Page 216 - Dynamic Loading and Design of Structures

Page 189

by the KC, Re numbers) and surface roughness (Sarpkaya and Isaacson, 1981). When
applying hydrodynamic coefficients to calculate loading on platforms consisting of many
members, additional uncertainties are encountered and should actually be reflected in the
coefficients.
Under such circumstances the coefficients are chosen so as to adequately represent the
loading in view of the wave kinematics formulation used.
The API (1993/1997) recommendation for calculating loads on jacket platforms may serve
to illustrate this point. The key points in this procedure for calculating extreme load effects
are:

●regular wave with appropriate height (e.g. corresponding to 100 year return period) and
period;
●wave kinematics according to two-dimensional Stokes fifth order (or other Stokes type)
methods and appropriate correction factors for shortcrested seas and current shielding or
blockage (i.e. the effect of the structure on the kinematics);
●the input current velocity profile, which refers to MWL, is modified by stretching to
provide current velocities over the total wetted surface;
●the effective diameter of the member is calculated by D=D +2t, where D is the clean outer
c
c
diameter and t is the thickness of the marine growth;
●drag and inertia coefficients for calculation of global loads are selected as:
smooth cylinders: CD=0.65, CM=1.6
rough cylinders: CD=1·05, CM=1.2
Members located 2 m above MWL may be considered smooth and those below are considered
to be rough.
The hydrodynamic coefficients were calibrated to fit in-service measurements (Heideman
and Weaver, 1992).
The relevant hydrodynamic loads for fatigue analyses correspond to more moderate waves
(i.e. with smaller KC numbers than for extreme waves). The implication may be to apply the
same C for smooth cylinders and reduce the C for rough cylinders and increase C to 2.0
D
M
D
(API, 1993/1997).
Morison’s equation accounts for in-line drag and inertia forces, but not for the ‘out of
plane’ (plane formed by the velocity vector and member axis) lift force due to periodic,
asymmetric vortex shedding from the downstream side of a member. Due to their high
frequency, random phasing and oscillatory (with zero mean) nature, lift forces are not
correlated across the entire structure. Their effect on global loads can therefore be ignored
while they may have to be considered for local loads. Morison’s equation also ignores axial
FK, added mass and drag forces, which will be of increasing importance with increasing
diameter to member length.
For (dynamic) spectral or time domain analysis of surface piercing framed structures in
random Gaussian waves and use of modified Airy (Wheeler) kinematics with no account of
kinematics factor, the hydrodynamic coefficients should, in absence of more detailed
documentation, be taken to be (NORSOK N-003, 1999) C =1.0 and C =2.0.
D
M