Tall Buildings: The Proceedings of a Symposium on Tall Buildings with Particular Reference to Shear Wall Structures, Held in the Department of Civil Engineering, University of Southampton, April 1966

Tall Buildings provides information and research on tall buildings. This book presents the advances in structural analysis, in methods of design, in methods of construction, and in the properties of materials. Organized into three sections encompassing 27 chapters, this book begins with an overview of the important features of the interaction of a tall building with the wind. This text then examines the reasons for requiring a more rational and refined approach to the wind loading of tall buildings. Other chapters consider the different solutions to the layout of plans for offices and flats using shear walls. This book discusses as well the comparisons made in respect of construction, design, and economy. The final chapter deals with the increase in the number of tall buildings, for both residential and commercial purposes, under construction throughout the world. This book is a valuable resource for civil, structural, consulting, and research engineers.

• Language: English
• Publisher: Elsevier Science
• Release date: Jun 28, 2014
• ISBN: 9781483180960

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Section 1

Wind Loading

Outline

Chapter 1: THE TREATMENT OF WIND LOADING ON TALL BUILDINGS

THE TREATMENT OF WIND LOADING ON TALL BUILDINGS

A.G. DAVENPORT,     Professor, Faculty of Engineering Science, The University of Western Ontario, London, Canada

Publisher Summary

This chapter discusses the significant features of the interaction of a tall building with the wind and to indicate the approaches available for making quantitative estimates of key design parameters. Reasons for requiring a rational and refined approach to the wind loading of tall buildings have become compelling. The new opportunities for carefully tailored design afforded by development of new architectural forms and structural systems, the introduction of a broader range of materials, especially higher strength steels and concrete, the formulation of new methods of analysis, and the application of the computer to the design and analytical processes have created a demand for an exact description of the wind loading that traditional approaches cannot supply. The traditional approach to wind loading that has been used in conjunction with the design of tall buildings and other structures is one in which the wind pressure is assumed to act statically. There is an adjustment for the variation of velocity with height that is sometimes based on the maximum gust variation with height and sometimes on the mean speed variation with height.

INTRODUCTION AND SCOPE

The purpose of this paper is to survey the significant features of the interaction of a tall building with the wind and to indicate the approaches available for making quantitative estimates of key design parameters. Reasons for requiring a more rational and refined approach to the wind loading of tall buildings have recently become more compelling. The new opportunities for more carefully tailored design afforded by development of new architectural forms and structural systems, the introduction of a broader range of materials, especially higher strength steels and concrete, the formulation of new methods of analysis, and, last but not least the application of the computer to both the design and analytical processes have created a demand for a more exact description of the wind loading which more traditional approaches cannot always supply.

The traditional approach to wind loading that has been used in conjunction with the design of tall buildings and other structures is one in which the wind pressure is assumed to act statically. This is convenient in that it has enabled the appropriate coefficients of pressure to be estimated from wind tunnel tests carried out in a uniform steady velocity in a wind tunnel. The velocity used in design has been variously determined from maximum gust speeds, or average velocities measured over a minute of a mile of wind, depending on the nature of the routine meteorological measurements. There is usually an adjustment for the variation of velocity with height which is sometimes based on the maximum gust variation with height and sometimes on the mean speed variation with height. The resulting pressures usually are in the range 15–50 lb/ft² and are applied to various elements of the structure such as the main frame and the glass. For steel structures higher stresses are normally permitted in the case of wind loads.

Although convenient, this quasi-static approach to wind loading is unrealistic in several respects as this paper describes. Furthermore, there is a need for broadening the basis of design against wind to include more explicitly such factors as allowable deflections, comfort of occupants and fatigue of the frame, as well as strength. The diversity of structures now being built makes the problem of formulating wind loads using simplified umbrella loadings more and more difficult if at the same time they are to be economical and satisfactory from a performance standpoint.

Recent research such as that presented at the 1963 Conference on the Wind Effects on Structure held at the National Physical Laboratory has indicated some of the directions that these improvements should take.

OBSERVATIONS OF THE BEHAVIOUR OF TALL BUILDINGS IN THE WIND

The use of static wind loads in the design of tall buildings, although convenient, can at times lead to a false impression as to the real behaviour of a tall building—or any structure for that matter—in the wind. In the natural wind over a city a tall building is constantly buffeted by gusts and other aerodynamic forces and although it does tend to deflect toward a mean position it is continuously swaying with an amplitude which may be at least as large as the steady deflection. This continuous swaying motion is illustrated in Fig. 1, which is taken from actual observations on tall buildings.* In describing the observations on the Empire State Building, Rathbun (1940) states that the building tended to vibrate continuously like the tines of a tuning fork. All the traces show that the sway motion occurs primarily in what turns out to be the fundamental frequency of the building with little evidence of the higher harmonics.

