## Info

standard deviation. However, unlike the previous example, assume w and P are correlated. The correlation coefficient between them is 0.7. The task is to evaluate the risk or reliability index of the beam for this situation.

### Solution

This is a problem on correlated nonnormal variables. The limit state equation for the problem is given by Equation 12.21. As before, the uniformly distributed load w is normal, that is, w~ N(35.03kN/m, 5.25 kN/m), and P is lognormal with 1P = 4.706 and ZP = 0.1. However, they are now considered to be correlated. Assume that the the correlation coefficient pWpP is 0.7. The reliability index calculation is expected to be very complicated. As mentioned earlier, the limit state equation needs to be expressed in terms of the uncorrelated Y variables. However, since the equivalent normal mean and standard deviation need to be evaluated for P at the checking point and the coordinates of the checking point are expected to be different at each iteration, the limit state function will change for each iteration. Hand calculation is not recommended for this type of problem; a computer program is necessary. However, some important steps are discussed below for ease of comprehension.

The correlation matrix [C0] given by Equation 12.24 for the problem is

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