deck itself.

The derivation of the theoretical expressions for the prediction of the response of bridge deck to turbulent wind assuming quasi-steady aerodynamics have been described in details in previous papers [3]. We are reproducing here the simplified expressions.

Although the response of a suspension bridge has been represented by coupled vertical and torsional equations of motion in fact the aerodynamic coupling terms are usually negllgible~ and the aerodynamic stiffness terms are usually small in comparison to the stiffness of tile bridge itself. This leaves the aerodynamic damping as the most

1193

significan~ aerodynamic force induced by motion.

We can represent the peak response ~ by the following:

where g is a statistical peak factor, u~ is the mean square background response acting quasi-statically, and cr~j is the mean square modal response at or near the resonant frequency.

The background response covers a broad frequency band below the natural fre- quency; the resonant response is concentrated in a peak at the natural frequency, the height of which is controlled by the damping. The two components can be estimated from the following expressions:

2 fo ~ ¢r s .... o = f'SF=,.,o (f') " [J=,.,o(f*) 12 " d(Inf') (2)

2 (Ir/4) f;SF.,.,o (f;) • [J.,z,o (f;)[2 (3) . .... ., = (/:))

In the above the subscripts z, z, 0 imply the equations ate written for each variable in turn; f" and f~ are the reduced frequencies fB/Vtt and fjB/VH; ~s mad (~ (f*) are the structural damping and aerodynamic damping at frequency f ' ; f'St~.,,o (f*) is the power spectral density of the externally induced z,y, 0 components on a cross-section of the bridge deck at the reduced frequency f ' ; [ J~,z.o ( f ' ) [2 is the "joint acceptance function", relating the generalized modal force component with the mode shape and the force components at frequency f* at cross-sections of the bridge and involves the spanwise correlation of the forces.

Using quasi-steady aerodynamics, the spectrum of the force caused by turbulence can be written:

(/'sF(/ )),,,,b- (q,, B) 2 (cL,o I A(f') ,2) .(/ u,,,,wCf')) (4)

where f'&,~,,o (f') A(f')

q~, B

-- the power spectra of the turbulent velocity fluctuations;

= "aerodynamic admittance" which translates the

turbulent fluctuations into forces on a cross-section; = a reference steady aerodynamic coefficient; and

= the dynamic pressure at deck height H times

the deck width B.

The contributions of the turbulence to the expressions for ¢r 2 and ~r2j can be written as follows. To simplify the notation we will consider the lift (z) force and only include the vertical (w) component of turbulence, which normally will dominate.

1194

(°'~')=(q'BO'=))~\~H) L o'~, IA:(ff) IJ=(S') "dOnS') ( 5 )

(@21.,) : (qHITC")) 2 (~H)~ f~S~O.~ (f/') I A. (~)12]Jz (S~)I 1 (~. d-(=/4)~. (S~)) (6)

The coei~.cient C'= denotes (OC=/Oo~), the variation of the lift coemcient with angle of attack. Similar expressions for the torsion can be written with 0 replacing z and introducing an additional factor B 2. For the drag direction 2C~ replaces G'= and replaces w.

If the left hand terms are normalized by the (qHBC'~) 2 term, the response is a func- tion primarily of the reduced frequency S" and the intensity of turbulence (I,, = o , , / ~ ) , two homologous quantities which link the full-scale bridge behaviour with any dynam- ically scaled model. Otherwise, the turbulence controlled response is bound up in the functional form of the turbulence spectrum, S,,,, the aerodynamic admittance, A., the joint acceptance function, J~, and the aerodynamic damping ¢~.

