Civil Engineering Reference
In-Depth Information
(see Eqs. 4.15 and 4.49) or in a multi mode approach (see Eqs. 6.47 and 6.81). These
eigen-modes are most often given as more or less ample vectors along the span of the
structure, and their second and third order derivatives, which are required for the transfer
from displacements to cross sectional forces, may in many cases be difficult to calculate
with sufficient accuracy. It is therefore desirable (as indicated in Fig. 7.1.b), to split
2
F
σ
2
F
B
2
F
R
into a background part
and a resonant part
, such that
σ
σ
2
2
2
σσ σ
≈
+
(7.3)
F
F
F
R
B
It is seen that this implies that the total response is sub-divided into a low frequency
(background) part and a fluctuating (resonant) part that is centred on the eigen-
frequency.
Fig. 7.2
Background and resonant part in time domain
This is further illustrated in Fig. 7.2. In time domain the background part is equivalent
to a slowly varying process. Its contribution to inertia forces may therefore be
disregarded, and thus, the load effects from this part may be regarded as quasi-static.
Clearly, the quasi-static part of the load effects are more accurately determined from
static shape functions or more directly from simple static equilibrium conditions, rather
than a calculation based on the derivatives of eigen-modes.
The second motivation behind such a partition of
2
σ
is the following. As previously
described, when a structure is subject to a fluctuating wind field, the passing of the flow
will generate fluctuating drag, lift and moment load components on the structure. These
loads may cause the structure to oscillate. But in many cases the structure is stiff and its
eigen-frequency is high (e.g. beyond 5 Hz), and then the displacements are small.
