james clayton lecture - pennsylvania state university

301

James Clayton Lecture

WIND EFFECTS ON STRUCTURES c. Scruton, BSc, CEng*

After several spectacular collapses caused by wind, there has been increased interest in the accurate prediction of the wind loading to which buildings and structures are subjected. The reliability of these design wind loads depends to a very large extent on the accurate prediction of the most severe wind conditions to be experienced for many years into the future, and on the accuracy of the wind force and pressure coefficients applicable to the structure. Many factors influence these coefficients and hitherto many of these factors have not been reproduced in measurements on models in wind tunnels, so much of the existing data is of

uncertain reliability. For many structures it is suflicient to regard the wind as causing static loadings and for this purpose to use time-averaged wind forces. However, the advent of modern design and fabrication of structures has ren- dered them more prone to respond to the dynamic action of wind. Increasing attention is therefore being given to the time-dependency of the wind forces resulting either from the fluctuations of speed caused by the turbulence of natural wind, or from some form of aerodynamic instability arising from the interaction of the structure with the airstream. The calculation of the dynamic response to turbulent winds involves the application of statistical theories to calculate the maximum amplitude of the response (stress or displacement) and the frequency of its occurrence, coupled with the concept of an acceptable degree of risk that the

structure will not fulfil its functional requirements during its lifetime.

INTRODUCTION I VERY much appreciate the honour your Council has bestowed on me by asking me to deliver this James Clayton lecture. The lecture was first proposed nearly two years ago, and in selecting the topic ‘Wind effects on structures’ the Council was probably influenced by the public interest in the subject current at that time. In 1968 there had been considerable gale damage to housing and engineering structures near Glasgow and the collapse of a block of system built flats at Ronan Point, Newham, although not caused by wind, had managed to engender controversial publicity about the adequacy of the existing specifications of wind loading for the design of tall buildings. These incidents had followed the expensive collapse under wind pressure of three 150 m high reinforced concrete hyperbolic cooling towers at Ferrybridge in 1965. Indeed, engineering literature over the past two centuries is not lacking in references to major disasters to buildings and structures caused by wind, This lecture is published for delivery at an Ordinary Meeting in

London on 24th February 1971. The MS. was received on 3rd December 1970. * Deputy Chief Scientific Oficer, N P L Environmental Unit, National Physical Laboratory,Teddington, Middlesex.

It must be assumed that designers of buildings and structures have, from the earliest times, utilized experience and intuition in their designs to provide against wind action. However, it was not until the collapse of the Tay Bridge in 1879, which was attributed to the effects of wind, that engineers began to assign quantita- tive values to the wind loads; and the Forth Bridge was designed in 1881 on the assumption of a maximum steady wind load of 2-7 kN/m2-a value derived, it has been stated, from considerations of the plate glass windows near the bridge site which had been broken by gales. Since that time, with the aid of measurements on models in wind tunnels, our knowledge of these ‘time-average’ forces, sometimes referred to as ‘steady’ forces, caused by wind has greatly increased, and this knowledge is being refined and extended to the present day. For many structures it is considered sufficient to regard the wind as causing static loadings and for this purpose to use time- average wind forces. However, wind loads are not steady, but fluctuate with time, and increasing attention is now being given by research workers and designers to the dynamic effects produced by these unsteady wind forces. A well known result of the dynamic effects of wind was the destruction in 1940 of the suspension bridge over the

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302 C. SCRUTON

Tacoma Narrows Strait in the United States. This bridge oscillated violently in wind until it broke up. It was this disaster which prompted much research into the causes and prevention not only of the aerodynamic instability of bridges, but also of the wind-excited oscillations of other structures such as chimney stacks, towers, masts and tall buildings which, because of their low frequencies of oscillation and low amounts of structural damping, are especially prone to such oscillations. Unsteady wind forces may result from self-excited instability mechanisms due to the interaction of the structure, or of its motion, with the airstream, or they may arise from the fluctuations of wind speed (gustiness) which are always present in natural winds. Modern methods of design and fabrication, and the tendency to build more slender and econo- mical structures of lower structural density than hitherto are increasing the importance of dynamic effects of wind in design. However, only very exceptionally has structural collapse resulted from oscillations caused by wind. But the limits of amplitude which can be tolerated often depend on other factors, such as the human reaction to

the oscillations (whether judged by the anxiety induced in people in the vicinity or by the discomfort of the occu- pants of a swaying building) and the functional requirements of the structure, for example the requirement that an aerial tower for microwave transmissions shall not deflect to such an extent as to interfere with the direc- tional accuracy of the microwave beam.

A further related topic, involving the interaction between wind and buildings, is that of wind environment and air pollution. This is, perhaps, the concern of the architect and city planner rather than of the structural designer. The effective dispersal of smoke plumes from smoke stacks and of exhaust gases from motorized traffic in enclosed areas or in streets with high traffic densities should now be a matter of planning rather than be left to chance. Similarly, the possible nuisance of high speed and gusty winds induced near ground level by tall buildings, to the inconvenience and discomfort of pedestrians, should be considered at the design stages of the develop- ment. These environmental matters will not be discussed further here, and the remainder of my lecture will be

I 5 5

5d

5 so

5 0'

Fig. 1. Highest mean hourly wind speed a t 33 ft (10 m) likely to be exceeded only once in 50 years

Proc lnstn Mech Engrs 1970-71 Vol 185 23/71



WIND EFFECTS ON STRUCTURES 303

devoted to the steady and unsteady wind loading prob- lems of the structural designer.