Defining the resonant root-mean-square modal response Snq in the vertical direction by:

0"2 e L

where Kj a~j/, = = (7) ~u,j KS

K i = the generalized stiffness in mode j; and/ , is the span length;

and assuming i) the Kolmogoroff inertial subrange of wind frequencies and spectra; ii) linear variation of the aerodynamic damping with reduced velocity; and iii) evaluation of the joint acceptance function for the high frequency asymptote, the resonant rms modal response, vertical, can be represeated by a product of dimensionless parameters:

(8)

c , , , , , , i , ; i - nj pB'~ Wt

.,';S...(s;)

I J (f;) J '~

- mass ratio, p is the air density and m is the mass

per unit length of the deck;

= A., \~} , Kolmogoroff subrange (A,. = 0.24 ; A. = 0.045 [3]);

2 Vu --" c " fj-'L' c is the spanwise cross-correlation coel~cient.

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Equation (8) is valid for all modes where the deck is dominant and can be easily transformed to express the lateral and torsional responses. Note that if the structural damping is considered dominant in equation (8), neglecting the aerodynamic damping term, the resonant rms response will tend to be proportional to the reduced velocity at a power of 2~. On the other hand, if the aerodynamic damping is dominant, the exponent 2~ will be reduced to a value approaching 2, given the variation of ~awith reduced velocity in the dominator of equation (8). This equation does not include the variation of the aerodynamic admittance with reduced frequency and assumes it equal to 1 (A (f . ) --- 1) corresponding to quasi-steady aerodynamics.

2.2 Section model and Equivalent Static Loads

The theoretical basis for "extended" section model testing in turbulent flow stip- ulates that for the section model and full bridge responses to be similar the following restrictions must hold [4]:

• the aerodynamic forces on the cables and towers must be small compared to those of the deck;

• the motion-induced aerodynami,- forces at all locations across the span must have the same linear function of the local motion of the deck; and

• the scale of turbulence at the resonant frequency is small in comparison with the length of the model (hence the term "extended" section model).

Early section model tests have shown satisfactory qualitative agreement with full bridge model tests and adequately predicted unstable behavior of full-scale bridges [5, 6]. How- ever, significant deficiencies in this approach were noted [4, 7] and an alternative approach was proposed and vet;fled in the studies of the Sunshine Skyway Bridge. This approach, known as the determination of Equivalent Static Loads (ESL), is based upon the mea- sured response of an extended section model in turbulent flow, with suitable corrections for discrepancies in the intensity and spectrum of turbulence, the damping and the mode shape. The wind loads are determined from estimates of the dynamic motion in the lowest symmetric and asymmetric modes as well as the mean load for the lateral, vertical and torsional degrees of freedom. This method is described by Davenport [8].

3 C o m p a r i s o n s

3.1 Full Scale Observations versus Predict ion Models

The H u m b e r Br idge The Humber Bridge, with its 1410 m world's longest suspended span, has been and

still is the object of many full-scale measurements in order to characterize its response. Fig. 1 was derived from full-scale results obtained by Brownjohn et al. [1]. The rms

!196

e~

m

i

g o.

uJ

V E R T I C A L . J U .2 r - 1.7 x ="- ; - - -~ ' / o e~ = .wq,

• : . . . Y . - ' : , 7

i? • .a • o w~o2

• 3

LATERAL

r * 4,2 x t 0 - 7 [ ~

REDUCED VELOCITY U* - U/G'B]

Figure I Variat ion of Modal Responses of H u m b e r S u s p e n - s ion B r l d s e w i t h M e n . Wind Speed (Full-scale Observations, Brcwnjohn et al(19S7))

16.5,2.-.

13.:~ Cablu~

21 080

A 8S0 m ~rp=n "=UUl~rmlon ~Hdme 9w: t" Cr~s SeeUon A

3.00

I I °'J.O00 , ¢Sbl,m I i

FiKure 2

HUMBER BWDCE DP.C'g I~.O'~l ~ ' r l o l l

S n s p e n s l o n B r i d g e D e c k C r o s s - s e c t l o n s ( A l l D i -

m e n s i o n s in Meters)

response, normalized by the Ba~, was found to be proportional to the reduced velocity at the power 2 in the vertical direction, and 2.36 in the lateral direction. This trend was observed for all the modes of vibration measured.

