## Seismic Energy Balance

In the design of structure subjected to earthquake loading, the energy equation can be used to study the energy absorbtion of different components. In a satisfactory design, the energy supply must be larger than the energy demand. In this regard, two approaches can be considered for the energy equation. Uang and Bertero (1990) used absolute and relative energy formulations for a single degree of freedom system. They found that absolute energy formulation is simple and more straightforward. Filiatrault et al. (1994) used energy balance to study the nonlinear behaviour of different structures under variable earthquake ground motion. Different time stepping algorithms were used to investigate the effect of numerical damping. Without the numerical damping, exact energy balance can be achieved. The two approaches to energy formulation were found to give different energy responses.

The energy equation of the dam structure governed by equation (2.1), can be written as:

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