Engineering Transactions, 11, 2, pp. 377-386, 1963

Próba Probabilistycznej Oceny Bezpieczeństwa Mostów Stalowych

W. Wierzbicki


The admissible stress k (or the safety factor) of a steel bridge under a moving load can be deter- mined by means of Eq. 13 where Ωs expresses the probability that in the case of a static load none of the increases of the stress σ expressed by Eqs. (1) exceeds the value Ω  - the probability that the increase of the stress σ due to dynamic factors will not exceed σdg, and Ωm the probability that the stress at the yield point is greater than the limit stress expressed by Eq. (10). The quantity p is the safety index constituting the probability that a catastrophe (in our case the fact of exceeding the plastic limit at an element) will not take place, The probabilities Ωd and Ωm will be obtained in the form of areas of the regions BCD on the graphs of the Gauss curves for the dynamic coefficients (Fig. 4) and stresses at the yield point (Fig. 5). If the increases of a may be considered to be non-random quantities, Ωs = 1 and the Eq. (13) becomes (14). For this case numerical computation has been performed. The curve of Fig. 5 has been plotted on the basis of experimental data represented in the form of the histograph of Fig. 3.
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[in Russian]

W. WIERZBICKI, Obiektywne metody oceny bezpieczeństwa konstrukcji budowlanych, PWN Warszawa 1961.