Environmental Engineering Reference
In-Depth Information
where d(y) is the diameter and C
d
is the drag coefficient which is usually specified
in the appropriate standard. The variation in U can be determined from formulae
similar to those used in
Sect. 1.5
, e.g. Uys et al. [
8
]. However, some standards,
such as Australian Standard AS1170.2 [
12
], require the use of the maximum wind
speed at all heights. For simplicity, a constant U will be used here. The stress due
to the drag is determined by first calculating the shear force V:
V
¼
Z
D
ðÞ
dy
ð
10
:
2
Þ
and then the moment M(y):
M
¼
Z
V
ð
y
Þ
dy
ð
10
:
3
Þ
with the appropriate boundary conditions at y = 0. Equations
10.2
and
10.3
are
derived in standard textbooks on structural design. For a linear taper
d
ðÞ¼
d
0
þ
d
h
d
0
h
y
¼
d
0
þ
d
1
y
ð
10
:
4
Þ
when the deviation due to slip fitting is ignored. d
1
is the taper. Using (
10.3
) leads
to the following expression for the total moment M(y):
M
ðÞ¼
M
0
þ
T
max
y
þ
1
d
0
2
y
2
þ
d
1
2
qU
2
C
d
6
y
3
ð
10
:
5
Þ
with the inclusion of T
max
—the boundary condition on V—and a moment, M
0
,
acting on the tower. M
0
can arise from a number of causes such as gyroscopic or
cyclic loads on the turbine main shaft or a significant overhang of the tower top
centre of mass. For simplicity, it is assumed that T
max
and M
0
act at y = 0.
Equation
10.5
is of the form
M
ðÞ¼
a
0
þ
a
1
y
þ
a
2
y
2
þ
a
3
y
3
ð
10
:
6
Þ
which is used in the program to be described. At any height, the maximum bending
stress, r
b,max
, occurs at a distance d/2 from the centroid, and is given by
r
b
;
max
¼
M
ðÞ
d
ðÞ
2I
ðÞ
ð
10
:
7
Þ
where I, the second moment of area for a regular octagon with wall thickness t,is
p
24 1
þ
2
2
h
i
I
ðÞ¼
10
þ
6
Þ
4
d
4
ðÞ
d
ðÞ
2t
ð
p
3
h
i
Þ
4
0
:
05474 d
4
ðÞ
d
ðÞ
2t
ð
ð
10
:
8
Þ
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