Maximum rotational response of asymmetric structures: estimation through a simple (code-like) but effective formula

Eccentric structures when subjected to dynamic excitation, develop a coupled lateral-torsional response that may increase the local peak dynamic response. In this paper, a key system parameter which controls the maximum rotational response of such systems under free and forced vibration, is introduced. This parameter, called ALPHA, is defined as the mass radius of gyration of the structure multiplied by the ratio of the maximum rotational to the maximum longitudinal displacement response developed by a one-story eccentric system in free vibration. A compact exact closed-form solution for the ALPHA parameter is given for undamped linear elastic three-degrees-of-freedom systems, while approximate empirical analytical expressions obtained through least square fitting are provided for damped systems.