Dynamic Wind Effects on Bridges

Prem Krishna

Professor of Bridge Engineering Department of Civil Engineering, University of Roorkee, Roorkee-247667

wincen@rurkiu.ernet.in; civil@rurkiu.ernet.in

Abstract

Wind being a randomly varying time-dependent phenomenon evokes a dynamic response from structures exposed to it. It is convenient to consider the wind loading to consist of a quasi-static (mean) and a dynamic (fluctuating) component. Bridge structures can range in span from a few meters to a couple of kilometers and their structural arrangement as well as sensitivity to the dynamic action of wind is dependent thereon. Long span bridges are generally cable bridges and their inherent flexibility makes them vulnerable to aerodynamic oscillations of different nature. The paper concentrates mainly on the issues concerning the aerodynamic response and design of such bridges to make them safe and stable under wind action. INTRODUCTION Wind is essentially a dynamic, randomly varying time-dependent force, and thus always evokes a dynamic response from a structure. The degree, however, varies with the type of structure and all the accompanying variations of the situation; likewise is the case with bridges.

Any record of wind shows that its velocity, V, at a point varies with time. It is convenient to look at this as consisting of a mean plus a fluctuating component, such that,

V ,VVV ′+= being the mean component and V' the fluctuating component. Both these components vary with height, as shown in Fig. 1. Another factor that affects the wind velocity at a certain location, besides the height above ground, is the nature of the approach terrain. Fig. 2 depicts typical velocity profiles for wind as it may approach bridges. It is also seen as to how the of surface roughness may affect the profile.

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The mean force, F, on a surface acted upon by wind can be expressed as,

F =Cp × p × A (1)

where p = 1/2 ρV2, ρ = mass density of air, V = wind velocity, Cp = pressure coefficient, and A = reference area of exposure

The effect of gustiness of wind can be accounted for by using a 'gust' factor on F. The value of the 'gust' factor depends upon the averaging period used for getting the mean wind velocity V. Typically, if a 15 min period is used for averaging, the peak gust speed is (1+gI) times the mean speed. Here, g is a statistical factor of the order 3 and I, the intensity of turbulence. The gust factor will be (1+gI)2. If, for evaluating F, the gust wind speed is used in place of V, the effect of gustiness is accounted for directly. The approach is satisfactory for small structures, which do not have a tendency to oscillate. For larger, more sensitive structures, the mean forces and the dynamic forces are usually not related in such a simple way, since the distribution of the two types of forces may be quite different. Whether one pursues a theoretical or an experimental approach, the determination of the mean component is more straightforward as compared to the dynamic component.

Whereas, generally it is sufficient to deal with the horizontal component of wind on structures, in case of bridges the inclination of wind incidence in the vertical plane becomes important. Such inclination results in wind velocity having a vertical component which affects the 'force' coefficients as seen later in this paper. (Fig. 5) BRIDGE RESPONSE

Short to medium span bridges can be assessed with methods for determining quasi-static wind effects, whereas long (or super-long) span bridges necessarily exhibit a marked dynamic behaviour. Girder, truss and arch bridges generally fall into the first category, and, cable bridges, being inherently flexible, by and large are in the latter category. Whereas failure of shorter bridges in high wind storms is not unknown, there are examples of a number of early suspension bridges (Table 1) having got damaged or failed during wind storms - the failure of the Tacoma Narrows bridge in 1940 under moderate wind is the most striking example of this type.

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One important factor governing bridge response is the energy spectrum of the approach wind. In this respect it is interesting to note that the influence of the approach site on the wind can manifest quite dramatically. There are examples of many suspension bridges which exhibited unusual aerodynamic behaviour, which could be explained by the environmental situation surrounding the bridge. Some of these are, Menai Straits bridge, Clifton bridge, Roebling bridge, Halifax bridge, Tacoma Narrows bridge, The Golden Gate bridge, Bronx Whitestone bridge, Normandy bridge (Miyata, 1999). Many long span bridges have sites with peculiarities and it follows thus that attention must be given to this aspect. Perhaps the best course is to study these situations through wind tunnel testing, as was done, for example, for the Tatara Cable Stayed Bridge in Japan.

The behaviour of bridges which are wind sensitive may be broken down broadly into 'static' and 'dynamic' categories. Static response can be best seen in terms of the force coefficients CD, CL and CM, representing drag, lift and pitching moment respectively, which are to a great extent dependent upon the shape of the deck as well as the angle of incidence of wind (measured in the vertical plane). Fig. 3 shows typical trussed and streamlined box cross sections for a cable bridge where the wind drag for the former can be as much as three times the latter. Fig. 4 depicts the effect of shaping the box on the drag coefficient and Fig. 5 the values of force coefficients for two long suspension bridges, as affected by the angle of incidence of wind.

