virtual wind tunnel

8/14/2019 Virtual Wind Tunnel

1/31


2/31

CONTENTS

1. Introduction (3)

2. Flutter phenomenon in bridges (5)

3. Hybrid method for the evaluation of wind-dependent static loads and flutter speed in

bridges

3.1. Hybrid method for the evaluation of wind-dependent static loads on bridge decks (7)

3.2. Hybrid method for the evaluation of the flutter speed in bridges (9)

4. Tests of full bridge models in boundary layer wind tunnel (15)

5. Comparative study of available methods for the analysis of the aeroelastic performance

of bridges (17)

6. Virtual wind tunnel: concept and achievements (19)

6.1.The Tachoma Narrows Bridge And Its Failure As Explained By VWT method (23)

7. Conclusions (28)

8. References (29)

2
http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#secx1#secx1http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#secx2#secx2http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#secx3#secx3http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#secx3#secx3http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#secx4#secx4http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#secx5#secx5http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#secx6#secx6http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#secx7#secx7http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#secx7#secx7http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#secx8#secx8http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#secx9#secx9http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#secx2#secx2http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#secx3#secx3http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#secx3#secx3http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#secx4#secx4http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#secx5#secx5http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#secx6#secx6http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#secx7#secx7http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#secx7#secx7http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#secx8#secx8http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#secx9#secx9http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#secx1#secx1


3/31

1. INTRODUCTION

Suspension and cable-stayed bridges are wind prone structures which require detailed and

complex studies in order to guarantee its safe behaviour under wind. Several wind-

induced vibrations have been described in bridge technical literature, although some of

those types are more critical or probable than others. In fact, one of the most important

aeroelastic instabilities is the flutter, as it can be responsible for the complete destruction

of a bridge, as it was the case with the Tacoma Narrows Bridge. On the other hand,

prevention against flutter phenomenon determines the fundamental design characteristics

of long span bridges.

Therefore, a lot of work and research has been done since November 1940, when the

aforementioned Tacoma Narrows Bridge collapsed, as in those days aerodynamic

performance of structures was a newborn subject and its study was reduced mainly to the

aeronautic realm.

In the civil engineering field wind effects on structures were first treated by means of

experimental studies using boundary layer wind tunnels. As time passed by, the out

coming of new technologies allowed the development of new techniques in experimental

testing, for instance the study of section models, as well as the incorporation of

computational methods for the analysis of bridge performance under wind flows. In this

dynamic and ever changing environment hybrid methods (combination of experimental

and computational techniques) for the study of aerodynamic and aeroelastic phenomena

appeared.

3


4/31

Nowadays, advances and improvements in computational power and computer aided

design technologies make possible a new pace in the way towards a feasible design

process of bridges considering its aerodynamic and aeroelastic behaviour. In this paper

are going to be presented the results obtained when the best of two worlds is joined

together: accurate experimental testing and computer aided design in order to bring out

what is going to be named as virtual wind tunnel (VWT). This VWT allows engineers to

get a detailed visualization of the complete bridge behaviour under wind flow while some

of the shortcomings and expenses of full bridge aeroelastic models are avoided.

2. AEROELASTIC FLUTTER

4


5/31

Fluttering is a physical phenomenon in which several degrees of freedom of a structure

become coupled in an unstable oscillation driven by the wind. This movement inserts

energy to the bridge during each cycle so that it neutralizes the natural damping of the

structure, thus the composed system (bridge-fluid) behaves as if it had an effective

negative damping (or hadpositive feedback), leading to a exponentially growing

response; in other words, the oscillations increase in amplitude with each cycle because

the wind pumps in more energy than the flexing of the structure can dissipate, and finally

drives the bridge toward failure due to excessive deflection and stresses. The wind speed

which causes the beginning of the fluttering phenomenon (when the effective damping

becomes zero) is known as the flutter velocity. Fluttering occurs even in low velocity

winds with steady flow. Hence, bridge design must ensure that flutter velocity will be

higher than the maximum mean wind speed present at the site.

