Page 472 - Marine Structural Design

448 Part IV Structural Reliability

The CDF for the largest of the individual combined bending moment can be expressed for a
total of the v, Trepetitions,

(25.22)

25.4 Procedure for Reliability Analysis of Ship Structures
25.4.1 General
Vast amount of publications are available now with regard to the reliability analysis of
existing ships since researchers first began to look at the desirability of using probabilistic
methods in the structural design of ships in the early 70's. The details of the analysis methods
may vary from one paper to another. However, generally speaking, reliability analysis of
existing ships should cover the basic steps of next section.
Step 1: Definition of the objective ship and its mission tasks
In order to carry out the reliability analysis of a ship, the basic geometry and scantlings of the
ship must be known. Furthermore, the environmental conditions including loading conditions
and sea conditions the ship has been exposed over its service life should also be defined.
Step 2: Definition of the limit state functions
Knowledge of the limiting conditions beyond which a ship will fail to perform its intended
function will undoubtedly help in assessing more accurately the true margin of safety of
the ship. The equations that can represent these limiting conditions are called limit state
equations. Establishing the limit state equations is a significant step within the reliability
analysis procedure. Generally speaking, there are two categories of limit state equations:
serviceability vs. strength. For each category, four different levels of limit states exist.
These are:
1. limit state functions for hull girder collapse;
2. limit state hnctions for stiffened panels;
3. limit state fimctions for buckling of plates between stiffeners; and
4. limit state functions for fatigue of Critical Structural Details (CSD).
Step 3: Definition of the statistical characteristics of the random variables
Step 4: Selection of the reliability calculation methods
Step 5: Calculate the probability of failure for each failure mode for the given ship
When the limit-state hction is complex, a response surface method may be applied to
approximate the limit-state surface using a polynomial type function. Using the response
surface, a standard FORM/SORM algorithm may then be used to estimate failure probability.
25.4.2 Response Surface Method

The limit state function at time t relating to the ultimate strength failure of an FPSO hull girder
is given by