FIG. 1 Dynamic response of tall buildings in the wind.

Although seldom considered explicitly in the design of tall structures, the sway motion is in fact probably the most significant aspect of the behaviour determining whether a structure performs satisfactorily or not in service. The sway acceleration directly determines the comfort of occupants and a large proportion of the total deflection, which governs the cracking of walls, is due to sway. The fact that the dynamic response is influenced by factors other than stiffness alone, such as the mass and damping, and the fact that the criterion of performance cannot be based on stress and strength considerations only but also on other factors such as deflection, acceleration and fatigue makes design for the dynamic effects of wind more subtle.

In order to develop an approach for the design of tall buildings against the wind it is first necessary to understandin general terms the character of the wind and the important factors which influence its action on buildings. While it cannotbe pretended that the understanding is yet complete, recent research has clarified a great deal and provided a framework in which to fit ideas.

THE RELATIONSHIP OF METEOROLOGICAL FACTORS TO WIND LOADING

†

The motion of the atmosphere, as it is manifested by the wind, is compounded of air movements of a very wide range of scales. On the very large scale there are seasonal fluctuations in the wind. On a scale comparable with the weather maps seen in the press or used on airlines there are large scale fluctuations identified by the patterns of isobars moving across the country. On a still smaller scale are fluctuations which are best observed on high speed anemometer records. Such a record is shown in Fig. 2 which was obtained from three instruments mounted on a tall mast.

FIG. 2 Record of wind speed at three heights on a 500 ft mast.

It is convenient for analytical purposes to separate the widely different scales of fluctuations into two categories. The large-scale fluctuations, down to the scale of weather map fluctuations, will be referred to as fluctuations in the mean velocity. Fluctuations of a much smaller character such as those appearing in the anemometer record will be referred to as gusts.

It turns out, for reasons stated elsewhere, that mean wind speeds averaged over a 10 min−1 hr period are reasonably stable quantities and are unaffected by slight shifts in the time origin. This is evident from the constancy of the mean velocity in Fig. 2. This is less true of shorter averaging periods, and speeds averaged over a minute may differ radically from minute to minute. This may also be seen from the anemometer record in Fig. 2. A 10 min or 1 hr average, therefore, represents a suitable unit to define the mean velocity. The characteristics of the mean flow and gusts are now described separately.

Properties of the Mean Wind

Reference to Fig. 2 suggests that the mean wind speed at each of the three heights remains more or less constant throughout the period of record and gust fluctuations take place about this mean. A further feature revealed by this record is that the magnitude of the mean velocity increases with height. This increase of the mean velocity with height is a fairly well understood phenomenon. The rate of increase is very much influenced by the roughness of the terrain as suggested in Fig. 3 (see Davenport, 1960, 1963a).

FIG. 3 Profiles of mean wind velocity over level terrains of differing roughness.

This variation of velocity with height is best considered as a gradual retardation of the wind nearer the ground due to surface friction. At heights great enough for the wind to be virtually independent of surface friction the wind moves freely under the influence of the pressure gradient and attains the so-called gradient velocity. The height at which this occurs is the gradient height. Figure 3 suggests typical mean velocity profiles (discussed elsewhere) for a nominal gradient wind speed of 100. This shows that the wind speed at 100 ft in a city is approximately one-quarter of that in open country. This reduction in velocity in a city is well confirmed by the figures in Fig. 4, which compares the wind speeds in cities and their local airports in the United States (see Davenport, 1963a). Although anemometers in the city are generally mounted higher above ground than at the airport, the mean wind speed is seen to be invariably lower.

FIG. 4 Comparison of one-in-50 year wind speeds at airports and city meteorological stations in the United States.

Climatological Properties of the Mean Wind

The properties of the mean wind can only be conveniently expressed statistically. Several statistical properties are ofvalue in structural engineering design. One is the overall distribution of wind speed not taking direction into account. This generally follows a Rayleigh distribution or a curve having similar characteristics as shown in Fig. 5. From this curve the total proportion of time during which the mean velocity is in excess of certain values may be determined.

FIG. 5 Rayleigh distribution of wind speeds at 500 m at the John F. Kennedy Airport, New York City.

