Wind direction effects on
cladding and structural loads
E m i l Simiu
Center for Building Technology, National Bureau of Standards, Washington, DC, USA
J a m e s J. Filliben
Center for Applied Mathematics, National Bureau of Standards, Washington, DC, USA
(Received February 1980; revised August 1980)
A simple procedure is proposed for estimating wind loads corresponding
to various return periods, which takes into account directional information
on both wind speeds and aerodynamic response. Examples of the application of the procedure are given, which show that cladding loads calculated
without taking directional information on extreme wind speeds into
account may in certain cases be larger than the actual loads by a factor of
two or more. It is also shoran that it is not appropriate, in general, to
account for wind direction effects by multiplying loads determined
without regard for these effects by a reduction factor of 0.8, as has
been suggested in the literature. In its present form, the procedure is
applicable to cladding panels and to members of relatively rigid structures
in regions not subjected to hurricane winds.
Introduction
Wind direction is, in general, an important design factor
for both climatological and aerodynamic reasons. As far as
the climatology of extreme winds is concerned, it is known
that as a result of basic atmospheric circulation patterns the
distribution of extreme wind speeds with respect to direction
is in general nonuniform. Aerodynamically, the effect of a
wind flow associated with a given gradient speed depends
(a), upon the nature of the terrain - which may vary with
direction and (b) upon the orientation of the structure
with respect to the mean flow.
Information on the directional characteristics of the
extreme wind climate in the United States can be obtained
for a large number of stations from records available at the
National Climatic Center (National Oceanic and Atmospheric Administration). Information on the dependence of
aerodynamic forces upon direction can be obtained, for
various types of structure, from full-scale or laboratory
experiments. The purpose of this paper is to present a simple
procedure for estimating design wind loads corresponding
to any specified mean recurrence interval by combining
these two types of information. The procedure is applicable
to building components and structural members that do not
exhibit any significant aeroelastic effects or resonant amplification of the response to the wind load, e.g., cladding
panels, exterior walls, rigid roof systems, and structural
members of low- and medium-rise buildings or other relatively rigid structures.
Examples of the application of the procedure presented
0141-0296/81/030181-06/$02.00
© IPC Business Press
here will then be given for a few cases of interest in design
practice. The numerical results obtained in these examples
will be used in an attempt to assess various approaches to
the question of how wind direction effects should be
accounted for in developing specifications on design
wind loads. In particular, it will be shown that the approach
employed in reference 2 may lead in certain cases to significant overestimates of the wind loads corresponding to any
specified mean recurrence interval. It will also be shown
that, on the other hand, it is legitimate to question the
appropriateness of accounting for wind directionality by
using a blanket reduction factor of the order of 0.8, as
suggested in references 3 and 5.
The procedure presented in this paper is based on the
description of the wind climate by series of recorded largest
annual speeds blowing from various directions at any given
station. While such a description is useful at stations where
the wind climate is well-behaved, it may be misleading in
regions that may experience hurricane winds or winds
associated with other types of exceptional storms. In these
regions a modified form of the procedure presented here
must be employed.