TIME-AVERAGE ('STEADY') WIND FORCES Despite the unsteady character of the loading because of wind, it has been the usual practice to regard wind loads as static loads, using time-average wind pressures, forces and moments. The assumption of steady wind loads is probably adequate for the design of most buildings and structures. The values and the distributions of the wind pressures on the external surfaces, the overall wind forces and moments and, for enclosed buildings, the internal pressures, may all be significant design loads. These loads are all dependent to a greater or less extent on the wind characteristics (speed, variation of speed with height, and turbulence) and on the shape and size of the structure and its orientation to the wind direction. Much simplification results from the reduction of wind forces to non-dimensional coefficients. Pressure, force and moment coefficients are expressed by

M and C, = ___ c , = p c . = r 2PV2A +pV2Ad

P F

respectively, where p is the air density, V is the wind speed, and A and d are, respectively, a typical area and a typical linear dimension of the structure. These coefficients are functions of the airstream characteristics, as will be discussed later, but with this limitation values found in small-scale model tests in wind tunnels may be used to estimate the values appropriate to the full-scale structure.

Maximum values of the wind forces which the structure will experience during its lifetime are required for design purposes and this requires the prediction of the maximum wind speed that the structure will encounter for many years into the future. Obviously such maximum wind speeds cannot be other than forecasts obtained by statistical theories using wind data acquired over a sufficient number of years previously. Fortunately in this country the Meteorological Office has very extensive wind records from which the maximum mean hourly wind speeds and short period gust speeds for a return period of 50 years have been predicted, and the information has been made available in the form of isopleth wind maps such as that in Fig. 1 (I)*. This information enables a design wind speed to be related to the anticipated lifetime of the structure and to the degree of risk which is considered acceptable. If T (years) is the return period for a wind speed V, the probability that V is exceeded in N years (i.e. the degree of risk) is

From this relation the return period T can be calculated to correspond to an assumed degree of risk and lifetime of the structure. The relationship between the wind speed V, for a return period T and that of V50 for the * References are given in the Appendix.

0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

B U I L D I N I ; L I F E FACTOR (B.L.F.)

Fig. 2. Factor for building life

return period of 50 years (the period for which wind data are presented in Fig. 1) has been calculated from the basic wind records by the Meteorological Office and presented in the form of a Building Life Factor (B.L.F.) = Vz/V50 in Fig. 2. The latter diagram clearly illustrates the wind load penalties incurred with increase of building life and reduction of the degree of risk.

The wind speed isopleths of Fig. 1 are for hourly means, recorded for the most part on instruments in- stalled in fairly open countryside with only low obstructions, and they have been reduced to refer to the standard meteorological height of 10m. Because of the turbulent nature of atmospheric winds, higher maximum wind speeds are obtained with shorter averaging periods, and the relation between the maximum hourly mean wind speed at height z, Vz and the maximum wind speed V,t averaged over a shorter period t may be expressed by a gust factor F," such that

V:=F,tVa . . . . (2) Within the height of the earth's boundary layer the

wind speed increases with height and for strong winds a simple power law variation is found to represent this wind shear adequately. A design wind speed can then be written (2)

where quantities with suffix 10 refer to values at the standard height of 10 m, K is an adjustment factor to allow for the influence of topography, and y is the exponent for the power law variation of the gust speed V,t with height. The shear and turbulence characteristics of the wind are influenced by the roughness of the terrain over which the wind flows, so that Flat, K and y also have

v," = F1~KtrlO(Z/10)~'Y . . . (3)




C. SCRUTON

1.2

1.0 0 8

0.6 0.4

0.2

CD

304

- Cate- gory

1 -

__ 2

- 3

- c ---.---. . \ \ I - I L---- -

-

--t I

Table 1

Topography

Extreme exposure: large expanses of grasslands, etc. 1.1

Medium exposure : open country with low obstructions- trees, hedges, 2-storey buildings 1.0

Low exposure : built-up areas and areas with high obstructions, towns and cities 10.8 118 1 2.0 1 1.6

values dependent on the topography. Typical estimates of the values for gust averaging periods of 3 seconds and 10 seconds are given for three terrain classifications in Table 1.

In the absence of the more direct information to be obtained from wind measurements at the site, an estimate of Vlo can be obtained from Figs 1 and 2.

The above approach to the assessment of a design wind speed is in broad principle, if not in detail, that adopted for the recently issued British Standard Code of Practice.

While the designer is confronted with some uncertainty with regard to the maximum wind speed which his structure will experience, for a variety of reasons he also lacks precise information on the pressure and force coefficients applicable to his structure. Most of the available information on these coefficients has been obtained from isolated models tested in the smooth uniform wind stream of a wind tunnel. These conditions are usually far different from the environment of the real structure, which is most likely to be in close proximity to other structures and, of course, is exposed to,the turbulent shear flows of atmospheric winds. Also, for Reynolds number sensitive structural shapes, the low Reynolds number at which most model tests are conducted makes for considerable difficulty and uncertainty in their extrapolation to the real structure. The available pressure and force coefficients for a considerable number of basic structural shapes are published in the British Standard Code of Practice and in other compilations, and no attempt will be made to discuss them here. It will be of interest, however, to examine some of the effects of wind characteristics and structural shape and configuration which have often not been reproduced in the tests on which much of the data in these compilations are based.

The influence of Reynolds number on the drag of bodies of simple sectional shape, such as the square and the circle, is demonstrated by Fig. 3. Unless the body has sharp edges or protuberances which fix the positions of the separation of the flow from the body, changes of the flow rCgime occur at critical values of the Reynolds number, resulting in a narrowing of the wake and a reduction in the drag. Quite a moderate rounding of the

r/d=0.167

r /d= 0,333

I

0.8

\d--

104 2 4 8105 2 4 8/06 sand 2 4

r/d=0,5 ( C I R C U L A R SECTION)

Fig. 3. Influence of Reynolds number, corner radius and surface roughness on the values of C, for prisms of square section and circular cylinders (AR = co )

corners of a long square section prism results in a decrease of the drag and in the drag coefficient becoming Reynolds number dependent (Fig. 3). The critical Reynolds number at which the sudden decrease of drag coefficient occurs is influenced by the surface roughness (Fig. 3d). The influence of Reynolds number on the external pressure distribution round the throat of a model cooling tower is shown in Fig. 4. There are large differences in the important peak side pressures as the Rey- nolds number is increased from the sub-critical [Re = 7 . 4 ~ lo4] through the critical [Re = 3 . 4 ~ lo5] and to the super-critical regime [Re = 6-5 x 107. The differences in the base under-pressures on the leeward side (0 = 18O0) are small, indicating that Reynolds number in this case had little effect on the total drag on the overturning moment.