Flutter is a self-starting and potentially destructive vibration where aerodynamic forces

on an object couple with a structure's natural mode ofvibration to produce rapidperiodic

motion. Flutter can occur in any object within a strong fluid flow, under the conditions

that apositive feedbackoccurs between the structure's natural vibration and the

aerodynamic forces. That is, that the vibrational movement of the object increases an

aerodynamic load which in turn drives the object to move further. If the energy during the

period of aerodynamic excitation is larger than the natural damping of the system, the

level of vibration will increase. The vibration levels can thus build up and are only

limited when the aerodynamic or mechanical damping of the object match the energy

input, this often results in large amplitudes and can lead to rapid failure. Because of this,

structures exposed to aerodynamic forces - including wings, aerofoils, but also chimneys

5
http://en.wikipedia.org/wiki/Degrees_of_freedom_(mechanics)http://en.wikipedia.org/wiki/Dampinghttp://en.wikipedia.org/wiki/Positive_feedbackhttp://en.wikipedia.org/wiki/Natural_frequencyhttp://en.wikipedia.org/wiki/Vibrationhttp://en.wikipedia.org/wiki/Periodic_motionhttp://en.wikipedia.org/wiki/Periodic_motionhttp://en.wikipedia.org/wiki/Positive_feedbackhttp://en.wikipedia.org/wiki/Vibration#Types_of_vibrationhttp://en.wikipedia.org/wiki/Degrees_of_freedom_(mechanics)http://en.wikipedia.org/wiki/Dampinghttp://en.wikipedia.org/wiki/Positive_feedbackhttp://en.wikipedia.org/wiki/Natural_frequencyhttp://en.wikipedia.org/wiki/Vibrationhttp://en.wikipedia.org/wiki/Periodic_motionhttp://en.wikipedia.org/wiki/Periodic_motionhttp://en.wikipedia.org/wiki/Positive_feedbackhttp://en.wikipedia.org/wiki/Vibration#Types_of_vibration


6/31

and bridges - are designed carefully within known parameters to avoid flutter. In complex

structures where both the aerodynamics and the mechanical properties of the structure are

not fully understood flutter can only be discounted through detailed testing. Even

changing the mass distribution of an aircraft or the stiffness of one component can induce

flutter in an apparently unrelated aerodynamic component. At its mildest this can appear

as a "buzz" in the aircraft structure, but at its most violent it can develop uncontrollably

with great speed and cause serious damage to or the destruction of the aircraft. Flutter can

be prevented by using an automatic control system to limit structural vibration.

Flutter can also occur on structures other than aircraft. One famous example of flutter

phenomena is the collapse ofGalloping Gertie, the original Tacoma Narrows Bridge.

Fig 1. Flutter of the Tacoma Narrows Bridge

6
http://en.wikipedia.org/wiki/Stiffnesshttp://en.wikipedia.org/wiki/Buzzhttp://en.wikipedia.org/wiki/Galloping_Gertiehttp://en.wikipedia.org/wiki/Stiffnesshttp://en.wikipedia.org/wiki/Buzzhttp://en.wikipedia.org/wiki/Galloping_Gertie


7/31

3. HYBRID METHOD FOR THE EVALUATION OF WIND-

DEPENDENT STATIC LOADS AND FLUTTER SPEED IN BRIDGES

3.1. Hybrid Method For The Evaluation Of Wind-dependent Static Loads On

Bridge Decks

The static load caused by the wind pressure acting on a bridge deck can be obtained by

means of a hybrid method. This method is well established in wind engineering[2] and

[3] and it begins with an experimental phase that must be completed in order to obtain the

deck aerodynamic coefficients, which depend upon the angle of attack between the

deck and the oncoming wind flow.

Fig 2.

In FIG a scheme of the lift, drag and moment aerodynamic forces acting on the deck is shown.

