Study of the aerodynamic measures impact on flutter stability of steel ...

The Eighth Asia-Pacific Conference on Wind Engineering,December 10–14, 2013, Chennai, India

Study of the aerodynamic measures impact on flutter stability of steel truss suspension bridge

BAI Hua 1, HUANG Sen-hua 2, LI Jia-wu 3 1 Master of School of Highway, Chang’an University, Xi’an, Shanxi, China, [email protected]

2 Master of School of Highway, Chang’an University, Xi’an, Shanxi, China, [email protected] 3 Professor of School of Highway, Chang’an University, Xi’an, Shanxi, China, [email protected]

ABSTRACT

The flutter stability of the steel truss suspension bridge is hard to reach the requirement of the wind

resisting stability when lacks the torsional stiffness. This essay discusses the influence of aerodynamic measure combination, such as central stabilizer, air director enclosed anti-collision bar and so on, towards the flutter stability of steel truss through the wind tunnel experiment of the bridge of Liu Jia gorge. The result shows: the effect of using both the upper and lower stabilized plate is better than separated; when sectionalized dispose upper stabilized plate, the flutter critical wind speed of attack angle will decrease rapidly. Outlaying the horizontal guide plate is better than internally installed; The flutter stability of different attack angle tend to be balanced by widening the horizontal guide plate. The anti-collision bar can be functionalized as the central stabilizer by heightening and enclosing, and effectively increase the critical wind speed of different attack angles of the high truss suspension bridge.

Keywords: Bridge engineering; Suspension bridge; Steel truss; Wind tunnel experiment; Flutter; Wind resisting measure

Introduction

The suspension bridge is one of the most concerned bridge type as its attractive appearance and large spanning ability. The Strait of Messina bridge(3300m) and the strait of Gibraltar bridge are both designed as suspension bridge recently. Because of the lightness of the suspension bridge structure and sensitiveness to wind effect, the wind resisting stability of suspension bridge is always the main factor on controlling and effecting the construction and designing of the large spanning suspension bridge. Especially, the 1940’s American Tacoma bridge destruction by wind aroused broadly attention towards suspension bridge flutter stability research and in recent years there are many researches towards this topic over the world. For instance, Zhang Xinjun’s three-dimensional finite element model analysis towards the influence by bridge span arrangement, main cable rise-span ratio and other design parameter of Run yang Bridge; Tong Ji University, Yang Yong xi’s researches on central digging box girder section’s flutter stability of Xihou Gate Bridge and the influence on flutter stability of suspension bridge after changing aerodynamic configuration of box girder and cutting width; Tongji University, Wei Zhigang’s research on wind resistant cable’s influence towards the flutter stability of long-span suspension bridge; ZHANG Wen-ming’s research and discussion on the evolution laws of double main span suspension bridges’ flutter form; Chen Hong’s research on laws of increasing the flutter critical wind speed of the Huang Pu Bridge, a bridge across the Pearl River in Guangzhou, by adjusting the width-span ratio of

Proc. of the 8th Asia-Pacific Conference on Wind Engineering – Nagesh R. Iyer, Prem Krishna, S. Selvi Rajan and P. Harikrishna (eds)Copyright c© 2013 APCWE-VIII. All rights reserved. Published by Research Publishing, Singapore. ISBN: 978-981-07-8011-1doi:10.3850/978-981-07-8012-8 239 499

Proc. of the 8th Asia-Pacific Conference on Wind Engineering (APCWE-VIII)

