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This paper presents theoretical investigation on the cros correlation between torsionalvibration (uq) and translation vibration (ux) of asymmetrical structure under white noise excitation. Theformula reveals that the cross correlation coefficient (r) is a function of uncoupled frequency ratio (W =wq /wx), eccentricity, and damping ratio (x). Simulations involving acceleration records from fifteendiferent earthquakes show correlation coefficients results similar to the theoretical correlation coefficients.The uncoupled frequency ratio is the dominating parameter to r; generally, r is positive for wq/wx>1.0,negative for wq /wx < 1.0, and close to zero for wq /wx = 1.0. When the eccentricity or damping ratioincreases, r increases moderately for small W (< 1.0) only. The relation among ux, uq and cornerdisplacement are best presented by r; a simple way to hand-calculate the theoretical dynamic cornerdisplacements from ux, uq and r is proposed as an alternative to dynamic analysis.