These tests must be carried out with the section model being fixed at different angles of

attack while the loads due to the oncoming flow are measured

7
http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#bib2#bib2http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#bib2#bib2http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#bib3#bib3http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#bib2#bib2http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#bib3#bib3


8/31

Drag aerodynamic coefficient vs. angle of attack for the Great Belt Bridge

The second phase in this methodology consists of the computational evaluation of the

static forces acting along the bridge deck. A finite element model of the studied bridge

must have been worked out (see Fig. 5) and the static loads can be evaluated using the

following expressions:

(1)

whereD is the drag force per unit of length,L is the lift force per unit of length, Mis the

moment per unit of length, is the air density, Uis the wind speed,B is the deck width

and CD, CL and CMare the aerodynamic coefficients obtained in the wind tunnel.

8
http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#fig5#fig5http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#fig5#fig5


9/31

Fig 3. Finite element model of the Great Belt Bridge.

3.2. Hybrid Method For The Evaluation Of The Flutter Speed In Bridges

The foundations of this method for solving the flutter problem were established by

Scanlan and Tomko in 1971, although new developments were published by several

researchers during the following years, until the present time. Analogously to the former

case, two different phases must be completed in order to evaluate the flutter wind speed

in bridges. The first task to be carried out is the experimental measurement of the flutter

derivatives, also called Scanlan derivatives, using a section model that can be undergoing

free oscillations or subjected to forced oscillations inside the wind tunnel test chamber.

9


10/31

Fig 4.a 4.b

a) Principle structural setup of a suspension bridge. b) Cross section of bridge deck

Up to 18 flutter derivatives can be obtained which depend upon the reduced frequency

K=B/U, where denotes circular frequency. In Fig. 5 an example of the flutter

derivatives of the Great Belt Bridge plotted vs. the reduced frequency is

presented.

Fig 5. Flutter derivatives to for the Great Belt Bridge.

10
http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#fig7#fig7http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#fig7#fig7


11/31

The second step consists in the numerical evaluation of the aeroelastic forces acting on

the bridge deck .

11


12/31

12


13/31

13


14/31

Fig 6. Evolution of aeroelastic damping vs. wind speed.

14


15/31

4. TESTS OF FULL BRIDGE MODELS IN BOUNDARY LAYER

WIND TUNNEL

The aim of this technique is to reproduce in the laboratory the aeroelastic behaviour of

the prototype. Therefore a model that replicates the future structure must be built and

immersed in an oncoming air flow. Several responses can be obtained from these tests

such as reactions, deflections under wind load or unstable behaviour at certain wind

speed caused by flutter.

The first full aeroelastic test of a bridge was that of the Tacoma Narrows Bridge in the

1940s used to investigate its collapse. Experimental techniques have evolved a lot, until

the present days when this keeps on being an active research field. Model scales common

in full bridge modelling are about 1:1001:500, depending upon several factors such as

wind tunnel dimensions or similarity requirements.

Nowadays a carefully planed experimental campaign must include the following tasks:

In first place, a section model test must be carried out on a relatively large model scale

(1:100 or even 1:25) in order to determine the deck aerodynamic behaviour. Then, a

second section model test must be performed using a model scale equal to the bridge full

model scale to be adopted. This second section model should be modified until it shows

an aerodynamic behaviour equivalent to that of the first section model. Once this

condition has been satisfied, the full aeroelastic model must be constructed replicating the

characteristics of the second section model which was built with the same model scale.

15


16/31

Therefore, full aeroelastic model must include previous section model tests in order to

guarantee a good model performance.

5. COMPARATIVE STUDY OF AVAILABLE MEHODS FOR

THE ANALYSIS OF THE AEROELASTIC PERFORMANCE

OF BRIDGES

This section is going to focus on the hybrid method and full model testing for study

bridge aeroelastic performance. Alternative approaches such as those based upon

computational fluid dynamics (CFD) are not considered due to the limited results

obtained to date, although continual progress is being made in this field.

