Page 247 - Dynamic Loading and Design of Structures

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convenient to include elements in the model which are only used to introduce loads properly.
This kind of model is indicated for the guyed tower in Figure 5.15. The first step is to
determine the DAF, as the ratio between the dynamic extreme response and the quasi-static
extreme response. It is important to determine these responses for representative sea states,
and to perform time domain simulations such that statistical uncertainties do not affect the
results too much (Karunakaran et al., 1993). Dynamic amplification will vary along the
structure. For a jacket with a fundamental natural period of about 4 sec, the DAF for the
overall bending moment may vary between 1.2 and 2.5 from the seabed up to the mean water
level. In particular, the quasi-static bending moment induced by wave loads in the structure
above the sea surface is zero. The dynamic amplification factor DAF=M dyn /M , for that part
stat
of the platform will actually be infinitely large (see moment diagram indicated for the sample
tower in Figure 5.13).
The dynamic effects are therefore, in general, most conveniently simulated by applying
inertia loads (mass×accelerations) on the deck and tower structure masses. Since the masses
are given, the acceleration field is tuned such that the DAF for the base shear and overturning
moment are fairly accurately represented for the extreme wave condition.
Obviously, the method outlined in this section is expected to yield accurate estimates when
the dynamic response is dominated by a single mode, the response is narrow-banded and the
dynamic response is associated with wave periods well separated from those that cause quasi-
static response. This approach is, for instance, adopted in design approaches for jack-ups
(SNAME, 1994).
The behaviour of compliant towers is more complex since dynamic contributions stem
from two modes, with natural periods on either side of the dominant wave excitation period.
This means that the inertia forces in the first mode balance excitation forces while the inertia
forces in the second mode add to the excitation. However, Vugts et al. (1997) show that fairly
accurate results can be obtained by calibrating a quasi-static approach with inertia loads for
this kind of platforms as well.
The magnitude of the load factor should reflect uncertainties involved in the determination
of load effects (see e.g. Moan, 1995). It is noted that steady-state wave-induced drag loads
normally are subject to more uncertainty than inertia loads. This is because the drag force is
more empirical in nature and also because it is more critically dependent on the kinematics
model for the splash zone. No design code currently reflects this difference in uncertainty
level by load factors dependent on the relative magnitude of drag and inertia forces.
Ringing and other higher order wave loads are subject to even larger uncertainties.
Uncertainties associated with lack of knowledge are often compensated by using conservative
approaches. Actually load model uncertainties may be so large that experiments are required
to determine the characteristic load effects, as discussed in Section 5.5.5.
When the inertia and damping forces are induced by the loading, uncertainties associated
with these reaction forces add to those in the excitation forces. When dynamic effects are
represented by an equivalent inertial load pattern as mentioned