Critical orientation of three correlated seismic components

Analytical formulae are developed for the determination of the critical angle of seismic incidence and the corresponding maximum value of a response quantity of structures subjected to three seismic correlated components: two horizontal components applied along arbitrary directions and a vertical component of earthquake ground motion. The developed analytical formulae, which are derived assuming that the structure behaves linearly, are simple and require the solution of two specific time history loading cases for the horizontal components and one for the vertical component. plication and the accuracy of analytical formulae are illustrated by means of response history analysis of an asymmetric multistory building due to several earthquake records. Also the same asymmetric structure is analyzed by using several earthquake records for different incident angles in order to illustrate the variation of the maximum structural response with the incident angle. The analyses results show that, for the earthquake records used, the critical value of a response quantity can be up to 80% larger than the usual response produced when the seismic components are applied along the structural axes.