Wind d i r e c t i o n a n d e x t r e m e w i n d speeds
Data published by the National Oceanic and Atmospheric
Administration (NOAA) do not include sufficient information to allow the description of the extreme wind speed
climate as a function of direction. However, such information can be obtained for a large number of stations from
Eng. Struct., 1981, Vol. 3, July 181
Wind direction effects: E, Simiu and J. J. Filliben
Table 1 Largest annual fastest-mile wind speeds at 10 m above ground in open terrain
Sheridan, Wyoming, 1958-1977
Huron, South Dakota, 1958-1977
Toledo, Ohio, 1959-1977
N
NE
E
SE
S
SW W
NW
N
NE
E
SE
S
SW W
NW
N
NE
E
SE
S
SW W
NW
28
41
36
25
22
31
22
33
36
44
36
28
28
33
23
28
24
22
31
44
20
25
21
18
23
14
15
31
21
14
19
16
13
15
19
23
28
22
24
20
23
19
16
30
22
23
18
20
19
16
19
15
20
22
26
19
19
19
28
19
50
29
34
36
36
33
34
33
34
40
35
36
35
31
36
32
37
27
33
40
23
25
26
27
16
36
19
18
14
36
21
22
37
22
37
18
25
28
38
36
50
40
43
47
47
63
54
67
51
51
39
54
61
49
55
46
57
39
47
34
51
38
45
38
52
48
54
43
45
42
40
34
37
31
44
39
49
33
33
44
70
61
61
60
61
57
61
55
61
62
47
67
54
47
47
65
56
51
47
56
34
56
41
34
32
36
38
38
55
36
44
55
36
39
43
47
39
35
46
44
40
25
33
47
37
39
35
35
32
51
49
42
30
37
27
37
48
28
36
49
37
25
35
26
51
48
35
25
34
30
27
26
26
37
25
34
28
36
27
28
32
31
63
42
46
40
38
39
36
42
39
38
36
37
34
49
46
61
36
39
48
49
45
41
51
44
46
38
37
42
42
38
46
49
47
38
39
37
44
38
31
45
29
63
44
28
56
46
37
38
37
37
39
42
34
34
77
46
59
49
56
55
52
45
71
65
62
51
59
62
79
61
46
47
55
50
47
57
48
49
37
25
34
33
28
28
32
33
38
34
26
23
22
25
30
23
28
27
37
31
30
30
38
26
37
35
34
28
36
33
39
25
30
23
30
29
26
29
32
32
31
24
22
28
26
30
27
25
18
24
25
26
26
20
21
26
23
34
23
23
21
39
32
18
21
31
25
35
26
17
28
26
24
35
18
39
20
35
22
28
33
31
24
27
25
23
27
24
29
20
35
25
26
32
26
42
38
39
43
46
40
45
34
61
44
36
44
46
36
44
41
44
42
39
39
37
51
39
42
39
51
36
42
42
51
36
48
48
39
39
43
39
43
44
38
32
56
38
37
42
38
34
34
54
55
43
39
39
39
51
34
28
Vma x
31
7.0
44
20
4.7
31
21
3.9
30
35
4.8
50
26
7.9
38
50
8.4
67
42
6.7
54
57
6.8
70
41
7.2
56
38
7.9
51
32
7.4
51
41
8.4
63
43
4.6
51
44 38
12.6 9.7
77 66
56
8.7
79
30
4.9
38
31
4.1
37
26
3.7
32
27
6.8
39
27
4.5
35
42
5.8
61
42
5.1
51
41
7.9
56
All directions
V = 59;s(V) = 6.5
s(V)
~'= 60; s(V) = 8.8
unpublished NOAA records. Given in Table 1 are largest
annual fastest-mile wind speeds blowing from each octant
at 10 m above ground in open terrain in mph (1 mph =
0.447 m/s) obtained for three stations from NOAA records.
Also given in Table i are summary statistics including the
sample mean, the sample standard deviation, and the
maximum value of the largest annual fastest-mile wind
speeds blowing from each octant, V, s(V), and Vmax,
respectively. The last line of Table l includes sample
statistics for the samples of data, Via, ( / = 1, 2 . . . . , n where
n = sample size), defined as follows:
V~ = max[ Vj(ai)]
(1)
in which Vi(ai) = largest annual fastest-mile wind speed
blowing from octant i (i = 1, 2 , . . . , 8), i.e., for any given j,
Vfl is the largest of the speeds Vj(ai). The wind speeds V~
(] = 1, 2 . . . . , n) are referred to as the set of largest annual
speeds from any direction. For example, at Huron, the
largest annual speeds from any direction for the years
1958-1961, which correspond to the first four lines of data
in Table I, are 56, 56, 63, and 63 mph.
Note that the characteristics of the extreme winds depend
strongly upon direction at each of the three stations of
Table 1. For example, east winds are considerably weaker
tha northwest or southwest winds in all three cases.
