Page 353 - Wind Energy Handbook

REFERENCES 327

ð
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R

ó MB (r ) K SMB (r ) c(r)[r r ]dr
¼ r ð (A5:58)
ó MB (0) K SMB (0) R
c(r)r dr
0

The ratio of the steady moment at radius r to that at the root is
Ð
Ð
R

R
r c(r)[r r ]dr= 0 c(r)r dr, so the ratio of the standard deviation of the quasistatic

fluctuations at radius r to the steady value there is
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ó MB (r ) ¼ ó MB (r ) ó MB (0) M(0) ¼ ó MB (0) K SMB (r ) (A5:59)

M(r ) ó MB (0) M(0) M(r ) M(0) K SMB (0)

Generally, the square root will be close to unity, so ó MB (r )=M(r ) will be nearly
constant.
A5.8.2 Resonant response
In Section A5.5 it was shown that the standard deviation of the first mode resonant
Ð
2 R
1
root bending moment is equal to ø ó x1 0 m(r)ì 1 (r)r dr (Equation A5.27). The
corresponding quantity at other radii can be derived similarly, giving
ð R
2
ó M1 (r ) ¼ ø ó x1 m(r)ì 1 (r)[r r ]dr (A5:60)
1
r
Hence the ratio of the standard deviation of the first mode resonant root bending

moment at radius r to the steady value there is
ð R ð R

ó M1 (r ) ó M1 (r ) ó M1 (0) M(0) r m(r)ì 1 (r)[r r ]dr 0 c(r)r dr ó M1 (0)
¼ ¼ ð ð

M(r ) ó M1 (0) M(0) M(r ) R R M(0)
m(r)ì 1 (r)r dr c(r)[r r ]dr
0 r
(A5:61)
References

Cramer, H. E., (1958). ‘Use of power spectra and scales of turbulence in estimating wind
loads.’ Second National Conference on Applied Meteororlogy, Ann Arbor, Michigan, USA.
Davenport, A. G., (1962). ‘The response of slender, line-like structures to a gusty wind.’ Proc.
Inst. Civ. Eng., 23, 389–408.
Davenport, A. G., (1964). ‘Note on the distribution of the largest value of a random function
with application to gust loading.’ Proc. Inst. Civ. Eng., 28, 187–196.
Dyrbye, C., and Hansen, S. O., (1997). Wind loads on structures. John Wiley and Sons.