Non-linear seismic response analysis using vector superposition methods

Computational algorithms based on the pseudo-force method (PFM) and the tangent spectrum method (TSM) for the seismic analysis of elasto-plastic MDOF structures by mode superposition are presented. The emphasis is put on the effect of the truncation of higher modes on the convergence of the ductility demand and energy dissipated during the earthquake. Eigenvectors and load-dependent vectors have been used in comparative analyses. Applications on a flexible 25-storey building and a stiff, 5-storey shear building indicate that, for a flexible structure, the ductility demand computed from the PFM is more sensitive to basis truncation than that computed from the TSM. However, for the stiff structure, the opposite behaviour is observed. The results indicate that the use of load-dependent vectors in inelastic analyses maintains the computational advantages found for elastic analyses in previous investigations. Although the PFM is more stable and computationally more effective than the TSM, it does not provide any information on the evolution of tangent modal properties in time that reflects dynamic response modification as the structure becomes inelastic.