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Codification of Wind Loads on

Wind-sensitive StructuresJohn D. Holmes

Director, JDH Consulting, Australia

Received January, 24, 2008; Revised version February, 24, 2009; Acceptation March, 03, 2009

ABSTRACT: Codified approaches for allowing for along-windresonant response of tall structures are reviewed. In particular the‘gust loading factor’ (GLF) format, used in codes and standardsbased on mean wind speeds (normally with an averaging time of 10minutes or 1 hour) is discussed. The alternative ‘dynamic response

factor’ (DRF) format, generally adopted by codes based on peak(nominally 3-second) gust wind speeds is also described. Theexplicit, or implicit, effective static wind load distribution inherentin these approaches is also discussed. The codification of the cross-wind response of tall structures of rectangular or circular cross-sections is also considered. A comparison of cross-wind forcespectra for some rectangular cross-sections used in current codesand standards is made. Some consideration of the codification of wind-induced fatigue is given. Finally the present use, and futurepotential, of internet-based design methods for dynamic wind loadsis discussed.

Keywords: Buildings; Codes; Dynamics; Fatigue; Towers; Vibration; Wind

loads.

1. INTRODUCTION

It is well known that as structures become taller (or

longer), they become more dynamically sensitive to

fluctuating wind loads in large-scale synoptic wind

events, arising from upstream turbulence, or from

wake- and vortex-induced forces. Many important

structures have specific wind engineering studies

carried out for them, usually involving wind-tunnel

tests. However, there is a large class of structures,

which have some dynamic sensitivity to wind, but for which the time and expense of special wind

engineering studies cannot be justified. In other cases,

such as chimneys, towers or masts of circular cross-

section, wind tunnels cannot give reliable results for

scaling reasons.

There is an important part to play by wind loading

codes and standards, and related desk-top approaches

in the design for wind of dynamically sensitive

structures – either for structures for which extensive

wind engineering studies (including wind-tunnel tests)

cannot be justified, or in preliminary design stages of

more complex structures. This paper reviews the basic

concepts and design approaches adopted by several

advanced wind codes and standards, and related

design-oriented sources, for resonant response to

wind. Both along-wind and cross-wind forces and

response are considered.

The paper primarily focuses on codification

approaches to the dynamic response of tall buildings

and towers, and smaller cantilevered structures such aslighting poles. Structures such as large roofs and

bridges are not discussed in this paper; generally the

behaviour of these structures to winds is too complex

to allow simplified code methods to be applied.

2. ALONG-WIND RESPONSE

2.1 History The earliest modern approach to codification of the

dynamic response of structures was the ‘gust

loading factor’ (GLF) approach proposed nearly

International Journal of Space Structures Vol. 24 No. 2 2009 87

•Corresponding author. E-mail Address: [email protected]

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88 International Journal of Space Structures Vol. 24 No. 2 2009

Codification of Wind Loads on Wind-sensitive Structures

Figure 1. A Simple Dynamic System for Determination of

Gust Loading Factors.

simultaneously by B.J. Vickery [1] and A.G.

Davenport [2]. This followed earlier pioneering work

by Davenport on the application of random process

theory to the wind loading of structures. Davenport

had earlier developed a gust loading factor for the

Danish Standard.

In 1968, Vellozzi and Cohen [3] developed asimilar approach for a ‘gust response factor’ (in fact

conceptually identical to the GLF) that was adopted in

the ANSI wind loading standard of 1972. It

introduced the effect of the along-wind correlation,

which was intended to account for the less than

perfect correlation between windward and leeward

pressure fluctuations on a building. There were a

number of other developments and refinements for

tall buildings in the nineteen-seventies and -eighties.

Amongst these, Vickery [4] in 1971 considered the

variability and reliability of GLF estimates,introduced a size factor based on the cross-spectral

density of the upwind velocity fluctuations, and

considered the effects of nonlinear mode shapes.

