Tamkang Journal of Science and Engineering, Vol. 8, No 1, pp.

43-56 (2005) 43

Effects of Deck Shape and Oncoming Turbulence on

Bridge Aerodynamics
Yuh-Yi Lin*, Chii-Ming Cheng, Jong-Cheng Wu, Tsang-Lien Lan and Kuo-Ting Wu
Department of Civil Engineering, Tamkang University,
Tamsui, Taiwan 251, R.O.C.

Abstract
The influence of deck geometry and oncoming turbulence on the flutter and buffeting
behavior of cable-supported bridges were investigated by using wind tunnel section model test. In
addition to smooth flow, homogeneous turbulent flow fields with various intensities and integral
scales were generated for the aerodynamic coefficient measurements. The flutter wind speed and
buffeting dynamic response were evaluated by incorporating the measured aerodynamic coefficients
into the analytical model of a cable-stayed bridge. The results show that the width-to-depth ratio,
B/H, of bridge deck plays an important role in bridge aerodynamics. Increasing B/H will improve the
bridge stability. This study also indicates that the critical flutter wind speed increases monotonically
with turbulence intensity, in other words, free stream turbulence tends to enhance the bridge’s
aerodynamic stability. Using the wind force coefficients and flutter derivatives obtained from
smooth flow condition may result in larger buffeting estimation than those obtained from turbulent
flows. These calculated results coincide reasonably with the measured results.

Key Words: Deck Shape, Turbulence, Section Model, Bridge

1. Introduction aerospace study. Scanlan and Tomko [1] are the pioneers
who modified Theodorsen’s flutter theory and then ap-
The development of advanced high strength materi- plied it to the bluff-body shaped long span bridges. In-
als and bridge construction techniques make cable- stead of using the analytical airfoil formulation, experi-
stayed bridge a suitable choice for long span crossing. mental approach was adopted to obtain the flutter deriva-
In many places such as Taiwan, the special aesthetic im- tives for the bluff body bridge decks. Three types of
pression and the high visibility put cable-stayed bridge bridge model tests, i.e., full model, section model, and
among the favorable choices of bridge types, some- taut-strip model, are currently being used in wind tunnel
times overruling the economic considerations. Because test to study the aerodynamic characteristics of the ca-
of the lightweight and the flexibility nature of this bridge ble-supported bridges. Among them, section model is
type, long span cable-stayed bridges are more vulnerable commonly used for the identification of bridge aerody-
to aerodynamic instability. The most important aerody- namic parameters.
namic phenomenon can be categorized as: (a) aerody- Generally speaking, bridge aerodynamic phenome-
namic instability - torsional divergence (static) and flut- non is the results of wind-structure interaction. It has
ter (dynamic); (b) buffeting and vortex shedding due to been established by many researchers that the character-
approaching flow. istics of bridge’s aerodynamic stability is under the influ-
Bridge aerodynamics, in its early stage, was spin-off ence of several factors: structural natural frequencies,
frequency ratio, deck geometry and wind conditions.
*Corresponding author. E-mail: yyl@mail.tku.edu.tw Bienkiewicz [2] studied section model of different cross
44 Yuh-Yi Lin et al.