The similarity between the deck crosHection of the Humber Bridge and a 850 meter span suspension bridge (cross-sectlon A), recently tested at the BLWTL is shown in Fig. 2. A full bridge aeroelastic model of the latter was built at a 1:170 scale and its response to turbulent boundary layer flow was measured for four levels of turbulence intensity. Fig. 3 shows the variation of the measured vertical rms modal response with reduced velocity and turbulence intensity. The solid line is given as a reference and represents a response proportions] to the V "2, The rms response for the aeroelastic model is clearly proportional to turbulence intensity and its slope tends to the reference value of 2.

Fig. 3 also compares the response of the aeroelastic mode] to the response of the full- scale Humber Bridge, represented by the chain-dash l~ue. The agreement is remarkable. Referring to equation (8), part of the explanation for this agreement is that the products

of the dimensionless parameters ( .a~, ~) (~)~ (~)~ are equivalent for both bridges. The quasl-steady theory predicts collapsing of the rms response if normalized by

the turbulence intensity~ as shown in Fig. 4. Here and in Fig. 5, The rms response of the aeroelastic model for different turbulence intensities collapse with the Humber Bridge full-scale results. Deviations from the collapsing trend are explained by variations of aerodynamic damping with turbulence and experimental errors.

The quasi-steady approach prediction for the aeroelastic model for the lateral di- rection is represented by the dash line in Fig. 5. The consistency of this theoretical

1197

prediction with the experimental results and full-scale measurements on the Humber Bridge is satisfactory, the quasi-steady prediction being slightly conservative for higher reduced velocity.

10 "~

Z

0

~10":

lO-,.J I

• - lu - 6Z | Wind Tunnel Results, • - I. • 9X I Aeroelasllc/IAodel In BLWT II . - lu • ISX ~ 1

~, - lu - 30XJ i " ~

D e c k Crosn Section A 6 a /

"° /

I " ,'.'2" , ~8 . , ~ m I a . x /

I tumber Bridge D e c k N ' / ; me

Croas Sect ion " / e I' R m

A N/ • /

,4,'-'" "';'-Humber Bridge

• / = • i = l . T x l O - S x V ' 2 ". Davenport, 1988

i i i

. . . . . . . 10

REDUCED VELOCITY (V/fB)

Figure 4

Vertical RMS Modal Response Normalized by Turbulence Inten- sity

~ 10",

N z 0 o .

~ I0"

10"

Figure 3

Comparisons of Full Bridge Aero- iastic Model RMS Modal Response (Bridge with Cross-section A) with Humber Bridge Full-scale Observa- tions

w- iu- 6X ] e = lu - 9X [ . - lu - ISX I

- lu - 3 0 X J

~ 281rp m ~=~

Wind Tunnel Results, Aeroelastlc Modal In 8LWT II

D~'ek Crosc~ fleetlo. A

. x

III!

l lumber Bridge Deck sp~ : ~ • Croaa Section A

G We/

• m~ A/

I E = 0.833 x i0 -s x V '2

REDUCED VELOCITY CV/fB)

1198

~ i0 °'

N "7 o

N

~ I0 "2

I 0 "

a ,, lu - W i n d Tunnel Rosnlts, • ,, lu = lSZ A e r o e | a s t l c M o d e l In B L ' ~ r I I . - lu - 3ozJ t

Deck Croes Section A

(~hsa.~.Steady Approach, , ~ , ~ Pzedlctlon . ~ P -

2a,~s m ~ "

Humber Bridne Deck ~,~ Cross Section 7

I0

REDUCED VELOCITY (V/fS)

F i g u r e S

L a t e r a l R M S M o d a l R e s p o n s e N o r - m a l l z e d b y T u r b u l e n c e I n t e n s i t y

The Far# Bridge The Far# Bridge is a 290 m span cable-stayed bridge with delta shape towers

and was inaugurated in 1985. Fig. 6 compares full-scale measurements obtained by Petersen et al. [2] during construction with predictions from the quasi-steady approach for turbulence intensity representative of the site, average values of structural damping and steady aerodynamic coe/~cients measured on a section model.

