Page 17 - Dynamic Loading and Design of Structures

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Figure 1.1 Partial factors and their significance in Eurocode 1 (European Standard, 2000).

In principle, there is a partial factor associated with each variable. Furthermore, the number of
load combinations can become large for structures subjected to a number of permanent and
variable loads. In practice, it is desirable to reduce the number of partial factors and load
combinations while, at the same time, ensuring an acceptable range of safety level and an
acceptable economy of construction. Hence, it is often useful to make the distinction between
primary basic variables and other basic variables. The former group includes those variables
whose values are of primary importance for design and assessment of structures. The above
concepts of characteristic and design values, and associated partial factors, are principally
relevant to this group. Even within this group, some partial factors might be combined in
order to reduce the number of factors. Clearly, these simplifications should be appropriate for
the particular type of structure and limit state considered. Figure 1.1 shows schematically the
system of partial factors adopted in the Structural Eurocodes.

1.2.3 Structural reliability

Load, material and geometric parameters are subject to uncertainties, which can be classified
according to their nature. They can, thus, be represented by random variables (this being the
simplest possible probabilistic representation; as noted above, more advanced models might
be appropriate in certain situations, such as random fields).
In this context, the probability of occurrence of the failure event P is given by
f

(1.5a)

where, M=g(X) and X now represents a vector of basic random variables. Note that M is also
a random variable, usually called the safety margin.
If the limit state function can be expressed in the form of (1 .2), eqn (1 .5a) may be written
as