A Simplified Approach to the Analysis of Torsional Effects in Eccentric Systems: the Alpha Method

Eccentric structures, characterized by non coincident center of mass and center of stiffness, when subjected to dynamic excitation, develop a coupled lateral-torsional response that may increase the local peak dynamic response of such a structure: this behaviour becomes particularly important for seismic isolated structures for which large displacements are developed in the isolators. The coupled lateral-torsional response can be estimated only through a three-dimensional analysis which is specifically carried out for a single structure subjected to a determined dynamic input. In this paper the authors present the analytical formulation of a simplified method which allows to understand, predict and govern the global trend of one-storey eccentric structures to develop a torsional response to dynamic inputs through the identification of a system key parameter named “alpha”. This parameter can be easily used to effectively estimate the maximum rotational response of a given eccentric system under a dynamic excitation through a simple linear elastic analysis of the “equivalent” non-eccentric system. Moreover, the results of the analysis in the non-linear field show that the linear elastic value of “alpha” acts as an upper bound for the corresponding value of elastic-perfectly plastic systems. In summary, this paper proposes a physically-based general theory which frames the problem of torsional phenomena of one-storey eccentric systems subjected to dynamic inputs and immediately allows the quantification of the system torsional response and the identification of the structural parameters governing it.