Simplified Response-Spectrum Seismic Analysis of Nonlinear Structures

A method is presented for a simplified seismic analysis of nonlinear multidegree-of-freedom structures. The method represents an improvement over an earlier attempt to extend the use of the conventional response-spectrum method to nonlinear structures, and is also based on the use of a modal superposition in combination with nonlinear response spectra. It involves the computation of their natural frequencies and mode shapes on the basis of their initial elastic properties, the calculation of a yield deformation for each of their modes using formulas proposed here, and readings from a nonlinear response spectrum. The procedure is formulated for plane rigid frames, but limited to elastoplastic force-deformation behavior. Its application is illustrated by means of numerical examples with a three-story shear building and a six-story plane frame. In a comparison with solutions obtained with a step-by-step integration method, the proposed approximate method predicts the maximum displacements of these two structures with an average error of about 5%.