Page 439 - Marine Structural Design

Chapter 23 Basics of Structural Reliability 415

Equation (23.2) is valid for small coefficients of variation (less than 0.10) only. However, the
above approximations are frequently used.

23.3 Basic Concepts

23.3.1 General
Structural engineering deals with load (S) and strength (R) in terms of forces, displacements
and stresses acting on the structures. Structural design codes commonly specify loads, strength
and appropriate safety factors to be used. Structural reliability theory is about the evaluation of
the failure probability taking into account the uncertainties in loads and strength. During the
last two decades, many efforts have been given on structural reliability and their application to
practical structural engineering.
23.3.2 Limit State and Failure Mode
A structural component can fall into safe or failure state. The border line (or surface) between
the safe and failure states is named as limit state, and expressed as g(Z) = R -S . The following
conditions describe the possible states of a structural component.
g(Z)<O represents a failure state where loads S exceeds the strength R.
g(Z)>O represents a safe state since strength R is larger than loads S.
g(Z)=O represents the limit state line (or surface).
The figure below shows the concept of limit state sketchily
For marine structures, the limit states are defined in accordance with the different
requirements, such as serviceability, ultimate strength, etc.
23.3.3 Calculation of Structural Reliability
By quantifying the uncertainties using probabilistic methods, Structural reliability can be
measured by means of failure probability.
For a structure described by a set of random variables Z with joint distribution fi(z), it must be
possible for each set of values of z to state whether or not the structure has failed. This leads to
a unique division of Z space into two sets, calIed the safe set and the failure set respectively.
These two sets are separated by the failure surface (limit state).