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Distribution of Earthquake Input Energy in Structures



P Khashaee, B Mohraz, Fahim H. Sadek, Hai S. Lew, John L. Gross


In developing an energy-based design approach and assessing the damage potential of structures, one must know the distribution of earthquake input energy among energy components: kinetic, elastic strain, hysteretic, and damping. This report examines the influences of the ground motion characteristics: intensity, frequency content, and duration of strong motion and the structural properties: ductility, damping, and hysteretic behavior on the distribution of input energy for a one- and a five-story building using 20 accelerograms, ten with short and ten with long duration of strong motion. Results indicate that for certain damping ratios, ductility has a significant influence on input energy and its distribution among energy components in a structure. For a given ductility ratio, small damping ratio (less than 5%) has a minor effect on input energy, but a major influence on the energy distribution. Damping ratios larger than 5% have a significant influence on the input energy and its distribution. Three energy ratios that relate to hysteretic energy were computed: the maximum ratio of hysteretic to input energy (Eh/Eir)m, the ratio of the maximum hysteretic energy to the maximum input energy Ehm/Eirm, and the equivalent number of yield excursions Neq = Ehm/(Fy, Up) where Fy is the yield strength, and Up is the plastic deformation. It is found that (Eh/Eir reflect the energy demand for the entire duration of accelerogram. The study shows that (Eh/Eir) m is independent of the duration of strong motion and period of structure; however, Ehm/Eirm is independent of both only for periods less then 1 s. Results indicate that as the duration becomes longer the equivalent number of yield excursions Neq increases indicating more structural damage. The influence of ground motion characteristics and structural properties on the distribution of energy parameters for a five-story building with fixed-base, base-isolation, supplemental damping and semi-active control are examined using the 20 accelerograms. The results show that: 1) the distribution of energy through the height of the building is mostly independent of the frequency content and the duration of strong motion, 2) base-isolation, supplemental damping, and semi-active control reduce the damage potential by reducing the input and hysteretic energy demands and have significant influences on the distribution of energy through the height of the building.
NIST Interagency/Internal Report (NISTIR) - 6903
Report Number


building technology, design spectra, earthquake energy, earthquake engineering, structural engineering


Khashaee, P. , Mohraz, B. , Sadek, F. , Lew, H. and Gross, J. (2003), Distribution of Earthquake Input Energy in Structures, NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg, MD, [online], (Accessed June 9, 2023)
Created December 31, 2002, Updated October 12, 2021