Turbulence in the airstream affects the wind forces in two ways: by modifying the airflow over the body, especially in promoting re-attachment of separated flows ; and by reducing the spatial correlation of the forces. The latter means that the force corresponding to the maximum wind speed is not produced instantaneously over





I I 180

L e e w a r d 50 -2.00

Windward 8 -degrees

Fig. 4. Influence of Reynolds number on the pressure distributions around the throat of a model cooling tower

Smooth s t r e a m

Turbu len t s t r e a m

-0.5 t ( l / U * / h 0.10) L,/D ~ 1 . 3 I

I I I I I 1

0 10 20 30 40

ANGLE OF INCIDENCE-degrees

Fig. 5. Variation of base pressure coefficient on a square- section prism (AR = co) in a smooth and a turbulent airflow

the whole length or area of the structure and so the total force is reduced. The former effect may produce changes of either sign. For a long square section turbulence produces marked changes in the pressure distribution and the base under-pressure is reduced (Fig. 5), indicating a marked reduction in the total drag force.

The pressure distribution and the drag and moment coefficients may be influenced strongly by the velocity profile of sheared winds, and markedly different distributions of pressure over house roofs have been found for the different profile and turbulence characteristics produced by various terrains. When the drag and moment coefficients are referred to the wind speed at the top of the building or structure their values, as would be expected, are less than those in uniform winds. The plot on Fig. 6 of the coefficients of the overturning moment, about the base C,, for circular stack and tank models of differing height/diameter ratios compares the values found for uniform winds with those in winds with shear expressed by the power law exponent of 0.2.

Last in this catalogue of factors with a marked influence on the wind forces are the proximity effects. These are

- O v e r t u r n i n g moment abou t b a s e I M - '12 p G2H2D I

Fig. 6. Moments on circular section cylinder (e.g. smoke stacks and storage tanks) in uniform and sheared flows

the most difficult to assess or discuss because of the end- less variety of configurations of juxtaposed buildings and structures, and because the effects on wind loading may be either adverse or beneficial. The shielding effect of windward structures may reduce the overall forces, but it may also produce an adverse distribution of these forces. An example of this is provided by the collapse in 1965 of three of the group of eight cooling towers at Ferrybridge. The grouping of the towers and the plots of the sectional drag coefficients found from model tests (Fig. 7) exemplify the marked influence of the grouping. Although the overall drag coefficient of a tower in the leeward row is less than that of an isolated tower or of a windward tower in the group, the differences in the sectional drag distribution affect the membrane stress ad- versely. In the three cases considered in Fig. 7 the calculated meridional stresses produced on a windward meridian are greater for Tower 1A and less for Tower 3A than for the isolated tower, and indeed it was the towers 2A, 1A and 1B in the leeward row which collapsed.

THE DYNAMIC RESPONSE OF STRUCTURES TO TURBULENT WINDS

We now depart from the simple deterministic approach to wind loading, in which time-average forces are used in static response calculations, to the more difficult statistical concepts involved in the determinations of the dynamic response. The speed of natural winds fluctuates randomly and because of this the wind will produce randomly fluctuating loads and a corresponding random stress or deflection amplitude response of a flexible structure exposed to it. Because we are now dealing with random variations we must be concerned with the statistical averages of the speed, the loads and the amplitude




C. SCRUTON 306

400

350

300

c cl cl c

I250 n z 3 0 d

W

> 0

4

200

m

$ I 5 0 W w r -

100

50

0

V

I ---- i s o l a t e d t o w e r

2- Tower I A o f

CD= 0.47

c o m p l e t e m o d e l

\ I \ 3- -Tower 3A o f I c o m p l e t e mode l I CD= 0.5 4 \

\\ /'- CD r e f e r r e d t o a v e r a g e d i a m e t e r

'\ Cob r e f e r r e d t o d i a m e t e r

a t local h e i g h t

Fig. 7. Sectional drag coefficients for members of a group of cooling towers

response. These developments, initially pioneered by Davenport (3), have taken place within the last ten years. The statistical concepts used were adapted from those of electrical communication theory and control engineering.

The general principles of the procedure for assessing the dynamic response of structures to wind loading can be most readily appreciated by considering the response of a very simple single-degree-of-freedom system to the random forcing produced by a turbulent wind. But first we must express the properties of the wind in statistical terms. Two relevant quantities are the variance uUa (the mean of the squares of the deviations of the wind speed from the mean F) and the rate of change of the mean square value with frequency (where the mean square value is that €or a narrow frequency band) which is termed the power spectral density function SU(n). For atmospheric winds a normalized spectrum for the longitudinal component of the turbulence u is assumed which is independent of height, wind speed and terrain roughness. In the form suggested by Harris (4), the normalized spectrum is

nSU(n) X * (4) Kplo2 - 4.(2+x2)2)5i6 - - --

where n is the frequency, K is the surface roughness coefficient, Plo is the mean wind speed at height 10m and X = n 9 / P l o , where L? is an arbitrary length to which Davenport assigned a value of 1200m but for

Table 2

gory ~ _ _ _ Gate- I a I 1 0.16 0.005

2 I 0.28 1 0.015 3 0.40 0.050

I I

which recent measurements in England by Harris sug- gest a value of 1800 m.

The above standard spectrum can be used to yield the following expressions for the variance of the wind speed and the turbulence intensity

uu2 = 6*7KPlo2 . . . . (5)

where a is the exponent in the expression for the variation of the mean wind speed with height

and K is the surface roughness. For the different terrains quoted in Table 1 values of a and K are given in Table 2.

