Cross-wind response of tall buildings

response of tall

Cross-wind buildings

-

K. C. S. Kwok School of Civil and Mining Engineering, The University of Sydney, Sydney, Australia fReceived June 1981; revised February 1982)

A design procedure was developed using random vibration theory and uses mode-generalized cross-wind force spectra and aerodynamic data to calculate the cross-wind displacement and acceleration responses of tall buildings. The force spectra of a number of building shapes and sizes in both suburban and city centre type wind flow are presented. The proposed design procedure gives reasonable estimates of the cross-wind response, compared with wind tunnel measurements, at reduced wind velocities and at structural damping values consistent with modern habitable tall building design. This allows assessment of the structural requirements of tall buildings to be made at an early design stage, and also allows the designers to assess the need for more detailed and expansive wind tunnel model tests. Key words: tall buildings, design procedure

Introduction In the design of most modern tall buildings, the cross-wind response often dominates over the along-wind response. The dynamic along-wind response can be predicted with reasonable accuracy using the gust factor approach. The cross-wind excitation mechanisms have proved to be much more complex and although there have been significant advances in the understanding of these mechanisms,‘. 2 no generalized analytical method is available to calculate the cross-wind response with sufficient degree of reliability. In many cases, aeroelastic model tests conducted in a wind tunnel are necessary to determine the response. The most common source of cross-wind excitation is wake excitation associated with vortex shedding. For a particular building shape, the shed vortices have a dominant periodicity which is defined by the appropriate Strouhal number. Hence the building is subjected to a periodic pressure loading which results in an alternating cross-wind force. A number of experimental techniques have been developed to estimate the forcing function from which the cross-wind response could be computed.3-5 A design procedure for the prediction of cross-wind displacement and acceleration responses of tall buildings is described in this paper. The computed responses are compared with experimental results from wind tunnel model tests. Sample computation of cross-wind response of a tall building is also presented.

256

Eng. Struct.,

1982,

Vol. 4, October

wind

excitation,

response, modal analysis,

Response of multi-degree to random excitation

of freedom systems

Most tall buildings and structures are essentially continuous systems free to move in a variety of ways. These continuous systems have an infinite number of natural frequencies PZi each represents a particular mode shape $Q(z). z is the vertical axis. The response (in a time domain t) of a lightly-damped multi-degree of freedom linear system to some arbitrary excitation w(z, t) per unit length can be expressed as a summation of the form: Y(z, t) = t

ai

(1)

GiCz)

i=l

The modal coefficients q(t) may be evaluated from the solutions of a set of equations of the form: da, d2ai mi 7 + Ci z + kiai = F,(t) in which: mi = mode-generalized

mass of ith mode

h

m(z) G?(z) dz

= I

(3)

0

0141-0296/82/040256-07/$03.00 0 1982 Butterworth & Co. (Publishers)

Ltd

Cross-wind response o f tall buildings: K. C. S. Kwok

h = height or length of structure

i SFi(n IHi(n)l 2 dn

m(z) = mass per unit height or length of structure c i = mode-generalized damping parameter of

=

ith mode

(10)

[Hi(n)[2 is the mechanical admittance function:

where

= 2~'i~

(27rni)4m~ o

(4)

S'i = damping in ith mode expressed as a fraction of critical

1

IH;(n)l 2 -

(11)

k i = mode-generalized stiffness of ith mode

= (27rni)2mi

(5)

Fi(t ) = mode-generalized force of ith mode h

The power spectral density function of the total response y(z, t) is given by the summation:

Sy(z)(n ) = £ Sai(n ) ~(z)

= ~ w(z, t) ~i(z) dz

(6)

(12)

i=1

i

where:

0 It can be seen that the solutions of a multi-degree of freedom linear system are the solutions of a set of equations each corresponding to a single degree of freedom linear system representing a particular mode shape. For most lightly-damped structures, the mean square displacement y - - ~ , or variance of displacement o2(z) assuming for convenience that the mean response is zero, may be expressed as:

4(z)

=

2

Sai(n ) -

(13)

M o d e - g e n e r a l i z e d cross-wind f o r c e s p e c t r a

(7)

i=1

The evaluation of ~ requires a knowledge of the power spectral density function (i.e. in a frequency domain) of the excitation forces which can be obtained as follows:

In the analysis of wind excitation of tall buildings and structures, it is seldom necessary to evaluate and sum the response over more than a few modes. In many cases the first tern1, corresponding to the fundamental mode of vibration is quite adequate. If the structure has a deflection mode shape given by qJ(z) = z/h, that is, a simple linear mode shape pivoted at the base of the structure, then from equation (12), the cross-wind displacement response spectrum is Sy(z)(n ) = Sa(n ) ~2(z). In particular, the cross-wind response spectrum at the top of the structure is:

Sy(n) = Sy(h)(n ) = Sa(n )

e~

SFi(n ) = 2 ( RFi(r ) e-j2~rrrr dT"

SFi(n) IHi(n)l 2 (27rni)4m~

(s)

and from equation (13):

1 --oo

where RFi(r) is the auto-correlation function, and z is a time lag. j = x/-~f. For a line-like structure excited by a distributed random load w(z, t) per unit height:

** h h

f f f W(zI't)w(z2't'-T) X I~/i(Z1) ~Ji(Z2) d z , dz2 e -j2nnr dr or

SF(n) IH(n)l 2 Sy(n)= (2rrno) 4m2

Extensive wind tunnel model tests were conducted by Saunders 6 and Kwok 2 on a range of tall buildings and tower-like structures. These scaled models were attached to a strain gauge balance system, and were constrained to pivot in a linear mode shape and about the base. The crosswind displacements spectra Sy(n) at the top of the structure were obtained by Fast Fourier Transformation of the displacement signals. The mode-generalized cross-wind force spectra SF(n) (for a linear mode shape ~(z) = z/h) were determined by using equation (14) such that:

h h SFi(n): f f C°(Zl'z2'n) ~/i(Z1) ~]i(z2)dZl dz2 (9) o o in which Co(zb z2, n) is the co-spectral density function for the fluctuating loads per unit height at positions Z l and z2. In general, Co(z1, z2, n) is a complex function; however, for excitation/response relationship where the phase information is not required, it is adequate to consider the real part only. The variance of the modal coefficient may then be evaluated as follows:

a7 = ; SFi(n ) IHi(n)l 2 dn e

(14)

h h SF(n) = o o

_ (27rno)4m2Sy(n) m

IH(n)l 2

(15)

The force spectra of some circular and square sectioned buildings are presented in Figures 1 and 2 in a normalized form:

nSy(n) [~ p02(h)

bh ]2

as a function of reduced velocity U(h)/nb and reduced frequency nb/U(h), p is air density. Uis mean wind

Eng. Struct., 1982, Vol. 4, October

257

Cross-wind response o f tall buildings: K. C. S. K w o k

A

,,/.:

_

a.-,

__..

lO -2 L-

Therefore, if the mode shape of a building varies significantly from a linear mode shape, the following approximate correction to the force spectra given in Figures 1 and 2 may be applied:

©Ib

+/ h

5

SF,,(n )

=~

I,~2(Z) dz

(16)

.SF(n )

o

2 ~'-~ 10 -3

/-

S

..:.<,.,f%. Prediction o f cross-wind displacement response of tall buildings - random excitation model

Suburban fetch h:b:d g:1(~ircular)J F r o m KwoK and

10-4 5

.........

2 10-5 0.02 t

I

,

50

_

6:1

1

~ Melbourne12

J

g:1 I

I

i

18:1

From

Saunders

and

I 31:1 11 iN~elb°urne~ 0.05 01 0.2 nb I

lu,~;J,,

I

20

10 O(h) nb

5

t

,

i

,

I i i 0.5 0.8 I

By assuming that wake excitation associated with vortex shedding is random, the cross-wind displacement response of tall buildings and structures can be computed by modal analysis outlined earlier. If response contributions from mode shapes higher than the fundamental mode of vibration

I

2 10 -1

Figure 1 Mode generalized cross-wind force spectra of tall buildings in a suburban fetch

lk

5 2 10 -2

velocity, b is width of the structure. The magnitude of the force spectra is at the maximum at the critical reduced velocity which represents the wind condition at which the vortex shedding frequency ns, as defined by the Strouhal number S = nsb/O , is very close to the natural frequency of the structure no. The mode-generalized cross-wind force spectra shown in Figures i and 2 apply to a linear mode shape. The sensitivity of the cross-wind force spectra SF,~(n ) of different mode shapes to the cospectral density function Co(z1, za, n) was examined 7 by considering the limiting cases of Co ~ 0 and Co = constant. The variations of the force spectra applicable to buildings with a cantilever mode shape and a sway mode shape are shown in Table 1. There is a -+16% variation on the force spectra which represents a -+8% variation on the displacement response. Therefore the force spectra are not particularly sensitive to the form of the co-spectrum. For tall, slender buildings in turbulent boundary layer flows, Co ~ 0 is the more likely assumption.

