Tower Design and Manufacture - Small Wind Turbines: Analysis, Design, and Application - page 220

where Dx k ¼

p Q

0 : 62
1 þ 1 : 91 Dx k = t

a ¼ rt ð 10 : 34 Þ

Þ 1 : 44 ð

where Q is the ''fabrication quality parameter'' which has the value of 40 for Class
A or excellent quality, 25 for Class B for high, and 16 for normal quality. Using
the last value of Q gives a = 0.537. In other words, the inevitable manufacturing
defects reduce the maximum allowable stress by nearly one half and this must be
considered in any interpretation of linear buckling analysis of the ideal structure.
With a = 0.537, r Rcr = 9.32 GPa from Eq. 10.31 . Now according to Eq. 8.17 of
Eurocode 3 [ 5 ], the ''relative slenderness parameter'' is

q

¼

p

F y r Rcr

k ¼

255 = 9320 ¼ 0 : 165 ð 10 : 35 Þ

This value is less than the ''meridional squash limit slenderness'' of 0.20 from
Section D.1.2.2 which means that ''the characteristic buckling stress'' is equal to F y
by Eq. 8.12 of the code rather than r Rcr . The result, in this case, is the same capacity
factor as the ASCE correlations. Both the ASCE and Eurocode 3 [ 5 ] correlations
imply a linear buckling factor of about half that determined from the FEA, the main
difference being that the codes contain some measure of manufacturing

imperfections.
Lattice towers can be made of non-circular sections: angles are the most
common. They also must be designed to avoid buckling in compression. The
relevant equations should be understandable to the reader who has progressed this
far, but they are often complex and convoluted and not of prime interest now that
the buckling of circular and octagonal members have demonstrated the general
design procedure.
The natural frequency of the lattice tower from the FEA analysis is 2.48 Hz
which is significantly higher than for the monopole tower. There are a number of
correlations for the natural frequency that may be of use. AS 3995 [ 17 ] estimates
the first natural frequency, n 1 (Hz), as

r

m 1
m 1 þ m tt

n 1 1500w a
h 2

ð 10 : 36 Þ

where w a is the average width of the tower, 1.032 m in the present case, and m 1 is
the ''generalized mass'' defined as

" #

2
þ 0 : 15 m 1 ¼ m t þ m tt

3

w a
w h

ð 10 : 37 Þ

where w h is the width at the base, equal to 1.975 m in this case. Thus
m 1 = 87.43 kg and n & 2.78 Hz. Another correlation for lattice towers with
ancillaries comes from [ 18 ]:

2 = 3 r

w h
h

270
h

n 1 ð 10 : 38 Þ