A second statistical distribution of use is the extreme value distribution of annual maximum wind speeds. A typical distribution of maximum annual wind speed is shown in Fig. 6 for New York City. Other results, including those from Shellard’s useful study of meteorological stations in the United Kingdom, are given by Shellard (1963), Hanai (1963) and Davenport (1963a). This type of distribution enables the estimates of the average recurrence interval of very strong wind speeds to be ascertained. Two parameters in this distribution are important—the mode U and the dispersion velocity 1/a. Knowing these two parameters the extreme wind speed expected on average every r years can be determined from the equation:

FIG. 6 Comparison of observed distribution of maximum monthly 5 min. wind speed in New York City at 450 ft (1884–1950) with type I extreme value distribution.

(1)

Usually a return period of 30 or 50 years has been adopted. This choice could be given greater consideration than it has been in the past and related more rationally to the specific item of consideration—whether it is design for strength, deflection of sway, whether it is the main structure being considered or the glass.

There are usually a number of difficulties in evaluating meteorological records, particularly when they are taken over a long period of time. It is more often than not the case that instruments are moved and replaced, elevated or lowered several times during the period of record. These translations generally significantly affect readings. More often than not the character of the surroundings changes due to the encroachment or removal of buildings, trees, etc. This also affects the indicated wind speed. A further problem exists in estimating the relationship of the wind speeds at the observing station to those at a building site.

To obviate some of these difficulties and in order to minimize the errors associated with using records obtained from single anemometers the writer has proposed using a gradient wind speed map (Davenport, 1961a). This was obtained by estimating the effective roughness of the meteorological station and hence estimating the statistical properties of the gradient wind from the surface estimates using a mean velocity profile corresponding to the roughness. The parameters derived from this study are shown in Fig. 7. Estimates of surface mean wind speeds are obtained from the extreme gradient wind speed using the profiles given in Fig. 3.

FIG. 7 Parameters of extreme mean hourly gradient wind speed over the British Isles.

Turbulence Structure

Study of Fig. 2 reveals a number of characteristics of gusts which are significant from the viewpoint of wind loading. As remarked above, the mean velocity at each height remains effectively constant throughout the period of record but increases with height. The amplitude of gust fluctuations is more or less constant with height with approximately the same rate of fluctuation. The similarity in the fluctuations at the different heights is very little in the case of the rapid changes but slower variations of a minute or so are detectable at all heights.

The character of turbulence is most conveniently and succinctly expressed in statistical terms. (For a full discussion see Lumley and Panofsky (1964); Davenport, 1963a.) The fluctuation characteristics of turbulence can be expressed in terms of the power spectrum of turbulence and the associated probability distributions. A procedure to obtain the spectrum is to represent the fluctuating velocities shown in Fig. 2 by an electrical voltage, record this voltage on magnetic tape, and play the tape through filters which suppress all fluctuations except those having a frequency close to a chosen frequency. If this filtered signal is fed to a wattmeter measuring power, the resulting level on the meter indicates the power at the chosen frequency. The plot of the power for various selected frequencies gives the power spectrum. The spectra of the various components of turbulence near the ground in strong winds can, it appears, be represented satisfactorily (see Davenport, 1961b) by universal functions of the type

(2)

in which S(n) is the power per unit frequency interval at frequency nis the mean velocity, L is a length scale, and K is the surface drag coefficient depending on the roughness.

The form of the horizontal spectrum of wind speed is illustrated in Fig. 8. As indicated, empirical expression is derived from experimental results from a wide variety of localities. Berman (1965) has recently reconsidered the problem. It appears that the length scale L is relatively invariant with height. The spectrum of vertical velocity is similar in form but of slightly smaller magnitude and the length scale is more or less proportional to height. The lateral velocity spectrum appears to be similar to the speed spectrum but the power is about two-thirds that of the speed.

FIG. 8 Spectrum of horizontal gustiness in high winds.

The similarity of the fluctuations at different heights can be expressed by the narrow band correlation (or coherence) function. The correlation coefficient varies between +1 and −1. A value of +1 indicates complete correlation between velocities, −1 a complete antiphasal correlation, and 0 a random association. It has been shown that the correlation in the velocity fluctuations of frequency n at two heights separated by a distance ΔZ is given closely by the expression

(3)

The value of C ). Two slower fluctuations in gusts which therefore have longer wave-lengths are effectively larger. Clearly, both the size and the power present in gusts influence the response of a structure to turbulence.

The third property that is required to define the turbulence characteristics is the probability distribution. (Perhaps the term relative frequency is more apt but this requires the word frequency to do double duty in describing the rate of fluctuation as well.) It appears, on both theoretical and experimental grounds, that turbulence has a probability distribution which is normal or Gaussian. Such a curve is depicted in Fig. 14.