Simiu [5,6] corrected the implementation of

windward-leeward wall correlation by Velozzi and

Cohen, and introduced more ‘meteorologically-

correct’ wind spectra and velocity profiles. Solari [7]

developed Simiu’s procedure with closed form

approximations for easier application.

As early as 1976, the Engineering Sciences Data

Unit in the U.K. introduced a detailed calculationmethod for along-wind response of flexible

structures [8]. This did not explicitly use the GLF

format, but was based on the same random vibration

concepts and theory. However, it introduced several

new refinements to the calculations: separate peak

factors for background and resonant response,

calculation of load action effect such as bending

moments and shear forces, and the inclusion of

aerodynamic damping. In these respects it was

significantly ‘ahead of its time’. In the Guide to the

British Standard on Lattice Towers and Masts of 1986 [9], detailed equations were given for the

evaluation of gust (loading) factors for lattice towers;

a particular innovation was the consideration of

cross-bracing members with influence lines with sign

reversal. However, the full dynamic method was not

implemented as part of the Standard itself.

Milford [10] developed a simplified GLF

calculation method for lighting poles and masts, using

simplifications resulting from the small frontal areas

exposed to wind forces. This method was incorporated

into a South African Code of Practice for LightingMasts.

2.1 Gust Loading Factor – Basic Derivation In all the references discussed previously, the gust

loading factor is calculated on the basis of the

generalized deflection of a structure assumed to move

in the first sway mode of vibration. In the derivation of the expressions for the GLF, the dynamic behaviour of

a building, or other tall structure, is usually simplified

to that of a simple single-degree-of freedom system, as

shown in Fig 1. Using this concept and random

process theory, the spectral density of the deflection, x,

can be simply related to the spectral density of the

applied (drag) force as follows :

(1)

where |H(n)|2 is a ‘mechanical admittance’ function.A modification of Eqn 1 replaces the response

variable x, by the internal spring force, k.x, denoted by

D*. Then Equation (1) becomes:

(2)

The velocity fluctuations do not occur

simultaneously over the windward face of a large

building, and their correlation over the whole area

must be considered. To allow for this effect, an

aerodynamic admittance, X 2(n), was introduced.

Then, (3)

X 2(n) is usually determined from the correlation

properties of the upwind velocity fluctuations, on the

assumption that the building does not distort the

approaching turbulence in the wind.

The expected maximum deflection response of the

simple system in Figure 1, can be written :

(4)x̂ x g x= + σ

S (n)1

kH(n)

4D

U. (n).S (n)x 2

22

2

2

u= X

S (n) H(n) S (n)D*

2

D=

S (n)1

kH(n) S (n)x 2

2

D=

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where is the mean deflection, σx is the standard

deviation of the deflection, and g is a peak factor,

which depends on the time interval for which the

maximum value is calculated, and the frequency range

of the response.

Then the gust loading factor is given by :

(5)

where σu is the standard deviation of along-wind

turbulence fluctuations, is the mean wind speed, B

and R are background and resonant terms, resulting

from the integration of the right-hand-side of Eqn 3

over all frequencies.

Thus, the GLF is essentially the ratio between the

expected maximum response (e.g. deflection or stress)

in a structure and the mean response, with the implied

representation of wind loading as a stationary random

process. It should be noted that in the simple model of

Figure 1, the GLF for deflection, Gx, is identical to that

for the internal force, GD*, since x and D* are related

by a constant factor, k. However, this simple

relationship does not apply for real structures with

distributed mass and stiffness. The variability of the

GLF with the response parameter is explored in the

following section.

The gust loading factor concept is retained, in its

original form, in the National Building Code of

Canada [11]. A similar form is adopted in the

Architectural Institute of Japan Recommendations

[12]. Other international codes and standards have

adopted a ‘dynamic response factor’ format, discussed

in a later section of this paper.

More details on the application of random process

theory to wind loading of structures are given in [13].

2.2 Modification for Cantilevered Towers The GLF was proposed primarily for tall buildings, in

which the resonant response to wind can often be

assumed to be restricted to the lowest sway dynamicmodes. Reducing the structure to a single-degree-of

freedom (mass-spring-damper) and calculating the

GLF for the deflection – as discussed in the previous

section - is equivalent to calculation of the GLF for the

generalized coordinate in the first mode of vibration.

