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ELASTIC AXIS OF BUILDINGS UNDER EARTHQUAKE EXCITATION

The elastic axis of multistory buildings is defined as the intersection of two vertical principal bending planes which are perpendicular. The elastic axis intersects each story at a point which has the property of the rigidity center. Single-story and special classes of multistory buildings, such as isotropic ones possess an elastic axis. Taking into account the dynamic nature of earthquake excitation the following question arises: under the action of a torsional earthquake component, is it possible to locate a stable vertical axis around which the structural system will be rotated under any torsional ground motion? For this purpose, monosymmetric single-story and isotropic monosymmetric multi-story buildings are studied analytically. The equation of motion is expressed in the time domain and transferred by Fast Fourier Transform in the frequency domain. Mathematical expressions of the coordinates of the torsional axis at each story level are produced, taking into account that each floor behaves as a rigid in-plane diaphragm. The derived equations indicate that the dynamic torsional axis depends not only on the geometrical and mechanical characteristics of the system but also on mass, damping and excitation frequency. Numerical examples are included for enhancing the comprehension of the derived equations. The divergence of the coordinates of the static and dynamic definition of elastic axis is discussed.