Table

I

5

~ ~-~ ~ ,~ ~ ~

2 l o .3

(3-

2

i~

¢

/

"\,,

%,-x,.

5

C i t y centre fetch h:b:d g : l 1 F r o m K w o k and M e l b o u r n e ~2 ....... 6 : 1 l / F r o m S o u n d e r s and . . . . . 3:1 1) Melbourne 3

lo-4 5 2 I

10 -5 0.02

I

1 L I I t 0.05 0.1

I 0.2

I

I

i

t

l 20

u,(h,), 10

,

L 5

t

~_

nb

Figure 2

Mode generalized cross-wind force spectra of tall buildings

in a city centre fetch

SF, ~ (n) SF(n)

C O~ 0

=

--

Colz I -- z2,n)

dlz 1 --z

2)

C o = constant

C o -+ 0

C o = constant

Co ' -

1.50

1.78

0.75

0.64

2.25 o

Cantilever,

- - Colz I --z~,n) dlz~--z 2) 4,1 o

258

Eng. S t r u c t . , 1 9 8 2 , V o l . 4, O c t o b e r

J

0 (h)

Sway,

~(z) =

J 2

Variations of mode-generalized cross-wind force spectra for buildings with a sway or a cantilever mode shape

M o d e s h a p e , ~ (z)

I 0.8

nb t 50

SF, ~ (n)

~(Z)

I l 0.5

Co'-6.25

Cross-wind response o f tar buildings: K. C. S. Kwok

could be neglected, the cross-wind response spectrum at the top of the building is given by equation (14):

0.5

Se,~(n) IH(n)12 Sy,,(n) -

0.2

(2zmo)4m 2

t . I '~' 0.0025 0.1

The variance of cross-wind response cr~ at the top of the building is determined by:

I~\

~ 005

~

Q05

Oy 2

~

0.015

~0.06

= f Sy , (n) dn 0.02

0 0.01

SF,~(n) IH(n)P dn

(2zrno)%n2

////

(17)

~" ~

~ ~

=W] l/

+

0. 005

0

This can be further simplified by applying the following approximations: /'/o

'If

o~ ,~ (2rrno)4m2

0

Sl~,~(n) dn + rm°SF'¢(n°) 4~s ]

o.ool o

5

10

and the standard deviation cross-wind response is proportional to ~.~u2. The wake-excited cross-wind displacement response of tall buildings can be readily determined from known modegeneralized cross-wind force spectra (Figures 1 and 2) as functions of reduced velocity and structural damping. As an example, the computed response of a 9 : 1 : I squaresectioned building in a suburban fetch is compared with experimental results from wind tunnel model tests in Figure 3. In general, there is reasonable agreement, to within + 25%, between computed and measured responses at damping values and design reduced wind velocities which are consistent with most modern habitable tall buildings; that is, at damping values between 1% and 5% of critical and at reduced velocities not much greater than the critical. It is recognized that some modern tower-like structures of unusual design could be exceptionally slender, flexible and lightly-damped so that wind-induced instabilities such as lock-in and galloping could cause significantly larger crosswind responses. Although the mechanisms of lock-in and galloping of tall buildings and structures in turbulent boundary layer flow are reasonably well understood and a few design models for the prediction of the resultant responses have been proposed, s-12 useful design data are extremely limited. In terms of design, these models are applicable only to a limited range of structures which would normally be subjected to extensive wind tunnel model testings. A similar design approach based on random vibration theory was proposed by Vickery and Clark 13 and Vickery t4 who suggested a Gaussian type cross-wind force spectrum due to vortex shedding in turbulent flow of the form:

0.01 0.005

equation (17)

15

20

25

O(h) nob

1

Predicted response, equotion (17)

1

0.5 --

0~[--~

k

LT(h)

(19)

- - ~ - - ,Predicted response

0.002

_

If excitation by low frequencies is small and the structural damping is low, less than 10%, so that the excitation bandwidth is large compared with the resonant band-width, the first term in equation (18) can be neglected. Hence:

o~ ~ rmoSF,~(no) ( 27rno)am24~s

at

2t 0.06 0.015

~

~

Expt.

ufJ

~

,ts

0 (h) 4 5

0.2 10 24~.