The main advantages of section model tests used in the hybrid method can be

summarized in the following:

Relatively low cost of sectional models themselves and the wind tunnel facilities.

The model scale must be large, about 1:251:100, although exceptions can be found in

literature. This allows proper modelling of important geometric details as well as

reducing possible distortions due to Reynolds number effects.

Section model tests can be carried out in small size wind tunnel facilities.

Both geometric and dynamic model properties can be modified easily.

The main shortcoming that can be found is

16


17/31

Standard section model techniques can offer inaccurate results due to three-dimensional

effects of topography or deck geometry.

The full aeroelastic model technique presents several strong points which are [9]

Full aerodynamic interaction between deck, towers, abutments and cables can be

modelled.

Wind characteristics across the span can be obtained when a model of the topography is

also included.

A complete set of aerodynamic responses can be obtained, such as reactions,

displacements or aeroelastic instabilities.

A clear visualization of the model deflections under wind flow can be obtained.

However, due to similarity requirements the oscillation frequencies are higher than the

correspondent ones in the prototype. In fact, when Froude scaling is respected, the

frequency scale is equal to the inverse of the square root of the length scale , for instance,

for a length scale of 1/100 the frequency scalen is 10, therefore, for this considered

example, full model oscillations are going to be 10 times faster than the real ones in the

prototype. This circumstance darkens the perception of the real bridge dynamic behaviour

under wind flow.

Additional weak points of this method are listed below:

17
http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#bib9#bib9http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#bib9#bib9


18/31

High cost of both boundary layer wind tunnel facilities and the full aeroelastic models

to be used. In addition, section model tests must be carried out in order to ensure the

experiment reliability.

It is difficult to introduce modifications in full models if their aerodynamic behaviour is

inadequate.

Due to the existing trend of building bridges with longer spans each time, the size of

wind tunnels must also be increased in order to maintain adequate model scales.

Both methods, hybrid method and full model testing can be used to identify the wind

flutter speed, as the two usually offer close results.

18


19/31

6. VIRTUAL WIND TUNNEL: CONCEPT AND

ACHIEVEMENTS

What do wind engineers dream about? For the authors envision the answer to the former

question is to be able to anticipate the real structural behaviour of long span bridges

under wind flow. The virtual wind tunnel (VWT) is the tool that can turn dreams in facts.

The VWT applies the hybrid method, explained in previous sections, to evaluate the

bridge response to an oncoming wind flow and additionally produces a realistic

animation of the bridge behaviour by means of a digital visualization model. Therefore

the real deflection of the bridge can be obtained and realistically reproduced for a wind

speed range between zero and the flutter speed. Two different situations must be

considered.

For a uniform wind speed lower than the critical flutter speed, the VWT obtains the static

deflection of the bridge under wind load. The structural problem to be solved is

Ku = p (U),

where p(U) is a vector containing the aerodynamic wind loads, which depend upon the

aerodynamic coefficients obtained using a conventional wind tunnel and the flow speed.

Wind loads are different for different wind speeds, therefore the VWT is able to simulate

19
http://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml13&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=4ea434860ad23880d5b4a7168af8f5bchttp://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml13&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=4ea434860ad23880d5b4a7168af8f5bchttp://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml13&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=4ea434860ad23880d5b4a7168af8f5bchttp://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml13&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=4ea434860ad23880d5b4a7168af8f5bchttp://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml13&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=4ea434860ad23880d5b4a7168af8f5bchttp://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml13&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=4ea434860ad23880d5b4a7168af8f5bc


20/31

the changes in the static bridge deflection for a wind speed increment form U= 0 up to

any speed U< Uf in a time interval t.

The second phase to be considered is the one that corresponds to U= Uf as this is the

critical wind speed for flutter. In this case the bridge deflection is obtained throughout the

eigenvector problem defined in (5), which leads to the following expression for the time-

dependent bridge deck deflection:

u (t)= wjejt=wje

ijt,

where is the modal matrix, and subindexj corresponds to thejth aeroelastic mode

which satisfies j = 0. Eq.(9) gives the bridge deck movements as a function of time for

the situation of neutrally stable motion previous to the instable state associated with

flutter. The VWT reproduces that steady harmonic oscillation, without frequency scaling,

which is added to the bridge previously evaluated static deflections caused by the wind

aerodynamic load by means of a realistic visualization computational model.

