WIND TUNNEL TEST AND VIBRATION TEST FOR RATIONALIZATION STEEL BOX-GIRDER BRIDGE

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25 Νοε 2013 (πριν από 3 χρόνια και 9 μήνες)

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WIND TUNNEL TEST AND VIBRATION TEST FOR
RATIONALIZATION STEEL BOX-GIRDER BRIDGE

Yoichi YUKI
1)
, Koichiro FUMOTO
2)
, Manabu OKUMURA
1)
,
Hiroo INOUE
1)
, Masao Miyazaki
1)
and Hidesaku UEJIMA
1)

1) Japan Bridge Association, Technical Committee, Design Subcommittee, Vibration Group
2-2-18, Ginza, Chuo-ku, Tokyo, 104-0061
y.yuuki@ybhd.co.jp
2) Honshu-Shikoku Bridge Expressway Co., Ltd., Planning Department, Planning Section
4-1-22, Onoe-Dori, Chuo-ku, Kobe City, Hyogo Prefecture, 651-0088



ABSTRACT

“Steel narrow-box-girder bridge” is rationalized about main structure of steel box-girder bride. Points of
rationalization are following. The first, it is possible to reduce number of girder because slab span is
widely by using durable slab such as composed slab of steel and concrete, or prestressed concrete
slab. The second, cross beam and lateral bracing are leaved or simplified. The third, construction of
box rib is simplified by being web space narrow.
Recently, steel narrow-box-girder bridge is increasing in Japan, because constructional cost and
maintenance cost are economically compared with former steel box-girder bride. On the other hand,
steel narrow-box-girder bridge has low frequency on torsion, because of its small torsion stiffness. So,
one of the not cleared subjects of steel narrow-box-girder bridge is endurance for wind.
We have carried out wind tunnel test and vibration test for steel narrow-box-girder bridge to obtain
characteristics of wind. We used second-dimensional scale down model supported springs in wind
tunnel test, and used real steel narrow-box-girder bridge which max span is110 meter in vibration test.
This paper reports results of these tests.

1. INTRODUCTION

A PC slab, steel-concrete composite slab or other durable slab is employed for steel road
bridges from the viewpoint of cost reduction. By using these types of slabs, cross girders, lateral
bracing or other transverse tie members can be simplified or omitted. Instances of employing such
rationalized bridge types have increased in recent years. The steel narrow box-girder bridge, whose
main girders have a box-shaped cross-section, is a rationalized bridge developed for use where there
are curves or long spans (60 to 100 meters or so) in bridges and its track record in terms of
construction is growing. One feature of the steel narrow box-girder bridge is that the number of
longitudinal and cross ribs can be reduced by reducing the web distance. In this way, the structure
inside the box is simplified and the number of construction components is substantially reduced
(Figure 1).
Conventional box-girder
Narrow box-girder
Conventional box-girder
Narrow box-girder
Asphalt pavement t = 80 mm
RC deck t = 220 mm
Left-in-place form
Asphalt pavement t = 80 mm
Composite deck t = 240 mm
H-900 or other shape steel used
for intermediate cross girder
Omission of longitudinal
and cross ribs
Neat inside box-girder
[View inside girder (Direction B)]
[Bird’s eye view (Direction A)]
Conventional box-girder
Narrow box-girder
Cross girder spac
ing 5000
Cross girder spacing 50
00
Cross rib spacing 4×1250=5000
Cross
rib spacing 4
×1
2
50
=5000
Web distance 2300
Girder height 2500
Web distance 1200
Girder height 2900
Cross girder spacing 10000
Diaphragm spacing
5000
Diaphra
g
m spacing
5000