~ 1 ~

:

1 15

0.1

0.05 8.3 ~

~

~

~

v

° o 0.01

0.005

4.5~

0.002 0.001

t

~, I O.Ol G

o.1

F i g u r e 3 Predicted and measured cross-wind response of a 9 : 1 : 1 square sectioned building in a suburban fetch

"1 n. 2 exp

-

(20)

in which: Cr. = standard deviation cross-wind force coefficient; and B = effective band-width measured as a fraction of the centre frequency.

Eng. Struct., 1982, Vol. 4, October

259

Cross-wind response of tall buildings: K. C. S. Kwok

It has been shown by Vickery and Clark, 13 Davenport and Novak, is and Vickery 14 that the modal coefficient of cross-wind response of a tall building in a turbulent boundary layer flow is:

CLpb4k3/27rl/4

[

x~i~x/ff(s(47rS)2mi

/1--!~21 1/2 exp-~kT)

j

-C

(21)

in which:

1+--o 2l l = correlation length; 3' = power law exponent of longitudinal mean velocity profile and k = S(U(h)/nib ). The modal cross-wind response is close to a maximum when ni = ns, that is k = 1, and:

N~i2max ~

CLP b47rl/4

X/~s(4rrS)2m i C

(22)

If contributions of response from mode shapes higher than the fundamental mode of vibration could be neglected, the cross-wind response at the top of the building is given by:

tTy =

CLPbaTr1/4 •C

b

(23)

x/~-s(47rS)2m

Typical values of CL, S, B and l can be found elsewhere•2,1a-is For design purposes, values shown in Table 2 for circular and square sectioned buildings may be used. These coefficients are function of height to breadth ratio, turbulence intensity level, velocity profile and for circular buildings, also the Reynolds number. Due to the limited amount of available data, they tend to be conservative and will probably result in over-estimation of the response. The cross-wind response of a range of buildings were computed from known mode-generalized cross-wind force spectra (Figures I and 2) and also from aerodynamic data (Table 2). At close to the critical reduced velocity, at which the response is at a maximum, and which probably represents the design maximum cross-wind response for many habitable tall buildings, there are reasonable agreements between computed response and experimental results, as is shown in Figure 14.

Table 2 Aerodynamic data for circular and square sectioned buildings in a turbulent boundary layer flow

CL Standard deviation cross-wind

Generalization of the prediction of cross-wind response of tall buildings and structures, in the form of general design equations and aerodynamic data, have been described in the previous sections• Due to the limited amount of available data, which is virtually non-existent so far as full scale structures are concerned, the application of the design approach and the interpretation of the computed response should be treated with caution• If the computed response amplitudes are excessive, wind tunnel tests of an aeroelastic model should be conducted. The designer may also consider: (a) (b) (c) or (d)

increasing the damping; adding aerodynamic spoilers; strengthening and/or stiffening the structure; increasing the mass.

Of these, the first two alternatives are generally more effective and easier to implement• An example is given here to demonstrate the practical application of the design approach.

Example: A building of square cross-section (a) Structural data Height h = 180 m Breadth and depth b = d = 30 m Fundamental natural frequency no = 0.2 Hz Mode shape ~(z) = (z/h) l"s (cantilever) Structural density Ps = 190 kg/m 3 uniformly distributed Damping ~'s = 1% of critical Modal mass

h

m = I m(z) tkZ(z) dz 0 ~t

= 7.695 x 106 kg (b) Meteorological data Suburban (Melbourne): AS 1170 Terrain Category 3 Mean wind velocity profile:

O(z)

, .

Regional design wind speed for Melbourne (from AS 1170): Uso yr = 39 m/s 10m Cat. 2 Adjust design mean wind speed at top of building for Terrain Category 3. (c) Determine operating reduced velocities:

O(h)

Circular cross-section

Square cross-section

0.25

0.5

nob (d) Select an appropriate mode-generalized cross-wind force spectrum (6 : 1 : 1 square, suburban fetch, Figure 1).

