«Dangerous Directions of Seismic Excitation» in Linear Spectral Analysis

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Key words: seismic response, linear spectral method, modal analysis in the time domain, dangerous directions of seismic excitation
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This paper opens the discussion on the «dangerous directions of seismic excitation» concept. This concept is popular for linear spectral analysis in our country. The author compares this approach with conventional «multi-component» approach used in the international practice for nuclear structures. It is shown that in case all components of seismic excitation have similar response spectra, both approaches give similar results, in spite of the principal physical difference in excitations (no correlation between components in the «multi-component» approach versus full correlation in the «directional» approach). The reason of this similarity is a math analogy between SRSS (Square Root of Sum of Squares) rule used for (i) the combination of maximums for the statistically independent functions; (ii) combination of vector’s components along orthogonal axes to get absolute value of vector. Similarity of the component response spectra is commonly adopted for two horizontal axes. However, vertical component usually has different spectrum; therefore the «directional» approach in the initial form cannot be applied. On the other hand, if spectral shapes are not very different (e.g. for the widespread case when vertical spectrum is taken as 2/3 of horizontal spectrum), the «directional» approach can be easily modified. One has to envelop normalized spectral shape curves and also scale participation factors for all natural modes in vertical direction.