ANALYSIS OF SUSPENSION BRIDGE CONSTRUCTION

ANALYSIS OF AERODYNAMIC FORCES ON SUSPENSION BRIDGE STABILITYIka Herawati1 ( 40669 ) ; Legi Pratama2 ( 40687 ) ; Satria Antariksa Ramadhan3 ( 36945 ) ; Yunanto4 ( 40665)

Jurusan Teknik Fisika Universitas Gadjah Mada

Jl. Grafika No. 2, Yogyakarta

Abstract :

Bridge is an important device used for connecting two separated sides of land and it has many types. In this time, we will focus on the suspension bridge, especially that construction which has important rule. Some factors of the bridge construction can affect strength and durability. They are structure, necessity, and materials. Besides that, the external factors are also affected, like the aerodynamic forces. These forces which is on the suspension bridge are lift force and drag force. Lift force affect the strain of the cable and drag force caused by wind vortex happened around the bridge sides. Here, we will analyze it use regression methods from numerical methods rapprochement. The regression methods is used to analyze the relationship between the angle of attack of wind velocity and the aerodynamic coefficient of the suspension bridge forces. It is important because it has relationship with the suspension bridge stability. The bridge is the flexible bridge which has the sensitive structure with the wind velocity around it, so it will be easy to tremble. So, using numerical methods, the suspension bridge can be built in the stability.

Keywords : The suspension bridge stability, aerodynamic forces, Regression methods.

I. INTRODUCTION

The suspension bridge is one of long span bridge type which has the cable made from steel or rope on its sides of the bridge. The load and the wind pass the bridge will influence the strain of the cable. It affects the bridge stability. The structure of the bridge is it has the portion of bluff or non aerodynamic shape which is very susceptible with the wind velocity. Interaction among them can make the dangerous problem if the wind velocity spectrum is larger.

Aerodynamic forces affect the interaction between the bridge and the wind are lift force ( FL ) and drag force ( FD ). Lift force is the vertical force at the bridge caused by the difference of the surface area of the bridge.

Lift force, drag force, the strain of cable, and the wind velocity are very important because they are affected the stability of the suspension bridge. And the stability has relationship with safety.

The analysis is done for determine the bridge stability relations with the wind velocity and the strain cable which suspends the bridge. It is hoped to help the bridge construction become more durable and it can restrain the tremble.

II. METHOD

In the analysis, we use regression methods to analysis the relation between the wind velocity and the strain of cable which is caused by aerodynamic forces. In this case, they are lift force and drag force.

Regression methods is used to study and determine the relation between two or more variable. The simple regression is studied about two variables, while the compound regression is studied about more than two variables.

In the analysis of regression, the regression equation will be determined and used to describe the function of the relation among the variables. Variable will be estimated its value is called dependent or response variable. In the analysis, dependent variable is the strain of the cable. And variable which is assumed give the effect in variety of dependent variable is called independent or axplanatory variable. The wind velocity in this analysis is independent variable.

The common regression line equation for the simple linier regression is :

= a + bx

Where :

=the estimate value of the dependent variable

a=intersection of regression line at y axe

B =gradient of line regression

x=the value of independent variable.

The value of a and b are defined below :

a = bx

III. ANALYSIS

Have you ever crossed a suspension bridge alone ? It must be terrible. Especially if you crossed when the wind was blowing fast. You had to feel the motions of the bridge. It will be easily found in small suspension bridge. Small suspension bridge are many built at the semi isolated district. For the such place, its hard to built a permanent bridge, most of the bridge are connecting deep valley. And off course, lots of wind blows there. Due to the phenomena, we are attracted to make an analysis about the wind effect for suspension these bridges stability. When the wind blows and hit a suspension bridge construction, it will affect the tension content of the wire(or rope) where the bridge is tied. This will be very dangerous if there is a person who across the bridge alone, moreover if he is a child. He can be thrown from the bridge down. We conclude that the wind blow causes two forces. Lifting force and Drag force. The lifting force is a force in vertical direction, while the Pushing force is in horizontal direction. Then, we will name the Lifting Force as FL (Force caused by Wind) and the Drag force will be named as FD .