steel box girder and increasing the guide plate; Hunan University, professor Chen Zhengqing’s research on function mechanism of central stabilizer towards the enhancement of flutter stability of steel truss suspension bridge, which believes that the central stabilizer’s function is to make the flutter form change from unidirection to bend torsion coupled flutter and thus increase the flutter critical wind speed LIU Gao’s calculation analysis on applying active control wing and fixed wind plate on main span to restrain the flutter of suspension bridge. The researches on flutter stability of suspension bridge above mainly focus on flat steel box girder, but comparatively less on stiffening girder flutter stability of truss section. Since the truss suspension bridge bears the merits of large torsional stiffness, high leak rate and convenient for construction in the area that is difficult for transportation, there are many such bridges in mountainous and valley areas in China, such as Aizhai bridge, Sidu River bridge, Beilin River bridge and so on. But it is always hard for such type of bridges to reach the flutter stability requirements and besides, the complex and changing wind environment in valley attributes the engineering practice value of assuring the flutter stability of the main section of the truss. To deal with such problem, the Akashi-Kaikyo bridge uses the lower central stabilizer and opening on bridge deck and by adding horizontal deflector to the middle of the steel truss, the Sidu River bridge get enhancement of aerodynamic stability. This essay bases on the background of enhancing the flutter stability of Liujiaxia Bridge to discuss the influence of aerodynamic measure combination, such as central stabilizer, horizontal deflector, installed lean deflector, changing handrails and so on, towards the flutter stability problem on truss suspension bridge. And further discusses the pneumatic mechanism under these controlling measures through CFD flow field simulation. This research results can be used as reference for this type of truss suspension bridges’ wind resistant design. Project Overview

The Liujiaxia Bridge crossed the tributary of Gansu Liujiaxia reservoir. The main

beam of the Liujiaxia Bridge section is steel stiffening truss girder, span combination of (20 +536 +20) meters, and the bridge is 581 meters in length. The theoretical sag of the bridge is 48.70 meters, the vertical span ratio is approximately 1:11, two-way driveway is 11 meters wide, center to center spacing of main cables is15.6 meters near the support, distance between main cable at the mid-span of the bridge and bridge deck is 4.0 meters.The girder elevation layout is shown in Figure 1: Because of the deck of Liujiaxia Bridge is narrow, the wind resistance stability needs investigation through wind tunnel test.

Fig.1 Steel truss stiffening girder (unit: cm)

500


Coupled flutter aerodynamic theory According to Scanlan self-excited aerodynamic force expressions, the unit length of

stiffening girder in wind field flowing from U suffered the resistance of the D, lifting and lifting moment M L, which can be expressed by a linear combination of the main girder displacement and speed:

2 * * 2 *

1 2 3

2 * * 2 *

4 5 6

1( ) (2 )(

2

)

se

h BL t U B KH KH K H

U Uh p p

K H KH K HB U B

αρ α= + +

+ + +

1

2 * * 2 *

1 2 3

2 * * 2 *

4 5 6

1( ) (2 )(

2

)

se

p BD t U B KP KP K P

U Up h h

K P KP K PB U B

αρ α= + +

+ + +

2

2 * * 2 *

1 2 3

2 * * 2 *

4 5 6

21( ) (2 )(

2

)

se

h BM t U B KA KA K A

U Uh p p

K A KA K AB U U

αρ α= + +

+ + +

3

Where: ρ = air density;U is wind speed; B = bridge width; /K B Uω= = reduced frequency;ω is circular frequency; *

iH *iA *

iP i =1 … 6 is flutter derivatives, and the function of reduced speed /( )U U fB= , related to the cross-section shape of the main beam, usually provided by the wind tunnel test. f = vibration frequency.

Can also be expressed as a matrix expression:

a a aF K u C u= + 4

where aF =wind load vector aK and aC =pneumatic stiffness matrix and damping matrix, respectively

The stiffening girder dynamic equilibrium equation considering the aerodynamic effect:

aMu Cu Ku F+ + = 5

where M K and C =Structural mass matrix , stiffness matrix and damping matrix, respectively M-order modal systems free vibration displacement vector:

1

m

i ii

u q qϕ=

= = Φ 6

where Φ = Modal matrix; q =modal participation mass, merge 4 , 5 , 6 together , premultiply ΤΦ :

( ) ( ) 0a aM q C C q K K qΤ Τ ΤΦ Φ + Φ − Φ + Φ − Φ = 7

501


Define: RM MΤ= Φ Φ ( )R aC C CΤ= Φ − Φ ( )R aK K KΤ= Φ − Φ , Considering the quality of Orthogonality (7) can be turned into:

0R RIq C q K q+ + = 8

By introducing the aeroelastic response, to solve the eigenvalue[10,11] . m couples conjugate complex eigenvalues:

j j jiμ α β= + j j jiμ α β= − 9

The aerodynamic damping and frequency of the j-th order eigenvalue, respectively:

2 2/( )j j j jαζ α α β= − + j jαω β= 10

When flutter occurs, both the real minimum damping and the characteristic value are 0, so: 0jα = ;

2 2

min min( ) min( / ) 0j j j jαξ ξ α α β= = − + = 11

Original design Program flutter stability test

The segmental model flutter experiment of the Completion state of Liujiaxia Bridge was carried out. Models of geometric scale ratio was 1:40;Wind speed ratio was 1:4.38; The design parameters of Sectional model is shown in Table 1.

Table.1 The design parameters of sectional model

Name of parameter symbol unit Real length Design value measured value

equivalent mass m kg/m 12800 8.00 8.13

Equivalent mass moment of inertia Jm kg.m2/m 557000 0.22 /

Vertical base frequency fb Hz 0.1964 1.79 1.78

Reverse frequency ft Hz 0.4534 4.14 4.17

contortion frequency ratio ε 2.31 2.31 2.34

According to the meteorological statistics combined with the relevant specification, we can deduce that flutter wind speed of Liujiaxia Bridge will be 51.14 m/s. The flutter divergence wind speed of model from wind tunnel test are 48.18m/s 43.80m/s 41.61m/s respectively for an angle of attack of wind of -3° 0° +3° .It is clear that the original deck configuration can not satisfy the requirement of flutter stability, therefore we should take the appropriate measures to improve the aerodynamic stability of Liujiaxia Bridge.

502


Aerodynamic Measures 1.Central Stabilizer

The central stabilizer is a very effective measure to improve bridge flutter stability. The set of upper and lower central stabilizer should consider the deck carriageway, construction feasibility, aesthetics and other factors. For this bridge deck, several different combinations of central stabilizers were selected. In Program 1, a 1.12m lower central stabilizer, with height 0.28 times of the steel truss was selected. In Programs 2, 3and 4 , keeping the size of the lower stabilizer constant, the height of the upper stabilizer was varied, the upper stabilizer height in Programs 2, 3and 4 is respectively chosen as 0.53 times, 0.85 times, 0.91 times the height of crash barriers. In Program 4, as the deck of Liujiaxia Bridge is relatively narrow, setting a long-pass upper stabilizer may get easily clogged during traffic accidents, so there was a need to set the central stabilizer into component section. The size of every stabilizer section is 30 m, every 30 meters setting a stabilizer.

Table 2 shows the test results of these Programs. As table 2 shows: Compared with those don't use the stabilizer, the stabilizer will increase the flutter critical wind speed significantly under -3°Angle of attack. The impact is little to 0 ° Angle of attack. Due to the use of the lower stabilizer, the flutter critical wind speed in+3 ° angle of attack will decrease. When both upper and lower central stabilizer simultaneously being used, flutter critical speed in each angle of attack will be improved. Remaining stabilizer height unchanged, with the stabilizer height increasing, the flutter critical speed increases. In Program4, if the stabilizer arrange in segments, 3 ° and 5 ° angle of attack of the critical flutter speed would drop dramatically, especially for 5 ° angle of attack.

Conclusion: upper central stabilizer can increase the flutter critical wind speed in negative angle of attack; the effect of using both upper and lower central stabilizer simultaneously was better than using lower central stabilizer alone.Increasing the height of upper central stabilizer, the flutter critical speed would generally increase; when upper stabilizer segmentation is made, the flutter critical wind speed will decrease dramatically in positive angle of attack.

