Summary 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.

No abstract

No abstract

No abstract

No abstract

No abstract

Seismic input energy per unit mass ( EI/m) imparted into a structure is a function of earthquake (duration, frequency content, amplitude etc.), soil (shear velocity, dominant period etc.) and the structural (vibrational periods etc.) characteristics. Generally, the damping properties of the structure is assumed negligible for seismic input energy. Most of the existing spectral equations derived for SDOF systems generally use a constant damping ratio of 5%. In this study, the damping effect on EI/m is investigated experimentally and numerically on SDOF systems with distinct damping ratios. Experimental investigation and numerical computations proved that seismic input energy is very sensitive to variation of damping within the vicinity of fundamental frequencies. Specifically, up to 50% increment was observed in the plateau region of the input energy spectrum, where maximum EI/m values occur, by variation of damping from 2% to 10%. Hence, a novel damping modification factor ( DMF), which could be utilized for existing energy spectra, is proposed in this paper. Validation studies of the proposed DMF are achieved through the various energy spectra found in the literature.

This paper discusses closed-form demonstrations of the damping effect for a basic mass, spring, and damper (MSD) and a single degree of freedom (SDOF) system that are exposed to harmonic loading. Initially, the energy balance equations of the systems were solved in closed form by considering the damping ratio and loading frequency. Verification of the solutions obtained for SDOF systems is achieved by shake table tests. Based on the analytical and experimental results, it was found that the damping effect is highly related to the ratio of loading frequency to the natural vibrational frequency of the system. For the lower and higher values of the ratio, damping is found to be almost ineffective. However, the effect becomes substantial when the ratio reaches unity i.e. at the resonant frequency. Damping has a reverse relation with seismic energy at the dominant frequency. In contrast, the relation is proportional in the vicinity of resonance frequencies. Hence, considering the damping as a parameter for the energy-based design of structures is suggested.