Combination coefficients for yielding structures under tri-directional earthquake excitations

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. This study uses the spectrum intensity concept to investigate the tridirectional effects of earthquakes on structures. For this purpose, a set of recent and past thirteen earthquakes (M>6) are selected to predict tri-directional effects. Inelastic velocity response spectra for 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 (e.g. base isolated) structures. Spectrum intensities for both orthogonal and vertical 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 the proposed analysis way, well-known building regulations are reviewed and evaluated by emphasizing the prescribed combination rules. Numerical results show that coefficients for the tri-directional contribution varies largely in the range between 0.01~0.68 for the selected force reduction factors of μ=2 and 8, revealing that in some cases the code defined combination values may yield unconservative seismic designs.