Page 244 - Dynamic Loading and Design of Structures

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the total wave loads. For instance, for a regular wave of length λcancellation occurs for
/
members with a distance λ2. For identical vertical members with a distance of 40 m,
complete wave force cancellation in deep water then would occur for a wavelength of 80 m,
or a wave period of 7.2 sec. This means that it is possible to obtain a very beneficial
cancellation of forces for waves with a period close to the natural period of flexural vibration.

5.5.2 Calculation of extreme load effects for ULS check

Modern design codes require environmental design load effects to be determined based on
−
2
characteristic loads which correspond to an annual exceedance probability of, say, 10 and
appropriate load factors (API, 1993/1997; NORSOK N-003, 1999), using appropriate models
of sea loading, structure and soil. Models of different refinement are used at different design
stages—conceptual, pre-engineering and detailed engineering—with a balance of probabilistic
and mechanics features.
The simple global behaviour (like ‘stick’ models of platforms) used in early design phases
are refined towards detailed design. At this stage a detailed finite element model (Figure 5.15)
of the structure is required to determine the relevant load effects for each structural
component.
Design analyses for fixed platforms, like jackets, gravity platforms and jack-ups are
commonly based on a regular (design) wave. When dynamic effects are of concern, an
improved model—recognizing the stochastic features of waves—is necessary. It is then
important to ensure that the refined model is properly based on current design practice. This
means, for instance, that a stochastic analysis approach should be consistent with the design
wave approach for structures with quasi-static behaviour. Moreover, dynamic effects should
preferably be considered by their additional forces as compared with their quasi-static ones.
To illustrate these two issues consider wave load effects obtained for a three-legged jack-up
platform (Karunakaran et al., 1994). With typical member diameters in the range of 0.15 to
0.8m, drag forces predominate in extreme sea states. (This fact is observed in Table 5.1 which
shows that load effects are proportional to CD.)
The structural damping was taken to be 2 per cent and hydrodynamic drag damping was
included by the relative velocity term. A non-linear soil-structure model for the spud can
foundation was used. The first natural period is 5.7 sec at extreme load levels. In stochastic
analyses C and C were taken to be 1.0 and 2.0, respectively. C for the design wave is 0.7.
D
M
D
A Gaussian and non-Gaussian model for surface elevation are considered. The non-Gaussian
model is based on a second order Stokes expansion. The kinematics is based on the Wheeler
modification. The regular design wave is modelled by a Stokes fifth order theory.
The results in Table 5.1 show that the quasi-static and dynamic load effects increase by
introducing second order (non-Gaussian) waves.
The comparison between quasi-static load effects obtained by the stochastic time domain
and a design wave approach (in terms of the factor RQS) shows the importance of consistent
definition of the total procedure for calculating load effects. In