Abstract: In this paper, the translation-torsion coupling earthquake responses, of single-story eccentric factory buildings with consideration of whole-space-work of the roof in 3-dimension non-inertia system are analysed and studied; and its calculation model has been established. And what is more, corresponding motion equations of earthquake responses have been derived, analysed and discussed. And it points out that under the action of the earthquake including rotational component, the principle of superposition of independent action for each earthquake component and mode-superposition method of dynamic responses analysis are already not applicable.In this paper, the translation-torsion coupling earthquake responses of some single-story eccentric factory building are calculated and analysed by comparison methods without consideration of the earthquake torsional component. The conclusion is that when whole-space-wcrk of the roof is considered, the results of calculation are more conformable to the actual earthquake damage. Moreover, this paper gives its simplified method for calculation and conditions in which the deformation of the roof can be neglected.

Key words: generalized continua, incremental rate type, principles of power and energy rate, generalized Piola’s theorem