Civil Engineering Reference
In-Depth Information
A useful empirical approach has been proposed by Wirsching and Light (1980). They
proposed that the fractional fatigue damage under a wide-band random stress variation
can be written as:
D
=λ
D
nb
(5.55)
where
D
nb
is the damage calculated for narrow-band vibration with the same standard
deviation,
σ
(Equation 5.53). A is a parameter determined empirically. The approach used
to determine λ was to use simulations of wide-band processes with spectral densities of
various shapes and bandwidths and rainflow counting for fatigue cycles.
The formula proposed by Wirsching and Light to estimate λ was:
λ=
a
+(1−
a
)(1−
ε
)
b
(5.56)
where
a
and
b
are functions of the exponent
m
(Equation 5.48) obtained by least-squares
fitting as follows:
(5.57)
(5.58)
ε
is a spectral bandwidth parameter equal to:
(5.59)
where
µ
k
is the kth moment of the spectral density defined by:
(5.60)
For narrow-band vibration
ε
tends to zero and, from Equation (5.56), λ approaches 1. As
ε
tends to its maximum possible value of 1, λ approaches
a
given by Equation (5.57).
These values enable upper and lower limits on the damage to be determined.
5.6.4
Effect of varying wind speed
Equation (5.53) applies to a particular standard deviation of stress,
σ,
which in turn is a
function of mean wind speed, Ū. This relationship can be written in the form:
σ=
A
U
n
(5.61)