A frame from the animation of the Messina Strait Bridge deflections under aerodynamic

loads caused by a wind speed lower than the critical is shown.

20
http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#fd4#fd4http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#fd4#fd4http://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml14&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=980aa924ee37d72893fe7e8d93aa03d6http://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml14&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=980aa924ee37d72893fe7e8d93aa03d6http://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml14&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=980aa924ee37d72893fe7e8d93aa03d6http://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml14&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=980aa924ee37d72893fe7e8d93aa03d6http://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml14&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=980aa924ee37d72893fe7e8d93aa03d6http://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml14&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=980aa924ee37d72893fe7e8d93aa03d6http://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml14&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=980aa924ee37d72893fe7e8d93aa03d6http://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml14&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=980aa924ee37d72893fe7e8d93aa03d6http://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml14&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=980aa924ee37d72893fe7e8d93aa03d6http://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml14&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=980aa924ee37d72893fe7e8d93aa03d6http://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml14&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=980aa924ee37d72893fe7e8d93aa03d6http://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml14&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=980aa924ee37d72893fe7e8d93aa03d6http://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml14&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=980aa924ee37d72893fe7e8d93aa03d6http://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml14&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=980aa924ee37d72893fe7e8d93aa03d6http://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml14&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=980aa924ee37d72893fe7e8d93aa03d6http://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml14&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=980aa924ee37d72893fe7e8d93aa03d6http://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml14&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=980aa924ee37d72893fe7e8d93aa03d6http://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml14&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=980aa924ee37d72893fe7e8d93aa03d6http://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml14&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=980aa924ee37d72893fe7e8d93aa03d6http://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml14&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=980aa924ee37d72893fe7e8d93aa03d6http://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml14&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=980aa924ee37d72893fe7e8d93aa03d6http://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml14&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=980aa924ee37d72893fe7e8d93aa03d6http://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml14&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=980aa924ee37d72893fe7e8d93aa03d6http://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml14&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=980aa924ee37d72893fe7e8d93aa03d6http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#fd6#fd6http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#fd6#fd6http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#fd4#fd4http://www.sciencedirect.com/science?_ob=MathURL&_method=retrieve&_udi=B6V1P-4T5S4BC-1&_mathId=mml14&_user=4501256&_cdi=5680&_rdoc=1&_ArticleListID=791719587&_acct=C000059971&_version=1&_userid=4501256&md5=980aa924ee37d72893fe7e8d93aa03d6http://c/Documents%20and%20Settings/Anand/My%20Documents/Anand/anand/science.html#fd6#fd6


21/31

Fig 7.Static deformation of the Messina Strait Bridge under static wind load.

Four frames from the digital animation of the steady state oscillation plus the static

deflection caused by the aerodynamic wind loads of the Messina Bridge when the flutter

speed is reached are presented

21


22/31

Fig 8.Realistic frames of the aeroelastic response of the Messina Strait Bridge for critical

wind speed.

The VWT was applied for the first time to the collapsed Tacoma Narrows Bridge as a

movie showing the vibrations that lead to the failure existed and the computer animation

produced using this technology could be compared to identify the similarity. This was a

way to pay tribute to the bridge that opened the way for the wind engineering science. In

fig 9,picture of the real oscillations of the Tacoma Bridge and a frame from the animation

of the Tacoma Bridge performance under wind flow obtained using VWT techniques are

shown.

22


23/31

Fig 9.a 9.b

Tacoma Narrows Bridge deflections under wind flow: (a) Real picture and (b) VWT

visualization.