The above information relates to the wind speed and turbulence at a point in space. For the design of structures we need to know how extensive the effects of the gusts are, i.e. the spatial correlations of the wind speed, particularly the lateral and vertical correlations of the streamwise component of turbulence. Information on the spatial correlations is scanty, but standard expressions are available (see Harris (5)).

The single-degree-of-freedom system under consideration is shown schematically in Fig. 8.

The equation of motion is m Q + c Q + k Q = P / k . . . (7)

from which we can separate a time-average response = p/k and for the fluctuating component write

mq+ccj+kq = p ( t ) . . . (8)

F o r c e D isp lac

Fig. 8. Single-degree-of-freedom system





If p(t) is expressed in terms of a power spectral density function SP(n) such that

p(t>" = jOm SP(n) dn . . . (9) the response is given in terms of another spectral density function S ( n ) : -

uqz = q(t)2 = lorn Sq(n) dn

= $1" IH(n)12.Sp(n) dn. (10)

1 S y n ) = p IH(n)I2S"(n) . . . (11)

where IH(n)I2 is the transfer function between the power spectral density functions for q(t) and p( t ) and is termed the structural admittance. For the system of Fig. 8

where no = 1/27rd(k/m) is the natural frequency and 1 = c/c, = c / d ( k m ) is the critical damping ratio. An expression for the fluctuating force on a small area A immersed in a turbulent stream is

where V(t) = P+u(t), A and D are typical area and linear dimensions, C, is the drag coefficient and C, is a virtual mass coefficient.

Substituting V(t) = P+u(t) and neglecting the virtual mass term C, and the terms in ~ ( t ) ~ this yields

P = % p A P 2 C D . . . - (14) p ( t ) = pVAu(t)CD . . . (15)

and a relation between the force spectrum and the gust spectrum

P2

V2 SP(n) = 4 - ~ . S " ( n ) . . . (16)

This expression is only valid for a point area where the scales of turbulence are much greater than the typical dimension of the body. For the more practical case where the dimensions of the structure and the turbulence scales are of the same order, we introduce another function, termed the aerodynamic admittance, and write

P2 SP(n) = IX(t~)l~*4.--.S~(n) . . (17)

P2

When this and P = k e are substituted in equation (11) we arrive at a final expression for the spectrum of the response e2

v2 nSq(n) = 41 H(n) I I X(n)I 2 . - * nS"(n) (18)

The steps for arriving at the power spectrum of the response are set out in Fig. 9. Since

uq2 = lorn S4(n) dn = jm nSq(n) d log (n) (19) the form of power spectrum plot of Fig. 9 can be used to find the variance (and hence the r.m.s.) of the response

I n 2 2 2 n)z . - "-'Ed ] + 4 2 (T i ,

Fig. 9. The spectral approach to the determination of the response of a flexible structure to turbulent air- f low (after Davenport)

by simple area integration. From a knowledge of the probability distribution (a Gaussian distribution is often assumed) the variance can be used to find two quantities of interest to structural designers. These are:

(1) The number of times the fluctuating response (stress or displacement) q(t) crosses through a specified value qs in a time T. This is of interest not only because of possible failure due to fatigue but also because of other functional requirements.

(2) The maximum response (stress or displacement) likely to occur within a given time T. For most structures this peak response is found to be roughly 3.5 to 4 times the r.m.s. fluctuation.

The above fluctuating responses have to be added to the mean response due to the mean wind speed to obtain the total response. The mean response is, of course, simply 0 = Flk.

The foregoing treatment for the calculation of the dynamic response of a flexible structure requires a knowledge of the aerodynamic admittance lX(n)I2. Its value will depend on the spatial correlations of the turbulence velocities over the surface of the structure and no reliable theoretical method that can be generally applied exists for its calculation. However, for square flat plates normal to the wind direction Vickery in a N.P.L. Aero Report (1965) has given a theory which is in fair agreement with the measured value, m, when the scale of the turbulence is greater than the plate dimension (Fig. 10). Discrepan- cies between theory and experiment are found when the scale of turbulence is less than the plate dimension.

For a particular structure recourse can be made to wind tunnel tests to obtain more accurate values of the aerodynamic admittance. However, such wind tunnel tests are not simple since to be meaningful the mean shear profile and the turbulence characteristics of the atmospheric wind must be correctly modelled in the wind tunnel. This is not easy, but may be attempted by




308 C. SCRUTON

nD/v

Fig. 10. Comparison of theoretical and experimental values of the aerodynamic admittance for a square flat plate

introducing turbulence producing obstructions at the entry to the working section and as much of the neigh- bouring ground roughness as is practicable (Fig. 11).

The calculation procedures so far discussed refer to a simple spring-mass system and become very much more

complicated when flexible structures are considered and the oscillation mode shapes of a multi-degree of freedom system become involved. The procedures are perhaps too complicated and involved for use in design offices. Attempts have therefore been made to simplify the procedure to such an extent that it can be incorporated in Codes of Practice. This is done by providing tables and charts giving data which enable a dynamic gust factor to be determined, where the gust factor G is defined as the ratio of the expected peak value of displacement in a period T to the mean value. The mean value can, of course, be calculated by conventional methods, but perhaps it would be as well to mention that the design wind speed for such calculation is the long-period (1 hour) mean and not the design wind speed based on the extreme gust as used in the present British Standard Code of Practice, C.P.3, Chapter 5. A typical expression for the gust factor is

G = I+@ { B+- yy’z . . (20)

where g is a ‘peak factor’, the ratio of the peak value expected in a period T to the root mean square of the displacement and is usually equal to 3.5; r is a ‘roughness factor’ depending on the terrain roughness, building height and

Fig. 11. Models of tall buildings in wind tunnel for tests to predict sway amplitudes caused by wind

Vol 185 23/71 Proc lnstn Mech Engrs 1970-71




mode shape; S is a ‘size reduction factor’ which involves the lateral and vertical correlations of the longitudinal component of turbulence and size of building; F is a ‘gust energy factor’ involving the gust or turbulence energy near the natural frequency of oscillation of the building; and 7 is the critical damping ratio for the structure (6).