The dynamic behaviour of the bridge under the action of wind loads is dependent upon the flow; particularly in terms of the turbulence characteristics, and the structural as well as aerodynamic characteristics - the mass, stiffness, frequency, geometrical shape and damping. These characteristics are often related to the bridge form and span. For example, see Figs. 6 and 7 for suspension and cable stayed bridge frequencies of vibration-it is noteworthy that the frequencies for truss or arch bridges would be in the order of 1/2 - 1 Hz. The various forms of aerodynamic response can be described as - buffeting, vortex induced oscillations, and, self excited oscillations such as in vertical bending, torsional bending, galloping in towers, or, flutter. It is seen from Figs. 8 and 9 that there is a sharp increase in the span range of cable bridges, and consequently issues of aerodynamic response are going to assume greater significance. | The preceding discussion is making it obvious that there is a close link between bridge aerodynamics and the Cable Bridge form. It is best, therefore, to proceed by studying the problem in terms of the three major components in a cable bridge superstructure - the deck, towers and cables. | The Deck The deck is the most important component of a bridge from the standpoint of the aodynamic behaviour of a cable bridge, and is therefore the one most investigated. Initially cable bridges

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used stiffening girders of trusses alongwith a concrete or a steel deck. This trend continued until the collapse of the Tacoma Narrows suspension bridge mentioned earlier. Following this failure, the idea of using box girder decks took roots to meet the requirements of adequate flexural as well as torsional stiffness, as well as to minimise wind loading. One of the major design concerns thereafter has been to choose a deck and stiffening system to raise the critical wind speed for the initiation of flutter above the design wind speed, while introducing adequate stiffness. From that point of view the comparison of the flat plate to a box, a truss, and, a split - box (or a separate box system) makes an interesting study. This may be seen from Fig. 10. It is seen that the critical wind speed for the initiation of flutter for a flat plate is the maximum. The split-box is better than a single box, which is better than a truss. This of course is only a qualitative comparison, and a family of curves could be obtained for the different deck forms with their varying frequencies and mass dispensation. | The turbulence in the flow and its span-wise correlation can affect the deck oscillations to a substantial degree. It is therefore important that both intensity and scales are suitably modelled in the wind tunnel. It is to be noted that the turbulence in the flow would be modified by the presence of the bridge structure and thus influence response. Fig.11 shows the torsional response of the Lion's Gate bridge. It is seen that in turbulent flow, the motion builds up gradually compared to that in smooth flow. Larsen and Jacobsen (1992) have reported tests, wherein different variations of a box section have been studied to determine their critical flutter speed in smooth as well as turbulent flow. Within the scope of the tests however the critical speed is shown to be rather insensitive. This may be true particularly for very long span applications as well as in cases where the topography is unusual. To study these bridges the role of instrumenting prototypes can be invaluable. There is now a growing trend towards this.

Construction Stage Analysis A long span bridge of 'cable supported' types or otherwise, is often constructed by the 'cantilever' method of erection. This implies that the bridge will consist of long cantilever portions before it is completed. The aerodynamic stability of the bridge will consist of long cantilever portions before it is completed. The aerodynamic stability of the bridge during the construction phase therefore needs to be carefully studied and safeguarded. Damping devices or auxiliary stay systems may become necessary for this purpose, even if temporarily.

Provision of Wind Screens The idea of providing wind screens (porous) on both sides of a bridge deck has been in serious consideration for the purpose of creating a more comfortable and safer environment for vehicles during a wind storm. These screens nevertheless attract greater drag force and lead to the possibility of enhanced aerodynamic instability.

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CONCLUDING REMARKS

The paper attempts a brief overview of the subject of wind effects on bridges, with greater emphasis on the dynamic aspect which necessarily becomes important for long span bridges of the cable supported type. Most aspects of bridge aerodynamics are addressed without attempting any detailed treatment. The state-of-the-art brought forth implies a fair understanding and information on most issues to attempt the application of 'long' as well as 'super-long' spans. | REFERENCES |

1. Brown W.C. (1999), “Long Span Bridge Projects - A Personal View”, Proc. of the International Seminar on Long-Span Bridges and Aerodynamics, T. Miyata, et al. (Eds.), Springer.

2. Hurty and Rubinstein, (1967), Dynamics of Structures, Prentice-Hall of India, New Delhi.

3. Archer, J.S. (1963), “Consistent mass matrix for distributed mass systems”, J. Struct. Div., ASCE, 89, 161-178.

4. Diana G. (1993), “Analytical and Wind-Tunnel Simulations for the Aeroelastic Design of the Messina Straits Bridge”, Proc. of the International Seminar on Utilization of Large Boundary Layer Wind Tunnel, Tsukuba, Japan.

5. Diana G., Falco M., Cheli F. and Cigada A, (1999), “Experience Gained in the Messina Bridge Aeroelastic Project”, Proc of the International Seminar on Long-Span Bridges and Aerodynamics, T. Miyata, et al. (Eds.), Springer.

6. Larsen A. and Jacobsen A.S. (1992), “Aerodynamic Design of the Great Belt East Bridge”, Proc. of the Int. Symp. on Aerodynamics of Large Bridges, A. Larsen (Ed.), Copenhagen, Denmark, Balkema.

7. Miyata T. (1995), “Full Model Testing of Large Cable-supported Bridges”, A State-of-the-Art in Wind Engineering, 9th International Conference on Wind Engg., New Delhi, India, Wiley Eastern.

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Table 1 Some Early Bridges Suffering Wind Induced Damage (After Brown 1999)

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Failure Date

Bridge Location Main Span (m)

Width (m)

1818 Dryburgh Abbey Scotland 79.3 1.22

1834 Nassau Germany 74.7 ----

1836 Brighton Chain Pier England 77.8 3.86

1838 Montrose Scotland 131.8 7.98

1839 Menai Straits Wales 176.9 7.32

1852 Roche-Bernard Scotland 79.3 1.22

1854 Wheeling USA 208.1 7.32

1864 Lewiston-Queenston

USA 317.3 5.95

1889 Niagara-Clifton USA 386.7 5.19

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Fig.1 Variation of Wind Velocity with (a) Time, (b) Height

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Fig. 2 Wind Characteristics in the Boundary Layer and Relative Bridge Location