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
Search WWH ::




Custom Search