Also VWT has been applied to some of the most outstanding suspension bridges existing

in the world such as the Great Belt Bridge or the aforementioned Messina Strait Bridge.

The two methods presented are widely accepted nowadays in order to carry out the

identification of the wind flutter speed. The presented strategy for visualize the

aeroelastic behaviour under wind flow represents an interesting extension of the hybrid

method while additionally avoids some of the drawbacks associated with the response

visualization in full model tests. To date VWT allows realistic real time visualization of

long span bridge movements for static wind loads as well as flutter instability under

smooth flow. Extensions of this methodology can be developed, for instance,

incorporation of turbulent flow, vortex-shedding response or buffeting response amongst

23


24/31

other phenomena. Currently this is an ongoing research that the authors are carrying out

with the aim of incorporating those capabilities in the VWT.

Evaluation of flutter speed is a computer time consuming task. Additionally, realistic

animations of the bridge movements require the generation of 24 frames per second of

animation. Therefore, application of parallel computing techniques in both cases allows

substantial reductions in the computer time required to elaborate the bridge aeroelastic

performance visualization.

6.1 The Tachoma Narrows Bridge And its Failure As Explained By VWT Methods

The bridge was solidly built, with girders of carbon steel anchored in huge blocks of

concrete. Preceding designs typically had open lattice beam trusses underneath the

roadbed. This bridge was the first of its type to employ plate girders (pairs of deep I

beams) to support the roadbed. With the earlier designs any wind would simply pass

through the truss, but in the new design the wind would be diverted above and below the

structure. Shortly after construction finished at the end of June (opened to traffic on July

1, 1940), it was discovered that the bridge would sway and buckle dangerously in

relatively mild windy conditions for the area. This vibration was transverse, meaning the

bridge buckled along its length, with the roadbed alternately raised and depressed in

certain locationsone half of the central span would rise while the other lowered.

Drivers would see cars approaching from the other direction disappear into valleys that

dynamically appeared and disappeared. Because of this behavior, a local humorist gave

the bridge the nickname Galloping Gertie. However, the mass of the bridge was

considered sufficient to keep it structurally sound.

24
http://en.wikipedia.org/wiki/Steelhttp://en.wikipedia.org/wiki/Concretehttp://en.wikipedia.org/wiki/I-beamhttp://en.wikipedia.org/wiki/I-beamhttp://en.wikipedia.org/wiki/July_1http://en.wikipedia.org/wiki/July_1http://en.wikipedia.org/wiki/1940http://en.wikipedia.org/wiki/Windhttp://en.wikipedia.org/wiki/Transverse_wavehttp://en.wikipedia.org/wiki/Steelhttp://en.wikipedia.org/wiki/Concretehttp://en.wikipedia.org/wiki/I-beamhttp://en.wikipedia.org/wiki/I-beamhttp://en.wikipedia.org/wiki/July_1http://en.wikipedia.org/wiki/July_1http://en.wikipedia.org/wiki/1940http://en.wikipedia.org/wiki/Windhttp://en.wikipedia.org/wiki/Transverse_wave


25/31

The failure of the bridge occurred when a never-before-seen twisting mode occurred,

from winds at a mild 40 MPH. This is a so-called torsional vibration mode (which is

different from the transversal orlongitudinal vibration mode), whereby when the left side

of the roadway went down, the right side would rise, and vice-versa, with the centerline

of the road remaining still. Specifically, it was the second torsional mode, in which the

midpoint of the bridge remained motionless while the two halves of the bridge twisted in

opposite directions. Two men proved this point by walking along the center line,

unaffected by the flapping of the roadway rising and falling to each side. This vibration

was caused by aeroelastic fluttering.

Eventually, the amplitude of the motion produced by the fluttering increased beyond the

strength of a vital part, in this case the suspender cables. Once several cables failed, the

weight of the deck transferred to the adjacent cables that broke in turn until almost all of

the central deck fell into the water below the span.

Here is a summary of the key points in the explanation.