sections and Nagao et al. [3] studied box girder with two as:
B/H ratios and different forms of fairing. In these studies
1
they concluded that the better streamlined deck cross D f (t ) = rU 2 (2 B)( K )
2
section leads to better bridge aerodynamic stability. In-
é z& (t ) Ba& (t ) ù
vestigations conducted by Matsumoto and his associates ´ ê P1* ( K ) + P2* ( K ) + KP3* ( K )a (t ) ú
[4,5] on plate section with various B/H ratios indicated ë U U û
that the bridge deck with smaller B/H ratio is less aerody- (4)
namically stable and tends to result in the single-degree-
1
of-freedom flutter. As for the effects of turbulence on L f (t ) = rU 2 (2 B)( K )
2
bridge stability, Scanlan and Lin [6] and Huston et al. [7]
é y& (t ) Ba& (t ) ù
studied the flutter derivatives of section model and then ´ ê H1* ( K ) + H 2* ( K ) + KH 3* ( K )a (t ) ú
ë U U û
concluded that turbulence has insignificant influence on
bridge flutter. However, Wardlaw et al. [8] found that (5)
turbulence can suppress the vortex shedding and buffet- 1
ing responses. M f (t ) = rU 2 (2 B 2 )( K )
2
This paper intends to study the effects of deck shape é y& (t ) Ba& (t ) ù
and oncoming turbulence on bridge flutter and buffeting ´ ê A1* ( K ) + A2* ( K ) + KA3* ( K )a (t ) ú
ë U U û
characteristics. Two basic deck sections-closed box girder
(6)
and plate girder-each with various B/H ratios were tested
in smooth and turbulent flow fields. The static wind force Bw
where K = is reduced frequency, w is the circular
coefficients and the flutter derivatives were measured in U
these wind tunnel tests. Based on the measured aerody- frequency, B is the deck width, r is air density, U is average
namic coefficients, bridge’s flutter wind speed and buffet- wind speed, y, z, a represent drag, lift and torsional dis-
ing response were then analyzed. The calculated results placements, respectively. H *j ( K ), Pj* ( K ), A*j ( K ) (j = 1,3)
were compared with the measured section model re- are non-dimensional aerodynamic coefficients, called
sponses reported in the authors’ another paper [9]. flutter derivatives, which represent certain aeroelastic
phenomenon induced by wind-structure interaction.
2. Flutter and Buffeting Analysis The flutter derivatives are functions of deck geometry,
reduced frequency and flow field, the first two factors
Consider a 2-DOF section model of bridge deck cast most of the influence on them.
subjected to turbulent oncoming flow. Fluctuating wind The buffeting forces on a bridge deck section in the
loads that act on the deck can be represented by a com- drag, vertical, and torsional directions can be simplified
bination of a motion-induced self-excited force and a as follows:
buffeting force. The equations of motion in the drag, lift
(heave) and torsional (pitch) directions are expressed as 1 æ 2u ö
Db (t ) = rU 2 BCD (a 0 ) ç ÷ (7)
[1]: 2 èU ø

1 ìï 2u é dCL ù w üï
mx ( &&
x + 2x xw x x& + w x2 x) = D f + Db (1) Lb (t ) = rU 2 B íCL (a 0 ) +ê + CD (a 0 ) ú ý
2 îï U êë da a =a 0 úû U þï
m y ( &&
y + 2x yw y y& + w y ) = L f + Lb
2
y (2) (8)
1
I (a&& + 2xa wa a& + wa2a ) = M f + M b (3) M b (t ) = rU 2 B 2
2
ìï é Ar ù 2u dCM w üï
in which the subscript f and b are self-excited force and ´ í êCM (a 0 ) + CD (a 0 ) 2 ú + ý
turbulence induced buffeting force, respectively. The ïî ë B ûU da a =a 0 U ïþ
linearized form of the self-excited force can be written (9)
 Effects of Deck Shape and Oncoming Turbulence on Bridge Aerodynamics 45

in which b represents buffeting effect, u, w are veloc- For the cross-spectrum of horizontal and vertical wind
ity fluctuations in the drag and lift directions, C D, CL, speed fluctuations
CM are the drag, lift and torstional wind force coeffi-
cients, a0 is mean wind angle of attack, A is the deck’s é Cr n xi - x j ù
SrCi rj (n) = Sr (n) exp ê - ú ; (r = u, w) (12)
projected area on the vertical axis, and r is the dis- êë U úû
tance of deck mass center from the effective axis of
rotation. where n is frequency; u* is the friction velocity; z is the
Substituting the empirical flutter derivatives into height above ground; Cr is the empirical constants, 16
Eqs. (4)-(6), the self-excited forces can be found. and 8 are used for the horizontal and vertical wind speed
Then substituting the self-excited forces into deck fluctuations, respectively; xi and xj are the longitudinal
equations of motion, Eqs. (1)-(3), the aerodynamic coordinates of nodes i and j, respectively.
stiffness and aerodynamic damping effects are incor- A cable-stayed bridge with a major span of 720 m
porated with the structural system. The system natural and two side spans, each of 220 m, is used for the flut-
frequency and critical velocity for onset of flutter can ter and buffeting analysis. A finite element model,
be found by using the complex eigen-value analysis. consisting of beam-column elements and cable ele-
As for the bridge’s buffeting response, the mechanic ments, is used to model the bridge deck, tower, and ca-
admittance for the structural system and the aerody- bles in the structural analysis. The geometry of the
namic effects are put to use with spectra for various bridge and the general view of the deck cross sections
wind speed fluctuations [10]. The dynamic responses are shown in Figures 1 and 2. The structural properties
can be obtained through a simple spectral analysis. A and the vibration mode characteristics of the bridge
unit admittance function is assumed in this analysis. are listed in Tables 1 and 2. Only the first lift mode and
The spectra and cross-spectra of horizontal and verti- torsional mode were used in the flutter analysis. As for
cal wind speed fluctuations used in this study are the buffeting analysis, the first ten structural modes
stated as follows [11]: were included.