Table.2 Flutter test results for bridge deck with central stabilizer

Program Conversion bridge flutter critical wind speed (m/s)

-5° -3° 0° 3° 5°

1 70.4 50.6 37.4

2 70.4 70.4 70.4 70.4 48.2

3 70.4 70.4 70.4 70.4 70.4

4 70.4 70.4 70.4 68.2 39.6

For the convenient of analyzing from the aspects of pneumatic mechanism of flutter divergence, Figure2 shows: under the 0 °angle of attack, the comparison results of several

flutter derivatives. *2A is direct derivative (dominant), reflects the reverse speed α on the role

503


of the pneumatic lifting moment, characterized by reversing pneumatic damping effect. *2A is

positive, equivalent to negative damping, opposite is positive damping. Fig. 2 shows: the original Program and Program1 are flutter derivatives from negative to positive situation, namely appeared the negative aerodynamic damping. But due to Program1 set up the lower stabilizer, from negative to positive reduced wind speed is higher than that without stabilizer. While the flutter derivatives of Program 2 and Program 3 has been negative, which indicated that positive aerodynamic damping in a role to play, and the numerical value in Program 3 is larger than others, the flutter stability of Programs 3 is the best Program of all.Another

dominant function *3A has little influence on the flutter critical speed of Truss suspension

bridge, Flutter Derivatives*3A in different Programs remain the same law, and numerical value

has little difference. Coupled derivative (vice derivative) *2H reflect the aerodynamic lift

produced by speed of twist motion. As is shown in Figure 2: the *2H value in Program 3,which

has the best flutter stability property, far more than others. This indicated that different aerodynamic measure would result in the Aerodynamic shape cross section changed, which Aerodynamic coupling effect has changed under the self-excited force. *

2H value increased ,which benefit to the flutter stability of the Truss suspension bridge.

0.0 1.5 3.0 4.5 6.0 7.5 9.0 10.5-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

Original design solutionProgram 1Program 2Program 3

A* 2

U/fB0.0 1.5 3.0 4.5 6.0 7.5 9.0 10.5

-0.2

0.0

0.2

0.4

0.6

0.8

1.0Original design solutionProgram 1Program 2Program 3

A* 3

U/fB

0.0 1.5 3.0 4.5 6.0 7.5 9.0 10.50.0

0.5

1.0

1.5

2.0

2.5

3.0 Original design solution Program 1 Program 2 Program 3

H* 2

U/fB

(a) *2A (b) *

3A (c) *2H

Fig.2 Compared with different Programs of flutter derivatives

2 The Position Of Deflector

Since the width of carriageway of the Liujiaxia Bridge merely has 11m, using central stabilizer will cause certain impact on passing vehicle. So, under the condition that the central stabilizer is unchanged, we set up 1.28m wide deflector, and change the position of

504


deflector on the truss to research the influence on flutter stability of the truss suspension bridge due to the different combinations of stabilizer and different deflector.

Different Programs schematically shown in Table 3:

Table.3 The different wind-resistance measures

Program wind-resistance measures

schematic diagram introductions

5

lower central stabilizer+Horizontal guide plate

6

lower central stabilizer+Inclined guide plate, Angle of 30

7

lower central stabilizer+Built-in oblique guide plate, dip - 30 °

8

lower central stabilizer+Built-in oblique guide plate, Angle of 30

Table 4 shows that the result of the flutter test of different deflectors program. From Table 4 we can see that using central stabilizer can achieve a better performance of wind-proof than using deflectors. Under -3°to 0°wind attack angle placing deflector horizontally or in a certain inclination outside the steel truss will achieve a better performance of wind-proof that put it into the internal of truss. Under the 3°wind attack angle, using the horizontally external deflector is most inefficient. Overall, deflector cannot significantly improve the flutter stability of the steel truss suspension bridge, especially under 3°wind attack angle.

Table.4 Flutter test results of bridge deck with deflector

Program Conversion of real bridge flutter critical wind speed (m/s)

-3° 0° 3°

5 70.4 66.0 17.6

6 70.4 66.0 39.6

7 66.0 48.2 41.8

8 57.2 39.6 33.0

505


Figure 3 shows that under -3°wind attack angle the comparison of the major flutter derivatives of different deflectors programs. From the Figure 3 we can see: the major flutter derivatives of Program 5 and 6 are constantly negative, and compared to other several programs the absolute values of the two are much greater. The reason that the flutter stability of the two programs is better than others is that aerodynamic positive damping generated by the aerodynamic self-excited force limits flutter instability of steel truss. The aerodynamic positive damping in Program 7 and 8 is relative small so that flutter stability is inferior.