1. In general, the 1940 Narrows Bridge had relatively little resistance to torsional

(twisting) forces. That was because it had such a large depth-to-width ratio, 1 to 72.

Gertie's long, narrow, and shallow stiffening girder made the structure extremely flexible.

2. On the morning of November 7, 1940 shortly after 10 a.m., a critical event occurred.

The cable band at mid-span on the north cable slipped. This allowed the cable to separate

into two unequal segments. That contributed to the change from vertical (up-and-down)

to torsional (twisting) movement of the bridge deck.

25
http://en.wikipedia.org/wiki/Vibration_modehttp://en.wikipedia.org/wiki/Transverse_modehttp://en.wikipedia.org/wiki/Longitudinal_modehttp://en.wikipedia.org/wiki/Aeroelastic_flutterhttp://en.wikipedia.org/wiki/Vibration_modehttp://en.wikipedia.org/wiki/Transverse_modehttp://en.wikipedia.org/wiki/Longitudinal_modehttp://en.wikipedia.org/wiki/Aeroelastic_flutter


26/31


27/31

vortex so the two were synchronized. The structure's twisting movements became self-

generating. In other words, the forces acting on the bridge were no longer caused by

wind. The bridge deck's own motion produced the forces. Engineers call this "self-

excited" motion.

It was critical that the two types of instability, vortex shedding and torsional flutter, both

occurred at relatively low wind speeds. Usually, vortex shedding occurs at relatively low

wind speeds, like 25 to 35 mph, and torsional flutter at high wind speeds, like 100 mph.

Because of Gertie's design, and relatively weak resistance to torsional forces, from the

vortex shedding instability the bridge went right into "torsional flutter."

Now the bridge was beyond its natural ability to "damp out" the motion. Once the

twisting movements began, they controlled the vortex forces. The torsional motion began

small and built upon its own self-induced energy.

In other words, Galloping Gertie's twisting induced more twisting, then greater and

greater twisting.

This increased beyond the bridge structure's strength to resist. Failure resulted.

27


28/31

7. CONCLUSIONS

The aeroelastic analysis of bridges based upon computer calculations fails to represent

graphically aeroelastic responses.

Full aeroelastic models tested in boundary layer wind tunnels show wind-induced

instabilities, although oscillation frequencies are affected by similarity requirements.

Boundary layer wind tunnel testing is complex and associated costs are high, therefore is

an unaffordable technique for many research groups and engineering companies

worldwide.

28


29/31

Virtual wind tunnel technique gives a realistic visualization of the aeroelastic

performance of long span bridges as an extreme detailed digital model of a future

structure is worked out. In fact, for the Messina Strait Bridge even the screws or the grids

have been modelled reproducing the ones defined in the project planes. VWT

methodology relies on section model testing which are far less expensive and complex

than full aeroelastic model testing.

In the engineering field advanced visualization has been widely used in the conceptual

design, in the detailing part of the design process of structures as well as in describing the

structural behaviour under certain time-dependent loads for digital models of simple

geometry. A new pace consists in its application to describe the structural behaviour

under a specific and complex time-dependent load as the wind-induced one and with the

high level of accuracy shown in the pictures.

8. REFERENCES

[1]E.H. Dowell et al., A modern course in aeroelasticity. In: G.M.L. Gladwell, Editor,

Solid mechanics and its applications (4th ed.), Kluwer Academic Publishers (2004), p.

746.

[2] E. Simiu and R.H. Scanlan, Wind effects on structures: fundamentals and applications

to design (3rd ed.), John Wiley & Sons, Inc., New York (1996) p. 688.

[3] J.D. Holmes, Wind loading of structures, Spon Press, London (2001).

[4] R.H. Scanlan and J.J. Tomko, Aircraft and bridge deck flutter derivatives, J Eng Mech

Div, ASCE 97 (1971), pp. 17171737.

