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Equations 3. There is a slight dependence of the topographic multipliers on the Jensen Number Section 4. For slopes between about 0. The topographic multipliers, at or near the crest, are therefore also fairly constant with upwind slope in this range. Thus for this range of slopes, equations 3. An additional complication for steep features is that separations can occur at or down wind of the crest see Figure 3. This has the effect of decreasing the mean velocity, and increasing the turbulence intensity, as shown in Figure 3.

Tropical cyclones are large storms with similar boundary layers to extra-tropical depressions on their outer edges. Near the region of strongest winds, they appear to have much lower boundary-layer heights — of the order of m. Topographic features greater than this height would therefore be expected to interact with the structure of the storm itself.

Letchford and Illidge, ; Wood et al. However the effect of forward motion of the storm may modify these conclusions. The adjustment starts at ground level and gradually moves upwards.

The result is the develop- ment of an internal boundary layer over the new terrain as shown in Figure 3. However the magnitude of the mean velo- city continues to reduce for many kilometres, until the complete atmospheric boundary layer has fully adjusted to the rougher terrain. Melbourne found the gust wind speed at a height of 10 m, adjusts to a new terrain approximately exponentially with a distance constant of about m.

Thus the peak gust at a distance x in metres into the new terrain 2 can be represented by equ- ation 3. These include the effects of topographic and terrain changes. Cook has described, for the designer, a structure of the atmospheric boundary layer, which is consistent with the above models. These references are strongly recommended for descriptions of strong wind structure in temperate zones. However, as discussed in this chapter, the strong wind structure in tropical and semi-tropical locations, such as those produced by thunderstorms and tropical cyclones, is different, and such models should be used with caution in these regions.

The main focus has been the atmospheric boundary layer in large synoptic winds over land. However some aspects of wind over the oceans, and in tropical cyclones and thunderstorm downbursts, have also been discussed. References Amano, T. Bendat, J. New York: J. Black, P. Busch, N. Charnock, H. Choi, E. London: Building Research Establish- ment and Butterworths. Deacon, E. Deaves, D. Durst, C. Fujita, T. Garratt, J. Glanville, M. Part II. Harris, R. Report Ishizaki, H. Jackson, P.

Krayer, W. Letchford, C. Atmospheric boundary layer and wind turbulence 67 Lettau, H. Melbourne W. Oseguera, R. Taylor, P.

Wilson, K. Wood, G. Figure 4. It can be seen in Figure 4. Basic bluff-body aerodynamics 69 to a surface. These layers are unstable in a sheet form and will roll up towards the wake, to form concentrated vortices, which are subsequently shed downwind.

However, the shear layer is not fully stabilized and vortices may be formed on the surface, and subsequently roll along the surface. Often A is a projected frontal area. Aerodynamic forces are conventionally resolved into two orthogonal directions. These axes are shown in Figure 4. These variables can be grouped together into non-dimensional groups, using pro- cesses of dimensional analysis, or by inspection. Equation 4. Wind-tunnel testing techniques are discussed in Chapter 7.

However for bodies with curved surfaces, such as circular cylinders or arched roofs, the separation points are dependent on Reynolds number, and this parameter should be considered.

Examples are: elevated hoardings and signboards, which are normally mounted so that their plane is vertical. Solar panels are another example but, in this case, the plane is inclined to the vertical to maximize the collection of solar radiation. The effect of free-stream turbulence is to increase the drag on the normal plate slightly. The increase in drag is caused by a decrease in leeward, or base pressure, rather than an increase in front face pressure. The hypothesis is that the free-stream turbulence causes an increase in the rate of entrainment of air into the separated shear layers.

This leads to a reduced radius of curvature of the shear layers, and to a reduced base pressure, Bearman, The reason for the increase on the wide plates can be explained as follows. A formula given by E. These contribute greatly to the increased entrainment into the wake of the two-dimensional plate. Basic bluff-body aerodynamics 75 Figure 4. The mechanism that produces the reduced drag at the critical spacing of 1. Cook discusses in detail the effect of porosity on aerodynamic forces on bluff bodies.

