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<p>The commonly used 30%-, 40%- and square root of the sum of squares (SRSS)-rules for the spatial combination of the peak responses obtained by the traditional unidirectional response spectrum superposition method for individual components of excitation along the structural principal axes do not explicitly consider the effect of the angle of excitation to arrive at the maximum value of the response amplitudes. Consequently, the conservatism of these methods remains undefined and potentially unreliable. This paper presents a critical evaluation of the relative performance of the conventional combination rules in comparison with the complete quadratic combination rule in three dimensions (CQC3)-Rule for three plausible types of response spectra used in engineering applications. As the CQC3-Rule and response spectra of two horizontal principal components of motion as input can be considered the most accurate and realistic method on theoretical grounds, it has been used as a reference in the present study. The percentage error with respect to this benchmark has been computed for the various response quantities of a typical six-story illustrative building using 12 different pairs of the combination rule and the response spectra. The combination rules considered are the CQC3-, SRSS-, 30%-, and 40%-Rules, and the types of response spectra used are the actual principal spectra, the same shape of principal spectra with a minor component of 0.75 of the major component, and the spectra of the as-recorded components of motion. A large set of 56 recorded accelerograms with widely differing amplitude and frequency characteristics has been used to compute the example results. It has been concluded that the approximations made in defining the input response spectra are more crucial than the combination rules as such. Due to the difficulties in realistically defining the actual principal spectra and the somewhat complex nature of the CQC3-Rule for implementation by practicing engineers, the simple 30% rule and as-recorded response spectra are shown to be acceptable choices for designing common buildings.</p>

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Critical evaluation of spatial combination rules for bidirectional earthquake design: Insights from three plausible definitions of input response spectra

  • 期刊论文

  • 发表日期：

    2026年5月27日

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  • P B Kote,
  • S N Madhekar,
  • V B Dawari,
  • I D Gupta

摘要

The commonly used 30%-, 40%- and square root of the sum of squares (SRSS)-rules for the spatial combination of the peak responses obtained by the traditional unidirectional response spectrum superposition method for individual components of excitation along the structural principal axes do not explicitly consider the effect of the angle of excitation to arrive at the maximum value of the response amplitudes. Consequently, the conservatism of these methods remains undefined and potentially unreliable. This paper presents a critical evaluation of the relative performance of the conventional combination rules in comparison with the complete quadratic combination rule in three dimensions (CQC3)-Rule for three plausible types of response spectra used in engineering applications. As the CQC3-Rule and response spectra of two horizontal principal components of motion as input can be considered the most accurate and realistic method on theoretical grounds, it has been used as a reference in the present study. The percentage error with respect to this benchmark has been computed for the various response quantities of a typical six-story illustrative building using 12 different pairs of the combination rule and the response spectra. The combination rules considered are the CQC3-, SRSS-, 30%-, and 40%-Rules, and the types of response spectra used are the actual principal spectra, the same shape of principal spectra with a minor component of 0.75 of the major component, and the spectra of the as-recorded components of motion. A large set of 56 recorded accelerograms with widely differing amplitude and frequency characteristics has been used to compute the example results. It has been concluded that the approximations made in defining the input response spectra are more crucial than the combination rules as such. Due to the difficulties in realistically defining the actual principal spectra and the somewhat complex nature of the CQC3-Rule for implementation by practicing engineers, the simple 30% rule and as-recorded response spectra are shown to be acceptable choices for designing common buildings.