where H is the height of the building, m(z) is the mass per unit length, n; is the frequency of the ¿th mode in the across wind direction, Z is the damping ratio in the ¿th mode, f(z, t) is the across wind force per unit height, and f (f) is the generalized across wind force in the ¿th mode. The spectral density of each normal coordinate can be determined from

where |H(n)| is the mechanical admittance function and Sf is the power spectral density of the generalized across wind force. The variance of the normal coordinate r; is given by pi g2t = Sr. (n) dn (22.53)

Hence, the variance of the across wind displacement is obtained from

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