Civil Engineering Reference
In-Depth Information
The mean wind speed,
Ū,
itself, is a random variable. Its probability distribution can be
represented by a Weibull distribution (see Sections 2.5 and C.3.4):
(5.62)
The total damage from narrow-band vibration for all possible mean wind speeds is
obtained from Equations (5.53), (5.61) and (5.62) and integrating over all wind speeds.
The fraction of the time
T
during which the mean wind speed falls between
U
and
U+δU
is
f
U
(U)
·
δU
.
Hence the amount of damage generated while this range of wind speed occurs is from
Equations (5.53) and (5.61):
The total damage in time
T
during all mean wind speeds between 0 and ∞ is given by,
(5.63)
This can be integrated numerically for general values of
k
. Usually
k
is around 2, in
which case,
This is now of the form of Equation (5.54), so that:
(5.64)
This is a useful closed-form expression for the fatigue damage over a lifetime of wind
speeds, assuming narrow-band vibration.