Figure 1. Structural outline of steel narrow box-girder bridge

With a rationalized bridge, the torsional rigidity and structural damping are small compared to a
conventional steel girder bridge, so attention must be paid to the evaluation of aerodynamic stability.
When dealing with aerodynamic stability, the evaluation of vibration characteristics and aerodynamic
characteristics is important. No systematic study has been conducted on aerodynamic stability for
steel narrow box-girder bridges yet, and current understanding on basic vibration and aerodynamic
characteristics is insufficient.
This study was aimed at gaining an understanding of the basic vibration and aerodynamic
characteristics of a steel narrow box-girder bridge and in order to do so a vibration test
1)
using an
actual bridge and wind tunnel test
2), 3)
using a two-dimensional section model were conducted. The
actual bridge vibration test was conducted on a three-span continuous steel narrow box-girder bridge
with a maximum span length of 110 meters. Exciters were used in a steady-state excitation test and
damped free vibration test to measure the natural frequency and structural damping. The wind tunnel
test was conducted on two sections with aspect ratios of B/D = 2.6 and 3.4 (B: width, D: height) to
investigate the effects of flow angle of attack, structural damping and turbulent flow on the
aerodynamic characteristics.

2. VIBRATION TEST USING AN ACTUAL BRIDGE

It is important to evaluate the natural frequency, structural damping and other vibration
characteristics when dealing with aerodynamic stability. For the steel narrow box-girder bridge,
however, there have so far been very few cases of using exciters to examine the vibration
characteristics in an experimental way. Thus, a vibration test using exciters was conducted on an
actual steel narrow box-girder bridge with a maximum span length of 110 meters to ascertain the
natural frequency, structural damping and other vibration characteristics.


2.1 Test method
The bridge in question is a three-span continuous steel narrow box-girder bridge with a bridge
length of 244 meters, width of 16.15 meters and maximum span length of 110 meters (Figure 2). For
the bearings, a seismic force distributing natural rubber bearing was employed and the bridge surface
was not paved when the vibration test was performed.

Brid
g
e len
g
th 244000
(
alon
g
CL
)

Girder length 243600 (along CL)
(along CL)

Figure 2. Continuous 3-span steel narrow box-girder bridge

For the vibration test, two exciters (0.1 to 2 Hz, exciting force: 120 kN per unit) were placed in
the center of the center span (Figure 3), and two vibration modes, the first vertical bending mode and
first torsional mode, were used. The vibration of the main girder was measured by 10 servo
accelerometers installed on the bridge surface. Eight laser displacement meters were installed on the
rubber bearings on intermediate supports to check the behavior of the rubber bearings. During the
measurement, the signals from the servo accelerometers and laser displacement meters (layout
drawing, Figure 4) and the control signal data to the exciters were sampled simultaneously, and time-
series data processing was performed to display the vibration measurement condition on a personal
computer in real time. An outline of the measurement and analysis system is shown in Figure 5.

Bridge length 244000 (along CL)
Girder length 243600 (along CL)

(along CL)

(along CL)
(along CL)

(along CL)

(along CL)
Asphalt pavement thickness t = 100 mm

Precast PC slab thickness t = 270 mm


Figure 3. View of exciter installation

A1
A2 A3 A4
A5
A6
A7 A8 A9
A10
D1
D2
D5
D3
D4
D6
D7
D8



Bridge length 244000 (along CL)
Girder length 243600 (along CL)
(along CL)

A1
A2 A3 A4
A5
A6
A7 A8 A9
A10
D1
D2
D5
D3
D4
D6
D7
D8
(along CL)
(along CL)
 Servo accelerometer
 Laser displacement meter
 Exciter

Figure 4. Measuring instrument layout



Figure 5. Outline of measurement and analysis system

The test included observation of ambient vibration, steady-state excitation test and damped
free vibration test. The observation of ambient vibration was for determining the excitation frequency
range of the exciters, and the observation of ambient vibration was observed by the servo
accelerometers installed on the slab. The steady-state excitation test was for searching for the natural
frequency of the main girder. The natural frequency was estimated from the observation of ambient
vibration for each vibration mode and the excitation frequency of the exciters was swept over the
range within about 20 percent of the estimated natural frequency to obtain a resonance curve. The
damped free vibration test was for searching for the structural damping factor at the natural frequency
of the main girder. When the amplitude of vibration excited by the exciters reaches a steady state, the
exciters are suddenly stopped to obtain a damped vibration. Then the natural frequency and structural
damping factor can be found from this data.
24bitA/D

