This paper proposes the methods for automatically selecting the probabilistically dominant failure modes in plane frame structure by using a matrix method and a branch-and-bound technique and for evaluating the system's reliabilities based on the selected modes. The characteristics of the proposed methods are investigated through application to several structures. The conclusions are summerized as follows: (i) The efficiencies of the one-and two-dimensional branching criteria are dependent on the configurations of the structures. (ii) The value of the bounding constant has great effect on the numbers of the selected failure paths and the computation times but not so much on the resulting estimation of the system's failure probabilities. The computational experiences show that taking γ=0 is recommended for evaluating the reliabilities of large structures. (iii) The proposed methods are successfully applied to reliability analysis of the transverse structure of a tanker, which shows the importance of taking account of correlation between loads.
