Civil Engineering Handbook

E yn2

n n n where {e(i)} is the normalized eigenvector of the ¿th mode of the correlation matric [C'] and e(i), e(i),..., e() are the components of the ith eigenvector. Eigenvalues are the variances of Y. Y will have zero means [14]. Using Equation 12.25, the correlated X variables can be transformed into uncorrelated Y variables. Then it is straightforward to rewrite the performance function in terms of the Y variables. FORM can then be used to evaluate the corresponding risk and reliability. The additional steps required to evaluate the reliability corresponding to a performance function containing correlated random variables are elaborated further with the help of an example. The example considered in the previous section for uncorrelated variables is modifed for this purpose.