In this case the resultant force remains primarily at right angles to the plate surface, i. Basic bluff-body aerodynamics 77 about 0. As previously shown in Figure 4. Bearman and Trueman, These variations can be explained by the behaviour of the free shear layers separating from the upstream corners.

These shear layers are unstable, as was shown in Figure 4. During the formation of these vortices, air is entrained from the wake region behind the prism; it is this continual entrainment process which sustains a base pressure lower than the static pressure. Thus the same entrainment process acts Figure 4. Basic bluff-body aerodynamics 79 4. As shown in Figure 4. This results from increased mixing and entrainment into the free shear layers induced by the turbulence.

Observations have also shown a reduction in the radius of curvature of the mean shear layer position Figure 4. This is due Figure 4.

This is representative of the pressure distribution on a tall building in the atmospheric boundary layer. For a given height, h, greater values of roughness length, zo, and lower values of Jensen number, implies rougher ground surface and hence greater turbulence intensities at the height of the body.

The pressure distributions at sub-critical and super-critical Reynolds numbers are shown in Figure 4. Basic bluff-body aerodynamics 83 Figure 4. If the body dimensions are small relative to the length scales of the turbulence, the pressure and force variations will tend to follow the variations in velocity see Section 4. Basic bluff-body aerodynamics 85 Figure 4. This is the basis of many codes and standards that use a peak gust as a basic wind speed see Chapter Also when applied to wind pressures over large areas, it is conservative, because full correlation of the pressure peaks is implied.

These effects and the way they are treated in codes and standards are discussed in Chap- ter The regular vortex shedding into the wake of a long bluff body results from the rolling- up of the separating shear layers alternately one side, then the other, and occurs on bluff bodies of all cross-sections.

Vibration of the body may also enhance the vortex strength, and the vortex- shedding frequency may change to the frequency of vibration, in a phenomenon known as lock-in. As each vortex is shed from a bluff body, a strong cross-wind force is induced towards the side of the shed vortex.

In this way, the alternate shedding of vortices induces a nearly harmonic sinusoidal cross-wind force variation on the structure. It may be expressed in a non-dimensional form, known as the Strouhal number, St.

The Strouhal number varies with the shape of the cross-section, and for circular and other cross-sections with curved surfaces varies with Reynolds number. Some representa- tive values of Strouhal number for a variety of cross-sections, are shown in Figure 4. The variation with Reynolds number for a circular cylinder is shown in Figure 4. Basic bluff-body aerodynamics 89 Scruton, ; Schewe, A slightly decreasing Strouhal number to about 0.

Helical strakes Figure 4. A is a reference area — usually the frontal area. With the quasi-steady assumption Section 4. Similarly the r. The value is around 0. Reproduced by permission of C. This was previously discussed in relation to atmospheric turbulence in Section 3.

The integrand in equ- ation 4. Then equation 4. Then from equation 4. This is an important result that is applicable to structures such as slender towers. The effect of turbulence and the ground surface are covered. Fluctuating pressures and forces, particularly those generated by upwind turbulence, and the regular shedding of vortices by a bluff body are discussed. References Baines, W. Bearman, P. Basic bluff-body aerodynamics 95 Cook, N. Part 2 Static Structures. Building Research Establishment and Butterworths, London.

Engineering Sciences Data Unit E. International , E. Data Item International, Lon- don, U. Gartshore, I. Laneville, A. Jensen, M. Macdonald, P. Marchman, J. Journal of the Structural Division — Melbourne, W.

Wiley Eastern Limited. Schewe, G. Scruton, C. Oxford University Press. Aero Report unpublished. Vickery, B. Wootton, L. There is a potential to excite resonant dynamic response for structures, or parts of structures, with natural frequencies less than about 1 Hz.

The resonant response of a structure introduces the complication of a time- history effect, in which the response at any time depends not just on the instantaneous wind gust velocities acting along the structure, but also on the previous time history of wind gusts.

