**4. Wind tunnel testing**

#### **4.1. Introductory notes**

*2.2.2. Railings*

92 Bridge Engineering

*2.2.3. Supporting cables*

cables are even more prone to vibration than the deck.

cables exceeds that of the bridge deck.

**3. Codes of practice**

Changes in the porosity of the outermost railings, be it through the use of panels to deflect the wind (and thus improve the comfort of pedestrians or servicing personal) or by snow accumulation [29], would seem, at first glance, inconsequential for the bridge aerodynamics. However, making that area impermeable to the wind can render the deck section highly unstable. As the solidity ratio (considered high above 0.3) of edge safety barriers increases, so does the overall bluffness of the section, increasing drag and reducing mean lift; the effect is more relevant as the bare deck shape is more streamlined [20]. Decks with higher porosity railings have higher flutter critical wind speed [21]. The effect of the barriers contributed to the mechanism respon-

Deck equipment, such as median dividers, edge safety barriers, or parapets, can have a great impact on the bridge aerodynamics. In numerical simulations, the barriers should be included despite the

Cables are essential components of long-span bridges and they present small mass, higher flexibility in comparison to other bridge components, and low mechanical damping. Therefore,

Wind-induced flutter instability is a major concern in the design and construction of superlong-span cable-stayed bridges. While the aerodynamic contribution from the cables is generally despised when resorting to sectional models in wind tunnel experiments of cable-stayed bridges, this cannot be maintained when assessing super-long-span cable-stayed bridges. The influence of cable aerodynamic forces on the deck's flutter instability may be significant when the main span exceeds 1000 m and the frontal area (as viewed in the flow direction) of all stay

Due to the importance of the assessment of the response of bridges to the action of wind, codes of practice have been developed to aid the bridge engineer in the design calculations.

Most countries and regions of the world have their own codes of practice for bridge design, for example: "EN 1991, Eurocode 1: Actions on Structures" [8] in Europe; the "Specifications for Highway Bridges" by the Japan Road Association [30] or the "Design Standards of Superstructures for Long-Span Bridges" by the Honshu-Shikoku Bridge Authority [31], in Japan; the "LRFD Bridge Design Specifications" by the American Association of State Highway and Transportation Officials [32] in the USA; the "Wind-Resistant Design Specification for Highway Bridges" [33], in China; the "CAN/CSA-S6-00, Canadian Highway Bridge Design

They provide definitions, establish best practices, and give recommendations.

Code" [34], in Canada; and the Australian standard "AS 5100" [35], in Australia.

sible for the vortex-induced oscillations of the Great Belt East Bridge in 1998 [20].

increased computational effort, in order to take into account their effects on the flow [20].

It should be said that wind tunnel tests will not directly provide, as an outcome, a design of a bridge or of an optimal deck geometry non-susceptible to aerodynamic instabilities. What the design engineer can expect from wind tunnel tests is a confirmation that the design is good from the aerodynamics point of view or, otherwise, clues that will help him/her in finding the causes of oscillations and remedy them. Nowadays, it is possible, and even advisable, to complement wind tunnel tests with numerical simulations, which are addressed in the next section.

Given the discussion in the preceding sections, it is not surprising that wind tunnel testing is an integral part of the design and analysis of most long-span bridges and is often a requirement in many codes and national standards. All over the world, many laboratories equipped with wind tunnels have been committed to such studies. In these studies, the goal is to reproduce, at a reduced scale and in the best possible way, the full-scale situation in a wind tunnel and to address whether the wind action on the bridge can possibly excite any of the bridge's vibration modes. When such excitation is possible to be foreseen, then it is necessary to propose corrective modifications and test their effectiveness in the wind tunnel.

#### **4.2. Similitude parameters**

Confidence in the translation to the real prototype of the results obtained with the wind tunnel models for the dynamic behaviour of bridge deck models imposes the compliance of certain similarity criteria. In what follows, the subscripts *m* and *p* refer to the model and to the prototype, respectively.