(e) Calculate force spectrum SF(no) from:

force coefficient

S

Strouhal number

0.15

0.1

B

Bandwidth

0.3

0.25

/

Correlation length (diameter or breadth)

1

3

260

Sample c o m p u t a t i o n o f cross-wind response o f a tall building

Eng. Struct., 1982, Vol. 4, October

noSF(no) [-~pG2(h) bh ]2 for given values of (U(h)lnob).

Cross-wind response of tall buildings: K. C. S. Kwok 005

70 \

0.2-

6.~X \ \~

7 o ~ 0.02 --

O(h_)

D---,,-

nob

110~

1

10Z3~

~

0.1 •

Y

~1~OOl-

0.005 --

0.07. I

0002 0.001

0.005

I

0.01

t

002

tl

t

005

I I I 0.1

001 0.001

9:1

i

~ [~ 0005

~Ltl 001

nob 10

11

1 1 L ~

C 18:1:1 Square

0.2 U

0.02

002

I

b

,

= I~,,Jl 0.005

t 0.01

l

I i i ii 0.1 0.05

I

t

I I, 0.05

building, suburban fetch

0.1 005

0.002

i

~ L~J

10~ 0 " ` . - 1 / 2

t:~,l4a0 ' 0 5

0.01 0 001

l 0.02

~5

building, surburbon fetch

Circular

~(h)

0 1 --

0.02

i

t I I III 0.05

0.1

001 0.001

I 0.002

I

~ IL lltl 0.005 001

I 0.02

,t 0.1

;s Square building, surburbon fetch

9:1:1

d

-------.-o-.--

Figure 4

l 0002

gs

a 0.2

~ [ It~tl

~

0002

~.~

9:1:1

Square building ,city centre fetch

Predicted response from rondon excitation model Equation (17) and mode-generalised cross-wind force spectra Equation (23) and aerodynamic data in ruble 2 Experimental results from wind tunnel model tests

Cross-wind response of circular and square sectioned buildings at close to the critical reduced velocity

(f) Correct SF(no) to give SF,~(no) for a cantilever mode

shape. From equation (16):

h SF'qj(n°)

h

=

-

The computed cross-wind displacement and acceleration responses are tabulated in Table 3 and plotted in Figure 5. The peak acceleration for a five-year return period does not exceed the criterion for human comfort of 2% of gravity.

dz.SF(no)

0

3 =-- SF(no)

4

(g) Calculate standard deviation cross-wind displacement response at the top of building from equation (19) (random

excitation model): Uy --

rrnoSF, q~(no) (2rmo)4m24~s

(h) Calculate standard deviation cross-wind acceleration response at the top of building from:

o~ = (27rno)2 ay (i) Calculate peak acceleration from:

# =ga~

Conclusions A design procedure based on a random excitation model was developed from modal analysis and random vibration theory. Using mode-generalized cross-wind force spectra and aerodynamic data, the cross-wind displacement and acceleration responses of tall buildings could be readily obtained. In general, there are reasonable agreement, to within _+25%, between computed and experimentally measured responses at damping values and design reduced wind velocities which are consistent with most modern habitable tall buildings. The design procedure allows assessment of the structural requirements of tall buildings to be made at an early design stage, and also allows the designers to assess the need for more detailed and expansive wind tunnel model tests.

Eng. Struct.,

1982,

Vol. 4, October

261

Cross-wind response o f tall buildings: K. C. S. K w o k Table 3 Computation of cross-wind displacement and acceleration responses of a 180 m by 30 m square building by random excitation model Return U(h) period O(h) (year) (m/s) nob

nob

n o SF(n o)

O(h)

SF(no)

[½PO2(h)bh] 2 (N2/Hz)

5

22.1

3.68

0.271 0.00055

6.94x109

25

25.5

4.25

0.235 0.0010

50

26.9

4.48

100

28.3

4.72

/lr noSF ~(no) - "~ - -~/ ~/ (2trno)4m2~"s b

SF,~(no) = ¼SF(no) aM = (N2/Hz) 5.21x109

0.0372 [0.38% ]

3.5

0.130 [ 1.33%]

2.24x10 ~° 1.68x10 ~°

0.0423

0.00141

0.066% [0.68%]

3.5

0.234 [2.38%)

