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8/14/2019 Virtual Wind Tunnel
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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)
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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.
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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
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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
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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
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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
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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.
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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.
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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.
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The second step consists in the numerical evaluation of the aeroelastic forces acting on
the bridge deck .
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Fig 6. Evolution of aeroelastic damping vs. wind speed.
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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.
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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
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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:
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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.
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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
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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.
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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
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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.
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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
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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.
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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.
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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.
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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.
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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.
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