However this GLF is not necessarily identical to the

GLF s for responses such as bending moment or shear

force at any elevation on the structure, or even the

actual deflection at the top of a tall structure. The

model developed by Holmes [14,15] enables the GLF

as a function of response variable to be determined.This model was originally developed for lattice towers,

U

G Gx

x1 g

x1 2g

UB Rx D*

x u= = = + = + +ˆ σ σ

x but can be applied to any prismatic or tapered structure,

for which a uniform drag coefficient is applicable.

The formulae for determination of the GLF s are as

follows:

Generalized co-ordinate:

(6)

Shearing force at any elevation:

(7)

Bending moment at any elevation:

(8)

Deflection at the top:

(9)

Bs, S and E are background, size and gust energy

factors, respectively. r is a roughness factor, equal to

twice the turbulence intensity (σu / ), evaluated at the

top of the structure. gB and gR are peak factors

separately evaluated for the background and resonant

response. s is the height at which the bending moment

or shearing force is required.

The factors F1,F2, ….…… F12 are defined in Refs 14

and 15, and account for the exponents of the mean

velocity profile and mode shape, and the mass

distribution and taper ratio on the structure. They alsoincorporate the elevation at which the shearing force or

bending moment are being evaluated. Note that, unlike

the simple structure of Fig 1, the GLF s for deflection,

and for internal forces such as shearing force and

bending moment, are not identical to each other.

Eqn 6 is representative of the usual GLF

calculations in codes and standards.

Comparisons of GLF calculated for the generalized

coordinate (using Eqn 6), and for the bending

moments and shear forces at various heights (using

Eqns 7 and 8) on a 160-metre tall tapered lattice tower,and a 183-metre tall building, of uniform cross section,

U

G

r g B F gSE

F F F

Fx

B

2

0 11 R

2

1

3 4 12

1

= +

+

1η

00

G

r g B F gSE

F F F

Fm

B

2

s 7 R

2

1

3 4 8

6

= +

+

1η

G

r g B F gSE

F F F

Fq

B

2

s 2 R

2

1

3 4 5

1

= +

+

1η

G 1 r g B gSE

B

2

s R

2

1

= + +

η

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Table 1. Comparison of GLF’s for Various Load

Effects – 160m Tapered Tower

(mean wind speed at top of tower = 30 m/s)

Load effect GLF

Generalized coordinate 1.69

BM at 0 m 1.74

BM at 80 m 1.89

BM at 120 m 2.02

SF at 0 m 1.77

SF at 80 m 1.87

SF at 120 m 2.00

Table 2. Comparison of GLF’s for Various Load

Effects – Tall building (183 m)

(urban terrain – mean wind speed at top of tower

= 30 m/s)

Load effect GLF

Generalized coordinate 2.14

BM at 0 m 2.21

BM at 90 m 2.31

BM at 135 m 2.36

SF at 0 m 2.25

SF at 90 m 2.31

SF at 135 m 2.36

are tabulated in Tables 1 and 2, respectively. These

Tables show that the GLF for the generalized

coordinate underestimates the GLF for both BM and

SF at all elevations. The GLF increases with elevation

of the load effect, for both the tower and the tall

building In the case of the tower, the increase is more

significant. The reasons for the last effect are the

greater importance of both the background and the

resonant components at the higher elevations, in

comparison with the mean wind loading. In the case of

the background contribution, this is because of the

reduced height for correlation of the applied

fluctuating forces; for example for a load effect

evaluated at half height, the effective height over

which the wind forces are reduced due to correlation

effects is reduced by a factor of two. In the case of the

resonant contribution, the effective (inertial) loads are

more highly weighted to the top of the structure than is

the mean wind loading.

2.3 Dynamic Response Factor In codes and standards which are based on a gust

loading (typically a 3-second gust) rather than a meanwind loading, use of a ‘dynamic response factor’

(DRF) is more appropriate than a GLF or GRF. This

approach is also better for transient, or non-stationary,

winds, such as downbursts from thunderstorms.