0.223 0.0014

3.88x101° 2.91 xl01°

0.0556

0.00185

0.0879 [0.90%]

3.5

0.307 [3.14%]

0.212 0.0017

5.77x101° 4.33x101°

0.0679

0.00226

0.107 [ 1.09%]

3.5

0.375 [3.83%]

5

3

5

_

o Computed response random ex~ation model t3 Experimental results (fnDm Sounders and Melbourne 3 ) 600 ft by 1OOft square building, linear mode r~ shape ~/

~0"10-3 "0

2 ~> L

Peak acceleration criterion for humor 0.5 comfort 2% of gravity based on

©

5

yr return period 02

U

J

o L)

01

2 Return period (year) c,lif30

104

0

I

I

'

1

2

3

I ~IIT, 4

5 _

U(h) Reduced v e l o c i t y nob

6

I 7

Figure 5 Cross-wind displacements and acceleration responses of a 180m by 30m square building

References t 2

262

(m/s:) [% gravity]

0.000785

U---,--

2

y": = ga~/

0.0235

10 -2

i h~--~ "E ~;

aj2 = (2rrn 0) =oF (m/s z) [% gravity] g

Melbourne, W. H. 'Cross-wind response of structures to wind action', Proc. 4th Int. Conf. Wind Effects Buildings Struct., Cambridge University Press, pp. 343-359, 1975 Kwok, K. C. S. 'Cross-wind response of structures due to displacement dependent excitations', PhD thesis, Monash University, Australia, 1977

Eng. Struct., 1982, V o l . 4, O c t o b e r

Saunders, J. W. and Melbourne, W. H. 'Tall rectangular building response to cross-wind excitation', Proc. 4th lnt. Conf. Wind Effects Buildings Struct., Cambridge University Press, pp. 369-379, 1975 4 Kareem, A. et al. 'Cross-wind response of high-rise building', Proc. 5th Int. Conf. Wind Eng., Vol. 2, Pergamon Press, Oxford, pp. 659-672, 1979 5 Rheinhold, T. A. and Sparks, P. R. 'The influence of wind direction on the response of a square-section tall building', Proc. 5th Int. Conf. Wind Eng., Vol. 2, Pergamon Press, Oxford, pp. 685-698, 1979 6 Saunders, J. W. 'Wind excitation of tall buildings with particular reference to the cross-wind motion of tall buildings of constant rectangular cross-section', PhD thesis, Monash University, Australia, 1974 7 Saunders, J. W. and Melbourne, W. H. 'Wind-excited building - design sway stiffness', J. Struct. Div., ASCE (submitted) 8 Novak, M. and Davenport, A. G. 'Aeroelastic instability of prisms in turbulent flow',J. Eng. Mech. Div., ASCE, 1970, 96 (EM2), Proc. Paper 7076, pp. 17-39 9 Iwan, W. D. and Blevins, R. D. 'A model for vortex induced oscillation of structures', J. AppL Mech., ASME, 1974, 41, 581 10 Vickery, B. J. 'A model for the prediction of the response of chimneys to vortex excitation', 3rd Int. Syrup. Chimneys, Munich, Oct. 1978 11 Kwok, K. C. S. and Melbourne, W. W. H. 'Freestream turbulence effects on galloping', J. Eng. Mech. Div., ASCE, 1980, 106 (EM2), Proc. Paper 15356, pp. 273-288, 12 Kwok, K. C. S. and Melbourne, W. H. 'Wind-induced lock-in excitation of tall structures', J. Struct. Div., ASCE, 1981,107 (ST1), pp. 57-72 13 Vickery, B. J. and Clark, A. W. 'Lift or across-wind response of tapered stack',J. Struct. Div., ASCE, 1972, 98 (ST1), pp. 1-20 14 Vickery, B. J. 'The cross-wind response of slender structures'. (Ch. 7) Course notes on the structural and environmental effects of wind on buildings and structures (ed. Melbourne, W. H.), Monash University, Australia, May 1981 15 Davenport, A. G. and Novak, M. 'Vibration of structures induced by wind' (Ch. 29, Part II), 'Shock and vibration handbook', Second Edition, (eds. Harris, C. M. and Crede, C. E.), McGraw-Hill, London, 1976 16 AS 1170, Part 2. SAA Loading Code, Part 2 - Wind Forces. Standard Association of Australia, 1975