For the spectrum of horizontal wind speed fluctuations 3. Experimental Apparatus

z 2
200 u* The section model test was conducted in the Bound-
Su ( n ) = U
5/3 (10)
æ nz ö
ç 1 + 50 ÷
Table 1. Sectional properties of the prototype
è Uø
Model
Prototype
Properties
For the spectrum of vertical wind speed fluctuations
Width (m) 35 (20 for model 2)
Mass (kg/m) 25400
z 2
3.36 u* Polar mass moment of inertia (kg-m2/m) 3,600,000
S w ( n) = U Vertical frequency (Hz) 0.167
5/3 (11)
æ nz ö Torsional frequency (Hz) 0.368
1 + 10 ç ÷
èU ø Torsional-to-vertical frequency ratio 2.2

Table 2. First 10 structural modes of the cable-stayed bridge

Mode Frequency (Hz) Dominant axis Mode Frequency (Hz) Dominant axis
1 0.167 Lift 06 0.439 Lift
2 0.174 Drag 07 0.488 Drag
3 0.229 Lift 08 0.494 Tower
4 0.348 Lift 09 0.497 Lift
5 0.368 Torsional 10 0.500 Drag
46 Yuh-Yi Lin et al.

130 M
50 M

220 M 720 M 220 M

Figure 1. Geometry of the prototype bridge.

B
2.0
1.
1. 0

Model 1-1 1-2 1-3 1-4

H(cm) 1.75 2.4 3.2 5
b(cm) 27.7 25.4 21.8 15.4
(closed box girder)

1. 0

Model 2-1 2-2 2-3 2-4

H(cm) 1.5 2 3 5
(plate girder)
Figure 2. Geometry of section models.
 Effects of Deck Shape and Oncoming Turbulence on Bridge Aerodynamics 47