Since 1.28m wide deflector didn't significantly improve flutter stability of the Liujiaxia Bridge, of which the stabilizer is inadvisably set on the bridge deck, we increase the width of deflector from 1.28m to 2.00m, and simultaneously decrease height of the crash barriers from 1.50m (Program 5) to 0.90m (Program 9). The comparison result of flutter test of Program 9 and 5 shows in Table 5:

0.0 1.5 3.0 4.5 6.0 7.5 9.0 10.5 12.0

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

U/fB

A* 2

Original design solution Program 5 Program 6 Program 7 Program 8

Fig.3 Compared with different Programs of flutter derivatives

Table.5 Flutter test results of the guide vane widened


-3° 0° 3°

five 70.4 66.0 17.6

nine 66.0 43.8 41.6

From Table 5 we can see: widening horizontal deflector and reducing the height of crash barriers can significantly increase the critical flutter wind velocity of 3°attack angle but decrease that of 0°. Under different attack angle, the flutter stability of cross section of truss has been enhanced so that extremely unfavorable wind attack angle will not be generated.

506


3 Crash Barriers

Since that it is inadvisable to be set up central stabilizer on the bridge deck, we take measures to close crash barriers of both sides of bridge deck so that the closed crash barriers will play the role of stabilizer. We suggest the following Program: Program 10: set the height of the crash barrier to 2.12m, of which the upper 1.04m uses structure "2 closed blocks and 3 empty blocks and 1 closed block and 2 empty blocks and 2 closed blocks" and the lower 1.08m uses structure "1 closed block and 2 empty blocks and 2 closed blocks and 3 empty blocks and 1 closed block", and the width of every block is 0.5meters. Program 11: close the upper 1.04m and the lower 1.08m uses structure "1 closed block and 3 empty blocks and 1 closed blocks and 3 empty blocks and 1 closed block". Program 12: reduce the height of the crash barrier to 1.50m, close the upper 0.60m and the lower 0.90m uses structure "1 closed block and 2 empty blocks and 1 closed block". The crash barriers are illustrated in Figure 4. The unit of length is mm. The ventilation rates of Program 10, 11 and 12 are 60%, 36% and 45%,respectively. These three programs all set 1.12m central stabilizer and 2.00m horizontal deflector, similar to Program 5.

Table 6 shows the result of flutter test of the three program. Vividly we can see: Canceling central stabilizer and closing part of crash barriers will cause as the effect as if central stabilizer works, and critical flutter wind velocities of different attack angles all be increased. Compare and contrast Program 10 and 11 we can see: Reducing ventilation rate of crash barriers will increase the critical wind velocity of negative attack angle and decrease that of positive attack angle. Compare and contrast Program 11 and 12 we can see: Keeping the crash barriers closed and reducing the their height will result in that flutter stability declines. Under comprehensive consideration, Program 11 is the optimal aerodynamic Program of Liujiaxia Truss Suspension Bridge.

1040

1080

500

1. Program10 500

1040

1080

(b) Program11

507


900

600

(c) Program12

Fig.4 The Programs of the crash barrier closed

Table.6 Flutter test results of the crash barrier


-5° -3° 0° 3° 5°

10 57.2 70.4 66.0 70.4 70.4

11 66.0 70.4 66.0 70.4 61.6

12 57.2 57.2 57.2 57.2 50.6

numerical simulation

In this section we use Fluent software to numerical simulate that setting up the upper and lower central stabilizers and horizontal deflectors. We suggest using Gambit software and unstructured grids to generate total approximately 1.86 million grids. Because that the size of barriers of suspension bridge is smaller than other rod members and bridge deck, using the finite grids to divide resulting in that the difference of the size of partial grids will be too great, we take measures to simplify the barriers of bridge deck, three uprights merging together and a horizontal barrier strips two merging into one, remaining positions are simulated according to the actual size. We simulate the 16 sections of main beam cross section along the bridge, and each section length of 8m. In order to contrast with main beam force measurement wind tunnel test results we take aerodynamic forces of among 12 sections to calculate Force Coefficient of Two, both sides of every two sections playing as compensation model. Figure 5 shows the pressure distribution when we set up central stabilizer deck: after setting up the central stabilizer, the pressure distributions of bridge upstream and downstream are significantly different. In the upstream bridge deck most of the region as the "windward", distribution with positive pressure. The downstream bridge deck which forms leeward are negative pressure.

