An improved input energy spectrum verified by the shake table tests

Input energy is the principal component of the energy balance equation. It is beneficial to determine, through its components, how the recoverable and irrecoverable energies are distributed within the structural elements. Several equations and attenuation relations to define mass-normalized input energy spectra exist in the literature. They are mainly proposed for elastic systems subjected to far-fault EQs. There is a lack of experimental verification of these proposed spectra. In this paper, experimental assessment was performed to the existing spectra, and further improvements were accomplished. For this purpose, steel cantilever columns were tested on the shake table for two specific historical EQs coincidently having similar spectral acceleration values. Based on the experimental results, a three-part mass-normalized relative input energy spectrum was formulated including soil type, EQ (corner period, intensity, duration, spectral acceleration, and velocity), and structural behavioral characteristics (period and structural damping). The proposed input energy spectrum was experimentally calibrated and numerically validated for various EQs featuring near-and far-field types. Analytical and experimental comparisons were made between the previously developed spectrum and the newly proposed one. The validation studies and the statistical evaluations exposed that the proposed spectrum yielded better agreement with the experimental and numerical results.