The most natural criterion is geometric similarity, being expressed by the equation:

$$L\_p/L\_m = \text{ } \text{C} \tag{1}$$

The similarity parameter that involves the mass of the model, or of the prototype, together with the respective logarithmic decrements of the damped responses in the various oscillation modes remains to be discussed. Strictly, these variables should be addressed separately. However, when the main concern of wind tunnel studies is the analysis of vortex shedding, mass and damping can be brought together into a single non-dimensional parameter. That is to say, the system's response to the forced periodic excitation due to vortex shedding can

appropriate in situations of low damping linear systems, and in such cases, the amplitudes of the resonance peaks are inversely proportional to damping. The similarity parameter, which

(i.e., the structure's depth, specifically the section at which resonant vortex shedding occurs). Thus, the denominator in the definition represents a characteristic value of the mass of the air displaced by the structure. The Scruton number describes how sensitive a structure is to vibrating as a result of vortex shedding; the response amplitude will significantly increase at

Being extremely difficult in practice to build a model and an experimental apparatus leading to the same values of *Sc* in the model and prototype, the common practice is to build a model and suspension system as light and as least damped as possible, in order to bring out in the

A pertinent issue for researchers planning wind tunnel tests of long-span bridges is the choice between a full aeroelastic model of the bridge and a sectional model of the deck [37]. In the former, besides the full three-dimensional geometry of the bridge, the dynamic attributes of the several components must also be adequately reproduced in order to obtain a valid global response of the bridge as a whole structure and of the interaction between its structural members. For large-span bridges, full model aeroelastic studies are undertaken because of the important role of towers and cables in the overall bridge response. Nowadays, large wind tunnels exist that can accommodate this type of studies, although at the expense of smaller scales of the model.

This is not the aim of sectional model tests, where the objective is rather studying the dynamic stability of the section proposed for a bridge. Thus, a sectional model reproduces a representative section of the bridge's deck, which is extruded over a length, to produce a twodimensional body for tests in the wind tunnel. For this purpose, the dynamic properties of the

Full aeroelastic model tests are usually conducted taking into consideration the effects of the terrain on the wind, whereas sectional models are usually tested in smooth flow. Therefore, in full model tests, the turbulence response is obtained directly and the effects of turbulence on flutter and vortex shedding are intrinsic and all three-dimensional aeroelastic effects are modelled implicitly. However,

is a mass per unit length, *ρ* is the air density, and *h* is the cross-wind dimension

, which is itself non-dimensional. This is

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*<sup>ρ</sup> <sup>h</sup>*<sup>2</sup> (5)

be represented by the logarithmic damping factor, *δ<sup>s</sup>*

*Sc* <sup>=</sup> <sup>2</sup> *<sup>δ</sup>* \_\_\_\_\_ *<sup>s</sup> <sup>m</sup><sup>i</sup>*

where *m<sup>i</sup>*

low values of this parameter.

is named Scruton number, is defined by the following expression [8]:

laboratory any tendency for instability due to the action of the flow.

**4.3. Full aeroelastic bridge models vs. sectional models**

sectional model must be judiciously chosen.

where *C* is a constant that establishes the scale factor between the model and prototype. Geometric similarity implies the homothety of the shapes of the surfaces contacting with the air, excluding of course all the details that are of very difficult construction and not significant, or even completely irrelevant given the precision with which the parameters of interest are measured.

Kinematic similarity implies that the relation between the characteristic velocities of the flow over the model, *Vm*, and of the oscillatory movement of the model, *f <sup>z</sup> Lm*, is the same for the prototype. This leads to the definition of a non-dimensional parameter known as reduced velocity:

$$V\_r = \frac{V}{f\mathcal{L}}\tag{2}$$

Here, *f* is one of the structure's eigen-frequencies, and it is often the frequency of the fundamental vertical motion, *f z* . Then, the relation between kinematically equivalent velocity scales between the prototype and the model can be defined as:

$$\frac{V\_p}{V\_n} = C \frac{f\_{\epsilon,p}}{f\_{\epsilon,n}} \tag{3}$$

The ratio of frequencies in (3) constitutes a relation for kinematically equivalent time scales, *Tm*/*T<sup>p</sup>* , which is useful to estimate the sampling time interval in order to obtain the mean values of the parameters measured in the laboratory.

