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and CEN (European Committee for Standardization)/TC250 code drafting committees, which
provide an excellent up-to-date overview of reliability methods and their potential application
in developing modern codes of practice (ISO, 1998; Eurocode 1.1 Project Team, 1996;
European Standard, 2001). Finally, it is worth mentioning that many of the topics presented in
this chapter have been discussed and clarified within the Working Party of the Joint
Committee on Structural Safety (JCSS), of which the author is privileged to be a member. The
present chapter draws from the JCSS document on Existing Structures (JCSS, 2001) and in
particular the Annex on Reliability Analysis Principles, which was drafted by the author and
improved by the comments of the working party members.

1.2 PRINCIPLES OF RELIABILITY-BASED DESIGN

1.2.1 Limit states

The structural performance of a whole structure or part of it may be described with reference
to a set of limit states which separate acceptable states of the structure from unacceptable
states. The limit states are generally divided into the following two categories (ISO, 1998):

●ultimate limit states, which relate to the maximum load carrying capacity;
●serviceability limit states, which relate to normal use.
The boundary between acceptable (safe) and unacceptable (failure) states may be distinct or
diffuse but, at present, deterministic codes of practice assume the former.
Thus, verification of a structure with respect to a particular limit state may be carried out
via a model describing the limit state in terms of a function (called the limit state function)
whose value depends on all design parameters. In general terms, attainment of the limit state
can be expressed as

(1.1)

where X represents the vector of design parameters (also called the basic variable vector) that
0
are relevant to the problem, and g(X) is the limit state function. Conventionally, g(X)≤
represents failure (i.e. an adverse state).
Basic variables comprise actions and influences, material properties, geometrical data and
factors related to the models used for constructing the limit state function. In many cases,
important variations exist over time (and sometimes space), which have to be taken into
account in specifying basic variables. It will be seen in Section 1.4.1 that, in probabilistic
terms, this may lead to a random process rather than random variable models for some of the
basic variables. However, simplifications might be acceptable, thus allowing the use of
random variables whose parameters are derived for a specified reference period (or spatial
domain).
For many structural engineering problems, the limit state function, g(X), can be separated
into one resistance function, g ( · ), and one loading (or action effect)
R