| Structural fatigue failure is closely related to the number of stress cycles.Therefore,the number of the intersections between stochastic response process and zero-boundary(equivalent to the number of stress cycles)is one of the key problems in structural fatigue reliability analysis.In this paper,Wiener-type stochastic stress process is studied,the probability distribution of the number of the intersections between stochastic response process and zero-boundary is analyzed,a new method of structural fatigue reliability analysis is established,and an example is applied.The main research contents and achievements of the paper include:(1)Firstly,based on the calculation formula of linear fatigue random cumulative damage index D,the relationship between the number of zero-crossing of stochastic response process and fatigue cumulative damage index D is deduced.(2)Then,the Wiener process is infinitely approximated with random walk,the probability distribution of the first zero-crossing time of the Wiener process is infinitely approximated with the probability distribution of the first return to the origin steps of the random walk;and then according to the translation invariance and Markov properties of the Wiener process,based on the renewal process theory,the probability distribution law of the number of the intersections between Wiener process and the fixed boundary in the determined time is further obtained.Monte-Carlo method is used to verify the theoretical formula of the probability distribution of the number of the intersections between Wiener process and zero-boundary.(3)Considering the randomness of the fatigue failure threshold Dcr,a formula for calculating the structural fatigue reliability is derived based on the fatigue failure criterion.Using the proposed structural fatigue reliability evaluation method based on probability analysis of the number of zero-crossing of stochastic response process,the fatigue reliability of key stay cable on coastal long-span cable-stayed bridge is analyzed as an example.The result show that reliability indexes of stay cable descent speed are slightly fast in the first 30 years,management and maintenance work of stay cable at the initial stage of operation should be done well;the reliability indexes of the stay cable are lower than the safety threshold[β]more than the operating time of 107 years. |
