For a simply supported beam with a concentrated load P at midspan and uniformly distributed load of intensity w over the entire span L, the maximum shear force (V) and the maximum bending moment (M) are given by

Find the covariance of V and M, Cov(V, M), using first-order approximations. Assume P and w to be random variables with known mean values and variances of μP, σP, μw, and σw, respectively.

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M WL P 2 WL + 2 PL 8 4