Determination of orthogonal combination coefficients using inelastic velocity response spectra

Abstract eng:
Seismic regulations and guidelines for buildings and bridges prescribe simplified combination rules to obtain the maximum structural response under multi-directional earthquake effects. An unfavorable internal force usually develops under the combined effects of an earthquake motion. In this study, the spectrum intensity concept is used to investigate the bi-directional effects of earthquakes on structures. For this purpose, a set of recent and past fifteen earthquakes (M>6) are selected to predict bi-directional effects. Inelastic velocity response spectra of these earthquakes are numerically obtained and plotted for damping ratios of ξ=0.05 and 0.20, representing a wide range of damped and heavily damped structures. Spectrum intensities for both orthogonal directions and for the resultant direction are calculated using a computer program developed for this purpose. Unfavorable response is then calculated by equating the resultant spectrum intensity to principle direction’s intensity plus the other direction’s contribution as a percentage of the principle component, or equating the resultant spectrum intensity to principle direction’s intensity plus a percentage of the other direction’s contribution, or vice versa. The results obtained are strongly earthquake-dependent. Based on this analysis, well-known building regulations are reviewed and evaluated by emphasizing the prescribed combination rules. Numerical results show that coefficient for the bi-directional contribution varies largely in the range between 0.01~0.98 for the selected force reduction factors of µ=2 and 8.

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