Civil Engineering Reference
In-Depth Information
to include any dynamic amplification. It is taken for granted that the wind load may be
split into a mean and a fluctuating part, i.e.
()
( )
q
q
x
q
x t
,
=
+
(2.97)
y
y
y
tot
()
(
)
y
qxt
is a stochastic variable.
Correspondingly, the load effect is split into a mean and a fluctuating part
y
qx
is a deterministic quantity and
,
where
()
(2.98)
M
=+
MMt
tot
Fig. 2.14
Cantilevered tower type of beam subject to fluctuating wind
()
Since
M
may be obtained from
y
qx
alone it is then also a deterministic quantity.
Thus, the prediction of
M
only involves the calculation of a simple static load effect,
and it will not be pursued herein. The instantaneous value of
()
M t
involves the same
()
M t
is a stochastic variable, and it is only its statistical
properties (i.e. its variance and auto spectral density) that can be predicted. From Fig.
2.14 it is readily seen that
simple static calculation, but
L
()
( )
(
)
M t
∫
Gx
qx t
,
x
=
⋅
⋅
(2.99)
M
y
0
()
M
Gx
is the influence
where
L
is the total (or flow exposed) length of the beam and
()
M
Gx x
function for the bending moment at the base [in this case
=
]. The variance of
()
M t
is then given by