If it can be determined that the terrain roughness depends
upon direction at the anemometer site, the data should be
corrected accordingly. This can in principle be done on the
basis of the short-term wind profile measurements, or from
comparisons of short-term records of wind speeds at upper
elevations with the surface data. 6
The dependence of the extreme wind speeds upon
direction can in principle be described by fitting a joint
probability distribution of the wind speeds and directions
to data such as those of Table 1. Research on the appropriate functional form of such joint distributions is, to date,
quite scant. Indeed, to the writers' knowledge, no model
182
Eng. S t r u c t . , 1981, V o l . 3, J u l y
29
44
30
41
66
54
36
24
49
37
33
36
36
40
38
37
26
37
32
32
Q = 47;s(V) = 6.5
for the joint distribution of wind speeds and directions is
currently available that would satisfy the requirements of
(a), providing an adequate fit to actual data and (b), yielding, by integration with respect to the azimuthal parameter,
a marginal distribution consistent with accepted probabilistic
models of the extreme wind speeds from any direction (e.g.,
the extreme value type I or the Weibull distribution). It will
be shown subsequently that a rigorous statistical analysis of
wind forces on cladding, exterior walls, rigid roofs, and
structural members of low- and medium-rise structures or
of other relatively rigid structures, can be carried out without any recourse to joint probability distribution models of
the wind speeds and directions.
Wind direction and a e r o d y n a m i c forces
As previously mentioned, the aerodynamic forces induced
on a structure by a flow associated with a given gradient
speed will in most cases depend upon the flow direction,
owing to the following two factors:
(1) The oncoming flow in the atmospheric boundary
layer depends significantly upon the terrain features upwind of the structure (i.e., the terrain roughness, or the
possible presence of obstructions). If the terrain features
vary with direction, so will the oncoming flow and, consequently, the aerodynamic forces on the structure.
(2) Even if the terrain features around the structure are
the same for all azimuths, the magnitude of the aerodynamic
forces will depend upon the orientation of the structure
with respect to the mean flow, except in the case in which
the structure has a circular shape in plan.
With few exceptions, aerodynamic forces on structures
and their dependence upon direction cannot be determined
analytically and must therefore be obtained by measurements. The peak aerodynamic force (or pressure) acting on
a component or member, and induced by a flow with mean
Wind direction effects: E. Simiu and J. J. Filliben
0.158
speed blowing from octant i (i = 1, 2 . . . . . 8) can be expressed as:
p~(~i) aCp(~i) v~(~i)
where Cp(cq) = peak force (or pressure) cofficient, Vt((~i) =
mean wind speed at top of boundary layer, and a = factor
with the dimensions ofpp/V~.
Coefficients Cp(~i) are given in Figures I to 4 for the
following four cases. Case I [1, p. F19] (Figure 1) corresponds to the uplift force induced by wind on one column
of an interior symmetrical frame in a building surrounded
on all sides by open terrain. (Building dimensions: 30.5 m
long, 24.4 m wide, 4.9 m eave elevation, 1 : 12 roof slope.)
Note that, owing to the unsteady nature of the flow around
the building, the wind induces an uplift force regardless of
the direction from which it blows. Case II (Figure 2)
corresponds, for the same building as in case I, to the larger
of the uplift forces acting on either of the two columns of
the frame. Case III (Figure 3) corresponds, approximately,
to the compression force on the upper horizontal member
of an end braced frame in a building with the same dimensions as the building of case I, but in which all lateral loads
are transmitted to braced frames located at the end walls
[reference 1, p. A4.1, columns Cp9 and Cplo]. Case IV
(Figure 4) corresponds to the absolute values of the sections on the exterior wall at a point (identified as tap 127
in reference 2, p. 26) located 33.7 m above ground near
the corner of a 101 m tall building in urban terrain. (For
a description of the building and its surroundings, see
reference 2). The coefficients shown in Figure 4 represent
0.3
0
0
,~
/
T
0158
0.162
l
0.41
~ T a p 127
2.90
1.47
\
T \
083
Figure 1 Coefficients Cp(ai) for case I
/
0.79
T \
Figure 2 Coefficients Cp(ai) for case II
Coefficients
Cp(c~i) for case IV
an envelope of coefficients measured for 24 mean wind
directions (reference 2, pp. 72-114).
