IABSE SYMPOSIUM LISBON 2005

Aerodynamic Problems of a Super-long Span Cable-stayed Bridge Airong CHEN Professor, Dr. Eng., Dept. Bridge ENG. Tongji University Shanghai, China a.chen@mail.tongji.edu.cn

Qingzhong YOU Director, Senior Engineer Sutong Bridge Construction Commanding Department

Xigang ZHANG Senior Engineer Design Group of Sutong Bridge

Rujin MA Dr. Eng., Tongji Univ. Shanghai, China rjma@mail.tongji.edu.cn

Zhiyong ZHOU Dr. Eng., Asscioate Professor Tongji Univ. Shanghai, China Z.zhou@mail.tongji.edu.cn

Summary Sutong Bridge over Yangtze River is a super long-span cable stayed bridge with a main span of 1088m. The wind resistant design was carried out at Tongji University. In this paper, several aerodynamic problems related with bridge are summarized briefly, including dynamic properties of considering vibration of cables, vortex-excited vibration of the deck, aerodynamic instability of bridge and wind loading of bridges.

Keywords: Super-long span cable-stayed bridge, dynamic properties, vortex excited vibration, aerodynamic instability, wind loading, high Reynolds sectional model testing

1. Introduction Along with the social and economical development, the great demand on highway engineering pushes this area a very fast development. More and more super long-span bridges are erected or in plan. As far as cable-stayed bridges are concerned, the maximum span length increased from several hundred meters to about one thousand meters in the last several decades. The problems due to the increase of the span length attract more and more attentions from the engineers and researchers. Since wind loading is a control factor for the designing of a super long-span cable-stayed bridge, some critical aerodynamic problems appear, which will be discussed in this paper. The first problem is how to discrete the long stay cables in the finite element model. In traditional analysis, the cables are simulated as link elements whose elastic modulus is modified by the Ernst formula. However, for super-long span bridges, this simulation is not appropriate any longer. A new method concerning aerodynamic forces on cables should be put forward. The second problem is the vortex-excited vibration of the deck, which has to be completely suppressed to avoid inner linear and nonlinear resonate vibration of cables. This kind of vibration often happens in low wind speed, and decreases the amenity of the bridges. Some techniques are required to ensure the aerodynamic stability. Moreover, the wind loading calculation is also a problem for a super-long span cable stayed bridge. In this paper, the wind resistant investigation results of Sutong Bridge over Yangtze River with a main span of 1088m under construction carried out at Tongji University will be given. The bridge connects Suzhou and Nantong cities and will be the longest cable-stayed bridge in the world when completed. It has the upside Y-type pylons of 300.4m high, oblique cable planes, steel box section of 4m high and 41m wide, as shown in figure 1 and figure 2.

2. Dynamic Properties of Cable-stayed Bridges with Super-long Cables Four different FEM models are adopted in the dynamic analysis for Sutong Bridge, in order to consider the super-long cables and the foundation of piles and cushion caps. Two simplifications for cable are performed. One is one-element cable model; the other is multi-element cable model. Also,

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two methods are applied for foundation. One is consolidation at the base of pylons; the other is consolidation at the build-in points of the piles. The four different FEM models are shown in figure 3.

Fig. 1 Elevation View of Sutong Bridge over Yangtze River (Units: m)

Fig. 2 Arrangement Plan of Standard deck section (Units: mm)

X

Y

Z X

Y

Z

CASE-1 CASE-2

X

Y

Z X

Y

Z

CASE-3 CASE-4

Fig. 3 Four different FEM models for Sutong Bridge

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Table 1 Comparisons of basic frequencies of the four different FEM models for Sutong Bridge

Mode Characteristics CASE1(Hz) CASE2(Hz) CASE3(Hz) CASE4(Hz)Longitudinal Floating 0.0637 0.0637 0.0648 0.0648

1st symmtric lateral bending mode 0.1009 0.1012 0.1034 0.1036 1st symmetric vertical bending mode 0.1894 0.1950 0.1901 0.1962

1st symmetric torsinal mode 0.6091 0.5307 0.5916 0.5647 From table 1, it can be concluded that, the frequencies of fundamental vertical bending, lateral bending and longitudinal floating are independent of the different models of cables and foundations. However, the torsional modes are dependent of the different models, which is an important factor for predicting the flutter instability. Therefore, validation through aerodynamics model is an effective way. Here, an aeroelastic full bridge model is designed considering the effect of multi-element cable system. The cables are simulated as spring plus wires and several masses. Dynamic checking are carried out and compared with Case-3 and Case-4, seen in table 2. It can be found that the dynamic characteristic of aerodynamic model is more close to the objective value of Case-3 than that Case-4. That is to say, the multi-element cable system is necessary for long span cable stayed bridge.