The comparison between the wind loads assessed on the static and the dynamic procedures depends on a number of factors, especially on the gust period adopted for the static approach and on the amount of structural damping assumed in the dynamic approach, The following comparisons have been extracted from the examples presented at the CIRIA Seminar held in June 1970, on ‘The modern design of wind sensitive structures’. The ratio given is that of the forces or moments assessed by the statistical procedures of the above mentioned seminar to those derived from the static approach of the British Standard Code of Practice, C.P.3, Chapter 5 (1968 Draft Revision) using the design speeds for gusts of 3 seconds’ duration. The assessments refer to a 50 year return period.

Ratio of loads

Lattice lighting rower (Z98 f t high) (a) Forces in leg 0.8 (b) Forces in bracing 0.g5

Rectangular building block (400 f t high) Base moment 0*go

Steel stack (55 ft high) Base moment 0.8

These examples all show that the statistical procedure yields somewhat less severe loading than the static procedures of the Code. It must be appreciated, however, that the comparisons depend sensitively on the characteristics of the structure under consideration and on the terrain roughness assumed. The assumption of a design wind speed of 10 seconds’ duration would considerably reduce the loading for the static approach, while structures of less dampings than were assumed in the above examples would attract larger design loads with the statistical approach.

AERODYNAMIC STABILITY Finally, I want to refer to the oscillatory or divergent instabilities of structures which can arise because of one of a number of possible self-excited aerodynamic instability mechanisms (7). The number of structures which have experienced oscillations from these causes is rela- tively small, but nevertheless these phenomena, because of their spectacular and often catastrophic results, merit very careful consideration in the design stage of any major project.

With the notable exception of the couplings essential to the classical flutter mechanism, which will be referred to later, it can be assumed that the unsteady wind forces

per unit length acting on a structure in one direction are independent of the motion and displacement in other directions, and can be represented by components in phase and out of phase with the motion, and can be written

F(t) = -(K,q+C,i) . . . (21) where q is the displacement, K,q and Cai are restoring and damping fdrces per unit length of the structure due to the wind and K, and C, can be referred to as aerodynamic stiffness and damping coefficients respectively. F(t) can be normalized by dividing by pV2D, where D is a typical dimension (e.g. width) of the structure, so that

1 - F ( t ) = -- (ka+i2ac,)i7 . . (22) pV2D V,2 where the quantities on the r.h.s. are all non-dimensional. Assuming 7 = yo ei2nA‘t, then 7 = q/D, V, = V/ND, C, = Ca/pND2, k, = Ka/pN2D2. Also 6, = Ca/2MN, where 6 , is the logarithmic decrement due to the aerodynamic damping.

If the aerodynamic damping is negative (a negative damping is referred to as an excitation) and is numerically greater than the structural damping 6, (-8, > as), the net log decrement is zero or negative and the oscillations will either maintain or grow in amplitude.

The frequency of oscillation in wind become

Often K, is negligible compared with K, so that N is not influenced by the wind. However, for some structural shapes K, can become negative and, because its value depends on V, - K, = K, at some critical speed, and the net stiffness and the frequency of oscillation become zero, the structure is then subject to a non-oscillatory divergent instability. An example of such a divergent instability is the buckling under wind pressure of thin cylindrical shells. This has occurred on steel tanks during construction and on models of cooling towers (Fig. 12).

With this background to the effects of self-excited unsteady forces caused by wind, we can now review the aerodynamic mechanisms which produce these unsteady forces and, in particular, those which produce the negative aerodynamic dampings which may cause structures to oscillate.

Vortex excitation Vortex excitation, sometimes referred to as aeolian excitation, is the excitation most commonly experienced by structures, and is the cause of most of the wind excited oscillations which have been reported. It is well known that when a fluid flows over a long body of aerodynamic- ally bluff section, the flow separates at the two opposite sides and forms a wake in which the flow is retarded and eddying strongly. The vortices may be regular and periodic in their formation, and be formed alternately, first from

Proc lnstn Mech Engrs 1970-71 * Val 185 23/71



310 C. SCRUTON

Fig. 72. Aeroefastic models of a cooling tower before and after a buckling test in a wind tunnel

one side and then from the other side of the body (Fig. 13). This alternation of the vortices produces an alternating force in line with the direction of the fluid stream but also, and with much greater intensities, in a direction transverse to the stream.

If the body is elastically mounted, oscillations may ensue, particularly when the predominant frequency of eddy shedding coincides with a natural frequency of oscillation of the structure. The frequency of the cross-flow excitation is that of the shedding of complementary pairs of vortices (one from each side of the body) which are shed at a frequency defined by the Strouhal number

- nD s=- V so that cross-flow oscillations would be expected to occur at a wind speed defined by

ND y = - S The Strouhal number is a constant for a specific sec-

tional shape except for its dependence on Reynolds number for those sections the flows around which are sensitive to Reynolds number. Amplitude of oscillations also exerts an influence on the frequency of vortex shedding and in certain conditions can cause the vortex shedding to ‘lock in’ to the frequency of oscillation of the structure

Fig. 13. Schematic sketch of Karman Street from a two-dimensional bluff shape

for a fairly wide speed range. This effect, as well as the dependence of the oscillations on the structural damping, is shown by the stability diagram in Fig. 14 in which the wind speed range for cross-flow oscillations of a model circular section chimney stack is plotted against the structural damping. The Strouhal number for a circular cylinder is 0.2, so that correspondence of the eddy shedding and structural frequencies occurs at V / N D = 5. The oscillations start when the wind speed approaches this value and continue (with the same frequency of oscillation) to a high wind speed which decreases with the structural damping until finally, with sufficient structural damping, the oscillations are eliminated. This closed form of the stability diagram is typical of vortex excitation. In addition to chimney stacks, vortex excited oscillations have occurred on suspension bridges (e.g. the original Tacoma Narrows Bridge shown in Fig. 15), on tubular

