Critical response to three-component earthquakes of arbitrary direction

The method to calculate the critical responses, maximum and minimum, to three traslacional seismic components that may act with any orientation relative to the structural axes, is presented. Elastic behavior is assumed and the seismic action is specified by means of proportional response spectra for each component. The recent formulation GCQC3 is used to combine the responses to three seismic components, which is a generalization of the method CQC3 and allows that a principal seismic component can depart of the vertical direction. The critical responses to one seismic component are given by the square root of the maximum and minimum eigenvalues of the response matrix R, whose elements are defined by means of the modal responses used in the well-nown CQC. The critical responses to three seismic components of arbitrary directions are calculated combining the eigenvalues of R and the intensities of the components. The method can also be applied to the determination of the critical responses when restrictions are imposed in the maximum inclination and/or intensity of a principal seismic component. The bounds of the quotient between the maximum response and the SRSS response, defined as the most unfavorable response to the principal seismic components acting along the structural axes, are presented.