Development of techniques for seismic mitigation has become increasingly important for communities throughout the world. Of the many available techniques, structural control has emerged as a promising option for the last thirty years. Extensive investigation has been conducted for modeling, performance, and strategies of structural control. Studies of this method have centered on the use of passive, active, and semi-active control devices. Semi-active control devices have gained popularity because they combine positive aspects of both passive and active control. In particular, magneto-rheological dampers have been used extensively in research and implemented in practice. However, structural control studies are evaluated on a case by case scenario or over a few earthquakes. In recent years, a new approach known as consequence based engineering seeks to evaluate seismic risk reduction through probabilistic safety assessment spanning a large class of structures. The assessment is performed through the development of fragility relationships for a class of structures. Seismic fragility relationships determine the probability of exceeding some limit state over a range of seismic inputs based on a number of ground motions, thus allowing for more than one case scenario to be analyzed. This thesis focuses on the methodology used to develop fragility relationships for civil structures that have been retrofitted with semi-active control devices for seismic risk mitigation purposes.
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