Critical response of structures to multicomponent earthquake excitation

This paper aims to develop an improved understanding of the critical response of structures to multicomponent seismic motion characterized by three uncorrelated components that are defined along its principal axes: two horizontal and the vertical component. An explicit formula, convenient for code applications, has been derived to calculate the critical value of structural response to the two principal horizontal components acting along any incident angle with respect to the structural axes, and the vertical component of ground motion. The critical response is defined as the largest value of response for all possible incident angles. The ratio rcr/rsrssbetween the critical value of response and the SRSS response - corresponding to the principal components of ground acceleration applied along the structure axes - is shown to depend on three dimensionless parameters: the spectrum intensity ratio γ between the two principal components of horizontal ground motion characterized by design spectra A(Tn) and γA(Tn); the correlation coefficient α of responses rxand rydue to design spectrum A(Tn) applied in the x- and y-directions, respectively; and β = ry/rx. It is demonstrated that the ratio rcr/rsrssis bounded by 1 and √(2/1+γ2). Thus the largest value of the ratio is √2, 1.26, 1.13 and 1.08 for γ = 0, 0.5, 0.75 and 0.85, respectively. This implies that the critical response never exceeds √2 times the result of the SRSS analysis, and this ratio is about 1.13 for typical values of γ, say 0.75. The correlation coefficient α depends on the structural properties but is always bounded between -1 and 1. For a fixed value of γ, the ratio rcr/rsrssis largest if β = 1 and α = ±1. The parametric variations presented for one-storey buildings indicate that this condition can be satisfied by axial forces in columns of symmetric-plan buildings or can be approximated by lateral displacements in resisting elements of unsymmetrical-plan buildings.