Numerical verification of the effectiveness of the “alpha method” for the estimation of the maximum rotational response of eccentric systems

In previous research works, the authors, starting from the governing equations of motion of one-storey linear elastic asymmetric systems, have identified a key system parameter which controls the maximum rotational response of such systems under free and forced vibration. This parameter (called ALPHA) has also led to the identification of a simplified procedure (called ALPHA method) for the estimation of the maximum rotational response of such systems. Main goal of this paper is to illustrate the results of a comprehensive set of 11600 numerical simulations carried out (with reference to a number of representative structures, encompassing also torsionally flexible ones, subjected to historically recorded earthquake ground motions) to verify the properties of the ALPHA parameter, with special attention devoted to the identification of the sensitivity of the proposed ALPHA method upon the fundamental period of vibration of the structure (not yet considered in previous research works). The results obtained (a) confirm the effectiveness of the ALPHA parameter to capture the intrinsic propensity of an eccentric system to develop a torsional response, (b) confirm the capacity of the ALPHA method to effectively estimate the maximum rotational response of a given eccentric system under seismic excitation, and (c) indicate how the ALPHA method is only weakly sensitive upon the period of vibration of the structure. The paper also introduces a mechanical analog for three-dimensional one-storey asymmetric systems which provides useful insight to the dynamic properties of such systems.