ary Layer Wind Tunnel in Tamkang University. The wind in smooth flow are shown in Figures. 3-4. It shows that,
tunnel has a working section of 3.2 m(W) ´ 2.0 m(H) ´ for both model series 1 and 2, as the section model’s
18.7 m(L). The bridge deck model of 1.5 m was placed be- B/H ratio increases, drag coefficient (normalized w.r.t a
tween two end plates in the test. Two controlling parame- constant bridge width) decreases due to the smaller
ters were selected-the B/H ratio and the oncoming turbu- front projected area. The B/H ratio makes only slight
lence. Two types of decks, one of the box girder type differences on the lift coefficient of the closed box
(model 1 series) and the other of the plate girder type girder (model series 1). The absolute value of CL de-
(model 2 series), were selected to investigate the effects of creases significantly when the B/H ratio of the plate
B/H ratios on bridge aerodynamics. For each type of deck, girder (model series 2) decreases. In the case of the
four section models, with B/H ratios from 4 to 20, were model 2-4, the relationship between the lift coefficient
built and tested. The geometry of these decks is shown in and attack angle is quite different from those of the
Figure 2 and the B/H ratios are shown in Table 3. In this other three models. As for the torsional moment coeffi-
part of study, all eight models were tested under smooth cient CM, it increases with model’s B/H ratio in model
flow and zero wind attack angle condition. series 1. However, for the plate girder, a thicker deck
In the second phase of this study, the authors investi- (with smaller B/H) is subjected to a smaller torque at
gated the influence of turbulence on bridge aerodynamic negative wind attack angle, but a larger torque at posi-
behavior. Two sets of grids were used to generate homo- tive wind attack angle. It is worth to mention that the
geneous turbulent flow fields for model testing. By torsional moment coefficient of the model 2-4 is signif-
changing the distance between the grids and the section icantly larger than those of the other three models at
model, five turbulent flow fields were generated. The zero angle of attack. The influence of the oncoming tur-
turbulence intensity varies from 1% in the smooth flow bulence on the force coefficients, shown in Figures 5
up to 16% in the flow field E. Flow conditions and the and 6, are similar for both the closed box girder and the
turbulence length scale Lu are listed in Table 4. For this plate girder bridge decks. Higher free stream turbulence
part of study, only model 1-3 (B/H = 11) and model 2-3 tends to enhance the reattachment and weaken the wake
(B/H = 6.7) were used for wind tunnel testing. formation, and therefore, reduce the wind loads on all
In each of the test cases, wind force coefficients, three directions. Larger wind attack angle amplifies the
CD, CL, CM, and flutter derivatives, H *j , A *j (j = 1,3), turbulence effect. Although the higher turbulence in-
were measured. Force coefficients were measured when duces larger fluctuating wind load, the smooth flow
the bridge section model was stationary. For the identi- condition tends to make bridge deck have larger force
fication of flutter derivatives, section model was ar- coefficients which in turn will produce larger bridge’s
ranged in such a way that it could be either in a pure tor- dynamic response during the analytical buffeting calcu-
sional motion or in a coupled mode motion. The mea- lation.
sured aerodynamic coefficients were then substituted
into the analytical model for the subsequent bridge flut- Table 4. Properties of turbulent flows
ter and buffeting analysis.
Flow field S A B C D E

4. Experimental Measurements Turbulence intensity 1 5 8 11 14 16

(%)
Length scale ratio -- 4 4 8 8 8
4.1 Force Coefficients
(LU/H)
The force coefficients of section models measured

Table 3. Geometry of section models

Deck shape Closed box girder (model 1 series) Plate girder (model 2 series)
Model 1-1 1-2 1-3 1-4 2-1 2-2 2-3 2-4
B/H 20 14.6 11 7 13.3 10 6.7 4
48 Yuh-Yi Lin et al.

Figure 3. Effects of deck shape on force coefficient-box girder Figure 4. Effects of deck shape on force coefficient-plate
(a) drag coefficient (b) lift coefficient (c) torsional girder (a) drag coefficient (b) lift coefficient (c)
coefficient. torsional coefficient.
 Effects of Deck Shape and Oncoming Turbulence on Bridge Aerodynamics 49

Figure 5. Turbulence effects on force coefficients of model Figure 6. Turbulence effects on force coefficients of model
1-3. 2-3.
50 Yuh-Yi Lin et al.

Figure 7. Effects of deck shape on flutter derivatives-box Figure 8. Effects of deck shape on flutter derivatives-plate
girder (a) H1* (b) A*2 (c) A*3. girder (a) H1* (b) A*2 (c) A*3.
 Effects of Deck Shape and Oncoming Turbulence on Bridge Aerodynamics 51

Figure 9. Turbulence effect on flutter derivatives of model Figure 10. Turbulence effect on flutter derivatives of model
1-3 (a) H1* (b) A*2 (c) A*3. 2-3 (a) H1* (b) A*2 (c) A*3.
52 Yuh-Yi Lin et al.