This probability distribution can be written

(4)

This expresses the probability that a velocity less than V and the standard deviation or root mean square fluctuation σv, both of which are found straightforwardly. An important fact is that the mean square fluctuation is in fact a measure of the total power of the turbulence, and is, therefore, related to the spectrum by the equation

(5)

that is, the area under the spectrum. This is indicated in Fig. 14.

If the spectra, correlation functions and the probability distributions are known, all of the turbulence properties, significant from the viewpoint of wind loading, are defined.

The Action of the Wind on a Tall Building

The mechanism whereby pressures are induced on a bluff body by a flow field is still incompletely understood. This is particularly true of the fluctuating forces generated by gusts in the flow. An impression of the nature of the wind pressures can be obtained from the oscillograph traces shown in Fig. 9 which were obtained from a model in turbulent boundary layer. The test arrangement in the new boundary layer wind tunnel at the University of Western Ontario is similar to that shown in Fig. 27. The nature of the fluctuating pressures is similar to that found by Newberry (1965) in his experiments on tall buildings in London, England.

FIG. 9 Measurements of pressure on a model of a tall building in a turbulent boundary layer.

It is apparent from Fig. 9 that the fluctuating pressures are of the same magnitude as the mean pressures. The frequency of the more significant pressure fluctuations turns out to be of the same order as the natural frequency of a typical building. This accounts for the sway amplitudes shown in Fig. 1. (The reduced time scaling can be converted to real time by substituting the real wind velocity and building diameter. For example, for a 100 ft/sec wind speed and building 100 ft in breadth the time between marks is 500 sec or about 8 min real time.)

It is convenient to treat the effects of steady and fluctuating pressures separately.

Steady Pressures

The steady pressures arising on structural shapes have been the subject of considerable research, the ground work for which was laid by such persons as Gustaf Eiffel (1914), Irminger and Nokkentved (1930), Ackeret (1936) and Stanton (1907–8). In these studies pressures were measured by means of pressure taps in the faces of the model and connected to manometer boards. It is unfortunate, perhaps, that with only one exception, due to a singular series of tests by Bailey and Vincent (1943), all these tests were carried out in a uniform airstream. Justification for this was based on the assumptions that this approach would be conservative, and that the real structure of the wind in nature could seldom be established accurately anyhow. It would seem today that the first reason is not necessarily true and the second is perhaps unduly pessimistic.

The importance of testing in a representative boundary layer profile was stressed by Jensen (1958) in his important paper entitled The Model Law for Phenomena in the Natural Wind. Comparison of the pressures on a simple structural shape in two different boundary layer flow conditions are shown in Fig. 10 (cf. Jensen, 1965). Baines (1963) has used graduated screens to generate velocity profiles in the wind tunnel and has also demonstrated that the steady pressures developed in a boundary layer are highly dependent on the mean velocity profile.

FIG. 10 Comparison of distribution of mean pressure coefficients on a tall building in two boundary layer velocity profiles (after Jensen). H = building height, Z0 = roughness length. Reference velocity pressure at top of building.

DYNAMIC ACTION OF THE WIND

The dynamic action of the wind on tall buildings can be associated with the following influences.

(1) Buffeting by gusts.

(2) Buffeting by turbulence and vortices shed by the structure itself.

(3) Buffeting by the wake from another structure.

(4) Aerodynamic damping.

Buffeting by Gusts

Although it may be some time before the action of turbulence on a bluff obstacle is fully understood, some progress in describing its action has been made through the application of statistical concepts as described by Davenport (1961a, 1962, 1963, 1964a). Some insight into the action of turbulence on a tall building can be obtained by considering the typical section depicted in Fig. 11. This diagram indicates that the fluctuating forces acting on the section due to small fluctuations in velocity δu and δv are, assuming quasi-steady conditions,

FIG. 11 Response of a single tower to fluctuations in velocity.

(6)

is zero through symmetry and we have typically

(7)

and the torque. It is apparent that the spectrum of the force on the section in the x direction nSFx (n) can be written

(8)

0 is a reference velocity at the top of the building where nSu(n) and nSv(n) are the velocity spectra of u and v. Similar expressions for the δFy and δT spectra can be written.

To determine the response of the structure as a whole the response can be analysed in terms of its principle modes of vibration. This is appropriate in view of the predominance of the fundamental mode of vibration. Assume that the rth mode shape is μr(z) and is chosen such that

(9)

where z is the vertical ordinate expressed as a fraction of the total height as shown in Fig. 12.

FIG. 12 Typical mode shapes and natural frequencies for a moderately tall building.

The mean square generalized force corresponding to this mode of vibration denoted by ϕr is