The Fundamental Mechanism Method
The second approach to structural systems reliability analysis, i.e. the fundamental mechanism
method takes basis in a definition of failure of the structural system at mechanism level.
Failure thus involves the formation of collapse mechanisms. Considering again the beam
structure from Figure 9.10 the formation of the mechanism is illustrated in Figure 9.12.
A
B
P
10
F
W
Figure 9.12: Collapse mechanism considered using the fundamental mechanism method.
The limit state function corresponding to this mechanism may be derived by consideration of
the internal and external work. Failure occurs if the external work exceeds the internal
work , i.e. there is:
AE
AI
gAArr(x) IE 2 5 w (9.22)In this case only one failure mechanism exists and it is seen that the corresponding limit state
equation (Equation (9.22)) is – not unexpectedly – identical to the limit state equations given
in Equations (9.17)-(9.18). Thus the probability of failure according to the fundamental
mechanisms method is:
1.47 10^3
PF
(9.23)Finally the effect of the mechanical behaviour after failure by reconsidering the limit state
functions given in Equations (9.17)-(9.18) is considered. Assuming now that the mechanical
behaviour after failure is brittle these limit state equations are changed to:
grmrBA(x) BA 2.5 w (9.24)grmrAB(x) AB 5 w (9.25)and the corresponding probabilities of failure are PF,B AO1.96 10-1 and PAB0.972.
An important aspect in the probabilistic modelling of failure of structural systems is the
correlation between the individual failure modes and/or the components of the system. The
individual components of the system will be dependent due to the fact that the limit state
equations used to describe the boundary between the safe domain and the failure domain, i.e.
the failure surface for the individual failure modes will to some extent contain the same basic
random variables and to some extent contain basic random variables which are correlated.