Page 239 - Dynamic Loading and Design of Structures

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relative magnitude of drag and inertia forces and possible dynamic amplification. For a quasi-
static response in an extratropical climate, like the North Sea with ‘continuous’ storms, γmay
be around 1.0 while γmay be as low as 0.4–0.6 for Gulf of Mexico platforms subject to
infrequent hurricanes (Marshall and Luyties, 1982). For structures with predominantly drag
forces, γwill be smaller than for predominantly inertia forces. Note, for instance, that if u is
2
=
Rayleigh distributed, F1=c1u will follow an exponential distribution (γ1), while for F2=C2u,
=
u will be Rayleigh distributed (γ2).
Dynamic effects may start to affect load effects relevant for fatigue when the natural period
exceeds 2.0 sec. As illustrated by Marshall and Luyties (1982), increasing the natural period
from 2 sec to 4 sec, may, for example, increase γrom 0.7 to 1.1 and from 0.9 to 1.3 for Gulf
f
of Mexico and North Sea structures, respectively. The implication is a factor of the order of
10 on fatigue damage. Odland (1982) indicated similar results for jack-up platforms.
The stress range level that contributes most to D corresponds to the value that yields the
m
maximum fatigue damage dD that is proportional to f (s)s . This stress range is found to be
s
, implying that fatigue damage is primarily caused by stress
ranges which typically are of the order of 10 to 20 per cent of s .
0

5.5 DYNAMIC ANALYSIS FOR DESIGN

5.5.1 Dynamic features of offshore platforms
The dynamic behaviour of platforms may be illustrated by considering two SDOF models
with reference to Figure 5.11. In both models the loading is assumed to be proportional to the
wave particle acceleration and hence written as:

(5.60)

where the co-ordinate z' refers to the seabed level and the mass consists of a deck mass M and
a uniformly distributed mass m.
Otherwise, the two models have the following properties:

Platform A (fixed platform) Platform B (compliant tower)
Stiffness Soil kψ Uniform buoyancy
Damping Soil cψand uniform damper c Uniform damper c

Model A will typically have a natural frequency above ωwhile the natural frequency for
Model B is below ω The dynamic equation of equilibrium for this stick model is established
.
by assuming that the motion is a rotation ψabout the support on the seabed. The horizontal
displacement is then The equation of dynamic equilibrium is obtained by moment
consideration and results in a SDOF version of eqn (5.43).