Maximum response of nonproportionally and proportionally damped structural systems under multicomponent earthquakes

Earthquake motions as felt by structures along three orthogonal directions are, in general, statistically correlated. The effect of this correlation on structural response was studied. Assuming the existence of principal axes of excitation along which the components of motion are uncorrelated, the mean square and design response are obtained in terms of spectral characteristics of the uncorrelated components. These responses depend upon the relative orientation of the structure with respect to the principal excitation components. For each response quantity, there exists a set of three orthogonal direction along which if principal excitations are applied, they will cause a maximum response. Identification of these directions is necessary to obtain the worst case response for design purposes. A methodology to obtain such a maximum response of a quantity of design interest is outlined.