This work summarises results of the evaluation of the physical earthquake vulnerability for the structural system of an essential building by using reliability methods. The research was based on the compilation of drawings and design memories, pathology studies, a structural surveying, and the assessment of the local earthquake hazard. In order to evaluate the shear capacity, non-linear pushover analyses in three (3) different models, by using Montecarlo simulation with 100 different concrete

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... rength data in each model, were performed. The first model is the original one, i.e. without reinforcement. The second one corresponds to a rehabilitated structure by using concentric steel diagonals. The third model is a structure retrofitted with a reinforced concrete wall. Demand was evaluated by performing dynamic spectral analyses for each model. Twelve different spectra corresponding to the same number of earthquake periods of return were used. Annual probabilities of failure were estimated by using the obtained distributions of shear demand and capacity. Moreover, the probabilities of failure were also evaluated utilizing spectral displacement distributions and demands at the performance points. Results showed imminent risk and inadequate levels of safety in the original un-reinforced structure. Annual probabilities of failure for the two retrofitted models were clearly lower than that of the original structure. An approximate cost-benefit analysis was also carried out, which is useful for decision taking.