Keywords: bridge, buckling load, imperfection sensitivity law, live loads, probabilistic variation.

In this paper, the Koiter law has been extended to be consistent with the evaluation of the probabilistic variation of buckling strength. The extension is the consideration of the second order (minor) imperfections, in addition to the first order (major) imperfections considered in the Koiter law. Explicit formulas are presented to be readily applicable to the numerical evaluation of imperfection sensitivity. As a revision of the results in [1], a procedure to describe the probabilistic variation of critical loads is presented for the case where initial imperfections of structures are subject to a multivariate normal distribution; the formula for the probability density function of critical loads is derived by considering up to the second order imperfections.

The framework of the probabilistic method based on the concept of imperfection sensitivity is extended to the description of the probabilistic variation of live loads. This extended method is applied to a truss arch structure subjected to dead and live loads. The mechanism of probabilistic variation of buckling strength of this arch due to the variation of live loads is successfully described by the proposed method, and the reliability of the arch is evaluated.

1

M. Ohsaki, K. Ikeda, Stability and Optimization of Structures - Generalized Sensitivity Analysis, Springer, New York NY, 2007.

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