換器
搭載パソコン



ボ型加速度計(10台)



位計(8台)



ボ型加速度計(10台)
24bitA/D

換器
搭載パソコン




位計(8台)
Servo accelerometers (10 units)

Personal computer equipped
with 24-bit A/D converter
Laser displacement meters
(8 units)

2.2 Test results

(1) Observation of ambient vibration

The time-series and power spectrum obtained by observation of ambient vibration are shown
in Figure 6. The object of measurement can be found from the results of observation of ambient
vibration, that is, the natural frequency of the first vertical bending mode can be estimated at f
h
= 0.95
Hz or so and the natural frequency of the first torsional mode at f
θ
= 1.76 Hz or so.
Time-series
Acceleration 3
(sec)
(a) Time-series

Figure 6. Results of observation of ambient vibration

(2) Steady-state excitation test

A steady-state vibration test was performed with the amplitude of the exciter control signal kept
constant while only changing the excitation frequency, to obtain the amplitude of the accelerometers
on the main girder and the phase difference of the exciter control signal along with the resonance
curve. The measurement results of the steady-state excitation test for the first vertical bending mode
and first torsional mode are shown in Figures 7 and 8, respectively. The resonant frequency of the first
vertical bending mode was found to be f
h
= 0.89 Hz and that of the first torsional mode was found to
be f
θ
= 1.71 Hz. The frequency ratio of the first torsional mode to the first vertical bending mode was
f
θ
/f
h
= 1.92. These results were compared with the results of an eigen value analysis using a space
frame model. The comparison in natural frequency is shown in Table 1 and the comparison in vibration
mode shape is shown in Figure 9. Looking at both the first vertical bending mode and first torsional
mode, it can be seen that the measured values of natural frequency and vibration mode shape agree
well with the results of the eigen value analysis.
(b) Power spectrum
Frequency (Hz)

Figure 7. Results of steady-state excitation test
(First vertical bending mode)
Figure 8. Results of steady-state excitation test
(First torsional mode)

Table 1. Comparison of natural frequency with analytical values

Figure 9. Vibration mode shape and comparison with analytical values

(a) Resonance curve
Amplitude
Resonance curve of
first bending mode

First bending mode
Phase difference with exciter signal

Phase difference

Frequency (Hz)
Frequency (Hz)
Frequency (Hz)
Frequency (Hz)
Resonance curve of

first torsional mode
First torsional mode
Amplitude
Phase
difference
Phase difference with exciter
signal
(b) Phase characteristics
(a) Resonance curve
(a) Resonance curve
(b) Phase characteristics
振動モード
実測値
① ② ①/②
解析値 比 率
鉛直たわみ1次
f
h

0.89 Hz 0.885 Hz 1.006
ねじれ1次
f
θ

1.71 Hz 1.724 Hz 0.992
振動数比
f
θ
/f
h

1.92 1.948 0.986
Vibration mode
Measured value

Analytical value

Ratio
First vertical bending
First torsional
Frequency ratio
-1.00
-0.80
-0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
G1側 解析値
G2側 解析値
G1側 計測値
G2側 計測値
G1側 解析値
G2側 解析値
G1側 計測値
G2側 計測値
(a) First vertical bending mode
Measured value on G2 side
Analytical value on G1 side

Measured value on G2 side

Measured value on G1 side

Analytical value on G2 side

Measured value on G1 side
Analytical value on G2 side
Analytical value on G1 side
-1.00
-0.80
-0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
(b) First torsional mode
(3) Damped free vibration test

The time-series measured by the damped free vibration test is shown in Figure 10. To obtain the
logarithmic decrement, the damped free vibration was passed through a band-pass filter for noise
removal and the logarithmic decrement value was calculated for each amplitude. The relationship
between logarithmic decrement and amplitude is shown in Figure 11. In the small amplitude region,
the dependence of logarithmic decrement on amplitude is seen to be high. According to the Wind
Resistant Design Manual of Road Bridges
4)
, no combination of repetition rate and induced stress for
degrees of vibration that would produce acceleration levels up to 100 gal will reach a level at which a
risk of fatigue failure is judged to exist. Thus, for the structural damping used in evaluating
aerodynamic stability, it is believed to be appropriate to calculate its value as a logarithmic decrement
at a somewhat large amplitude (100 gal).

