Civil Engineering Reference
In-Depth Information
Fig. 4.5
Single mode shape containing three components
Adopting the same assumptions regarding motion induced load effects as presented in
chapter 4.2 above, the total cross sectional load is given by
(
)
(
)
(4.36)
xt
,
xt
, , , ,
q q
=
+
q
rrr
tot
ae
T
(
)
xt
,
⎡
q
q
q
θ
⎤
where:
q
=
⎣
(4.37)
⎦
y
z
is the flow induced part of the load, and
T
(
)
q
xt
,,,,
rrr
=
⎣
⎡
q
q
q
θ
⎤
(4.38)
⎦
ae
y
z
ae
is the motion induced part. The time domain modal equilibrium condition given in
Eq. 4.18 still holds, but for the expressions for
M
,
C
and
K
it is necessary to turn to
Eq. 4.10, i.e.
(
)
while the modal
T
2
M
∫
φ M φ
dx
,
2
and
=
⋅
⋅
CM
ω ζ
=
K
=
ω
M
i
i
0
i
i
i
i
i
i
i
i
L
flow induced part of the load is given by (see Eq. 4.12)
()
T
( ) (
)
Qt
∫
φ
x
xtdx
,
=
⋅
q
(4.39)
i
i
L
exp
