A FIXED LEG PLATFORM: STATISTICAL RESPONSES
245
Figure 9.7 Response spectra for the displacement coordinates of the fixed leg
platform.
Numerical results for these response spectra, computed using MathematicaO
(1999), and PSI-Plot (1999), are shown in Figure 9.7. As one would expect, the
higher spectrum is associated with , or the deck level at 76 m. These peaks
for 5(^,0?) and S(£2,w) are 111.2 x 10“4 m2-s/rad and 13-6 x 10"4 m2-s/rad,
respectively, where both peaks occur at üj = 0.372 rad/s. The variance of each
response was computed from these results using équation (9.81), where the limits
of intégration (0, oo) were replaced by (0.16,1.4) rad/s. Those results and their
rms values are as follows:
tr2(^) = 69.62 x 10~4 m2; cr(€i) = 0 0834 m
(9.98)
(9.99)
Assuming a Gaussian process, there is only a 0.026 percent chance that each
response exceeds the ±3 0.0878 m. Note that these latter two displacements of 0.250 mi an d 0 0878
are close to the respective values of $| — 0.1937 m and £2 — •
m er’
in Section 9.1 as the peak responses to a single incident harmonie wave v.1 a
significant wave height of 15 m.