Look at the picture below.

Lifting force is caused of the difference between the top and bottom surface area. It causes different velocity of the wind for both. This velocity difference will cause further effect, it is the different pressure which is caused by fluids velocity around it. Finally, different pressure will cause the difference force for those two surfaces. And the resultant of the forces will affect the bridge stability. It can make the bridge to be raised or pushed down. When it is raised up, it will reduce the value of the tension of the bridge rope, but is will be dangerous if the weight of the crosser is small, he can be thrown. Hence when the bridge is pushed down, it will make the tension of the rope bigger, but it cause a more stable condition of the bridge. Its analogical like when have two threads, you tie the one with a paper and the other one is tied to a stone. Put them together in front of a switched on fan, you will see that the position of the stone is more stable than the paper. Though, the raising force can help because reducing the tension, but we thought it will be better if we to the stability of the bridge.

Here, were going to analyze this phenomena. We will concern to the effect of wind velocity and its angle to the aerodynamic forces. We want to predict the value of drag, lift, and torsion coefficient.

First, we use the Bernoulli Pressure equation,

Or it can be simplified by

Because there is no high difference ( h1 = h2 ).

If we integrate the pressure p along the bridge surface, we will get the total forces and torsion. That is drag, lift, and torsion which affected too much by Reynold number ( Re ).In the study about long span bridge, Drybye and Hansen ( 1996 ) said that the aerodynamic forces can be found by :

FTotal = FQ + FT + FMwhere :

- FQ is averaged aerodynamic force by time - averaged mean wind load

- FT is aerodynamic force caused by buffeting, wind gusts

- FM is aerodynamic force caused by motion induced wind load

They are important to be analyzed but the most important force is averaged aerodynamic force ( FQ ) because it is the force which mostly happened and the bridge structure must restrain it.

The averaged aerodynamic force is consisted of FD as drag force, FL as lift force, and M as aerodynamic torsion.

Those forces can be written respectively as :

is the density of air, v is the wind velocity, and c ( D, L, M ) ( ) is the coefficient of drag force, lift force, and aerodynamic torsion respectively, is the angle of attack of wind velocity, and A is the bridge deck - width.

From those equations, we can find the aerodynamic coefficients from these formulas :

We know that the wind flow has direction. The direction of wind flow passes the side of the bridge ( Look at the picture above ) and it creates an angle between the wind and the bridge called angle of attack ( ). So the aerodynamic coefficient equation can be written as follow :

In this analysis we make the angle of attack as independent variable and the aerodynamic coefficient as dependent variable, while the density of air, the wind velocity, and the bridge deck - width are constant.

The aerodynamic coefficient respectively can be found by the equation as follow :

AR ( aspect ratio ) = h2 / A, h is the bridge thickness.

( This is the aerodynamic friction equation )

Because this analysis needs some data of the suspension bridge, so we try to search the data from the books and internet, but we find no data, so we use the data which it gets from Wind Tunnel Test and we modify it for this analysis which is suitable with the averaged - wind velocity in Indonesia, that is about 2.5 - 6 m/s and we takes the middle value, that is about 4.25 m / s. The data can be seen below :

and we take the value of angle of attack ( ) is about 0.5 - 2.5 rad.

The pictures below is the side section of the bridge model respectively :

a. Model 1

b.Model 2

c.Model 3

d.Model 4

Wind tunnel test gets the value of in the range of angle of attack is from 0.5 to 2.5 rad as follow :

Model 1

cDcLcM ( rad )

0.58880.57275.45 x 10 - 60.5

1.09500.93038.86 x 10 - 61

26.64547.10586.76 x 10 - 61.5

-0.3458-1.2078-1.15 x 10 - 52

-0.3313-0.6274-5.97 x 10 - 52.5

Model 2

cDcLcM ( rad )

0.60110.58245.54 x 10 - 60.5

1.11960.94609.01 x 10 - 61

27.45597.22576.88 x 10 - 51.5

-0.3412-1.2282-1.17 x 10 - 52

-0.3341-0.6380-6.07 x 10 - 62.5

Model 3

cDcLcM ( rad )

