Page 440 - Marine Structural Design

416 Part IV Structural Reliability

Figure 23.1 Limit State Concept

The structural failure probability Pf can then be calculated as
P, = P(g(Z) I o)= (23.3)

and the reliability R is
R = 1-P, = P(g(Z) > 0) (23.4)

The exact numerical integration is only practical for a very limited class of simple problems. A
variety of procedures representing different levels of sophistication may be used to calculate
the failure probabilities, namely safety index method, analytical approach and numerical
approach.
Cornell Safety Index Method
Assuming that the limit state function is given below
g(Z)=R-S (23.5)
where R and S are random variables representing the strength and load respectively. Cornell
(1 969) proposed to estimate the safety index using

(23.6)

where, and 3 are the mean values of R and S; OR and GS are standard deviations of R and S
respectively. ne safety index is uniquely related to the failure probability by
p/ = a(- P> (23.7)

where is the standard normal distribution function. see the table below.