A procedure for elasto-plastic seismic response analysis of spatial structures based on design response spectra

For the equivalent single-degree-of-freedom (ESDF) system of a spatial structure, the post-yielding stage of its load-displacement curve is relatively short, therefore, large errors would occur as the force-displacement (F-d) curve being bi-linearized via conventional methods. Besides, some iterative processes are needed in determining the inflection point of the F-d curve herein. In view of these problems, the Ramberg-Osgood model is adopted to describe the hysteretic curves of the ESDF systems of spatial structures. Based on an equivalent linearization procedure, the stiffness of the equivalent linearized system is set equal to the secant stiffness of the nonlinear ESDF system at its maximum displacement. The area of a hysteretic loop of the nonlinear ESDF system is calculated through integration of the hysteretic curve, and the equivalent viscous damping is derived by setting the energy dissipated equal to that dissipated by hysteresis. By transforming the linear acceleration response spectra into the period-damping ratio-displacement format, and solving the simultaneous formulas consisting of the transformed spectra and the equivalent period-damping ratio-displacement curve of the equivalent linear system through a graphic method, the seismic responses of the equivalent linear system is obtained. Accordingly, the overall seismic response of the spatial structure is got. Nonlinear seismic responses of a cylindrical latticed shell and a spherical latticed shell are computed by means of the proposed method. Results demonstrate that the proposed method is simple, efficient and involves no iteration. In addition, this method is easy for execution via computer programing, and could yield relatively accurate seismic displacement responses for spatial structures.