Example

Since each computer is expected to give different sets of random numbers, it may not be practical to give a detailed example to demonstrate the application of the simulation method in reliability analysis. However, a simple example is given to illustrate its many desirable features.

Suppose the probability of failure of a steel beam needs to be evaluated. The limit state function can be defined as g ()= Fy Z — Ma (12.41)

where Fy is the yield stress, Z is the plastic section modulus, and Ma is the applied bending moment. The statistical characteristics of these variables are given in Table 12.3.

The probability of failure of the beam can be calculated in several ways [22] and the results are summarized in Table 12.4. If distributional information on the three random variables is ignored, then according to MVFOSM, the probability of failure is found to be 0.007183. However, if FORM is used, the corresponding probability of failure is found to be 0.023270. These probabilities of failure are quite different. Simulation can be used to establish which number is correct.

In the third column of Table 12.4, the probabilities of failure for several simulation cycles are given for direct Monte Carlo simulation. The results indicate that if the simulation cycles are relatively small, the

TABLE 12.3 Statistical Characteristics of Random Variables

Variables

Mean value

0 0

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