Page 171 - Pipelines and Risers

144 Chapter 10

(10.6)

where:
n(E,m)= Rain Flow correction factor
A(E,m)= a + (1 - a)(l- Elb
a = 0,926-0,003m
b = 1,587m-2,323
m,,, = spectral zero moment of the hotspot stress spectrum
m,< = spectral second moment of the hotspot stress spectrum
E = band width of the hot spot stress spectrum

Based on Equation (10.6), the transformation of a stress range spectrum to a fatigue damage is
straightforward. Applying a spectral fatigue analysis, analytical expressions may be derived
as the transfer functions from wave spectra to bottom velocity spectra, to response amplitude
spectra and finally to stress range spectrum.

10.3 Force Model

10.3.1 The Equation of In-line Motion for a Single Span
The equation of in-line motion for a Bernoulli-Euler beam subject to wave forces represented
by the Morison force, damping forces and the axial force is given by:

(10.7)
azz
-(CM -l)-pD’-
4 at2

where:
Z is the in-line displacement of the pipe, and is a function oft and x.
x is the position along the pipe
t time
M is the mass of the pipe and the mass of fluid inside
C is the damping parameter
E1 is the bending stiffness parameter where E is the elasticity module and I is the
inertia moment for bending
T effective force (T is negative if compression)
U is the time dependent instantaneous flow velocity