066
065
"
0 83
0.72
Estimation of aerodynamic forces corresponding
to a specific r e t u r n period
083
0 52 - - ~
O. 65
T
05, ~
Figure 4
065
f
1.21
03
.'#
/
0.158
042
130
065
\
Figure 3 Coefficients Cp(c~i) for case III
/
0.52
0.158
(2)
=
0.3
0.162
0.52
0 65
Current approaches
Two approaches for estimating aerodynamic forces
corresponding to a specified return period are documented
in the literature. In one of these approaches, 2 it is assumed
that the conditional probability distribution of the extreme
winds, given that the wind blows from a specified octant,
is the same as the probability distribution of the extreme
winds from any direction (as defined in this paper immediately following equation (1)). The second approach requires
the fitting of a joint probability distribution to the extreme
wind data corresponding to various azimuth angles. From
this joint distribution, and from aerodynamic information
on the direction-dependent response, a joint probability
distribution of response and direction is obtained. The
probability distribution of the response is then, by definition, equal to the marginal distribution calculated by inte-
Eng. S t r u c t . , 1 9 8 1 , V o l . 3, J u l y
183
W i n d d i r e c t i o n effects: E. S i m i u a n d J. J. F i l l i b e n
grating this joint distribution with respect to the azimuthal
parameter.6
Proposed approach
While the approach presented in this paper does incorportate directional information on extreme wind speeds,
it does not require the estimation of joint probability
distributions of wind speeds - or wind-induced effects and directions. Rather, a random variable is defined which
consists of the maximum annual wind effect of concern
(e.g., pressure, force, stress, and so forth), or of a function
thereof suitably chosen for computational convenience. A
cumulative probability distribution function (CDF) is then
fitted to the data consisting of the values taken on by this
random variable in a sufficiently large number of consecutive years. The wind effect with a N-year return period
corresponds to the value of the variate for which the
ordinate of the CDF is 1 - I/N.
Application: estimated 50-yr pressure at a point on exterior
wall o f a high-rise building
To illustrate the application of the procedure, the 50-yr
pressure will be sought at the exterior wall location (tap
127 in reference 2) for which the pressure coefficients are
given in Figure 4. The following random variable will be
used:
rdir = max [C~/2 (ai) V(ai)]
(3)
It will be assumed that the structure is located in Huron,
S.D. (see Table 1), and that the building of Figure 4 is so
oriented that its short side is parallel to the north direction
and the point under consideration is northeast of the
centre of the building. The factors Cp(ai) and C~/2(~i) will
then have the absolute values given in Table 2.
Using these values in conjunction with the extreme wind
speeds at Huron listed in Table 1, the following set of values
of the random variable Ut i t is obtained :
62, 54, 59, 71,87, 82, 64, 52, 60, 56, 54, 46, 45, 63,
46, 58, 87, 61,67, 56
These data were subjected to a statistical analysis aimed at
determining the best fitting Weibull, extreme value type I,
or extreme value type II distribution and its parameters.
The computer program used in this analysis was similar to
that described in reference 4. It was found that the data
were best fitted by an extreme type I distribution, which
yielded d ~ r : 93.5 mph (41.8 m/s), where ~ r = estimated
value of rair corresponding to a probability of exceedance
0.02 in any one year (i.e., a return period N = 50 yr).
A random variable will now be defined, which is consistent with the procedure of reference 2, i.e., which, in
contradistinction to r ctir, does not reflect climatological
wind direction effects:
~od = max [C~/2(ai)] V~o
bution, it follows from the data of Table 1 that V~o =
82.5 mph (36.9 m/s), so that, with max[C~/2(a)] = 1.7
(Table 2), equation (4) yields rnso
a = 140.2 mph (62.7 m/s).
The ratio of the 50-yr pressure estimated by ignoring
climatological wind direction effects, p~oa, to the 50-yr
pressure estimated by taking these effects into account,
dir
Pso,
is then, in this example:
n d _ (140.2
Pso
air \ ~ . 5 - !
Pso
nd
P20
dir
P20
Values of
- 2.34
P air
20e
= a max [Cp(ai) V2max(~i)]
(7)
it follows from Tables 1 and 2 that:
nd
P20
dir
P 20e
= 2.22
(8)
This ratio is seen to differ rather insignificantly from the
_ndt_dir
ratio p:o/p2o - This is the case because the difference
between the estimated 20-yr pressure, pd~r, and the extreme
dir
pressure, P2oe, that would actually have been recorded in
the 20-yr period covered by Table 1, is only of the order
of 5%.