The DRF may be defined in the following way:

(10)

The DRF is an expression of the following ratio:

(maximum response including resonant and

correlation effects)

(maximum response calculated ignoring both

resonant and correlation effects)

Note that for codes and standards based on a gust

wind speed, the gusting effects are incorporated in the

wind speed itself. The DRF as defined in Equation

(10) simply modifies the loading to account for

correlation and resonant dynamic effects.

The denominator of Equation (10) is proportional to

the ‘gust envelope’ response calculated using ‘static’

methods in codes and standards. The dynamic response

factor, as defined above, will usually have a value close

to 1.0. A value greater than 1 can only be caused by a

significant resonant response. The turbulence intensity,

Iu in the denominator is usually taken as a single value

– i.e. that at or near the top of the structure. In this case,

a single value of cd results for all heights on the

structure. A direct conversion from a GLF approach

would require the turbulence intensity in the

denominator, and hence cd, to vary with height, z.

The dynamic response factor format has been

adopted for ASCE-7 [16], by the Australian/New

Zealand Standard [17], and by the Eurocode [18]. In

ASCE-7, it is known as a ‘gust effect factor’; this is a

rather confusing terminology (retained from earlier

versions of ASCE-7) as the gust effects are already

incorporated through the use of a 3-second gust speed.

2.4 Effective Static Loading Distributions In the original concept of the GLF, it is implied that thepeak effective loading should be distributed over the

height of the structure with the same distribution shape

as the mean wind loading, but factored by the GLF

itself. For codes and standards using the DRF format,

the basic effective distribution of wind loading with

height is the distribution of gust envelope loading; the

magnitude of this is factored up or down by the DRF.

Zhou and Kareem [19] recommended an approach

for the ASCE-7 Standard in which the resonant

component is distributed correctly as inertial loads,

with the mean and background components distributedas the mean loading. Although this approach is an

c1 2I g B g R

1 2gId

u B

2

R

2

u

=+ +

+

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John D. Holmes

improvement, it is also not completely correct. Figure

2 shows the correct effective distributions of mean,

background and resonant loads for the base bending

moment on the 160 metre tall tapered tower,previously discussed. These distributions are

consistent with Equation (8) for the gust loading factor

for base bending moment, Gm, with s set equal to 0.

The background component has its own distribution

which is neither the mean nor the inertial loading. On

average the distribution of background loading is

proportional to the correlation coefficient between the

load effect (i.e. the base bending moment in the case of

Figure 2), and the fluctuating wind pressure at each

height.

As discussed earlier, the effective static loaddistribution implied by the use of the DRF is

proportional to the peak gust envelope. For a structure

with a small resonant response, this is a better

approximation to the correct combined effective static

load distribution, than is an effective load distribution

based on the mean load distribution, as used in codes

and standards adopting the GLF format.

3. CROSS-WIND RESPONSE

The cross-wind dynamic response of structures can be

as significant as the along-wind response for several

classes of structure:

a) Tall buildings – say greater than about 100 metres

in height,

b) Cantilevered structures of circular cross-section,

such as chimneys or lighting poles,

c) Horizontal structures such as long-span bridges

or stadium roofs of very large dimensions.

On the other hand, open lattice structures, such as

communication towers, do not generally experience

large cross-wind response. The driving mechanism for

cross-wind response is usually regular vortex

shedding, with a lesser contribution from lateral

turbulence.

The codification cross-wind response of tall

cantilevered structures has proved to be difficult, buthas been attempted in a number of documents.

3.1 Tall Buildings of Rectangular Cross-section A random vibration approach to the cross-wind

response of tall buildings of simple rectangular cross-

section is the basis of the methods applied in the

Recommendations of the Architectural Institute of

Japan [12] (AIJ), and in the Australia/New Zealand

Standard [17]. In the former case, a series of

parameters are defined that are each a function of the

side aspect ratio of the cross section. However, in the

AIJ there is no dependence on the height aspect ratio.

