Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Civil and Environmental Engineering


Eric M. Lui


Ductiltiy, Hysteretic energy, Hysteretic model, Input Energy, Soil site class, Velocity index

Subject Categories



Current seismic codes for building design often utilize a force or a displacement-based approach in their implementation. In a force-based approach, a structure is designed to ensure it possesses sufficient strength to resist the maximum forces imparted to it by an earthquake. In a displacement-based approach, a target displacement is calculated or identified and the structure is proportioned to achieve a specified performance level, defined by strain or drift limits, under a specified level of seismic intensity. A third approach, which has gained momentum in the earthquake engineering community, is the energy-based approach. In this approach, a design is considered satisfactory if the capacity of a structure to absorb or dissipate energy exceeds its energy demand from an earthquake. In the present research, a new energy-based approach is proposed in which velocity index (VI), obtained as the product of two ground motion indexes - peak ground velocity (PGV) and cumulative absolute velocity (CAV), is used to normalize input energy spectra. The use of VI as a normalization factor not only allows for the creation of dimensionless input energy spectra, but can result in smaller values of coefficients of variation when compared to other normalization factors currently being used.

Earthquake input energy spectra for four site classes (Site Class B, C, D and E as per IBC 2012 soil classifications) and four hysteretic models (bilinear plastic, stiffness degradation, bilinear flag and bilinear slip) are developed for five ductility levels (=1, 2, 3, 4, 5) using ground motion ensembles of 38, 42, 38 and 26 recorded at site classes B, C, D and E, respectively. For purpose of design, the normalized input energy spectra are divided into three regions - short period, intermediate period and long period - that are consistent with the customary design response spectra contained in various seismic codes and standards. A close examination of these spectra has shown that regardless of the hysteretic models used, the normalized seismic input energy decreases as ductility increases, and increases as the soil gets softer. For each site class, empirical ductility dependent input energy expressions are developed, and hysteretic to input energy ratio relationships are formulated. The proposed design input energy spectra are validated using six major earthquakes and are found to reasonably match the spectra generated using time history analysis.

Since the input energy spectra are developed for single-degree-of-freedom (SDOF) systems, to facilitate the implementation of the proposed method in the design of multi-degree-of-freedom (MDOF) systems, simple expressions that relate earthquake input and hysteretic energies for MDOF system to its equivalent single-degree-of-freedom (ESDOF) systems are formulated. The energy relationships are verified using four (a three story, a five story, a seven story and a nine story) frames each subjected to six earthquakes wherein a very good estimate for the three- and five- story and a reasonably acceptable estimate for the seven-, and nine-story frames were obtained. A new method for distributing hysteretic energy over the height of moment resisting frames is also proposed. The new distribution scheme was used in determining the energy demand (hysteretic energy) component of an energy-based seismic design (EBSD). EBSD is a story-wise optimization design procedure developed using the relationship that exists between energy dissipating capacity and plastic analysis/design of structures. Finally, the entire process of determining the input energy for ESDOF systems to the distribution of hysteretic energy over the height of MDOF structures using the proposed EBSD design procedure is demonstrated using two design examples: a three-story one-bay frame and a five-story two-bay frame.


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