Approximate Design for Multicomponent Earthquakes

Current design criteria are intended to provide values of structural responses to a single component of a design earthquake, at a fixed exceedance probability. It is desirable to know whether a structure is safe, at that reliability level, under the combined effect of several simultaneous earthquake components. If the component accelerograms are idealized as zero-mean Gaussian processes and the structure behaves linearly, then structural responses associated with a given exceedance probability define an ellipsoid in the response space. In this space, points falling inside the failure surface (interaction surface) correspond to survival; those outside, to failure. A structure is safe, at the specified reliability level, if the corresponding ellipsoid falls entirely within the survival region. Computations to verify this condition are, however, quite awkward. An approximate method is developed which replaces computation of the ellipsoid coordinates with that of a linear combination of responses to individual components.