Energy damage index based on capacity and response spectra

Non-linear dynamic analysis and the damage index of Park-Ang have been often used to assess expected seismic damage to a structure. Depending on the size of the structure and the duration of the record, the computational effort in dynamic analyses is usually high. In this research, a new damage index is proposed based on nonlinear static analysis. The damage index is a linear combination of two energy functions: (1) the strain energy associated with the stiffness variation and the ductility of the structure, and (2) the dissipated energy associated with hysteretic cycles. These two energy functions are obtained from the capacity curve of the structure and from the energy balance with the spectral acceleration. To show the ability of the index to represent damage, low-rise steel buildings were studied under the seismic actions that are expected in Mexico City. The results obtained with the new method show good agreement with those calculated by means of dynamic analyses using the Park-Ang damage index. On average, the Park-Ang damage index is well-fitted by the combination of 62% of the strain energy and 38% of the energy dissipated by hysteresis. Moreover, the new damage index can link damage to certain characteristics of seismic actions, such as their intensity and duration. Therefore, the new approach results in a practical, powerful tool for estimating seismic damage in buildings, especially as probabilistic approaches require massive computations.