If we now define :
P2oend = d
max [Cp (ai)] {max [ Vmax(ai)] }2
(9)
where pn2de = pressure calculated by ignoring climatological
wind direction effects and based upon the maximum wind
speed from any diiection actually recorded in the 20-yr
period covered by Table 1, max[Vmax(C~i)], rather than
upon the estimated value V~o, we obtain the result:
nd
P 2oe
dir
- 2.37
(10)
P 2oe
i.e., this ratio differs by less than 2% from the ratio given
by equation (6). This shows that, in this example, deviations from actual data that are inherent in the estimates
p dir A
20 un the one hand and P2o
na on the other hand are of the
same order of magnitude.
Additional case studies:
dir
al-
I Cp(ai)land C~2(ai )
N
NE
E
SE
S
SW
W
NW
ICp(ai)l
C~/Z(ai)
0.42
1.21
2.90
0_72
0,79
1.30
1.47
0.41
0.65
1.10
1.70
0.85
0,89
1.14
1,21
0.64
Pso
nd
P5o
dir
P20
na
a3 =
a4 -
P 2oe
nd
P2o
dir
P20e
na
P2oe
Eng. Struct., 1981, Vol. 3, July
(6)
(lla)
(1 lb)
P2o
dir
ai
184
(5)
ncl
It is of interest to compare the 20-yr pressure, P2o,
estimated by ignoring climatological wind direction effects, to
the maximum pressure, pa~e , that would actually have
occurred during the 20-yr period covered by Table 1. Since:
a2Table 2
= 2.25
i.e., if the procedure of reference 2 - which ignores
climatological wind direction effects - were used, the
50-yr pressure would be overestimated by 225%. It can
be verified that for a 20-yr return period:
(4)
where V~o = estimated value of the 50-yr wind speed from
any direction. Assuming that the extreme winds from any
direction are described probabilistically by a type I distri-
12
(1 lC)
(11d)
W i n d d i r e c t i o n e f f e c t s : E. S i m i u a n d J. J. F i l l i b e n
Ratios al to a4 (for the Toledo station subscript 20 must
be replaced by subscript 19) were calculated in the cases
previously designated as I, II, III and IV (Figures 1, 2, 3
and 4, respectively) for various building orientations and
wind climates. The results of the calculations are given in
into account the directional characteristics of the wind
climate is clearly quite important for at least five of the
eight possible orientations of the building, even if allowance is made for possible sampling errors. This effect is seen
to be much less pronounced in cases II and III, and to
some extent in case I, owing to the less peaked character
of the variation of Cp with direction in these cases.
As previously mentioned, it was suggested 3,s that it is
appropriate to account for wind direction effects - particulady for the purpose of developing building code wind
loading provisions - by multiplying loads determined
without regard for these effects by a reduction factor of
about 0.8. The results of Table 3 suggest that this approach
is in general not justified. For example, if this approach
were adopted, the loads corresponding to case II (Sheridan)
would be underestimated by 20% for all buildings with a SE
(or NW) orientation of the short side and by about 12%
for all buildings with a NE (or SW) orientation. Thus, if a
uniform distribution of the building orientations were
assumed, the use of a reduction factor of 0.8 would lead
to the underestimation of the wind loads on half of the
buildings of the aerodynamic type represented in Figure 2.
Clearly, the underestimation would be even more severe in
case III.
Table 3 also shows averages of the quantities al to a4 for
all directions. In this connection it should be emphasized
that the use of such averaged reduction factors could well
be unacceptable as far as the safety of buildings with
certain unfavourable orientations is concerned. For
example, in case IV, if the average reduction factor 0.65
were used, the cladding load would be severely underestimated for all buildings oriented with the short side in
Table 3.
Interpretation of r e s u l t s
Note that in all cases the differences between the values o f
al and a2 are small for practical purposes. However, the
differences between the values of a2 and a3 are in certain
cases significant (e.g., case II, NE; case III, NE). The differences between the values of a2 and a4 are somewhat less
than those between a2 and a3, but are still relatively large in
a few cases.