Dynamic similarity concerns the dynamic interaction between a body and the flow around it and is of a rather complex nature and thus more difficult to assure. In order to be observed, the relative magnitudes of the various forces involved in the structure's dynamics—the inertial, gravitational, aerodynamic, elastic, and structural damping forces—shall be the same for the model and the prototype, and, consequently, the motion amplitudes will be in the same proportion as the geometric scale ratio. For the airflow, the relation between inertial and viscous forces is expressed by the Reynolds number:

$$\text{Re} = \text{VL}/\upsilon \tag{4}$$

Since the values of the kinematic viscosity of air, *υ*, are approximately equal in the model and in the prototype, dynamic similarity would require that *Vm* = *C V<sup>p</sup>* . This is in conflict with relation (3) established by kinematic similarity, which states that flow velocities in the wind tunnel represent much higher velocities of the flow over the prototype. However, when the model does not exhibit a streamlined section, recirculation zones are formed from flow detachments occurring at the model's sharp edges. This type of separation of the main flow from the solid surface is known to be independent of *Re* above a certain value. Therefore, it is important to warrant that the scale of the model and velocity in the wind tunnel result in a value of *Re* above that threshold.

The similarity parameter that involves the mass of the model, or of the prototype, together with the respective logarithmic decrements of the damped responses in the various oscillation modes remains to be discussed. Strictly, these variables should be addressed separately. However, when the main concern of wind tunnel studies is the analysis of vortex shedding, mass and damping can be brought together into a single non-dimensional parameter. That is to say, the system's response to the forced periodic excitation due to vortex shedding can be represented by the logarithmic damping factor, *δ<sup>s</sup>* , which is itself non-dimensional. This is appropriate in situations of low damping linear systems, and in such cases, the amplitudes of the resonance peaks are inversely proportional to damping. The similarity parameter, which is named Scruton number, is defined by the following expression [8]:

$$\text{Sc} = \frac{2\,\delta\_s m\_i}{\rho \, h^2} \tag{5}$$

where *m<sup>i</sup>* is a mass per unit length, *ρ* is the air density, and *h* is the cross-wind dimension (i.e., the structure's depth, specifically the section at which resonant vortex shedding occurs). Thus, the denominator in the definition represents a characteristic value of the mass of the air displaced by the structure. The Scruton number describes how sensitive a structure is to vibrating as a result of vortex shedding; the response amplitude will significantly increase at low values of this parameter.

Being extremely difficult in practice to build a model and an experimental apparatus leading to the same values of *Sc* in the model and prototype, the common practice is to build a model and suspension system as light and as least damped as possible, in order to bring out in the laboratory any tendency for instability due to the action of the flow.

#### **4.3. Full aeroelastic bridge models vs. sectional models**

The most natural criterion is geometric similarity, being expressed by the equation:

measured.

94 Bridge Engineering

*Tm*/*T<sup>p</sup>*

mental vertical motion, *f*

*L<sup>p</sup>* /*Lm* = *C* (1)

where *C* is a constant that establishes the scale factor between the model and prototype. Geometric similarity implies the homothety of the shapes of the surfaces contacting with the air, excluding of course all the details that are of very difficult construction and not significant, or even completely irrelevant given the precision with which the parameters of interest are

Kinematic similarity implies that the relation between the characteristic velocities of the flow

totype. This leads to the definition of a non-dimensional parameter known as reduced velocity:

Here, *f* is one of the structure's eigen-frequencies, and it is often the frequency of the funda-

<sup>=</sup> *<sup>C</sup> <sup>f</sup> <sup>z</sup>*,*<sup>p</sup>* \_\_\_ *f z*,*m*

The ratio of frequencies in (3) constitutes a relation for kinematically equivalent time scales,

