An Energy Spectrum Method for Seismic Evaluation of Structures

Seismic evaluation of structures generally involves determination of displacement demands from which story drifts, and component forces and deformations for specified hazard levels can be obtained for comparison with available capacities. A number of methods have been proposed by investigators in the past some of which are also used in current practice, such as MPA, FEMA 440, and Capacity Spectrum. Those methods generally involve non-linear pushover analyses. This paper presents adaptation of an energy based method that has been recently developed and successfully used by Goel et al., for design purposes, called Performance-Based Plastic Design (PBPD) method. In the PBPD method the design base shear for selected hazard level is determined by equating the work needed to push the structure monotonically up to a selected target drift to the corresponding energy demand of an equivalent SDOF oscillator. It turns out that the same work-energy equation can also be used to estimate seismic demands for existing structures. In this approach the skeleton force-displacement (capacity) curve of the structure is converted into energy-displacement plot (E_c) which is superimposed over the corresponding energy demand plot (E_d) for the specified hazard level to determine the expected peak displacement demand. The drift demands of two 20-story RC and steel moment frames as computed by the proposed energy spectrum method were in excellent agreement with those obtained from inelastic dynamic analyses using representative ground motion records.