The SLSV (single-loop-single-vector) method is modified for the reliability-based optimization problem with multiple reliability constraints. The design problem is formulated to minimize the structural volume of frame structure in terms of cross-sectional area of each frame element subjected to the two mode reliability constraints. The two mode reliability criteria consist of the mean compliance and mean eigenfrequency. The limit state functions are formulated as normalized form to achieve

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... ical stability of the SLSV method, because the functions are directly adopted as constraint conditions. That is a large difference from the conventional double-loop method, where the limit state functions do not appear in the optimization loop. Through numerical examples of 2-D and 3-D frame design problems, higher computational efficiency and sufficient reliability approximation accuracy by the SLSV method are demonstrated in comparison with the conventional double loop method that the mode reliabilities are evaluated by the first order reliability method (FORM) in each optimization step. Additionally, the importance of normalization of the limit state functions in the SLSV method is also demonstrated.