Dynamic similarity concerns the dynamic interaction between a body and the flow around it and is of a rather complex nature and thus more difficult to assure. In order to be observed, the relative magnitudes of the various forces involved in the structure's dynamics—the inertial, gravitational, aerodynamic, elastic, and structural damping forces—shall be the same for the model and the prototype, and, consequently, the motion amplitudes will be in the same proportion as the geometric scale ratio. For the airflow, the relation between inertial and vis-

*Re* = *VL*/*υ* (4)

Since the values of the kinematic viscosity of air, *υ*, are approximately equal in the model

with relation (3) established by kinematic similarity, which states that flow velocities in the wind tunnel represent much higher velocities of the flow over the prototype. However, when the model does not exhibit a streamlined section, recirculation zones are formed from flow detachments occurring at the model's sharp edges. This type of separation of the main flow from the solid surface is known to be independent of *Re* above a certain value. Therefore, it is important to warrant that the scale of the model and velocity in the wind tunnel result in a

and in the prototype, dynamic similarity would require that *Vm* = *C V<sup>p</sup>*

, which is useful to estimate the sampling time interval in order to obtain the mean val-

*Vm*

*<sup>z</sup> Lm*, is the same for the pro-

(3)

. This is in conflict

*fL* (2)

. Then, the relation between kinematically equivalent velocity scales

over the model, *Vm*, and of the oscillatory movement of the model, *f*

*Vr* <sup>=</sup> \_\_*<sup>V</sup>*

*z*

ues of the parameters measured in the laboratory.

cous forces is expressed by the Reynolds number:

value of *Re* above that threshold.

*<sup>V</sup><sup>p</sup>* \_\_\_

between the prototype and the model can be defined as:

A pertinent issue for researchers planning wind tunnel tests of long-span bridges is the choice between a full aeroelastic model of the bridge and a sectional model of the deck [37]. In the former, besides the full three-dimensional geometry of the bridge, the dynamic attributes of the several components must also be adequately reproduced in order to obtain a valid global response of the bridge as a whole structure and of the interaction between its structural members. For large-span bridges, full model aeroelastic studies are undertaken because of the important role of towers and cables in the overall bridge response. Nowadays, large wind tunnels exist that can accommodate this type of studies, although at the expense of smaller scales of the model.

This is not the aim of sectional model tests, where the objective is rather studying the dynamic stability of the section proposed for a bridge. Thus, a sectional model reproduces a representative section of the bridge's deck, which is extruded over a length, to produce a twodimensional body for tests in the wind tunnel. For this purpose, the dynamic properties of the sectional model must be judiciously chosen.

Full aeroelastic model tests are usually conducted taking into consideration the effects of the terrain on the wind, whereas sectional models are usually tested in smooth flow. Therefore, in full model tests, the turbulence response is obtained directly and the effects of turbulence on flutter and vortex shedding are intrinsic and all three-dimensional aeroelastic effects are modelled implicitly. However, compared to sectional model tests, full three-dimensional tests involve higher cost and longer lead time; larger wind tunnels, which are costly to operate; and smaller scale of the model, which limits the level of detail of the flow that can be studied and possibly introduces *Re* dependency effects. Consequently, full aeroelastic model tests are often complemented with sectional model tests, as was the case in the design stage of the Trans-Tokyo Bay Bridge [38], to give an example. An interesting discussion of advantages and limitations of sectional models, taut-strip models, and full bridge models is given in [29]. Alternatively, instead of the full bridge, parts of the bridge, retaining some three-dimensional aspects, may be tested throughout the design phase; for example, at a certain point of the Messina Bridge Project, just the main span was tested at 1:250 scale.

this technique has increased at the same rate as the increase of computational power, and, nowadays, the required post-processing is done swiftly. The duration of a wind tunnel test

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At present, three-dimensional unsteady numerical simulations where all the relevant physics of the interaction of turbulent wind with a flexible structure are completely described still involve a considerable investment of time, despite the steady increase in computational power over time. The case becomes even more difficult if wind gusts, surrounding complex terrain, or coupling with neighbour bridges, are to be included. Therefore, numerical simulations are carried out to look into a certain aspect of the whole problem. Often, numerical simulations complement wind tunnel testing. The engineer has to integrate the several pieces of information to come up with a design that not only is robust from the wind action point of

