1160 framed reinforced concrete buildings, holding 3–13 stories, have been modelled in a probabilistic way. Capacity spectra have been calculated and characterized by means of 5 parameters: initial stiffness, ultimate capacity (Sdu, Sau), µ and s. µ is related to ductility, and s controls the way the building strength degrades. A strong correlation among these five parameters has been found. Moreover, the also high correlation between the initial stiffness and the number of stories allows to define median and percentile capacity spectra starting from the number of stories. Afterwards, for each number of stories, a fragility analysis is performed for the median capacity spectrum. The Barcelona city, in Spain, is used to depict the expected physical damage for a probabilistic and a deterministic seismic hazard scenario. Two procedures, based on the bilinear form of the capacity spectrum and on the Park and Ang damage index, are used to define damage states thresholds. The probabilistic scenario is more damaging than the deterministic one is and, damage states thresholds based on the capacity spectrum lead to more damages than the ones based on the Park and Ang damage index. Mean damage states close to 2.0 are obtained, being 25% and 6% the probabilities of Severe, and Complete, damage states, which would have significant impact on the number of homeless people and victims. Maps of expected damages depict the physical seismic risk of the probabilistic scenario. These scenarios are very useful for emergency planning and for earthquake protection.