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 is the yield stress (strength) of the steel, d is the distance from the reinforcing steel to the top fibers of the beam, b is the width of the beam, and f′c is the ultimate stress (strength) of the concrete. If the random variables are assumed to be statistically uncorrelated, determine the first-order mean and variance of the moment capacity in terms of the means and variances of the random variables.

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where M-A,f, (d) a= Afy 0.85bf