3

Fig. 14. Stability diagram for a model circular stack (LID = 37.5)

Proc lnstn Mech Engrs 1970-71 Vol185 23/71




Fig. 15. The plate-girder stiffened suspension bridge crossing the Tacoma Narrows oscillating in wind in the antisymmetric torsional mode before collapse

television masts and suspended pipelines. Vortex formation is responsible for the ‘singing’ of telephone wires and marine propellors and, with the advent of taller slender buildings, vortex excitation may well manifest itself in the cross-flow swaying of such blocks. Bending- type oscillations parallel to the flow direction occur in sympathy with the shedding of discrete vortices, i.e. when V = ND/2S. The excitation is much weaker than the cross-flow excitation ond in-line oscillations are very rarely experienced. With the more powerful input because of the higher density, these streamwise oscillations are more likely to occur in water flow. Recent examples of this occurred during the construction of the deep water jetty at Immingham on the River Humber. The combina- tion of ebb tide and river flow produces flows of up to 2.5 m/s near the jetty. At an erectional stage piles 600mm and 900mm in diameter and about 27 m in length were immersed in the stream as cantilevers, and in this state they oscillated in the flow direction at about V I N D h 2 and more violently in the cross-flow direction at V/ND h 4.5. When the pile was restrained at the top by the concrete platform, violent streamwise oscillations still occurred, and the pile oscillated in a bow string mode. The frequency in this mode was sufficiently high to raise the critical speed for cross-flow oscillations beyond the maximum flow speed occurring at the site.

Another type of oscillation which can occur in response to the discrete vortex shedding is the ovalling or breathing

oscillations of cylindrical shell structures in which the section ovals or distorts as an elastic ring (8). A number of modes for such oscillations are sketched in Fig. 16 and the critical fluid speeds are given by

5ND v, = - r where r = 1,2,3, . . . etc. It seems that this phenomenon has occurred at the top of a number of chimney stacks

2: I

I :I

Fig. 16. Possible relationships between ovalling oscillations and vortex shedding




312 C. SCRUTON

Fig. 17. The ovalling mode of oscillation of a model chimney stack oscillating under wind action

with Y = either 1 or 2. It has been reproduced in model tests (8), as illustrated in Fig. 17.

Galloping-type excitation Fig. 18 shows the stability diagrams for long prisms of square and dodecagonal sections free to oscillate with parallel motions of their longitudinal axes and in winds directed normal to this axis. There are two speed ranges for instability, The lower one is of the enclosed loop type common to vortex excitation; the other is due to a

40

30

Q ‘2 2 c 3

I (

C

I n s t a b i l i t y

vo r t ex ex c i t a t i on/X +--o--~- M a x amp. for

+x--.X-

0.10

”Omax

0 . 0 5

20 40 6 0 80 90

mechanism termed ‘galloping’ because it was first used to explain the slow, large amplitude motions of iced-up transmission lines which attracted this descriptive term. The mechanism for galloping-type excitation depends on the destabilizing character of the variation of the steady ‘time-average’ wind forces with incidence or speed. In its simplest form the excitation is due to a negative lift slope, that is, to a force normal to the wind direction decreasing as the incidence of the wind increases. Some polygonal sections, and some sections created by the deposition of ice on circular wires, etc., have this charac- teristic. As for vortex excited oscillations, galloping excitation produces motion in the cross-flow direction. As the body moves across the wiEd direction, the motion induces a relative wind at incidence to the body and when (as with a negative lift slope) this change of incidence is such as to produce a wind force in the direction of the motion, work is done on the body and instability results. With a knowledge of the static lift and drag curves against incidence, it is comparatively simple to calculate the amplitudes and critical speeds for galloping excitation if a value for the structural damping is available or can be assumed.

For small amplitude oscillations the criterion for galloping excitation is

dC, dC, . . -- dor - -+c, dor < 0

and the slope of the boundary for small amplitude oscillation on the V , versus c, (= 2MS,/pD2) plot is

- 2 / ( Z + C , ) . . Here C,, C, and C, are non-dimensional normal lift and drag force coefficients.

4 0

30

Q 2 2 0 -2

--X--X- Ins t a b i I i t y b o u n d a r y

-O---O--O- M a x . amp. for v o r t e x e x c i t a t i o n , V/ND=5.2

x..x-x-x---x-x e x c i t a t i o n

20 40 60 80 90 Cs ( 2 Ma, /,a D21

0.10

“omox

0.05

0 Square s e c t i o n

Fig. 18. Aerodynamic stability diagrams for long prisms of square and dodecagonal section in smooth airflow

Vol 185 23/71 Proc l ns tn Mech Engrs 1970-71




0 -

The energy input per cycle can be calculated and used to find the aerodynamic excitation in the form of the non- dimensional coefficient (- c,) or the logarithmic decrement (- 8,) :

- S t a t i c p i tch ing moment

---- Ins tan taneous p i tch ing moment dur ing osc i l la t ion

c,=-- 2M8, - -= r C , ( l + t a n 2 a) cos wt dwt PD2 477’71~ o

J

2 5 0 . t: -

. . . (26)

2 Final s t a t e of s t r u c t u r e ( w i t h added moss d u e t o road pavement, ra i l ings ,

This expression can be evaluated by using graphical integration or, mathematically, if polynomial expressions for the variation of C, with cc can be derived.

Icing of the conductor is not the only cause of galloping of transmission lines. The power crossing over the River Severn spffered severely from conductor clashing because of the peculiar aerodynamic effects in quartering winds produced by the lay of the strands. The remedy here was to wrap tape round the conductors to give them a fairly smooth circular section-a section which, because of its symmetry to winds of all inclinations, can have no tendency towards galloping excitation.

