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Modal ductility factors of one‐story inelastic structures with simple eccentricity

A simple procedure is presented for constructing modal capacity curves of one‐story monosymmetric models with elastoplastic resisting elements. These curves may be used for an approximate decomposition of the equations of motion of the assumed structural models, when subjected to ground motions. The motive of applying a modal decomposition on inelastic structures is the simplicity and the consequent attractiveness of the response spectrum technique as applied in linear structures. By applying a modal decomposition on eccentric one‐story inelastic systems, modal ductility demands may be determined for the various resisting elements and the total demands may be estimated by an appropriate combination rule. The modal capacity curves are constructed by performing a nonlinear pushover analysis using the inertia force eccentricities of each mode. As at each loading step the modal eccentricity reflects the current state of stiffness, the incremental floor movement consists of a rotation about the corresponding natural center of vibration and this simplifies the calculation of displacements throughout the loading history. The method of constructing modal capacity curves is outlined for systems with different structural parameters: uncoupled lateral frequency, uncoupled torsional‐to‐lateral frequency ratio, stiffness eccentricity and relative values of element strength. A parametric analysis is also presented, based on a three‐element single mass model that has been extensively used in the past for similar analyses. In particular, two types of model structure are examined: systems with element strengths proportional to their stiffness and systems with element strengths determined by the static equilibrium of the eccentric model. The results of the present work are in good agreement with the findings of studies published in the past. Copyright © 2007 John Wiley & Sons, Ltd.