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Modal superposition method for seismic design of non‐linear multistorey structures
Author(s) -
Villaverde Roberto
Publication year - 1988
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.4290160505
Subject(s) - superposition principle , equations of motion , modal , linear equation , linear system , degrees of freedom (physics and chemistry) , inertia , mathematics , ground motion , response spectrum , mathematical analysis , structural engineering , engineering , classical mechanics , physics , chemistry , quantum mechanics , polymer chemistry
An approximate procedure is introduced to analyse non‐linear multistorey structures within the framework of the conventional response spectrum method. Its derivation is based on the use of non‐linear response spectra and an approximate decomposition of the equation of motion for multi‐degree‐of‐freedom non‐linear systems. The decomposition is attained by considering the non‐linear terms in this equation of motion as additional external forces and, thus, by interpreting it as the equation of motion of linear systems with the initial properties of the non‐linear ones when subjected to a modified set of inertia forces. For simplicity, the procedure is herein limited to elastoplastic systems of the shear‐beam type. Its accuracy is evaluated by comparing the approximate and step‐by‐step integration solutions of systems with three and ten degrees of freedom when subjected to three different earthquake ground motions.