The predicted peak vertical displacement at the tip of the cantilever in the half com- pleted bridge configuration are in good agreement with the measured values in full-scale for the ranf~e of interest of wind velocity. This validates equation (8) for bridges under construction as well as completed bridges, given that the deck motion dominates the re- sponse. The measured and predicted responses have a slope approaching the theoretical value of 2~ suggesting predominance of the structural damping over the aerodynmnic damping for this construction phase.

3.2 Sect ion Models versus Full Bridge Aeroelast ic Models

The method taken in the ]inking of the section model and full bridge model studies, was to use the Equivalent Static Loads (predicted from the section model study) for a given wind speed and apply these in turn to a static analysis of the prototype structure. For the lateral direction, the computer model needed only to consist of the deck itself.

1199

m'

"d

:£

m

IO"

• - ADer Work Hours x . During Work Hours

Full Stoic Measurement* During Construction (af ter Putersen • t •1.. 1987) , "

/ !,

[ I MN N I 22.9 m ~ m d l l i u ~ l l ~

, ~ o ~ o

. ~ , , / / ~ cc Y '

~ i - S t e a d y Apnroach ~ ,I, ° n Prediction, 71, = '4% ' /,e' •

/ / / T = 0.0185 ~. V W~

,,, (after Petersen et al.)

. . . . . . I0 WIND VELOCITY Ca/*)

F i g u r e 6

~ ' a r i a t i o n s o f C a n t i l e v e r T i p P e a k D i s p l a c e m e n t w i t h M e a n W i n d Ve- l o c i t y f o r t h e F a r , B r i d g e D u r l n 8 C o n s t r u c t i o n

For the vertical and torsional directions, however, the cables end towers play a vital role in the stiffness in these directions, therefore a more complicated model was needed. In these cases the mode shapes, frequencies and mass distributions were used to derive the Generalized Mass and Stiffness to provide a means of determlnin s the deck displacement for a given modal load. The deck displacements were used directly to predict both deck accelerations and deck bending moments. Corrections were made to the ESL results so that the dsmpins and turbulence characteristics were the same as that measured for the full bridp model tests.

A 845 m span Cable-Stayed B d d s e

This cable-stayed bridge with delta frame towers and a double plane of cables has recently been studied at the BLWTL. Comparisons between section model and full bridge model tests are summarized as follows:

Mean Dra~: The full bridse model lateral bending moment at midspan was 1.4 times that predicted by the ESL on the deck alone. A simplified estimate of the cable mean drag as an additional uniformly distributed load on the deck was made assuming: Cd = 1.1; 50% of the cable load was transferred to the deck and the remainder to the tower; no shielding of downwind cables by upwind cables. The load carried by the deck due to the cables, using these assumptions, brought the ratio of full bridge to ESL predicted midspan bending moment to 0.95, or only a 5% difference in the two tests•

Dynamic Dra~: The ratio of full bridge to ESL predicted bending moment was I•I without any correction for dynamic cable loading. This close agreement is understandable as the cable mass was not modelled explicitly in the full bridge model and hence, has only a minor contribution to the loading.

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Dynamic Lift and Torque: The fu l l bridge model responses in the vertical and tor- sional degree of freedom were s~ightly higher (10%) than those predicted with the ESL Analysis for the first three fundamental modes. It appears that the contribution of higher modes is required to bring the ESL responses closer to those observed in the full bridge model tests. Fig.7 shows predictions for m]dspan llft rms acceleration of the prototype bridge, normalized by Bw 2, plotted versus reduced velocity. Consistency between the section model and full bridge model results is shown.

Fig.7 also presents predictions of the rms response estimated using quasi-steady aerodynamics [3]. The predictions agree well with the wind tunnel tests for higher values of the reduced velocity. The differences observed can be explained by the limitations of this approach, e.g. mostly valid for small values of reduced frequency.

