Civil Engineering Reference
In-Depth Information
5.4.3
Background loading distributions
As discussed previously, the background wind loading is the quasi-static loading
produced by fluctuations due to turbulence, but with frequencies too low to excite any
resonant response. Over the duration of a wind storm, because of the incomplete
correlations of pressures at various points on a structure, loadings varying both in space
and time will be experienced. It is necessary to identify those instantaneous loadings
which produce the critical load effects in a structure. The formula which enables this to
be done is the 'Load-Response Correlation' formula derived by Kasperski and Niemann
(1992).
This formula gives the expected 'instantaneous' pressure distribution associated with
the maximum or minimum load effect. Thus, for the maximum value, of a load
effect,
r:
(5.34)
where and
σ
pi
are the mean and root-mean-square (r.m.s.) pressures at point or panel,
i;
ρ
r,
pi
the correlation coefficient between the fluctuating load effect and the fluctuating
pressure at point
i
(this can be determined from the correlation coefficients for the
fluctuating pressures at all points on the tributary area and from the influence
coefficients); and
g
B
the peak factor for the background response which normally lies in
the range 2.5-5.
A simple example of the application of this formula is given in Appendix F.
The second term on the right-hand side of Equation (5.34) represents the background
fluctuating load distribution. This term can also be written in the form of a continuous
distribution:
f
B
(z)=g
B
ρ(z) σ
p
(z)
(5.35)
where
ρ(z)
denotes the correlation coefficient between the fluctuating load at position
z
on the structure and the load effect of interest; and
σ
p
(z)
is the r.m.s. fluctuating load at
position
z
.
In Equation (5.34), the correlation coefficient,
ρ
r,
pi
,
can be shown to be given by:
(5.36)
where
I
k
is the influence coefficient for a pressure applied at position,
k
.
The standard deviation of the structural load effect,
σ
r
,
is given by (Holmes and Best,
1981):
(5.37)
