A simplified normalized cumulative hysteretic energy spectrum

For energy-based seismic design, a simplified normalized cumulative hysteretic energy spectrum proposed for obtaining hysteretic energy as energy demand is the main objective in this paper. The dimensionless parameter, βEh, is presented to express hysteretic energy indirectly. The βEh spectrum is constructed directly through subtracting the hysteretic energy of single degree-of-freedom (SDOF) system energy equation. The simplified βEh spectral formulation as well as pseudo-acceleration spectrum of modern seismic provisions is developed based on the regression analysis of the large number of seismic responses of SDOF system subjected to earthquake excitations, which considers the influence of earthquake event, soil type, damping ratio, and ductility factor. The relationship between PGV and PGA is established according to the statistical analysis relied on a total of 422 ground motion records. The combination of βEh spectrum and PGV/PGA equation allows determining the cumulative hysteretic energy as a main aseismic design indicator.