This chapter will introduce the principles and analysis of dynamic response to wind. Some discussion of aeroelastic and fatigue effects is included. Also in this chapter, the method of equivalent or effective static wind loading distributions is introduced.

Treatment of dynamic response is continued in Chapters 9 to 12 on tall buildings, large roofs and sports stadiums, slender towers and masts, and bridges, with emphasis on the particular characteristics of these structures. In Chapter 15 code approaches to dynamic response are considered. Figure 5. The background response, made up largely of low-frequency contributions below the lowest natural frequency of vibration, is the largest contributor in Figure 5. In the former case, the resonant, or vibratory component, clearly plays a minor role in the response, which generally follows closely the time variation of the exciting forces.

In fact, the majority of structures fall into the category of Figure 5. However the amount of resonant response also depends on the damping, aerodynamic or structural, present.

Lattice towers, because of their low mass, also have high aerodynamic damping ratios. Resonant response, when it does occur, may occasionally produce complex interactions, in which the movement of the structure itself results in additional aeroelastic forces being produced Section 5. In some extreme cases, for example the Tacoma Narrows Bridge failure of see Chapter 1 , catastrophic failure has resulted.

A further source are buffeting forces from the wakes of other structures upwind of the structure of interest. When a structure does respond dynamically, i. In the case of quasi-static loading, the structure responds directly to the forces acting instantaneously at any given time. The effective load distribution due to the resonant part of the loading Section 5. Dynamic response 99 At this point, it is worth noting the essential differences between dynamic response of structures to wind and earthquake.

This means that struc- tures will be affected in different ways, e. However, the eddy structure in windstorms results in partially-correlated wind forces acting over the height of the structure.

Vortex- shedding forces on a slender structure also are not full correlated over the height. Davenport outlined an approach to the wind- induced vibration of structures based on random vibration theory Davenport, , , Harris and B. Vickery , The approach uses the concept of the stationary random process to describe wind velo- cities, pressures and forces. However, we are able to use averaged quantities like standard deviations, Figure 5. The spectral density, which has already been introduced in Section 3.

The latter is calculated from the spectrum of the aerodynamic forces, which are, in turn, calculated from the wind turbulence, or gust spectrum. The frequency-dependent aerodynamic and mechanical admittance functions form links between these spectra.

The use of stationary random processes and equation 5. It may not Figure 5. Dynamic response be appropriate for some short-duration, transient storms, such as downbursts or tornadoes associated with thunderstorms. Methods for these types of storms are still under develop- ment. This is a single-degree-of freedom system, and is reasonably representative of a structure consisting of a large mass supported by a column of low mass, such as a lighting tower or mast with a large array of lamps on top.

The equation of motion of this system under an aerodynamic drag force, D t , is given by equation 5. Writing equation 5. By combining equations 5. The low frequency gusts are nearly fully correlated, and fully envelope the face of a structure.

For high frequencies, or very large bodies, the gusts are ineffective in producing total forces on the structure, due to their lack of correlation, and the aerodynamic admittance tends towards zero.

The approximation of equation 5. The background factor, B, represents the quasi-static response caused by gusts below the natural frequency of the structure. Importantly, it is independent of frequency, as shown by equation 5. For many structures under wind loading, B is considerably greater than R, i.

An example of such a structure is that whose response is shown in Figure 5. The term gust loading factor was used by Davenport , and gust factor by Vickery These essentially have the same meaning, although sometimes the factor is applied to the effective applied loading, and sometimes to the response of the structure. The expected maximum response of the simple system described in Section 5.

From equation 5. This is an approximate approach which works reasonably well for some structures and load effects, such as the base bending moment of tall buildings.

Holmes, ; Vickery, — see also Chapter For this case, Davenport derived the following expression for the peak factor, g. T is the time interval over which the maximum value is required. The gust response factor is also meaningless in cases when the mean response is very small or zero such as cross- wind response.