Stall hysteresis excitation Stall hysteresis excitation arises from the hysteresis effects on the cyclic attachment and detachment of the airflow from the surface of a body when the body is oscillating about a mean incidence near its ‘stall’ condition. Its effects are to be found in the stalling flutter of aircraft wings and of compressor blades and in the pitching oscillations of bowl-shaped structures such as are used, for example, for microwave beam reflectors and radio telescopes.

If we consider a reflector bowl mounted with freedom to perform pitching oscillations about a horizontal axis through a point near the vertex of the bowl, the static pitching moment curve is typical of the form shown as the full line in Fig. 19. From this it can be inferred that the bowl is stalled with almost complete detachment of the flow for all incidences below about 45 degrees. Above EC = 45 degrees the flow reattaches, at least partly, to the concave surface and the flow tends to become unstalled.

a - d e g r e e s

Fig. 19. Hysteresis of pitching moment of reflector bowl at stall

The instantaneous pitching moment during an oscillation is shown by the broken lines for mean incidences below B,, at A, and above Bz the stalling angle. Hysteresis loops are found in anticlockwise directions for B1 and B2, indicating that energy is transferred from the motion to the airstream and therefore that the reflector bowl has positive aerodynamic damping at these incidences. At a mean incidence near the stall, the motion delays the stall and the recovery from the stall to lower and higher incidences respectively, the resultant hysteresis loop runs clockwise, and energy is extracted from the stream to provide an aerodynamic exciting force.

Model tests for the 250 ft diameter radio telescope at Jodrell Bank showed such an instability in the region of cc = 45 degrees and it was for this reason that the huge ‘bicycle wheel’ damping device was incorporated in the final design.

Proximity and interference effects Wind excited oscillations of a structure may arise, or amplitudes may be increased, because of the proximity of other structures. One of these effects is termed ‘buffet- ing’ and refers to oscillations produced on a flexible structure such as a suspension bridge or chimney stack by the disturbed airflow in the wake of another windward structure. Structures which have no inherent aerodynamic stability may oscillate because of the direct forcing action of the fluctuating air forces produced, and the largest amplitudes will occur when the predominant frequency in the wake coincides with a natural frequency in the structure. Other instability mechanisms due to proximity are evident in the oscillations of arrays of tubes such as are found in condenser banks or in boiler tubes. The airflow and the instability mechanisms in these instances are complex and at the present time our understanding of them is incomplete.

Classical flutter The last instability mechanism which I wish to mention is in a somewhat different classification to those discussed previously in that at least two degrees of freedom are necessary, and the aerodynamic dampings remain positive, but the necessary energy to promote the oscillations




314 C. SCRUTON

Fig. 21. Sectional model of the Severn Bridge spring-mounted in a wind tunnel for tests to predict the oscillatory behaviour in wind

is extracted from the airstream because of the couplings between the freedoms. These couplings may be inertial, elastic, or aerodynamic. The basic theory for classical flutter was developed for the study of the flexure-torsion flutter oscillations of aircraft wings (9). These theories are directly applicable, and have a somewhat simpler application, to civil engineering structures.

Oscillations as a result of classical flutter have occurred in model tests of bowl-shaped microwave reflectors and they may become important considerations in the design and erection of long span suspension bridges. With the more conventional design of bridge suspended roadway

in which deep lattice or plate girder stiffening along the sides is used, the crucial type of instability is usually the single-degree-of-freedom instability either in bending or in torsion, and any tendency to such instability can be overcome by modifications to the structural shape. In- stabilities because of classical flutter are rare with this type of structure. However, following the example of the Severn Bridge, bridge decks of shallow plated box section are now favoured for suspension and cable stayed bridges. The single-degree-of-freedom instability of such decks can be eliminated (as was that of the Severn Bridge) by incorporating suitable edge fairings which ‘streamline’

Fig. 22. The British Pavilion at Expo 70, Osaka, Japan, showing the venting of the limbs of the towers

Proc lnstn Mech Engrs 1970-71 voi 1 a5 23171




the section to reduce the flow separations. It is then found that the aerodynamic characteristics of the section approxi- mate to a flat plate, and classical flutter with vertical bending and torsional freedom involved becomes the crucial type of instability. Classical flutter may become especially dangerous during the erection of the bridge when the full stiffnesses of the completed bridge are not realized, and the frequency in torsion approaches that in the corresponding vertical bending mode. This was so for the Severn Bridge. Flutter calculations indicated a dangerously low critical wind speed for the onset of flutter during erection unless measures were taken to maintain the torsional rigidity of the bridge during erection. With these measures in operation the variation of the critical speed with length of erected span was calculated. It will be seen from Fig. 20 that with about 230 m of the main span erected, the critical speed reached a mini- mum of only 45 m/s. This, however, was not considered to be serious because the probability of the occurrence of a wind of this speed being maintained for a sufficient time for the oscillations to build up to a dangerous level was negligibly small.

Wind excited oscillations of structures are difficult to predict in the design stages, both because of lack of quan- titative data on the unsteady aerodynamic exciting forces and because reliable methods for the estimation of the structural damping (on which the amplitudes of oscillation are sensitively dependent) are not available. The required aerodynamic data can often be provided by tests of models in wind tunnels. Rather than the direct determination of the aerodynamic data, which can then be used to calculate the structural response, the wind tunnel model can be designed for use as an analogue com- puter to give the response directly. For this purpose the model has to be constructed to be dynamically similar to its full-scale prototype and the wind stream required to reproduce the relevant characteristics of the atmospheric wind. The similarity requirements for model and airstream and the practical means of achieving them will not be discussed in this lecture, but they form a most interesting and complex subject for the experimental aeroelastician. The objective of wind tunnel tests may not be so much to predict the structural response as to devise means for the elimination of the excitation or of oscillatory response. Modifications which can be made to provide stability include those to the aerodynamic shape which eliminate or reduce excitation, those to the structure which increase the natural frequencies so that the wind speeds for oscillation are raised beyond the range of wind speed to be experienced, or those which increase the structural damping so that the balance of the energy dis- sipated by structural damping and received by the wind remains positive. Of the above three factors it is to be preferred if an aerodynamic shape can be found and adopted for which there is no tendency to oscillate in wind. Significant changes in the natural frequencies are, for most structures, difficult and costly to achieve, the provision of extra structural damping is not always prac-

ticable, and often damping devices require maintenance if they are to remain effective.