Table.2 dynamic characteristics of full aeroelastic model compared with objective ones

Mode type Measured frequency

(Hz)

Target frequency of CASE-3(Hz)

ERR%

Target frequency of CASE-4(Hz)

ERR%

1-S-L 1.376 1.4064 -2.2 1.4091 -2.3 1-A-L 3.858 3.8696 -0.3 3.8819 -0.6

2-S-L&1-S-T 6.885 7.1209 -3.4 6.9150 -0.4 1-S-V 2.490 2.5870 -3.7 2.6686 -6.7 1-A-V 3.090 3.1474 -1.8 3.2235 -4.1 2-S-V 4.440 4.5878 -3.2 4.5021 -1.4 1-S-T 8.057 8.0466 0.1 7.6808 4.9

Note: S means symmetric; A means asymmetric; L means lateral bending; T means torsional mode; V means vertical bending.

3. Vortex-excited Vibration of Super-long Span Cable-stayed Bridges Another aerodynamic problem for a long-span cable stayed bridge is the vortex-excited vibration, which is one of a main concern for a long span cable stayed bridge. Any vortex shedding at the deck and pylons should be suppressed to avoid any possible inner linear and nonlinear resonances of cables, which has to be verified with wind tunnel testings. Meanwhile the testing requirement of Reynolds number is much higher than other wind tunnel testings. Therefore, the similitude of Reynolds number is harder to simulate in normal boundary layer wind tunnel. In this circumstance, a large scale sectional model is designed and tested for vortex-excited vibration. In the aerodynamic performance study of Sutong Bridge, a sectional model with the scale of 1:13.5 is constructed. Figure 5 shows the detailed photo of railing and wind nose, the testing results show that vortex-excited vibration happened in the original design. Therefore, two measurements are taken to avoid this vibration, seen in figure 4. The testing results show that both measurements can reduce the vortex-excited vibration amplitude effectively, seen in figure 6. Except testing, numerical technique of the discrete vortex method is carried out to predict vortex-excited vibration. Figure 7 shows the vortex-excited vibration amplitude varying with the wind speed. Figure 8 shows the time-history response of vertical vortex-excited vibration.

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Fig. 4 Counter-measures to suppress vortex-excited vibration of deck

Fig. 5 Detailed photo of sectional model with the scale 1:13.5

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0.11 original design counter-measurement 1 counter-measurement 2measurement offered by COW

ver

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ude rms

value(

m)

Wind speed (m/s)

Fig. 6 Vortex excited vibration Amplitude vs. Wind speed

Counter-meaurement 1

Counter-meaurement 2

Measurement offered by COWI

Rail for tool car

Rail for tool car

Rail for tool car

Rail for tool car

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0 2 4 6 8 1 0 1 2 1 4 1 6 1 8

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

A ttack ang le= 0 o

U (m /s )

A m plitude (m m )

V ertica l respon se

Fig. 7 Numerical technique of discrete vortex method

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V e r t i c a l r e s p o n s e ; G e n e r a l i z e d m a s s 3 2 ( t / m ) F r e q u e n c y 0 . 1 7 5 4 ( H z ) ; A t t a c k a n g le = 0 0

V e r t i c a l r e s p o n s e ; G e n e r a l i z e d m a s s 2 2 .2 ( t / m )F r e q u e n c y 0 . 1 7 4 ( H z ) ; A t t a c k a n g le = 0 0 C O W I

y ( m )

t ( s )

A t t a c k a n g le = 0 0

Fig.8 Vertical response of vortex excited vibration (Re=105)

4. Aerodynamic Instability of Super-long Span Cable-stayed Bridges It is well known that cable-stayed bridge has more flutter stability reservation than suspension bridges. cable-stayed bridges, especially with close box girder and spatial cable planes, often can meet the requirement of aerodynamic stability. However, the flutter instability will decrease with the increasing of the span of cable-stayed bridges. The long-span cables will take many roles in the flutter instability. During the aeroelastic full bridge model design of Sutong Bridge, the dynamic characteristics of cables are considered, seen in figure 8. Several masses are added to a constantan wire to satisfy the similarity of wind force and dynamic characteristic of cables. Special phenomenon of the aeroelastic full model happened in wind tunnel testing. It can be described as the deck moves in single frequency and in the motion in vertical direction combined with lateral direction and torsional direction. Furthermore, the cable planes also took part in the flutter instability.

Table 3 Aerodynamic instability critical wind speed (m/s)

Attack angle

Full aeroelastic

model

Sectional model test

Coupled flutter

analysis

Coupled flutter analysis considering

static wind effect

Checking wind speed

(m/s) 0o 115.6 154 139.0 111.9

+3o 88.4 100 92.5 90.4 -3o >136.0 >142 >160 >160

71.6

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However, the aerodynamic instability wind speeds are close to those analyzed by coupled flutter analysis considering the static wind, seen in table 3. In next stage, the special instability mechanism will be studied.

Fig. 9 Full Aeroelastic model of Sutong Bridge in TJ-3 Wind Tunnnel

5. Wind Loading of Super-long Span Cable-stayed Bridges The calculation of wind load also takes an important role in the designing of cable-stayed bridges. Reasonable and accurate method to predict wind load will offer a safe design. The wind loading of long-span cable-stayed bridge can be considered in two basic directions. One is the longitudinal wind load; the other is the lateral wind load. The lateral wind loading can be divided in to three parts, which are wind load induced by mean wind speed, background response and resonance response due to fluctuation of natural wind. The former two parts can be combined, and named as equivalent static wind load, seen in figure 10.