The significance of the differences between a2 and a 3 is
the following. If a2 < 1, it would in theory be permissible
to reduce the load obtained as in reference 2 (i.e., ignoring
climatological wind direction effects) by using the reduction
factor a2. However, if a3 > a2, the load so reduced would
be smaller than the actual load that would have occurred
during the period under consideration. In view of the
errors inherent in the statistical handling of the data it may
therefore be prudent, judging from the examples of Table
3, to use for the design of structures with known orientation reduction factors that are larger than the estimated
ratios a2. In this context, the need for a study of sampling
errors in the estimation ofp~ r for various values of N is
obvious. Such a study would have to be conducted for
a large variety of aerodynamic and climatic situations.
Note, however, that in the case of cladding loads at a
specified point (case IV of Table 3) the effect of taking
Table3
Ratiosa~,a2, a 3 a n d a 4
Direction of short side of building
N
NE
E
SE
Sa
SW a
Wa
NW a
Average for
all directions
0.75
0.74
0.85
0.81
0.59
0.59
0.67
0.64
0.53
0.53
0.53
0.51
0.64
0.62
0.67
0.63
0.72
0.71
0.80
0.75
Case I
(Figure I)
Huron
aI
a2
a~
a4
0.66
0.65
0.79
0.75
0.84
0.81
1.00
0.95
0.80
0.79
0.79
0.75
0.94
0.94
1.07
1.00
Case II
(Figure 2)
Toledo
a~
a2
a~
a,
0.72
0.76
0.87
0.80
0.78
0.83
1.09
1.00
0.82
0.86
0.87
0.80
0.86
0.89
0.91
0.84
0.80
0.84
0.94
0.86
Case II
(Figure 2)
Sheridan
al
a2
a3
a4
0.79
0.80
0.78
0.79
0.85
0.84
0.89
0.91
0.79
0.80
0.78
0.79
1.00
0.98
0.98
1.00
0.86
0.86
0.86
0.88
Case I I
(Figure 2)
Huron
a~
a2
a3
a4
0.77
0.78
0.85
0.79
0.82
0.79
1.00
0.95
0.82
0.80
0.85
0.79
0.97
0.95
1.07
1.00
0.85
0.83
0.94
0.88
Case I I I
(Figure 3)
Huron
ai
a2
a3
a4
0.94
0.94
1.00
0.94
0.80
0.79
1.00
0.94
0.96
0.95
1.00
0.94
0.96
0.94
1.07
1.00
0.92
0.91
1.02
0.96
Case I V b
(Figure 4)
Huron
a1
a2
a3
a4
0.44
0.43
0.45
0.42
0.62
0.60
0.67
0.63
0.48
0.46
0.45
0.42
0.75
0.82
1.00
0.94
0.58
0.60
0.74
0.72
0.90
0.96
1.06
1.00
0.52
0.53
0.53
0.50
0.54
0.57
0.60
0.56
0.60
0.62
0.69
0.65
a If no entry is shown, values are same for S and N, SW and NE, W and E, NW and SE, respectively
b Point under consideration (pressure tap 127, see reference 2) is in the NE-E octant when short side is parallel to north direction, in E-SE
direction when short side is parallel to northeast direction, etc.
Eng. S t r u c t . , 1 9 8 1 , V o l . 3, J u l y
185
Wind direction effects: E. Simiu and d. J. Fill/ben
the SE or SW direction, with the possible consequence
that, for these buildings, the number of cladding failures
due to wind loading would be unacceptably large.
Conclusions
A simple procedure was proposed for estimating wind loads
corresponding to various return periods, which takes into
account directional information on both wind speeds and
aerodynamic response. Examples of the application of the
procedure were given, which show that (1), cladding loads
calculated without taking directional information on
extreme wind speeds into account may in certain cases be
larger than the actual loads by a factor of two or more,
and (2), it is not appropriate, in general, to account for
wind direction effects by multiplying loads determined
without regard for these effects by a reduction factor of
about 0.8, as suggested elsewhere. 3,s
The procedure presented in the paper is applicable to
building components and structural members that do not
exhibit any significant aeroelastic effects or resonant
amplification of the response to the wind load, e.g.,
cladding panels, exterior walls, rigid roofs, and structural
members of low- and medium-rise buildings or other
relatively rigid structures. Also, the application of the
procedure in its present form is limited to well-behaved
wind climates, i.e., to regions where hurricane or other
extraordinary winds may not be expected to occur or
are not taken into account in design. (A modified version
of the procedure, applicable to hurricane-prone regions, is
currently being developed by the writers.)