0.59610.57855.51 x 10 - 60.5

1.10960.93968.95 x 10 - 61

27.1287.17746.83 x 10 - 61.5

-0.3430-1.2200-1.16 x 10 - 62

-0.3330-0.6337-6.03 x 10 - 62.5

Model 4

cDcLcM ( rad )

0.58160.56705.40 x 10 - 60.5

1.08050.92108.77 x 10 - 61

26.17437.03526.70 x 10 - 61.5

-0.3483-1.1958-1.13 x 10 - 62

-0.3296-0.6211-5.91 x 10 - 62.5

We want to find the best model which it is suitable with the averaged - wind velocity in Indonesia, so we using MATLAB R2013A to find it with Regression Method from Numerical Method Rapprochement, and the result can be seen below :

a. Model 1

From the graphic we know that the value of cD is smaller than the value of cL and cM. And cL is the biggest of all. The model is a good model because the value of aerodynamic coefficient is like that, it means that lift force on this model is bigger than its drag force, so the bridge will be on stability in the range of angle of attack between 0.5 - 2.5 rad and the averaged - wind velocity is about 2.5 - 6 m / s.

b.Model 2

From the graphic above we know that the value of cD is bigger than the value of cL, it means that the model is worst to be used in Indonesia, because the model is the most sensitive model of all. It can be seen by the curl of curvature.

c.Model 3

From the graphic we know that the value of cD is bigger than the value of cL, it means that the model is also sensitive to be used in Indonesia, but it is less sensitive than Model 2, because the curl of the curvature is less than Model 2, so the model will be more stable than Model 2 if it is used in Indonesia.

d.Model 4

From the graphic we know that the value of cD is also bigger than the value of cL. But if we shows the curl of the curvature we can conclude that this model is more stable than Model 2 and Model 3 because the curl is less the both of them. So, if this model is used in Indonesia, this model will be more stable than Model 2 and Model 3, because it is less sensitive of them all.

Look at all of the equation and the graphic above, what will we conclude ? From the coding and the graphic, we know that cL dan cM equation is linear equation, while cD is the nonlinear equation or the polynomial equation. In the graphic above :

- x as

- v as cL- y as cD

- z as cM

IV.CONCLUSION

1.The best - bridge model which is suitable with the averaged - wind velocity in Indonesia is MODEL 1, because the value of the cL in this model is bigger than the value of cM, it means that the bridge will be in stability than the others model.

2.The sensitive - bridge model or the worst - bridge model is MODEL 2, because the graphic show that the curve of the cD in range of angle of attack ( 0.5 - 2.5 rad ) is the most curlest of all.

3.If MODEL 3 is compared with MODEL 4, we can conclude that the MODEL 4 is more stable than MODEL 3, because the line of cD shows that MODEL 3 is curler than MODEL 4.

4.This result is just for the averaged - wind velocity in Indonesia and in the range of angle of attack between 0.5 - 2.5 rad. The result will be different if the range of angle of attack and the averaged - wind velocity changed.REFERENSI

Anderson, John D. Jr. ; Fundamentals of Aerodynamics ; 2nd Ed., McGraw Hill, 1991.

Bisplinghoff, Raymond L. ; Holt, Ashley and Halfman, Robert L. ; Aeroelasticity , Addison Wesley Publishing Company Inc., Reading, 1955.

Dyrbye, Claes and Hansen, Svend Ole ; Wind Loads on Structures, John Wiley & Sons, Singapore, 1997.

Fung, Y.C. ; An Introduction to the Theory of Aeroelasticity, Dover Publication Inc., New York, 1969.

Gerhart, Philip M., Gross, Richard J.,b Hochstein, John I., Fundamentals of Fluid Dynamics, 2nd Ed., Addison - Wesley, 1985.

Gimsing, Niels J., ; Cable Supported Bridges : Concept and Design, John Wiley & Sons, 1983.

Hjorth - Hansen, E., ; Section Model Tests, Proceedings of the 1st. International Symposium on Aerodynamics of Large Bridges, A. A. Balkema, Copenhagen, 1992.

Huston, Dryver R., Bosch, Harold S.; Aerodynamic Design of Highway Structures; Dec, 14th 2000.

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