Dominant failure modes in stochastic structural systems

In an analysis of redundant structural systems in which either or both loading systems and/or member resistances are stochastic variables, all modes of failure are potentially of significance in the calculation of structural reliability. In practice, however, many modes do not contribute very much, and a problem has been to identify those modes which are stochastically dominant. In this paper a general, iterative procedure called the Truncates Enumeration Method [TEM] to determine the most stochastically dominant modes is derived from successive systematic curtailment of the results which would be obtained by complete enumeration. In this way, it is shown that the procedure presented has the capability to produce all dominant modes to within the accuracy of the criteria used for curtailment. The method is similar to that proposed by Murotsu et al. It is also shown that the incremental load method (ILM), proposed by Moses et al., has certain features common to TEM, that both techniques are essentially incremental in nature and that both methods produced the same mode failure probability statement, each using quite distinct procedures. It is finally argued that the methods are not restricted merely to the materials behaviour properties studied thus far by their proponents.