4.2 Flutter Derivatives decks.

The uncoupled flutter derivatives (H1*, A2*, A3*) of Figures 9 and 10 show the flutter derivatives of
all section models tested in smooth flow are shown in model 1-3 and 2-3 measured at various flow fields. For
Figures 7 and 8. Both model series 1 and 2 have negative the closed box girder 1-3, turbulence tends to increase
values of H1* which indicates a positive aerodynamic the absolute value of H1*, i.e., increase the positive aero-
damping effect on the lift vibration mode. The plate dynamic damping in the vertical direction. However, the
girder models in general have larger absolute values of flat plate girder 2-3 has a reverse effect; the higher the
H1* than the closed box girder model. It also can be found turbulence intensity, the lower the absolute value of H1*.
that the plate girder shows a more distinctive trend of H1* As for the torsional aerodynamic damping, the reduced
with B/H ratio than the closed box girder. Except at very wind speed corresponding to the sign change of A2* in-
low reduced velocities, both model series 1 and 2 exhibit creases with turbulence intensity in both models. It
positive value of A3* which represents a negative tor- shows that turbulence tends to make bridges more aero-
sional aerodynamic stiffness effect. Model series 1 has a dynamically stable. The effect of turbulence on flutter
slightly higher A3* than series 2, which suggests that derivative A3* is indistinct on model 1-3, but on model
model series 1 is more likely to exhibit coupled-mode 2-3. It can be observed that A3* decreases as turbulence
motion. For this flutter derivative, the B/H ratio does not intensity increases.
cast significant effect on model series 1, while it does on
model series 2. The value of A3* of the plate girder in- 5. Bridge’s Critical Flutter Wind Speed
creases with the B/H ratio. A2*, which represents the tor-
sional aerodynamic damping effect, is the most impor- The critical flutter wind speeds were evaluated by
tant flutter derivative on bridge aerodynamic stability. substituting the flutter derivatives into the numerical
Both types of models show negative A2* at low reduced model, for both single-degree-of-freedom flutter and
velocities and positive value of A2* at high reduced ve- coupled flutter analyses. Detailed analytical procedure
locities. For the closed box girders, A2* becomes positive is described in the reference [10]. Table 5 indicates that
at wind speeds Ur = 4.5-6.5. In the cases of plate girder bridge model series 1, which was more streamlined, has
models, sign change on A2* occurs at earlier wind speeds, significantly higher flutter wind speeds than model se-
Ur = 3-5.5. This indicates that the plate girder model ries 2. When B/H ratio of model series 1 varies from 7 to
tends to show negative aerodynamic damping in the tor- 20, the flutter wind speed increases by 1520%. For
sional mode at a lower wind speed than the closed box model series 2, the change of B/H ratio from 4 to 13, the
girder. The results imply that the plate girder is a less sta- increase of the flutter wind speed can be more than
ble bridge cross section. Also, it can be found that the in- 50%. In other words, selecting a flatter deck shape can
crease of B/H ratio will delay the occurrence of negative improve bridge aerodynamic stability. This phenome-
torsional aerodynamic damping for both types of bridge non is more effective for a “bluff body like” deck than a

Table 5. Flutter wind speeds and flutter frequencies for various model shapes
Model Flutter wind speed (m/s) Flutter frequency (Hz)
Uncoupled Coupled Measured Uncoupled Coupled
1-1 72 69.1 60.9 0.322 0.3244
1-2 66.2 63.9 59.7 0.326 0.3272
1-3 62.8 59.8 59.2 0.324 0.328
1-4 57 55.5 55.2 0.332 0.3359
2-1 45.5 45 42.3 0.365 0.365
2-2 41.9 37.8 39.6 0.367 0.367
2-3 36.9 36.7 36.3 0.367 0.367
2-4 29.2 29.2 29.4 0.369 0.368
 Effects of Deck Shape and Oncoming Turbulence on Bridge Aerodynamics 53

more “streamlined like” deck. Table 5 lists the flutter agreement with the measured results reported in refer-
wind speeds based on both the aerodynamically cou- ence [9].
pled and uncoupled analyses. For model series 1, the The flutter wind speeds of both model 13 and 23
flutter wind speed based on the coupled mode analysis were calculated for different flow fields, as listed in Ta-
is slightly lower than the one from the uncoupled analy- ble 6. For both bridge deck models under study, the crit-
sis. The little difference between two methods is due to ical flutter wind speed increases monotonically with
the fact that the frequency ratio of the first torsional turbulence intensity. Regardless of the geometric shape
mode to the first lift mode of the prototype bridge is 2.2, of bridge deck, free stream turbulence tends to enhance
which will not induce significant mode coupling. As for the bridge’s aerodynamic stability. For comparison, the
the model series 2, there is virtually no difference be- measured results obtained from reference [9] are also
tween coupled and uncoupled flutter analyses. In short, included. From the comparison of the results, it can be
the plate girder deck tends to flutter in a single-degree- seen that the calculated results in this study are consis-
of-freedom mode, whereas the box girder deck tends to tent with the measured results. Although there is some
flutter in coupled modes. The results in Table 5 also in- discrepancy found in model 2, the difference is not sig-
dicate that the calculated flutter wind speeds are in good nificant.

