For a given structural reliability problem, the (nonlinear) lmit state function is given by where all…

For a given structural reliability problem, the (nonlinear) lmit state function is given by where all three components of X, ie. XI, X, & Χ,, have mean values μι, μ2, & μ, respectively and equal standard deviation ơxi-Ox2 Ou Ox. Estimate the mean value, variance, standard deviation and coefficient of variations (Cov, see Eq. (3.4) on p. 99 of ‘An Introduction to Structural Reliability Theory’) of X. T-1 (3.3) where ε; and E, are the mean and the variance of the random variable Et The partial derivatives in equation (3.3) are to be evaluated at the mean value E . Equation (3.3) can be normalized and written in terms of the coefficient of variations (COV): (3.4) where Ss Ξ T is the strength COV, and ẫ: G, /E: are the cov ofti and the partial derivatives are to be evaluated at the mean values.