Page 468 - Marine Structural Design

444 Part IY Structural Reliability

powerful tool, in which the limit state function is approximated by a simple and explicit
hnction at the sampling points, e.g. Bucher (1990) and Liu, et al, (1994).
This Chapter presents a methodology for the time-variant reliability assessment relating to the
ultimate strength of the midsection for hull girders subjected to the structural degradations of
corrosion and fatigue. It includes three aspects: (1) closed form equations for assessment of
the hull girder reliability. (2) load effects and load combination, and (3) time-variant reliability.
The progressive collapse analysis of hull girder strength used in the time-variant reliability is a
modified Smith’s method (Smith, 1977). The modification is to account for corrosion defect
and fatigue crack, see Part II Chapter 13.

25.2 Closed Form Method for Hull Girder Reliability

For the vertical bending of the hull girder the limit-state function can be expressed by the
following expression for sea going conditions,

g(xi)=Mu -@Sw +~w) (25.1)
where,
Mu = ultimate vertical bending moment
MSW = still water bending moment for sea going condition
MWV = vertical wave bending moment for in sagging or hogging condition
Assuming these load and resistance variables follow normal distribution and have the same
COV, we may obtained the following equation based on the Cornell safety index method, Eq.
(23.6).

(25.2)

Moreover, taking into account the assumptions adopted for modeling of the random variables,
Eq. (25.2) shows that the safety index for sea going conditions is inversely proportional to the
COV. For an increase of the COV of SO%, the safety index is reduced by 35%.
The Cornell safety index method is also called the Mean Value First Order Second Moment
(MVFOSM) concept, where the reliability index reliability index P is defined as the mean of
the limit state hction divided by its standard deviation.
The limit state function g and reliability index p for different failure modes are
a. For Hull Primary Failure
g = M, - [MS + kw(Kv + kdMd 11 (25.3)

p=lg (25.4)
ag
where,
+kdpMd 11
Pg =PM. -1PMs +kw(pM, (25.5)