In the AS/NZS, data is given which enables estimation

of the cross-wind response of a limited number of

building geometries for two different turbulence levels.

The uncertainty for the designer with regard to

cross-wind response is illustrated in Figure 3, which

shows the non-dimensional spectral density of cross-

wind generalized forces for a simple building of

square cross section, with a height of six times the side

length – i.e. a building with proportions of 6:1:1. This

is the key aerodynamic parameter from which cross-

wind responses are calculated. The Figure shows

experimental data and specified data from the AIJ [12]

(12) and AS/NZS [17].

The ordinate is the non-dimensional cross-wind

force spectrum coefficient, Cfs, as defined in the

Australian/New Zealand Standard [17]. The abscissa

in Figure 3 is the reduced velocity given by:

(11)UU

n.br

h=


0

0.0 0.2 0.4 0.6 0.8 1.0

20

40

60

80

100

120

140

160

Effective pressure (kPa)

H

e i g h t ( m )

Combined

Resonant

Background

Mean

Figure 2. Effective Static Load Distributions for Base Bending Moment on a Tapered Tower.

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is the mean wind speed at the top of the

building; n is frequency, and b is the building width.

The usual range of reduced velocity in practical

situations is 2 to 8.

Considering the logarithmic axes in Figure 3, the

differences between the data lines in Figure 3 are very

large, and would result in very different cross-wind

responses if used by a designer. However, there are

currently moves to ‘benchmark’ wind-tunnel

measurements of tall buildings, with some standardized

building shapes; this may resolve some of the

variability in Figure 3, and similar comparisons for

other shapes.

3.2 Structures of Circular Cross-section Towers, chimneys, masts and poles of circular cross

section are prone to suffer cross-wind response at

lower and more frequent wind speeds than those with

sharp edged sections, such as square or rectangular.

The reason for this is that the fluctuating forces are

primarily induced by vortex shedding. For the same

wind speed and section breadth, the rate of shedding is

approximately twice for circular cross sections than it

is for sharp edged bodies. Hence, resonance with the

natural first-mode vibration frequency of the structureoccurs at a critical wind speed about half that for a

square structure of the same width. The critical wind

speed for circular sections corresponds to a reduced

velocity, as defined by Equation (11), of about 5.

For masts and poles of very small diameter, the

critical wind speeds can be very low (i.e. 2–3m/s) and

vibrations often occur in the early morning or evening

when atmospheric conditions are thermally ‘stable’

with low turbulence. The latter can lead to more

coherent and effective vortex shedding, and hence

more severe vibrations.

Although it is a common phenomenon throughout

the world, the prediction of vortex-induced vibrations

has resisted codification until fairly recently. In many

documents, the advice given does not go beyond a

simple expression for critical wind velocity.

There are two classes of calculation methods for the

cross-wind vibrations of circular sections:

a) Methods based on the assumption of sinusoidal

excitation forces

b) Methods based on random vibration theory.

The sinusoidal model has been adopted for the

Australian/New Zealand Standard [17] – in Section

6.3.3.1 of that Standard. The random model is used in

the American Standard for Steel Stacks ASME STS-1-1992 – Appendix 5.C [20]. Both methods have been

U h



0 . 0 0 0 0 1

0 . 0 0 0 1

0 . 0 0 1

0 . 0 1

0 . 1

0 1 0

1 0 0

Reduced Velocity

C f s

A I J - 2 0 0 4

A S / N Z S 1 1 7 0 . 2

I u = 0 . 2 0

A S / N Z S 1 1 7 0 . 2

I u = 0 . 1 2

N D s u b u r b a n 6 : 1 : 1

N D u r b a n 6 : 1 : 1

T K U u r b a n

T K U o p e n

H K U S T 5 : 1 : 1 o p e n

Figure 3. Cross-Wind Force Spectrum Coefficients for a 6:1:1 Building (Showing Code Values and Experimental Data).

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John D. Holmes

adopted as alternative approaches in the Eurocode for

Wind actions – Annex C [18].

