Page 383 - Marine Structural Design

Chapter I8 Fatigue Loading and Stresses 359

where d is the water depth. Numerically solve this equation, it gives W.0296 m-'
Setting x=O at the riser center, the horizontal wave induced water particle velocity is given by:

and the horizontal wave-induced acceleration is

H cosh(k * (x + d))
a(x)=w2 .-. COS(&)
2 sinh(k*d)
When the linear wave theory is used, one can simplify the calculations by separating drag and
inertia forces:
M(d) =M,(&)+M,(d)
where the moment due to the drag forces and inertia forces are given below.
MD(&)=MD,,, *sin'(&) = 4596*sin2(&)(Nm)

M,(d) = M,.,,m * cos(&) = 1306 * cos(unt)(Nm)
Maximizing M(ot) gives:

COS(0t) = MI,IMX = 0.142,wt = 81.8'
2 * Mo,,,
The maximum moment is then given by:
M,,,=4689 Nm
And the resulting stress range is,
MD
S = 2a,, - 12.9MPa
=
I
The procedure above is repeated for all waves and the analysis results are summarized in
Table 18.4 below for the establishment of a stress range exceedance diagram.

H (m) T (sec) F,, (NW s (MP4 LogN
0 0 0 6.72
3.0 7.2 28 1 .o 5.74
5.0 8.7 66 2.3 5.14
7.0 9.8 140 4.8 4.57
9.0 10.8 250 8.6 4.00
11.0 11.7 3 84 13.2 3.45
15.0 13.1 738 25.4 2.35
20.0 14.6 1326 46.7 1 .oo