Titel_SS06

Brittle Ductile

Figure 9.6: Symbolism used to identify the mechanical characteristics of failure modes/components
in structural systems reliability analysis.

For structural systems where failure is modelled by a series system the distinction between
brittle failure and ductile failures for the individual components is irrelevant. Failure will
simply occur when the weakest element fails.

For structural systems where failure is modelled in terms of one or several parallel systems the
distinction is, however important. This is because the event of failures of the individual
components in that case has an effect on the loading of the other components in the parallel
system. In case of parallel systems consisting of ductile components the strength of the
parallel system RS may thus be seen as the sum of the strength of the individual components,

i.e.:

1

n

S

i

R Ri



 (9.7)

where Ri is the strength of component i and n is the number of components in the system. It is

easily seen that the mean value and the variance of the strength of a ductile parallel system are
given as:

S 1

n

R

i i

 R



 (9.8)

2

S 1

n

R

i

2
 Ri (9.9)

and from the central limit theorem is known that (for sufficiently large n) RS will be Normal

distributed, independent of the type of distribution for the individual component strengths Ri.

Considering the case where RR 12 ... Rn and RR 12 ... Rn , the

coefficient of variation is determined by:

COV

n









(9.10)