**2.2. Influence of bridge features**

damping (considered positive) and an aerodynamic damping, related to *d CL* /*d* + *CD*. The system can develop divergent oscillations if the total damping becomes negative. The condition for negative aerodynamic damping to occur is known as the Den Hartog criterion [11].

Non-streamlined box-girders with relatively small width-to-depth ratio are particularly sus-

Galloping can occur at low, either steady or unsteady, wind speeds, for structures with low structural damping associated with bending, which is the case of suspension bridges, although the occurrence of galloping is more typical of overhead power lines subjected to ice deposition [11].

Coupled flutter, also named classic flutter, encompasses motion in both bending and torsion. It occurs in cases for which the structure has a pair of neighbouring frequencies in bending

Bridge decks that will exhibit coupled flutter if the wind speed exceeds a critical value are those with a streamlined trapezoidal cross-section, with large width-to-depth ratio, so that there are no large vortices shedding from the leading edge. Examples are the Great Belt and

Classic flutter was first perceived in aircraft wings and Theodersen [12] developed a thin airfoil theory aimed at describing analytically the flutter phenomenon. Since the aerodynamics of trapezoidal decks is far from being tractable as that of a thin airfoil, this theory cannot be directly applied to bridge decks without corrections [13]. Scanlan and Sabzevari [14] proposed a formulation in which the aeroelastic forces (lift and torque) are expressed as functions involving coefficients known as flutter derivatives. These derivatives (which cannot be obtained analytically) have to be obtained through wind tunnel testing. The resulting equations can be

In certain cases, designers may resort to simpler ways of estimating this critical speed. In the beginning of the 1960s, A. Selberg proposed a formula for thin plates. Under certain conditions, it can be adapted to bridge decks through the use of a factor that depends on the geometry of the cross-section. More recently, Bartoli and Mannini [15] proposed simple expressions for critically reduced wind speed and coupling frequency based on a reduced number of flutter derivatives.

Current design practice avoids coupled flutter, alias classic flutter, by having in mind from the beginning of the design sufficient separation between the lowest torsional natural frequency of the bridge and the fundamental bending frequency. For example, Section E.4.2 of

In the same way, torsional flutter is not a significant phenomenon in modern bridges due to

ceptible to galloping, since the flexural stiffness is much smaller than the torsional.

Galloping occurs above this critical wind speed.

the Izmit Suspension Bridges, as pointed out by [7].

solved for the critical wind speed for the onset of flutter.

the Eurocode 1 [8] establishes a minimum ratio of 2:1.

the necessary stiffness imposed by practical reasons.

*2.1.5. Coupled flutter*

and in torsion.

90 Bridge Engineering

*2.1.6. Comments*

The occurrence of aeroelastic phenomena on long-span bridges has been widely studied. Good starting points for further reading are the reviews of Miyata [17] and of Saito and Sakata [18].

In aerodynamics, minor details (from the point of view of design) in the body contour can lead to significant modifications of the flow pattern and aerodynamic response. While this means that the aerodynamic can be improved by introducing, still at the design stage, inexpensive and simple-to-implement modifications, it also means that it is important to consider in the aerodynamic study the various stages of the deck construction since the addition of equipment, such as median dividers, guard rails, and border beams, can noticeably change the deck's aerodynamic response [17, 19–22].

#### *2.2.1. Deck cross-section shape*

The overall shape of the bridge deck's cross-section strongly influences the occurrence of aeroelastic phenomena [23–25]. A numerical study of four generic cross-section shapes developed from the well-known plate girder section of the First Tacoma Narrows Bridge, by adding horizontal plates and fairings, showed that the closed section with fairings displayed the best aerodynamic performance (in terms of drag loading and oscillating lift) and the parent H-shaped cross-section, the worst [23].

In streamlined box sections, VIV can likely be avoided or kept at insignificant levels if the angle between the horizontal extension of the deck's bottom plate and the lower inclined panels is kept smaller than 15°, in order to avoid flow separation [25]. Streamlining of the deck can possibly result in improved aerodynamic performance, with an increase in the critical wind speed for torsional flutter and decrease in the vortex-induced response [19, 26]. Even though streamlined decks have lower drag and postpone the onset of possible divergent aeroelastic instabilities to higher wind speeds, they may nevertheless exhibit oscillations at low wind speed due to vortex shedding excitation.

It should be said that trapezoidal decks are far from being tractable as thin airfoils and analytical methods, such as Theodersen's thin airfoil theory for the study of flutter, are not successful if applied without appropriate modifications. Bridge decks have to be considered as bluff bodies.

The aerodynamic stability of super-long-span bridges can be effectively improved by introducing a slot at the centre of the girder [24]. This is the design being adopted for the proposed Messina Strait (**Figure 2**) and Gibraltar Strait crossings [27, 28].

## *2.2.2. Railings*

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

In the European Union, the named Eurocodes ultimately replaced the several National Codes, with differing rules, in the various Member States. It is worth mentioning the recommendations of the European Convention for Constructional Steelwork (ECCS) [13] or, in the case of

Wind Action Phenomena Associated with Large-Span Bridges

http://dx.doi.org/10.5772/intechopen.73061

93

Wind actions on bridges are covered in Section 8 of the Eurocode 1 Part 1–4. It is worth pointing out that the code does not apply to bridges involving civil engineering works with heights above 200 m or bridges having spans greater than 200 m. The Vila-Real Bridge to be discussed

Codes of practice tend to be conservative though, encouraging wind tunnel tests to address the susceptibility to undesirable aerodynamic phenomena, of long-span bridges and/or with atypical shape. In their numerical studies, Bruno and Mancini [20] found for decks with complex geometries errors up to 200% between the simulated forces and the predictions using standard rules (ENV 1991-2-4). Therefore, when it is difficult to fit up a bridge within the regulation in effect, it is unavoidable to resort to aerodynamic experimental studies to obtain design criteria that warrant structural safety and, in many cases, a reduction of the overall cost of the project.

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 pro-

pose corrective modifications and test their effectiveness in the wind tunnel.

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

the UK up to 2010, the British standard "BS 5400" [36].

in Section 8 exceeds both these criteria.

**4. Wind tunnel testing**

**4.1. Introductory notes**

**4.2. Similitude parameters**

prototype, respectively.

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

#### *2.2.3. Supporting cables*

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, cables are even more prone to vibration than the deck.

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 cables exceeds that of the bridge deck.