Table 6. Flutter wind speeds at various flow fields

Flow fields Model 1-3 Model 2-3
Calculated flutter Calculated flutter Measured flutter Calculated flutter Calculated flutter Measured flutter
wind speed (m/s) frequency (Hz) wind speed (m/s) wind speed (m/s) frequency (Hz) wind speed (m/s)
S 59.8 0.328 59.2 36.7 0.367 36.3
A 61.5 0.330 60.7 38.2 0.365 42.3
B 62.7 0.331 61.4 36.7 0.365 43.5
C 65.4 0.318 63.03 38.8 0.365 43.2
D 69.2 0.329 - 39.6 0.365 -
E 67.3 0.326 63.7 42 0.364 46.2

Table 7. Maximum RMS buffeting responses of Model 1 at 50 m/s (Ti = 10%)

Model 1 Drag (m) Lift (m) Torsional (degree)
Calculated Measured Calculated Measured
1-1 0.04994 0.811 1.057 0.5316 0.582
1-2 0.05525 0.8018 0.937 0.5139 0.556
1-3 0.05921 0.766 0.897 0.4629 0.52
1-4 0.06624 0.6585 0.863 0.5181 0.468

Table 8. Maximum RMS buffeting responses of Model 2 at 35 m/s (Ti = 10%)

Model 2 Drag (m) Lift (m) Torsional (degree)
Calculated Measured Calculated Measured
2-1 0.01 0.32 0.459 0.1133 0.196
2-2 0.02314 0.244 0.355 0.2165 0.181
2-3 0.0307 0.18 0.281 0.234 0.245
2-4* 0.0237 0.11 0.167 0.34 0.438
* Results were calculated and measured at 28 m/s.
54 Yuh-Yi Lin et al.

Table 9. Maximum RMS buffeting responses of Model 1-3 at 50 m/s

Flow field Lift (m) Torsional (degree)
Calculated Measured Calculated Measured
S* T** S* T**
A 0.3743 0.29 0.165 0.228 0.2023 0.1775
B 0.625 0.448 0.595 0.38 0.308 0.478
C 0.876 0.658 0.897 0.529 0.429 0.52
D 1.092 0.76 1.545 0.660 0.554 0.957
E 1.256 0.837 1.745 0.759 0.622 1.189
*Use the coefficients measured in smooth flow; **Use the coefficients measured in turbulent flow.

Table 10. Maximum RMS buffeting responses of Model 2-3 at 35 m/s

Flow field Lift (m) Torsional (degree)
Calculated Measured Calculated Measured
S* T** S* T**
A 0.083 0.077 0.12 0.1 0.064 0.108
B 0.136 0.12 0.19 0.17 0.15 0.17
C 0.189 0.215 0.254 0.23 0.144 0.193
D 0.236 0.194 0.343 0.287 0.185 0.295
E 0.2717 0.261 0.38 0.33 0.225 0.323
*Use the coefficients measured in smooth flow; **Use the coefficients measured in turbulent flow.