In the AS/NZS [17], the following simple formula is

given for the maximum amplitude of tip deflection:

(12)

bt is the average breadth (diameter) of the two third of

the structure, corresponding the region where the

exciting forces have their greatest effect.

Sc is the Scruton Number defined as follows:

(13)

The key parameters in Equation (13) are mt, the

mass per unit height over the top third of the structure,

and ζ, the ratio of structural damping to critical

damping. ρair is the air density.

It can be seen from Equations (12) and (13) that

increasing either, or both, of the mass or the damping

will reduce the vibration amplitude. Interestingly, the

amplitude of vibration given by Equation (12) is

independent of both wind speed and the natural

frequency of the structure. The theory on which

Equation (12) is based is given in Reference (13)

(amongst other places).

The sinusoidal approach to cross-wind response is

somewhat simplified, but enables a quick indication of

the likelihood of vortex-induced vibrations occurring.

If high amplitudes are predicted it is usually better to

reduce these by increasing mass or damping (including

auxiliary damping devices) or by other means (e.g.

aerodynamic devices such as helical strakes, or by

guying, or linking adjacent chimneys to each other).

4. FATIGUE

Fluctuating stress reversals from wind-induced

vibrations has often produced failures either or both of

along-wind and cross-wind vibrations involved. Since

an accumulation of fatigue damage over a period of time occurs with a range of wind speeds, the wind

loading component is complex. This was recognized in

some early work by A.G. Davenport [21] in 1966, in

which he derived an expression for the number of

exceedences of defined amplitudes under long-term

wind loading.

On the material side, the parameters relating to

fatigue damage are very uncertain. For these reasons,

the prediction of fatigue life under wind loading has

not been generally adopted by codes; hence, the

phenomenon has probably been largely ignored bydesigners, until a failure has occurred.

A usable method for estimating the fatigue life of

slender structures under along-wind loading is given in

Refs 22 and 23 (also discussed in Ref 13). A ‘closed-

form’ expression for upper and lower bounds of fatigue

life is given. This requires information on the parameters

of the Weibull distribution of 10-minute mean wind

speeds at the site, as well as the constants of the power law expression describing the fatigue s-N curve. The

simplified Palmgren-Miner Hypothesis for

accumulation of fatigue damage is also assumed. So far

this approach has not been adopted by any code or

standard; however, there is a potential for this to be done.

Since the critical velocity for vortex-induced

vibrations of small diameter steel structures is typically

a wind speed with a high probability of occurrence, a

large number of stress cycles may accumulate in a short

period of time. In that case, the simplest design

approach is to ensure that the maximum stress rangedue to cross-wind vibrations remains below the

‘endurance limit’ of steel [24] – thus theoretically

producing no fatigue damage. This may require

increasing the damping or mass of the structure, as

discussed in the previous section.

5. ESDU ENGINEERING DATA

The Wind Engineering series of ESDU data sheets

published by ESDU International of London, U.K.

contain three volumes of data items concerned with

dynamic response to wind. These are very detaileddocuments with comprehensive examples, and

sometimes with accompanying computer programs.

Along-wind response is covered in ESDU 87035

[25] and 88019 [26], for ‘line-like’ and ‘plate-like’

structures respectively. Cross-wind response, due to

both lateral turbulence and vortex shedding, is treated

in ESDU 89049 [27], 90036 [28] and 96030 [29].

Another volume in the ESDU series incorporating

ESDU 83009 [30] and 91001 [31] covers natural

vibration parameters of structures – i.e. damping and

natural frequencies.Although expensive and perhaps over-complex in

some areas, in relation to the uncertainties involved,

the ESDU Data Items are an alternative source of

design methods for dynamic response to wind, but

currently not widely used outside the U.K.

6. INTERNET DATABASES

Another alternative to codes and standards is provided

by internet databases such as the one compiled by the

Natural Hazards Modeling Laboratory of the University

of Notre Dame (www.nd.edu/~nathaz/database). Thelatter provides information on the spectral densities of

Scm .

