ABSTRACT
Generally, failure (i.e. an undesired or unsafe state of the structure) is defined in terms of a limit state function g(.), i.e. by the set F ={X : g(X)≤0}. Frequently, Z= g(X) is called safety margin. For the simple problem as shown in Fig. 6.1, the definition of the limit state function
is not unique, i.e. there are several ways of expressing the failure condition
F = {(F,L,Mpl) : FL ≥ Mpl} = { (F,L,Mpl) : 1− FLMpl ≤ 0
} (6.1)
The failure probability is defined as the probability of the occurrence of F :
pf = Prob[{X : g(X) ≤ 0}] (6.2)
This quantity is unique, i.e. not depending on the particular choice of the limit state function.