I0-~

N Z o

ilJ

| 0 "'1 ,

0.5

• - FULL BRIDGE MODEL

• - SECTION MODEL

~' - GUASI-STEADY AERODYNAMICS. PREDICTION

l - - a , . , ~, ~ I / / Quasi-Steady Approach,/ / P~ed~cclon ~',~_C- / /....." /

,.".:: / ./." / . • • V . ~

/ /'." / REDUCED VELOCITY CV/fS)

Figure 7

Comparisons of Vertical RMS Re- sponse for a 345m Cable-stayed Bridge: Full Bridge Model vs. Sec- tion Model vs. Quasl-steady Ae~'o- dynamics Prediction

Sunshine Skyway Bridl~e

The comparisons documented in Davenport [8] for the concrete and steel alternates of this 365 m main span cable-stayed bridge are summarized in Fig. 8. The midspan deflection of the prototype bridge, predicted from the section model tests and the full bridge model tests, is normalized by the deck width B and plotted versus reduced velocity. Excellent agreement can be seen for the dynamic response. The mean llft loading on the deck section alone is in the downward direction as shown by the section model tests. However, the effect of the drag on the cables in the full bridge model produces an up llft on the deck and a reversal in the direction of the total mean lift.

1201

O.e'

0.6'

- - - Q ' F U L L BKIDGE MOOE~ MEAN - - - e ' F U L L BRIDGE MODEL: DYNAMIC PEAl[

='SECTION MODEL; PREDICTED MEAN ------O-SECTION MODEL; PREDICTED pEAK

0.4' Q

0

~ O.a, Q

1"4 -'L

1 ~ 0.2.

| L

2 9 m '1

~ 4.3 m

Q&~m a~oIID $¢CtleU

Mean (downward) f

B.O .---- ~-- - "----~'-- .--------I D I

n~ouc~o,,~',-OC,TV,V,~'~ ' '

Figure 8

Normalized Midspan Lift Peak De- flection for the Sunshine Skyway Concrete Alternate

4 Conc lus ion

Comparisons between full-scale observations and prediction models have shown a satisfactory level of accuracy of these models in predicting the response of the real bridges in turbulent wind. Also, the high level of consistency demonstrated between the prediction models themselves namely the full bridge seroelastic model, the extended section model and a theoretical model known as the quasi-steady aerodynamic approach is very promising.

References

[1] Brownjohn, J.M.W., Dumsnoglu A.A.,Severn, R.T. and Taylor, C.A. "Ambient Vi- bration Measurements of the Humber Suspension Bridge and Comparisons with Cal- culated Characteristics", in Proc. ICE Part 2, Sept. 1987.

[2] Petersen A., Ostenfeld K.H., Andersen E.Y., "The Fare Bridges , Long Life at Low Costs", in Proc. ASCE Structures Congress'87, Orlando, Florida, August 1987.

[3] Davenport, A.G.,"Relisbility of Long Span Bridges under Wind Loading ", in Proc. of ICOSSAR '81, Trondheim, Norway, June 1981.

1202

[4] Davenport, A.G., Isyumov, N. and Miyata, T., "The Experimental Determination of the Response of Suspension Bridges to Turbulent Wind ", in Proc. of the Third Int'l Conf. on Wind Effects on Buildings and Structures, Tokyo, Sept. 1971.

[5] Farquharson, F.B. and Vincent, G.S., et al. " Aerodynamic stability of suspension bridges with special reference to the Tacoma Narrows Bridge ", Bull. No.16, Univ. Washington Eng. Station, Parts I-V, 1949-54.

[6] Frazer, R.A. and Scruton, C., " A Summarized Account of the Severn Bridge Aero- dynamic Investigation", Report NPL/Aero/222, H.M.S.O., 1952

[7] Wardlaw, R.L. "Sectional versus Full Model Wind Tunnel Testing of Bridge Road Decks ", DME/NAE Bulletin no. 1978(4), National Research Council Canada

[8] Davenport, A.G. and King, J.P.C., "A Study of Wind Effects for the Sunshine Skyway Bridge, Tampa, Florida - Concrete and Steel Alternates", Univ. Western Ontario, Research Report BLWT-SS24-1982 and BLWT-SS25-1982, October 1982.

[9] Davenport, A.G. "The Response of Tension Structures to Turbulent Wind: The role of Aerodynamic Damping", in Proc. Ist Oleg Kerensky Memorial Conference, London, June 1988.