However, in an arbitrary yaw angle of wind, the wind load of Sutong Bridge should be considered. Numerical technique of discrete vortex method is applied to obtain the drag coeffeicient of pylon, seen in figure 11. It can be found that, the drag coefficient of pylon is not the biggest in 0º or 90º, but is the biggest in the yaw angle between 40º to 60º. Therefore, the worst-case wind loads in these

Resonance response Equivalent wind load

Mean wind load

Background response

Equivalent wind load

Lateral

Wind loading

Longitudinal

Fig. 10 Classification of wind load

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yaw angles should be estimated, seen in table 4.

-10 0 10 20 30 40 50 60 70 80 90 100-0.5

0.0

0.5

1.0

1.5

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2.5

3.0

3.5

CV,C

Dx,C

Dy

Yaw angle

% (CV,Wind axis) % (CDx,Body X axis) % (CDy,Body Y axis)

Fig.11Drag coefficient of pylons of Sutong Bridge

Table4 Wind load of Sutong Bridge under certain load case ( smU /9.3810 = )

Yaw angle Selected sections

o3=β o30=β o45=β o60=β o87=βBase of pylon Mz(N.m) 3.78E+08 9.66E+08 1.43E+09 1.75E+09 1.73E+09

Middle of deck My(N.m) -9.29E+08 -7.02E+08 -4.71E+08 -2.36E+08 -3.15E+06Joint of pylon and deck My(N.m) 1.12E+09 8.32E+08 5.46E+08 2.69E+08 2.47E+06

Longitudial displacement of deck(m) -1.13E-01 6.87E-01 8.65E-01 9.09E-01 9.01E-01 UZ -1.65E+00 -1.26E+00 -8.68E-01 -4.42E-01 -8.12E-03middle of deck(m) UY 7.64E-01 5.48E-01 3.49E-01 1.67E-01 5.55E-04 UZ -2.11E-01 -1.80E-01 -1.34E-01 -6.99E-02 -2.74E-03Top of pylon(m) UY -2.98E-01 6.39E-01 8.85E-01 9.82E-01 1.01E+00

Confined force of deck at pylon Fx(N) 0.00E+00 0.00E+00 -0.39E+07 -0.96E+07 -0.97E+07Confined force of deck at pylon Fz(N) -1.03E+07 -0.77E+07 -0.51E+07 -0.25E+06 -0.02E+06

6. Comparison of Wind Loading Calculated and Tested

6.1 Comparison of static wind load The wind load calculation is compared with the testing results, seen in figure 12. It can be found that wind load calculated is very close to the testing result, except the vertical displacement at higher wind speed, because of strong nonlinearity of cable –stayed bridge.

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Test Calculate

(a) Vertical static wind displacement (b) Lateral static wind displacement

Fig.12 Comparison of Static wind Displacement

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0 20 40 60 80 100

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MS

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Test Sears NoAd

(a) Vertical Buffeting displacement (b) Lateral Buffeting displacement

Fig.13 Comparison of Buffeting Displacement

6.2 Comparison of buffeting response Figure 13 shows the buffeting response in wind tunnel testings and calculated buffeting response considering aerodynamic admittance as Sears function and not considering Sears function. It can be found that, the testing result are just less than the calculated results not considering the aerodynamic admittance, and are larger than those results considering the aerodynamic admittance as Sears function. It can be certificated that the testing result is reasonable and credible.

7. Conclusions and Prospects Based on study of wind performance of Sutong Bridge, several main conclusions can be made for super long cable-stayed bridges, such as,

1) Dynamic characteristics of cables should be considered during the modal analysis of super-long cable-stayed bridges.

2) Cable stayed bridge has sufficient flutter stability reservation. However, the aerodynamic stability will have different shapes. Lateral motion of deck, and cable planes, will participate in the instability mode.

3) Vortex-excited vibration should be avoided especially in super-long cable-stayed bridges; the location of the rail of tool car is sensitive factor of vortex-excited vibration. Large scale sectional model wind tunnel testing is necessary to verify it.

4) Comparison of testing results and calculated results reveals that calculated results are close to the testing results. It can be found that numerical technique combined with wind tunnel testing is successive way.

Aerodynamic problems still exist in super long-span cable stayed bridges, such as aerodynamic force on cables, explanation of aerodynamic instability, etc. Therefore, efforts should be made to receive challenge of longer span of cable-stayed bridges.

8. Acknowledgement The project is jointly supported by National Science Foundation under Grant No. 50478109 and Special Science Research Foundation of Doctorate Program for colleges and universities under Grant No. 20040247026, which are gratefully acknowledged. Also, gratitude should be given to Jiangsu Provincial Sutong Bridge Construction Commanding Department.

9. References [1] Airong Chen, Wind-resistance performance analysis of Sutong Bridge over Yangtze River,

State Key Laboratory for Disaster Reduction of Civil Engineering at Tongji University, Shanghai, China, 2004

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