.b

t

air t

2=

4π . ζ

ρ

y0.5.b

Scmax

t=


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three components of base moment for 27 different

building shapes, in two different terrain types. The nine

cross-sections considered are shown in Figure 4. This

information has been obtained from a high-frequency

base balance, the standard technique for determining

wind loading and response of tall buildings. By the use

of standard random vibration relationships, base

moments and tip accelerations can be determined for

basic building shapes. However, only orthogonal wind

directions are considered, and the effects of surroundingbuildings, and complex coupled mode shapes cannot be

treated. Special wind-tunnel studies are required to

adequately cover the latter.

It is likely that internet databases will be further

developed in the future with more comprehensive data

available to the designer.

7. LIMITATIONS OF CODIFIED

APPROACHES

There are many situations of response to wind that are

beyond the application of conventional codifiedmethods to the dynamic response of structures. Some

of these situations are as follows:

a) When modes higher than the fundamental sway

and twist modes contribute significantly to the

load effects. This would be the case for very large

structures such as tall cantilevered towers and

long span bridges. These may be particularly

important for calculation of deflections and

accelerations. Special wind engineering studies,

usually involving wind-tunnel tests, should

normally be undertaken for such structures.b) Cases when surrounding structures can

significantly modify the approach flow

conditions – particularly the turbulence

characteristics. Wind-tunnel testing is an

effective method of predicting the shielding and

interference effects of surrounding structures.

c) Structures such as stadium roofs – particularly

arched and domed roofs. Although the resonant

dynamic response for such roofs may not be

particularly significant, except for cantilevered

roofs and very long structures, the structuralresponses are sensitive to the variety of load

distributions that fluctuating wind pressures can

impose. In these cases simple load distributions

based on quasi-steady principles are inadequate.

Approaches to the development of wind loading

distributions for long span roofs, based on the

appropriate processing of wind-tunnel test data,

are discussed by Holmes [13].

8. CONCLUSIONS

This paper has considered the codification of dynamicresponse to wind of tall wind-sensitive structures.

Methods of treating both along- and cross-wind

response of tall buildings, and other structures such as

towers and chimneys, are discussed. It has been noted

that current codification approaches cannot easily

account for responses to wind in higher modes and for

structures such as long-span bridges and large stadium

roofs. Development of new approaches for these

structures is a topic for future research.

However, the approach to guyed masts adopted by the

British Standard BS8100 [32], in which numerous ‘patchload’ distributions are specified, is a case where a

successful codified approach to structures with a complex

response to fluctuating wind forces has emerged.

The possible future codification of fatigue

calculations has also been discussed in the present

paper. Alternative sources of information for designers

– namely the ESDU Wind Engineering Data items, and

internet databases are also mentioned briefly.

REFERENCES

[1] Davenport, A G, Gust loading factors, Journal of theStructural Division, A.S.C.E., 93, 1967, 11–34.

[2] Vickery, B J, On the assessment of wind effects on elastic

structures, Civil Engineering Transactions, I.E.Aust.,

CE8, 1966, 183–192.

[3] Velozzi J and Cohen, E, Gust response factors, Journal of

the Structural Division, A.S.C.E., 97, 1968, 1295–1313.

[4] Vickery, B J, On the reliability of gust loading factors,

Civil Engineering Transactions, I.E.Aust., CE13, 1971,

1–9.

[5] Simiu, E, Equivalent static wind loads for tall building

design, Journal of the Structural Division, A.S.C.E., 102,

1976, 719–737.

[6] Simiu, E, Revised procedure for estimating alongwind

response, Journal of the Structural Division, A.S.C.E.,

106, 1980, 1–10.



3:1 2:1 1.5:1 1:1 1:3 1:2 1:1.5 1:1 1:1.5

Figure 4. Cross Sections of Tall Buildings for Which Data is Given in the Internet Database of the University of Notre Dame

(www.nd.edu/~nathaz/database).

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John D. Holmes

[7] Solari, G, Alongwind response estimation: closed form

solution, Journal of the Structural Division, A.S.C.E.,

108, 1982, 225–244.

