Seismic Applications of Nonlinear Response Spectra Based on the Theory of Modal Analysis

Abstract

A fast nonlinear response spectra analysis algorithm based on the theory of modal analysis and superposition is proposed to overcome the drawbacks of using the time-consuming nonlinear response history analysis in seismic design. Because linear modal analysis has found great acceptance in performance-based seismic engineering, it is here extended to the nonlinear domain by using the force analogy method that links the global responses with local inelasticity of the structure. Geometric nonlinearity is incorporated into the analysis by modifying the initial stiffness matrices to consider gravity load effects. By ignoring geometric stiffness update, the theory of modal analysis and superposition is easily incorporated into the proposed algorithm. Numerical simulation is performed to demonstrate the accuracy of the algorithm in capturing both the maximum global and local responses.