29
http://e/anand/science.html#bbib2#bbib2http://e/anand/science.html#bbib3#bbib3http://e/anand/science.html#bbib4#bbib4http://e/anand/science.html#bbib2#bbib2http://e/anand/science.html#bbib3#bbib3http://e/anand/science.html#bbib4#bbib4


30/31

[5] P.P. Sarkar, N.P. Jones and R.H. Scanlan, System identification for estimation of

flutter derivatives, J Wind Eng Ind Aerodynam 42 (1992), pp. 12431254.

[6] Chen Chern-Hwa, Lin Yuh-Yi, Chen Jwo-Hua. Prediction of flutter derivatives using

artificial neural networks. In: The fourth international symposium on computational wind

engineering. Yokohama, Japan: 2006.

[7] J.A. Jurado and S. Hernndez, Theories of aerodynamic forces on decks of long span

bridges, J Bridge Eng 5 (1) (2000), pp. 813.

[8] J.P.C. King, The foundation and the future of wind engineering of long span bridges

the contributions of Alan Davenport, J Wind Eng Ind Aerodynam 91 (2003), pp. 1529

1546.

[9] ASCE, Wind loading and wind-induced structural response 1987, Committee n Wind

Effects of the Committee on Dynamic Effects of the Structural Division of the American

Society of Civil Engineers.

[10] Jones NP, Scanlan RH. Advances (and challenges) in the prediction of long-span

bridge response to wind. In: International symposium on advances in bridge

aerodynamics. Copenhagen, Denmark: 1998.

[11] S. Hernndez, L.A. Hernndez and A. Antn, Virtual laboratories for analysis and

design of civil engineering structures, Applications of high performance computing in

engineering VI, WIT Press (2000).

[12] Hernndez S, Jurado JA, Mosquera A. Multidisciplinary and multiobjective

approach to aeroelastic design of long span bridges. In: International workshop on long

span aerodynamics, IN-VENTO2002, SGE Editoriale, 2002.

30
http://e/anand/science.html#bbib5#bbib5http://e/anand/science.html#bbib6#bbib6http://e/anand/science.html#bbib7#bbib7http://e/anand/science.html#bbib8#bbib8http://e/anand/science.html#bbib9#bbib9http://e/anand/science.html#bbib10#bbib10http://e/anand/science.html#bbib11#bbib11http://e/anand/science.html#bbib12#bbib12http://e/anand/science.html#bbib5#bbib5http://e/anand/science.html#bbib6#bbib6http://e/anand/science.html#bbib7#bbib7http://e/anand/science.html#bbib8#bbib8http://e/anand/science.html#bbib9#bbib9http://e/anand/science.html#bbib10#bbib10http://e/anand/science.html#bbib11#bbib11http://e/anand/science.html#bbib12#bbib12


31/31

[13] S. Hernndez et al., An application of virtual wind tunnel techniques to the proposed

Messina Bridge, The fourth international symposium on computational wind engineering,

Japan Association for Wind Engineering, Yokohama, Japan (2006).

[14] Hernndez S, Nieto F. Distributed computing of the aeroelastic analysis and

sensitivities of flutter speed of bridges. Application to the Messina Bridge. In: 9

Convegno Nazionale di Ingegneria del Vento IN-VENTO-2006. Pescara, Italy:

Associazione Nazionale per lIngegneria del Vento; 2006.

[15] http://en.wikipedia.org/wiki/Tacoma_Narrows_Bridge_Collapse

[16] http://en.wikipedia.org/wiki/Aeroelastic_flutter#Flutter

[17] http://raphael.mit.edu/Java/

[18] http://www.wsdot.wa.gov/tnbhistory/Machine/machine3.htm
http://e/anand/science.html#bbib13#bbib13http://e/anand/science.html#bbib14#bbib14http://en.wikipedia.org/wiki/Tacoma_Narrows_Bridge_Collapsehttp://e/anand/science.html#bbib13#bbib13http://e/anand/science.html#bbib14#bbib14http://en.wikipedia.org/wiki/Tacoma_Narrows_Bridge_Collapse