Information on the dependence of extreme wind
speeds upon direction can be obtained for a large number
of US weather stations from unpublished records of the
National Oceanic and Atmospheric Administration. The
writers believe that it would be useful (1), to extract and
publish such information, and (2), to undertake on its
basis studies of sampling errors in the estimation of the
dependence of wind effects upon direction.
Acknowledgements
The writers wish to thank M. J. Changery, of the National
Climatic Center, National Oceanic and Atmospheric Administration, who provided the data used in Table 1, and M. E.
Butts of the Center for Building Technology, National
Bureau of Standards, for useful exchanges and valuable
contributions to this paper. The work presented here was
partly supported by the National Science Foundation
under agreement No. ENV-7716113 and the Department of
Energy, Office of Assistant Secretary, Conservation and
Solar Applications. Any opinion, findings and conclusions
or recommendations expressed in this publication are those
of the authors and do not necessarily reflect the views of
the National Science Foundation or the Department of
Energy.
186
Eng. Struct., 1981, Vol. 3, July
References
1 Davenport, A. G. et al. "Wind loads on tow-rise buildings: Final
report of phases I and II, parts 1 and 2, BLWT-558-1977',
Boundary Layer Wind Tunnel Laboratory, The University of
Western Ontario, London, Ontario, Canada, 1977
2 Peterka, J. A. and Cermak, J. E. 'Wind tunnel study of Atlanta
office building', Department of Civil Engineering, Colorado
State University, Fort Collins, Colorado, 1978
3 Ravindra, M. K. et al. 'Wind and snow load factors for use in
LFRD', J. Struct. Div., ASCE, 14, (ST9), Prec. Paper 14006,
September, 1978, pp. 1443-1457
4 Simiu, E. and Fill/ben, J. J. 'Probability distribution of extreme
wind speeds', J. Struct. Div., ASCE, 102, (ST9), Prec. Paper
12381, September, 1976, pp. 1861-1877
5 Stathopoulos, T. Discussion of Paper, "Wind and snow load
factors for use in LRFD', J. Struct. Div.. ASCE, 105, (ST10),
October, 1975, pp. 2132-2133
6 Surry, D. and Davenport, A. G. 'Modeling the wind climate: an
overview', Prec., Workshop on Wind Climate, Asheville, North
Carolina, November 12-13, 1979, Texas Tech. University,
Institute for Disaster Research, Lubbock, Texas, 1980
Notations
a, d = factors in equations (2), (7) and (9)
ax, a2, a3, a4 = ratios defined by equations (11)
Cp = peak force or pressure coefficient
dir = superscript indicating that climatological
wind directionality effects are taken into
account
max[ ] = denotes maximum value
nd = superscript indicating that climatological
wind directionality effects are ignored
N = return period
p~r, p~va = wind effect (e.g., pressure, force) with an
N-year return period, estimated by taking
into account and by ignoring climatological
wind directionality effect, respectively
pdir
_nd
.
.
Ne, PNe = wlnd effect that would have actually
occurred in given N-year record, calculated
by taking into account and by ignoring wind
directionality effect, respectively
pp = peak aerodynamic force or pressure
r air, r~ zr = random variable defined by equation (3),
value of r air corresponding to a N-year
return period, respectively
r ha, r~ a = random variable defined by equation (4),
value of r na corresponding to a N-year
return period, respectively
s(V) = sample standard deviation of V
V, V, Vmax= wind speed, sample mean of V, sample
maximum value of V, respectively
Vi(ai) = largest annual fastest-mile wind speed
observed in jth year of record from octant i
Vja, V} = largest annual fastest-mile wind speed blowing in ]th year of record from any direction,
fastest-mile with N-year return period blowing from any direction, respectively
Vt = wind speed at top of boundary layer
a i = denotes octant i (i = 1, 2 . . . . . 8)