The ultimate moment capacity, M, of an under-reinforced concrete rectangular section is given by

in which the following are random variables: As is the cross-sectional area of the reinforcing steel, fy the yield stress (strength) of steel, d the distance from the reinforcing steel to the top fibers of the beam, b the width of the beam, and fc the ultimate stress (strength) of the concrete. If the random variables are assumed to be statistically noncorrelated, determine the mean and variance of the moment capacity using the following information:

Use 100 simulation cycles. Is this a sufficient number of cycles? Why? Provide a discussion.

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where M = A, f, (d) a= Af 0.85bfc