9.1 Introduction
In the analysis of structural components considered previously, only one failure mode for a
given structural component or system has been considered. To the extent that one failure
mode is governing the structural reliability of the considered structural component or system
this is of course sufficient but in many practical applications this is not the case. Often several
failure modes either associated with one particular cross-section or associated with a number
of different cross-sections in a structural system contribute to the failure probability. This is
very much depending on the definition of failure for the considered component or system.
Consider as an example the structure illustrated in Figure 9.1a).
BDCA EB C DA ECB DA ECB DA Ea) b)F
H FFFHHHFigure 9.1: a) Illustration of a redundant structural system and b) corresponding bending failure
modes.
Obviously the structural system illustrated in Figure 9.1 will not collapse if only one cross-
section of the structure fails. In fact for this structural system a total of three degrees of
freedom must be introduced before the structure will collapse. However, if failure is defined
as the occurrence of first yield at any point in the structure’s failure at any one possible
location is sufficient for system failure to occur. To make a clear differentiation between
components reliability analysis and systems reliability analysis it is denoted by component
failure the event of failure for one failure mode, remembering that a component in this sense
does not necessarily correspond to a structural component of the structural system.