Civil Engineering Reference
In-Depth Information
6.3 Buffeting response
As previously discussed in chapter 4, for practical reasons it is in the following
distinguished between three cases. First a case of single mode single component
response will be shown. This will render a suitable solution if eigen-frequencies are well
separated and there is insignificant structural or flow induced coupling between
horizontal, vertical and torsion displacement components. Second, a case of single mode
three component response will be shown. This is a suitable solution strategy if there is
significant structural or flow induced coupling between any of the three displacement
components, and if eigen-frequencies are still well separated. Finally, a full multi mode
approach is presented.
The buffeting load is given in chapter 5.1. As shown in Eq. 5.8 (see also Eqs. 5.15 and
5.16), it comprises a time invariant mean part
()
, previously dealt with in chapter 6.2
q
x
above, and a fluctuating part
(
)
xt
,
q
=⋅
B v C r K
+⋅
+⋅
r
(6.10)
q
ae
ae
Cr
that contains a flow induced contribution
Bv
and two motion induced parts
⋅
⋅
q
ae
and
ae
Kr
. The content of Eq. 6.10 is defined in Eqs. 5.9 - 5.14. It is applicable in time
domain as well as in frequency domain. Improved frequency domain counterparts to
B
,
a
C
and
a
K
are given in Eqs. 5.19, 5.24 and 5.25. As shown in chapter 4.2 - 4.4, in a
modal frequency domain solution the flow induced part of the load (i.e. the modal
versions of
Cr
and
Kr
) are moved to the left hand side of the equilibrium
equation and included in the modal frequency-response-function. Thus, the development
of a modal buffeting load needs only consideration of the flow induced part
⋅
⋅
ae
ae
Bv
, while
the motion induced parts need consideration in the development of the modal frequency-
response-function.
Single mode single component buffeting response calculations
The response spectrum of an arbitrary displacement component at span-wise position
x
due to excitation in a corresponding mode shape number
i
is given in Eqs. 4.28 -
4.30. The variance of the displacement response at
⋅
q
x
is then obtained by frequency
domain integration, i.e.