508


Fig.5 Pressure distribution of the central stability board

(a) The central stabilizer plate flow field

(b) Horizontal deflector flow field

Fig.6 Flow field

Conclusion

1. Lower central stabilizer can raise the critical flutter wind velocity of negative attack angle of truss suspension bridge; Using upper and down stabilizers simultaneously is more effective than using alone; Increasing the height of upper stabilizer will result in the gradual increase of the critical flutter wind velocity; when the upper stabilizer is made of segmented layout, critical flutter wind velocity of positive attack angle will be drastically reduced.

2. When horizontal deflector located outside of the truss, the critical flutter velocity of the negative attack angle will be increased. Since the critical flutter velocity of the positive attack

509


angle is lower, widening horizontal deflector can make flutter stability of different attack angles tends balanced. The external deflector is more effective than the internal one.

3. When it is inadvisable to set up a central stabilizer on bridge deck, we can heighten and close the crash barrier to make the crash barrier play the role of central stabilizer. Experiment shows that: this measure can effectively improve the flutter critical wind speed of different attack angles of truss suspension bridge.

References ZHANG Xin-jun, SUN Bing-nan.Study on Flutter Stability of Long-span Suspension Bridge[J]. China Journal of Highway and Transport.2004,21(8):34-37

YANG Yong-xin, GEYao-jun,CAO Feng-chan. Flutter Performance of Central-slotted Box Girder Section for Long-span Suspension Bridges [J]. China Journal of Highway and Transport . 2007,20(3):35-40

WEI Zhigang, GE Yaojun, YANG Yongxin.Effectiveness of storm ropes for long suspension bridge's flutter control [J]. State Key Laboratory for Disaster Reduction in Civil Engineering, Tong ji University, Shanghai 200092,China 2008,36(12):1628-1632

ZHANG Wen-ming,GE Yao-jun,ZHOU Zhi-yong,ETC. Experiment on Flutter Stability of Suspension Bridge with Double Main Span [J]. China Journal of Highway and Transport, 2010,23(4):58-62

CHEN Hong,HUANG Chengzao,XIE Jun. Study of enhancing flutter critical wind speed for suspension bridge of huangpu bridge over zhujiang river in Guangzhou [J]. Bridge Construction. 2007,3:30-32

CHEN Zheng-qing, OU YANG Ke-jian, NIU Hua-wei, etc. Aerodynamic Mechanism of Improvement of Flutter Stability of Truss-girder Suspension Bridge Using Central Stabilizer[J]. China Journal of Highway and Transport, 2009,22(6):53-59

LIU Gao, QIANG Shi-zhong, WANG Xiu-wei. The Study of Suppressing the Flutter of Suspension Bridges by Active Aerodynamic Wings[J]. Chinese Journal of Applied Mechanics, 2002,19(4):52-57

LI Chun-guang, ZHANG Zhi-tian, CHEN Zheng-qing, etc. Truss stiffening girder suspension pneumatic stabilization measures Experimental Research [J]. Journal of Vibration and Shock, 2008,27(9):40-43

Makoto Kitagawa. Technology of the Akashi Kaikyo Bridge[J]. Structural Control and Health Monitoring, 2004, (11):75-90

TANG Mian, CHEN Zheng-qing. Flutter stability of long span self-anchored suspension bridges and wind-tunnel tests [J]. Journal of Central South University JCR Science Edition , 2007,38(1):164-169.

Hernandez S, Jurado J A. A review of the theories of aerodynamic forces in bridges[J]. Journal of Bridge Engineering, 2000, 5(1):8-11

510

Study of the aerodynamic measures impact on flutter stability of steel ...

Documents

Transcript of Study of the aerodynamic measures impact on flutter stability of steel ...