6. Bridge’s Buffeting Response and torsional RMS responses of model series 1 increase
with B/H ratio. These trends coincide with the variation
The buffeting responses were calculated assuming of the corresponding force coefficients. The drag buf-
that the prototype bridge is subjected to the turbulent feting responses of model series 1 and 2 increase as the
wind with the turbulence intensity of 10%. The wind B/H ratio decreases. These results can be expected be-
force coefficients and the flutter derivatives of the cause the deck with the smaller B/H ratio has the larger
decks used in the calculation were measured in smooth depth and results in the larger drag force. The lift buffet-
flow. Using the buffeting theory, the maximum RMS re- ing response of model series 2, similar to model series
sponses of bridge decks with model 1 and model 2 are 1, also increases with B/H ratio, but the torsional re-
respectively calculated at wind speed of 50 m/s and 35 sponse decreases with it. The calculated lift and tor-
m/s. The results are listed in Table 7 and Table 8, respec- sional responses are in a similar trend with the results
tively. The measured results obtained from reference measured in reference [9]. Inspected from this table, it
[9] are also included in these tables. It should be pointed can be found that all of the calculated responses are
out that the two series of bridge models have different smaller than the measured results and the differences
widths and assumed under the same scaling ratio. In are about 20%. The reason is that the calculated re-
other words, the prototype bridges also have two differ- sponses are based upon the buffeting theory that fol-
ent widths, therefore, the responses should not be com- lows the quasi-steady assumption. The wind spectra
pared between the two types of bridges. The data listed and the span-wise correlation used in the calculation are
in Tables 7 and 8 indicates that, although the effects of not the same as those in the wind tunnel testing. Fur-
structural mode coupling and bridge aeroelastic effects thermore, the measured responses are transformed from
are included in the buffeting analysis, the bridge dy- the section model responses in which only two modes
namic responses basically follow the same trend as the are considered. The transformation from the section
corresponding force coefficients. For example, the lift model responses into the full bridge responses is simpli-
 Effects of Deck Shape and Oncoming Turbulence on Bridge Aerodynamics 55

fied based upon many assumptions [9]. Therefore, the shape.

measured and the calculated results will not be the same (2) A flatter deck shape can improve bridge aerody-
and the discrepancy is reasonable. namic stability. This phenomenon is more effec-
The buffeting responses of the prototype bridge tive for the plate girder deck than the closed box
based upon the wind force coefficients and the flutter girder deck.
derivatives obtained in different flow fields are listed in (3) The bridge has the better aerodynamic stability
Tables 9 and 10. The buffeting responses were calcu- in a turbulent flow than the smooth flow field.
lated assuming that the bridge is subjected to the turbu- (4) Applying the wind force coefficients and flutter
lent wind with the turbulence intensity in the range of derivatives acquired from a section model test in
5% to 16%. In each case, the wind force coefficients smooth flow condition may result in more con-
and the flutter derivatives measured in smooth flow and servative buffeting estimation.
in the corresponding turbulent flow were respectively
used in the calculation. It clearly shows that the buffet- References
ing response of the bridge increases with turbulence.
The calculated results based upon the wind force coeffi- [1] Scanlan, R. H. and Tomko, J. J., “Airfoil and Bridge
cients and the flutter derivatives measured in smooth Deck Flutter Derivative,” J. Eng. Mech. Div., Vol. 97
flow are larger than those measured in the turbulent (EM6), pp. 1717-1737 (1971).
flow. Comparison between the calculated and measured [2] Bienkiewicz, B., “Wind Tunnel Study of Effects of
buffeting responses indicates that all of the calculated Geometry Modification on Aerodynamics of a Cable
responses are smaller than the measured responses. The Stayed Bridge Deck,” J. Wind Eng. Ind. Aerodyn., Vol.
reason is similar to those stated earlier. From the com- 26, pp. 325-339 (1987).
parison, it can be also found that the calculated re- [3] Nagao, F., Utsunomiya, H., Oryu, T. and Manabe, S.,
sponses using the wind force coefficients and the flutter “Aerodynamic Efficiency of Triangular Fairing on
derivatives measured in smooth flow are closer to the Box Girder Bridge,” J. Wind Eng. Ind. Aerodyn., Vol.
measured responses than those measured in the turbu- 74, pp. 73-90 (1993).
lent flow. However, this does not imply using the aero- [4] Matsumoto, M., Kbayashi, Y. and Shirato, H., “The In-
dynamic coefficients measured in smooth flow in the fluence of Aerodynamic Derivative on Flutter,” J. Wind
calculation is more reasonable than those measured in Eng. Ind. Aerodyn., Vol. 60, pp. 227-239 (1996).
the turbulent flow. This is because the measured buffet- [5] Matsumoto, M. and Abe, K., “Role of Coupled Deriva-
ing responses, transformed from the section model re- tive on Flutter Instabilities,” Wind Struct., Vol. 1, pp.
sponse, are also the approximated values. From these 175-181 (1998).
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