Page 452 - Marine Structural Design

428 Part IV Siructural Reliability

assumed to follow normal probability distribution with mean value ps=20,000 ft-ton
and pz=30,000 ft-ton, respectively, and standard deviations of 0~=2,500 ft-ton and
0~=3,000 ft-ton, respectively. What is failure probability for the hull?
Solution
The reliability index, p, may be estimated using Cornel1 safety index method

Substituting in the numerical values for p~, ps, OR and (SS, we may get

30000 - 20000 = 2.56
P=
J2500’ +30002
The corresponding failure probability is
Pf = 5.23YE-3

Random variable

Figure 23.6 Load and Strength Probability Density hnctions

23.11.2 Example 23.2: p Safety Index Method
Problem
Assuming the random variables R and S are corresponding to the bending moments
of a ship hull girder with normal distributions. The mean value and standard
deviations of R and S are p~=150, 0R=20 and ps=90, os=30 respectively. What is
the p index value and Pr using Hasofer Lind method?
Solution
The limit state function can be formed as
g(Z)=R-S
Based on Eqs. (23.12) and (23.13), the random variables R and S can be expressed
using variables in standard normal space as