Page 457 - Marine Structural Design

Part IV

Structural Reliability

Chapter 24 Random Variables and Uncertainty Analysis

24.1 Introduction

Strictly speaking, all the variables in the engineering structures are stochastic to a certain
degree. Structural reliability analysis deals with the rational treatment of random variables and
uncertainties in the structural engineering design, inspection, maintenance and decision
making.
This Chapter presents the basics of statistical description of random variables that are the
foundation for reliability analysis. Measures of uncertainties are discussed, loads and capacity
of ship structures are used to illustrate the uncertainty analysis. Further reading is referred to
Ang and Tang (1975), Benjamin and Cornel1 (1970), Thoft-Christensen and Baker (1982),
Mansour (1 997) and Melchers (1999).

24.2 Random Variables
24.2.1 General
Marine structures are subjected to loads that are random in nature, such as wave, current and
wind actions. It is not possible to forecast deterministically, e.g. the height and direction of the
next single wave that will act on the structures. Neither it is possible to predict
deterministically the structural response to those actions for a certain coming instant.
Random variables may be used to describe the uncertainties in the basic variables such as
spatial and time variation of external loads, material properties, dimensions, etc. In practice,
these variables are basic in the sense that they are the most fundamental quantities used by
engineers and analysts in structural analysis and design. For instance, the yield stress of steel
can be considered as a basic random variable for the purposes of structural reliability analysis.
It should be mentioned that it is generally impracticable to obtain sufficient statistical data to
model the variations in the loads and strength for structures. Reliance must be placed on the
ability of the analyst to synthesize this higher level information when required.
24.2.2 Statistical Descriptions

A random variable X is a real function defined on a sample space. For every real number x
there exists a probability P[X 5x1. A realization x of the random variable Xis any outcome of
the random phenomenon X. In this Section, the random variables are denoted by capital letters
and the corresponding small letters denote their realizations.