Generally speaking, structural aspects are studied with the finite element method (FEM), whereas aerodynamic aspects are studied with the finite volume method (FVM), or some other common method in computational fluid dynamics (CFD). It should be said that,

In FEM, the structure of the bridge, or a part of it, is discretized into simple structural elements. Values of interest are then obtained at the ends (nodes) of the element, by solving the numerical model equations, and a weighting function is used within an element to obtain the values at intermediary positions on it. There is a wide variety of elements that may be used and a large choice of weighting functions ranging from simple to more elaborate and precise. In CFD, the common approach is the Eulerian approach, in which the fluid around the deck, or pylons, or even the whole bridge, up to a long distance from the structure, is discretized into small control volumes for which transport equations (mass, momentum, turbulence, and

The challenge has been to couple these two tools to describe the coupling that exists in the real world between structure and wind, in order to be able to study aeroelastic phenomena.

Finite element (FE) is the method of choice to model the structural dynamics of a bridge and can provide insight into its dynamic response, such as the main modes of oscillation and associated natural frequencies. This is especially important for bridges with low structural damping, as is the case of cable-stayed or suspension bridges. Among many studies, a few published examples on suspension bridges are The John A. Roebling Bridge in Kentucky, USA [44]; Tamar Bridge in Plymouth, UK [45]; and the Bosphorus Bridge and the Fatih Sultan

recently, there have been advances towards using FEM for the study of the flow field.

campaign using this technique has been reduced, making them more affordable.

view but also complies with economic and structural constraints.

scalars) are solved. Another approach is to employ meshless methods.

**5.2. Modelling of the structural dynamics**

Mehmet Bridge, in Istanbul, Turkey [46].

**5. Numerical modelling**

**5.1. Introductory notes**

The test of sectional models has been widely understood as a good tool to predict critical flutter instability as well as critical vortex-induced vibration. This is particularly accurate for box-girder and plate girder decks, when sectional model testing appears to predict full scale vortex shedding excitation, and there is evidence that turbulence has only but a minor effect on critical flutter speeds.

#### **4.4. Instrumentation**

To study in the wind tunnel the susceptibility of a bridge to aerodynamic instabilities, the model has to be free to oscillate in response to the action of the flow. This is a completely different situation of static testing. In what concerns sectional models, there are a few solutions, along with the associated instrumentation, to adequately support them in the wind tunnel. Typical suspension systems are based on helical springs. One configuration (used by e.g., [39]) is based on a single pair of suspension columns, which support the extremities of a shaft on the sectional model's axis of rotation. Other sets of helical springs, not contributing to the suspension though, can govern the torsional stiffness, and the setup also includes means of preventing rolling and horizontal displacements of the model. Another configuration employs four suspension columns to support the sectional model through two horizontal arms, one at each end of the model. The four columns tackle both torsional and flexural stiffness. Each suspension column includes two helical springs, one above and one below the suspension arm. Two horizontal wires limit the translation of the model in the horizontal plane. The entire assembly remains outside the test chamber. Systems of this type have been used, for example, by Larsen and Wall [40], and by the present authors [41].

Various types of sensors may be used with the suspension systems to monitor the windinduced motions of the deck model: laser reflexion sensors, piezoelectric accelerometers, or ring strain sensors [41].

The dynamics of the flow pattern around the model can be understood using diagnostic techniques such as laser sheet visualisation (LSV) [40]. Computational fluid dynamics (CFD), to be discussed in the next section, is becoming more often used also for this purpose, and the term CFD visualisation has been employed (e.g., [10, 42]). The classic techniques of smoke lines and wool tufts are still valuable for expedite assessments.

Another possibility is the simultaneous measurement of turbulent pressure fluctuations at multiple points on the surface of the model (e.g., [43]). By analysing the spectra correlation, the development and movement of recirculation bubbles can be understood. The interest in this technique has increased at the same rate as the increase of computational power, and, nowadays, the required post-processing is done swiftly. The duration of a wind tunnel test campaign using this technique has been reduced, making them more affordable.