For suspension bridges it is usual to modify the shape or configuration of the roadway deck to obtain the required degree of aerodynamic stability, and these required modifications are indicated and verified by tests on models in wind tunnels. The basic structural shape for the Severn Bridge deck was that of a rectangular plated box. Such a shape, however, was susceptible to oscillation because of the marked flow separation from the edges. Therefore edge fairings were suggested and these, with the overhung sidetracks, provided the necessary streamlining to provide stability. The photograph (Fig. 21) shows a model used for the aerodynamic investi- gation for the Severn Bridge in the wind tunnel at the National Physical Laboratory. Only a short span of the suspended roadway was represented, but this was mounted on a spring system to enable vertical bending and pitching oscillations, corresponding to the vertical bending and torsional oscillations of the complete bridge, to

Fig. 23. A perforated shroud fitted to the top of a model chimney stack to prevent vortex excited oscillations




316 C. SCRUTON

occur. This method of test enables the aerodynamic characteristics of a bridge section to be determined; it also permits modifications of the bridge section to be made easily and their effects on the stability to be readily examined.

For many structures there is not the same freedom to modify the shape to prevent serious flow separations, but with even bluff bodies it is often possible to devise some aerodynamic means of preventing a vortex or other types of excitation. Several schemes of fitting spoilers to cylindrical structures such as stacks and tubular masts have been devised for stabilizing purposes, and in general these operate either by breaking up the airflow pattern, thus destroying the lengthwise correlation of the dis- turbing forces, or by reducing the strength of the vortex formation. Where it is practicable, the latter objective can be achieved by venting the oncoming airstream into the wake formed by the structure, the simple and obvious way of doing this being to perforate the structural shell, One interesting application of this principle was to the twin-legged towers of rectangular section supporting the British Pavilion at Expo 70. Because of their similarity to suspension bridge towers-and with the knowledge that suspension bridge towers, while free-standing, are liable to oscillate in winds (peak amplitudes of 1 m were observed on the Forth Bridge towers during erection)- model tests were conducted to establish whether the Pavilion towers would be prone to instability. These tests

indicated that oscillations as a result of both vortex shedding and galloping excitation were possible. The remedy was to perforate the legs of the tower in the manner shown in Fig. 22. The interesting feature was that the two types of excitation could be controlled and suppressed separ- ately : the galloping oscillations were suppressed by per- forating the faces of the legs running parallel to the wind direction, while the vortex excitation required perforations in the faces normal to the wind direction for its suppression.

For cylindrical structures when perforations of the shell are not permissible, two other devices which can be attached to the structure have proved successful. The perforated shroud device illustrated in Fig. 23 is effective in suppressing vortex excitation, and was used suc- cessfully to stop the oscillations of some experimental piles at Immingham. The helical strake device illustrated in Fig. 24 has been widely used to suppress the oscillations of steel stacks and tubular television masts.

CONCLUDING REMARKS Modern developments in design and fabrication of buildings and structures have increased the importance of wind loading and wind effects. In consequence in recent years wind effects have received more attention than hitherto from both research workers and practising engineers. The deterministic assessment of wind loading in which

Fig. 24. Helical strake devices fitted to the steel stacks of a chemical plant to prevent wind excited oscillations

Proc lnstn Mech Engrs 1970-71 Vol 185 23171




time-average ‘steady’ wind loads are used to obtain a static structural response is giving way to the more realis- tic ‘probabilistic’ approach in which statistical concepts are used to estimate the dynamic response caused by the random fluctuations of the speed of atmospheric winds. Increased attention is also being given to the self-excited oscillations of structures exposed to wind, and to the means for their prevention.

ACKNOWLEDGMENTS The lecture is published by permission of the Director of the National Physical Laboratory.

APPENDIX

REFERENCES

(I) SHELLARD, H. C. ‘Extreme wind speeds over the United Kingdom for the period ending 1959’, Met. Mug. Lond. 1962 91,39.

‘On the estimation of wind (2) SCRUTON, C. and NEWBERRY, C.

loads for building and srructural design’, Proc. Znstn civ. Engrs 1963 25,97.

‘The application of statistical concepts to the wind loading of structures’, Proc. Instn civ. Engrs 1961 19, 449.

(4) HARRIS, R. I. ‘On the spectrum and auto-correlation function of gustiness in high winds’, E.R.A. Report No. 5273 1968.

( 5 ) HARRIS, R. I. ‘The nature of wind’, Proc. CIRIA seminar on the modern design of wind sensitive structures, 1970.

(6) DAVENPORT, A. G. ‘Gust loading factors’, Proc. ASCE engineering conference, Dallas, Texas, 1967.

(7) SCRUTON, C. and FLINT, A. R. ‘Wind excited oscillations of structures’, Proc. Instn Ciu. Engrs 1964 27, 673.

(8) JOHNS, D. J. ‘Wind-induced ovalling oscillations of circular cylindrical shell structures such as chimneys’, Proc. symp. on wind effects on buildings and structures, Loughborough, 1968.

‘The fundamentals of flutter’, Rep. Mem. Aeronaut. Res. Coun. 1948,2417.

‘Preventing wind- induced oscillations of structures of circular section’, Proc. Instn civ. Engrs 1970 47, 1.

(3) DAVENPORT, A. G.

(9) DUNCAN, W. J.

(10) WALSHE, D. E. and WOOTTON, L. R.

Proc Instn Mech Engrs 1970-71 Vol185 23171



james clayton lecture - pennsylvania state university

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