Figure 10. Damped free vibration
(sec.)
Time-series
Acceleration 9 First bending mode

A
mplitude (gal)
Logarithmic
decrement
Logarithmic
decrement
First torsional

First vertical bending


Figure 11. Dependence of logarithmic decrement on amplitude

The logarithmic decrement at about 100 gal was found from the damped free vibration test
results, namely, that the first vertical bending mode was δ
h
= 0.051 and that the first torsional mode
was δ
θ
= 0.056.
During the vibration test, the behavior of the rubber bearing was measured. As a result, it was
confirmed that the longitudinal and rotational displacements of the rubber bearing were very small and,
for large amplitudes around 100 gal, they mostly agreed with the analytical displacement values.

3. WIND TUNNEL TEST

It is important to evaluate aerodynamic characteristics when dealing with aerodynamic stability.
For steel narrow box-girder bridges, however, even basic aerodynamic characteristics are not fully
understood.
Thus, a wind tunnel test was conducted using a two-dimensional section model of a steel
narrow box-girder bridge to examine the effects of flow angle of attack, structural damping (logarithmic
decrement) and turbulence on aerodynamic characteristics.

3.1 Test method

The wind tunnel test assumed the two three-span continuous steel narrow box-girder bridges
shown in Figure 12. The bridge A has a width of 11.5 meters while the bridge B is 16 meters wide.
They differ in cross-sectional aspect ratio B/D, namely, B/D = 2.6 for the bridge A and B/D = 3.4 for the
bridge B. The wind tunnel test models are two-dimensional section models made to a scale of 1/40 (for
bridge A) and to a scale of 1/45 (for bridge B). The various model dimensions are shown in Table 2
and a view of the tunnel test is shown in Figure 13. In the wind tunnel test, a response test was
performed first in a smooth flow with the angle of attack set to α = -3, 0 and +3 degrees to examine the
effect of flow angle of attack. To examine the effect of the structural damping of the steel narrow box-
girder bridge, a response test was performed with the angle of attack set to α = 0 degrees and the
structural damping varied from δ = 0.03 to 0.06. Then, generating two kinds of grid turbulence in the
wind tunnel, a response test in a turbulent flow was performed with the angle of attack set to α = 0
degrees and the structural damping set to δ = 0.03 and 0.04. The turbulence was generated by a grid
turbulence installed upstream in the wind course and two levels of turbulence intensity were used, a
low turbulence of approximately Iu = 5 % and a high turbulence of approximately Iu = 10%.

Figure 12. Bridge section under consideration

Table 2. Dimensions of model



Figure 13. View of wind tunnel test

11500<16000>
10500<15000>
500
500
2900<3100>
100
アスファルト舗装厚 80mm
合成床版<PC床版>厚 240<270>mm
調整コンクリート
2.0% 2.0%
支点部 中間部
1200
G1
G2
5200<6000>
1200
1950
1950
<3000> <2000> <2000> <3000>
注記)<>内は幅員16m断面の値を示す。
4344<4700>
Support portion

Intermediate portion

Asphalt pavement thickness 80 mm
Composite slab <PC slab> thickness 240 <270> mm
Adjusting concrete
Note: < > shows the value for the section of 16-meter width.
実 橋 模 型 実 橋 模
縮 尺
幅 ) 11.5m 287.5mm 16.0m 355.6mm
4.344m 108.6mm 4.700m 104.4mm
2.6 2.6 3.4 3.4
2.9m 72.5mm 3.1m 68.9mm
163kN/m 101N/m 248kN/m 123N/m
228 0.0887 391 0.0953
kN・s
2
・m/m N・s
2
・m/m kN・s
2
・m/m N・s
2
・m/m
1.17Hz 3.03Hz 0.89Hz 2.75Hz
2.28Hz 5.90Hz 1.72Hz 5.32Hz
振 ) 1.95 1.95 1.93 1.93
 型
   