[8] Engineering Sciences Data Unit, The response of flexiblestructures to atmospheric turbulence, ESDU Data Item

76001, September 1976, Engineering Sciences Data

Unit, London, U.K.

[9] British Standards Institution, Lattice towers and masts. Part 2. Guide to the background and use of Part 1 ‘Codeof practice for loading, BS 8100: Part 2: 1986, British

Standards Institution, London, U.K.

[10] Milford, R V, Gust loading factors for lighting masts,

Engineering Structures, 11, 1989, 62–68.

[11] National Research Council (Canada), National Building

Code of Canada, N.R.C. Ottawa, 2005.

[12] Architectural Institute of Japan, AIJ recommendations for

loads on buildings, AIJ, Tokyo, 2004.

[13] Holmes, J D, Wind loading of structures, 2nd Edition,

Taylor and Francis, U.K. 2007.

[14] Holmes, J D, Along-wind response of lattice towers: part

I – derivation of expressions for gust response factors.

Engineering Structures, 16, 1994, 287–292.[15] Holmes, J D, Along-wind response of lattice towers: part

II – aerodynamic damping and deflections, Engineering

Structures, 18, 1996, 483–488.

[16] American Society of Civil Engineers, Minimum designloads for buildings and other structures, ASCE/SEI 7-05,

A.S.C.E., New York, 2005.

[17] Standards Australia and Standards New Zealand,

Structural design actions. Part 2: Wind actions,

Standards Australia, Sydney, and Standards New

Zealand, Wellington, Australian/New Zealand Standard

AS/NZS1170.2:2002.

[18] C.E.N. (European Committee for Standardization),

Eurocode 1: Actions on structures – Part 1-4: Generalactions – Wind actions, prEN 1991-1-4.6, C.E.N.,

Brussels, 2004.

[19] Zhou, Y, and Kareem, A, Gust loading factor: new

model, Journal of Structural Engineering, 127, 2001,

168–174.

[20] American Society of Mechanical Engineers, Steel Stacks,

American National Standard. ASME STS-1-1992.

[21] Davenport, A G, The estimation of load repetitions on

structures with application to wind-induced fatigue and

overload, RILEM International Symposium on the Effects

of Repeated Loading of Materials and Structures ,

Mexico City, September 15–17, 1966.

[22] Holmes, J D, Fatigue life estimates under along-wind

loading – closed form solutions, Engineering Structures,

24, 2002, 109–114.[23] Robertson, A P, Holmes, J D, and Smith, B W,

Verification of closed-form solutions of fatigue life under

along-wind loading, Engineering Structures, 26, 2004,

1381–1387.

[24] van Koten, H, The response of tall structures, Seminar onSafety of Structures under Dynamic Loading, Trondheim,

Norway, June 1977.

[25] ESDU International. Calculation methods for along-wind

loading. Part 2. Response of line-like structures toatmospheric turbulence, ESDU Data Item 87035,

December 1987.

[26] ESDU International. Calculation methods for along-wind loading. Part 3. Response of buildings and plate-like

structures to atmospheric turbulence, ESDU Data Item88019, October 1988.

[27] ESDU International. Response of structures to

atmospheric turbulence. Response to across-wind turbulence components, ESDU Data Item 89049,

December 1989.

[28] ESDU International. Structures of non-circular crosssection. Dynamic response due to vortex shedding ,

ESDU Data Item 90036, December 1990.

[29] ESDU International. Response of structures to vortexshedding. Structures of circular or polygonal cross

section, ESDU Data Item 96030, December 1996.

[30] ESDU International. Damping of structures. Part 1: tall

buildings, ESDU Data Item 83009, September 1983.[31] ESDU International. Structural parameters used in

response calculations, ESDU Data Item 91001,

December 1991.

[32] British Standards Institution. Lattice towers and masts.

Part 4. Code of practice for loading of guyed masts, BS

8100: Part 2: 1995, British Standards Institution, London,

U.K.


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