This approach has been adopted recently in some codes and standards for wind loading. The use of the gust response factor and dynamic response factor in wind loading codes and standards, will be discussed further in Chapter A load effect is not the load itself but a parameter resulting from the loading which is required for comparison with design criteria.

Dynamic response ence lines for the bending moment and shear force at a level, s, halfway up a lattice tower. These are relatively simple functions; in the case of the shear force loads or wind pressures above the level s have uniform effect on the shear force at that level.

It should be noted that loads or wind pressures below the level s have no effect on the shear force or bending moment at that level. Thus wind pressures applied in the same direction at different parts of the roof may have opposite effects on the bending moment at C, Mc. Modal analysis is discussed in most texts on structural dynamics e. Clough and Pen- zien , Warburton Equation 5. If the structure is moving, this should be a relative velocity, which then generates an aerodynamic damping force Section 5.

Then from equation 5. Bendat and Piersol Analogously with equation 5. For the vast majority of structures, the natural frequencies are at the high end of the range of forcing frequencies from wind loading. Thus the resonant components as j increases in equation 5. For example, Vickery found that over twenty modes were required to determine the mean value of a response, and over ten values were need to compute the variance.

Also for the background response, cross coupling of modes cannot be neglected, i. This approach is illustrated in Fig- ure 5. The background component is derived making use of a formula derived by Kasperski and Niemann , and depends on the load effect in question. The resonant component comprises an inertial loading, similar to that used in earthquake engineering.

The approach will be illustrated by examples of buildings with long-span roofs and freestanding lattice towers and chimneys. The main advantage of the effective static load distribution approach is that the distri- butions can be applied to static structural analysis computer programs for use in detail structural design.

The approach can be applied to any type of structure Holmes and Kas- perski, The mean value of any load effect e. However, if the purpose is to derive an equivalent static loading, then equation 5.

Over the duration of a windstorm, because of the incomplete correlations of pressures at various points on a structure, loadings varying both in space and time will be experienced.

It is necessary to identify those instantaneous loadings which produce the critical load effects in a structure. A simple example of the application of this formula is given in Appendix F. The second term on the right-hand side of equation 5. In equation 5. For a vertical structure, the integrations in equation 5. Figures 5. These distributions fall within an envelope formed by the maximum and minimum pressure distri- butions along the arch.

It should also be noted that the distribution for the bending moment at C includes a region of positive pressure. The maxima for these distributions occur at around 70 m height for the base shear and about m for the base bending moment.

An approximation Holmes, b to these distributions, which is independent of the load effect but depen- dent on the height at which the load effect is evaluated, is also shown in Figure 5. Dynamic response Determination of the r. An alternative to equation 5. Examples of the combined distribution, calculated using equation 5. Equations 5. This is the case with the along-wind vibration of tall structures, such as lattice towers of relatively low mass.

The subject of aeroelasticity and aerodynamic stability is a complex one, and one which most engineers will not need to be involved with. However, some discussion of the prin- ciples will be given in this section. A number of general reviews are available of this aspect of wind loads e. Scanlan, When transferred to the left-hand-side of the equation of motion equation 5.

It is a pure translational, cross-wind vibration. Consider a section of a body with a square cross-section as shown in Figure 5. The aerodynamic force per unit length, in the z-direction, is obtained from the lift and drag by a change of axes Figure 4. Dynamic response 5. The body shown in Figure 5. This effective angle of attack can generate both a vertical force, and a moment if the centre of pressure is not collinear with the centre of rotation of the body.

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You must be logged in to Tag Records. Broken link? The nature of windstorms and wind-induced damage 2. Prediction of design wind speeds and structural safety 3. The atmospheric boundary layer and wind turbulence 4. Basic bluff-body aerodynamics 5. Dynamic response and effective static load distributions 6. This paper briefly examines reliability. A report is A form of professional documentation. A working document that could be one page in length or EBSCOhost e- books. You are granted free resale rights of this ebook.

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