1/40 1/45
80m 110m最大支間長
  員 (B
代 表 高 (D)
断面辺長比 (B/D)
主 桁 高
単位重量
極慣性モーメント
たわみ振動数(f
η
)
ねじれ振動数(f
θ
)
動数比(f
θ
/f
η
A橋 (幅員11.5m) B橋 (幅員16m)
Frequency ratio (f
θ
/f
h
)
Torsional frequency (f
θ
)
Vertical bending frequency (f
h
)
Polar moment of inertia
Unit weight
Main girder height
Maximum span length
Width (B)
Representative height (D)
Cross-sectional aspect ratio (B/D)
Actual bridge
Model
Actual bridge
Model
Scale
Bridge B (16 meters wide) Bridge A (11.5 meters wide)
3.2 Test results

(1) Effect of flow angle of attack

A response test was performed in a smooth flow with structural damping set to δ = 0.03 and
0.04 and the angle of attack set to α = -3, 0 and +3 degrees. The response test was performed for
vertical bending vibration and torsional vibration at the different air flow angles of attack, and the
results are shown in Figures 14 and 15. V is wind speed, f is the natural frequency of vertical bending
vibration or torsional vibration, and B is the overall width of the slab.

With regard to vertical bending vibration, the occurrence of galloping was confirmed for bridge
A in the high wind speed region while bridge B was stable with respect to galloping. For bridge B,
vortex induced vibration occurred near a dimensionless wind speed of V/fB = 2. Vortex induced
vibration of torsion occurred with both bridges; however, for bridge B, it was confirmed that it made a
direct transition to torsional flutter at α = 0 and 3 degrees and δ = 0.03.
One of the effects of the angle of attack was that the response amplitude of vortex induced
vibration tended to decrease at α = -3 degrees and to increase at α = +3 degrees for either cross-
sectional aspect ratio.

(2) Effects of structural damping

A response test was performed in a smooth flow with the angle of attack set to α = 0 degrees
and structural damping (logarithmic decrement) varied from δ = 0.03 to 0.06. The response test was
performed for vertical bending vibration and torsional vibration at the different levels of structural
damping and the results are shown in Figures 16 and 17.
Figure 15. Aerodynamic response (Effect of angle of attack for bridge B)
(a) Vertical bending
(b) Torsional
0 1 2 3 4 5 6 7 8
0.00
0.01
0.02
0.03
0.04
0.05
0 1 2 3 4 5 6 7
0 10 0 80 90 100 11020 30 40 50 60 7
0
2
4
6
8
10
12
14
16
18
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
WIND VEL.
V / f B
Vm [ m / s ]
Vp [ m / s ]
η
/ B
[ mm ][ m ]
η
m
η
p
[Maximum span length 110 m, smooth flow]

-◊-: δ = 0.03 (α = +3°)
-○-: δ = 0.03 (α = 0°)
-□-: δ = 0.03 (α = -3°)
[Maximum span length 110 m,

smooth flow]
-◊-: δ = 0.03 (α = +3°)
-○-: δ = 0.03 (α = 0°)
-□-: δ = 0.03 (α = -3°)


Figure 14. Aerodynamic response (Effect of angle of attack for bridge A)
(a) Vertical bending (b) Torsional




















[Maximum span length 80 m,
smooth flow]
-◊-: δ = 0.04 (α = +3°)
-○-: δ = 0.04 (α = 0°)
-□-: δ = 0.04 (α = -3°)














