Page 444 - Marine Structural Design
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420 Part IVStructural Reliability
t SORM
\
Figure 23.3 Illustration of FORM and SORM
23.3.5 Calculation by SORM
In the second order reliability method (SORM), the limit state surface is approximated by a
hyperparaboloid with the same tangent hyperplane and the main curvatures at the design point.
An approximation to the failure probability is then
(23.22)
where i in the third term is the imaginary unit, Re() denotes the real part, and kj (j=1727...,n-1)
are the principal curvatures at the design point. The first term is the asymptotic result for p-m
Using SOW, an equivalent hyperplane can be defined as a linear approximation to the true
failure surface with a reliability index
P smM = (p,.,RM ) (23.23)
The unit normal vector asom is, in practice, approximately set equal to that obtained by
FORM.
In SORM, the limit state surface is approximated by a curvature fitted hyperparaboloid at the
design point u*, as sketched in Figure 23.3 above. Compared SORM with FORM, the estimate
accuracy has been improved by second order approximation.
