New insight into and simplified approach to seismic analysis of torsionally coupled one-story, elastic systems

Abstract Structures characterized by non-coincident center of mass and center of stiffness, referred to herein as eccentric structures, develop a coupled lateral–torsional response when subjected to dynamic excitation. This phenomenon is particularly important for seismic isolated structures due to the potentially large deformations imposed on the seismic isolators by the earthquake ground motion. A careful examination of the governing equations of motion of linear elastic, one-story eccentric systems sheds new light and new insight into the coupled lateral–torsional dynamic behavior of such systems and leads to the identification of a basic system parameter, the “alpha” parameter, which controls the maximum rotational response of such systems under free and forced vibrations. The “alpha” parameter 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 under free vibration from a given initial deformation. Closed-form exact and approximate solutions for the “alpha” parameter are provided for undamped and damped eccentric systems, respectively, for a wide range of system parameters. A new basic result is that the “alpha” parameter has an upper bound of unity, thus physically limiting the maximum rotational response of an eccentric system in free vibration from an initial imposed deformation. A new physically based, simplified analysis procedure is developed, based on the “alpha” parameter to effectively estimate the maximum rotational response of a given eccentric system under seismic excitation. The extensive numerical and experimental verification of the simplified “alpha” method performed demonstrate that the proposed “alpha” method is accurate enough for design purposes, is robust and is significantly more accurate than the current International Building Code (IBC) design provisions. The experimental verification was performed through a suite of 88 shaking table tests performed on a versatile, carefully designed, one-story small-scale building model able to represent the dynamic characteristics of a wide range of eccentric systems. The dimensionless “alpha” parameter, bounded between zero and unity, can also be used as a formal index for the inherent property of a given structure to develop a rotational response under dynamic excitation. Sensitivities of the “alpha” parameter to various physical system characteristics are investigated and provide valuable guidance for eccentric system design.