[Maximum span length 80 m,

smooth flow]
-◊-: δ = 0.04 (α = +3°)
-○-: δ = 0.04 (α = 0°)
-□-: δ = 0.04 (α = -3°)
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
0 1 2 3 4 5 6 7
0 10 20 30 40 50 60 70 80 90 100 110
WIND VEL.
V / f B
Vm [ m / s ]
Vp [ m / s ]
Amp.
[deg.]
0.0
1.0
2.0
3.0
4.0
5.0

In terms of vertical bending vibration for bridge A, in which galloping occurred in the high wind
speed region, little effect of structural damping was seen. However, bridge B, in which vortex induced
vibration occurred in the low wind speed region, the excitation-inducing amplitude was confirmed to
decrease with increasing structural damping.
With regard to torsional vibration, it can be seen that vortex induced vibration almost
disappears with increasing structural damping for bridge A. For bridge B it was confirmed that the
flutter at dimensionless wind speeds of V/fB = 2.7 or higher was separated and stabilized with
increasing structural damping and vortex induced vibration alone occurred.
The effect of structural damping on aerodynamic response shows up more noticeably in torsional
vibration, so the setting of structural damping is important for rational aerodynamic stability design.





































[Maximum span length 80 m,
smooth flow]
-○-: δ = 0.04 (α = 0°)
-Δ- δ = 0.06 (α = 0°)














[Maximum span length 80 m,
smooth flow]
-○-: δ = 0.04 (α = 0°)
-Δ- δ = 0.06 (α = 0°)
[Maximum span length 110 m,
smooth flow]
-○-: δ = 0.03 (α = 0°)
-Δ- δ = 0.06 (α = 0°)
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
0 1 2 3 4 5 6 7
0 10 20 30 40 50 60 70 80 90 100 110
WIND VEL.
V / f B
Vm [ m / s ]
Vp [ m / s ]
Amp.
[deg.]
0.0
1.0
2.0
3.0
4.0
5.0
[Maximum span length 110 m,
smooth flow]
-○-: δ = 0.03 (α = 0°)
-Δ- δ = 0.06 (α = 0°)
(a) Vertical bending (b) Torsional
Figure 16. Aerodynamic response (Effect of structural damping for bridge A)
0
2
4
6
8
10
12
14
16
18
(a) Vertical bending
(b) Torsional
Figure 17. Aerodynamic response (Effect of structural damping for bridge B)
0 1 2 3 4 5 6 7 8
0.00
0.01
0.02
0.03
0.04
0.05
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 1 2 3 4 5 6 7
0 10 20 3 0 90 100 1100 40 50 60 70 8
WIND VEL.
V / f B
Vm [ m / s ]
Vp [ m / s ]
η
/ B
[ mm ][ m ]
η
m
η
p
(3) Effect of turbulence

A response test was performed with the angle of attack set to α = 0 degrees and structural
damping set to δ = 0.03 and 0.04 while generating two kinds of turbulence in the wind tunnel. The
response test was performed in a turbulent flow for vertical bending vibration and torsional vibration
and the results are shown in Figures 18 and 19. In these figures, the aerodynamic response in a
smooth flow is also shown for comparison.

Paying attention to vortex induced vibration, it can be seen that it has almost disappeared by
the low turbulence of Iu = 5% for both bridges A and B. Paying attention to galloping and flutter, the
galloping that had occurred in bridge A was stabilized in the turbulent flow and only a gust response
was observed. It was found that the flutter-inducing wind speed of bridge B shifted to V/fB = 3.5, which
is well within the high wind speed region. It was confirmed that either section was stabilized by
turbulence with respect to vortex induced vibration, galloping and flutter.

4. CONCLUSIONS

The vibration and aerodynamic characteristics of a steel narrow box-girder bridge are
important in evaluating its aerodynamic stability. To understand these characteristics, a vibration test
was performed using a actual bridge and a wind tunnel test was conducted using a two-dimensional
section model. Major findings obtained are as follows:

1) For the steel narrow box-girder bridge, its natural frequency of the first torsional mode tends to
be low because its torsional rigidity is lower than a conventional ordinary steel box-girder bridge. The
frequency ratio of the first torsional mode to the vertical bending mode was f
θ
/f
h
= 1.92.





















Maximum span length 80 m,
α
= 0°,
δ = 0.04
-○-: Smooth flow
-◊-: Turbulent flow (Iu = 5%)
Maximum span length 80 m,
α
= 0°, δ = 0.04
-○-: Smooth flow
-◊-: Turbulent flow (Iu = 5%)
0 1 2 3 4 5 6 7 8
0.00
0.01
0.02
0.03
0.04
0.05
0 1 2 3 4 5 6 7
0 10 20 30 40 50 60 70 80 90 100 110
0
2
4
6
8
10
12
14
16
18
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
WIND VEL.
V / f B
Vm [ m / s ]
Vp [ m / s ]
η
/ B
[ mm ][ m ]
η
m
η
p
Maximum span length 110 m,
α
= 0°,
δ = 0.03
-○-: Smooth flow
-◊-: Turbulent flow (Iu = 5%)
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0
0 1 2 3 4 5 6 7
0 10 20 30 40 50 60 70 80 90 100 110
WIND VEL.
V / f B
Vm [ m / s ]
Vp [ m / s ]
Amp.
[deg.]
0.0
1.0
2.0
3.0
4.0
5.0
Maximum span length 110 m,
α

=

0°,

δ = 0.03
-○-: Smooth flow
-◊-: Turbulent flow (Iu = 5%)
(a) Vertical bending (b) Torsional
(a) Vertical bending (b) Torsional
Figure 18. Aerodynamic response (Effect of turbulence for bridge A)
Figure 19. Aerodynamic response (Effect of turbulence for bridge B)












2) For the steel narrow box-girder bridge with a maximum span length of 110 meters, its structural
damping was δ
h
= 0.051 for the first vertical bending mode and δ
θ
= 0.056 for the first torsional mode.
However, structural damping is noticeably dependent on amplitude. Thus, for the structural damping
used in evaluating aerodynamic stability, it is believed to be appropriate to calculate its value as a
logarithmic decrement at a somewhat large amplitude (for 100 gal).

3) Of the aerodynamic characteristics of a steel narrow box-girder bridge, the response
characteristics differ for different cross-sectional aspect ratios. Specifically, for a cross-sectional aspect
ratio of B/D = 3.4, a tendency to become unstable to torsional vibration was observed. For both
sections with aspect ratios of B/D = 2.6 and 3.4, it was found that the turbulence effect could well be
expected and the aerodynamic stability was markedly improved in a low turbulent flow of a turbulence
intensity of approximately Iu = 5%.
The wind resistance of steel bridges is influenced by the wind and vibration characteristics at
the bridge site, presence or absence of noise barriers and juxtaposed bridges and other variable
conditions. Future studies on the wind resistance of steel bridges, including variations in these
conditions are necessary.



REFERENCES

1) Fumoto, Tsukuna, Arai, Kiyota and Miyazaki: Field Vibration Test of Long-Span Two- or Three-
Girder (Narrow Box-girder) Bridges, Proceedings of the 60th Annual Conference of the Japan
Society of Civil Engineers, I-543, pp. 1083-1084, Sep. 2005 (in Japanese).

2) Mineta, Inoue, Koyama and Miyazaki: On the Basic Aeroelastic Characteristics of Narrow Box-
girder Sections, Proceedings of the 62nd Annual Conference of the Japan Society of Civil
Engineers, I-163, pp. 325-326, Sep. 2007 (in Japanese).

3) Okumura, Koyama, Inoue, Takiguchi and Miyazaki: On the Aeroelastic characteristics of Narrow
Box-girder Sections, Proceedings of the 63rd Annual Conference of the Japan Society of Civil
Engineers, I-284, pp. 567-568, Sep. 2008 (in Japanese).

4) Japan Road Association: Wind Resistant Design Manual of Road Bridges, Dec. 2007 (in
Japanese).