Stochastic assessment of rocking masonry façades under real seismic records

This contribution assesses in stochastic terms the safety level of masonry façades potentially subjected to out-of-plane loading and the beneficial effect offered by horizontal restraints - such as steel tie rods - under earthquakes. A parametric analysis is performed on façades of different slenderness and size to state their influence on the response in probabilistic terms, showing that velocity and energy based Intensity Measures are optimal since they usually respect the efficiency and practicality criteria. In case of retrofitting interventions, the univariate FCs can be plotted in the two configurations (with and without steel tie rods). In order to effectively present the results, the graph of the difference of conditional probability is elaborated, which directly gives the information on the earthquake intensity for which the level of improvement is more relevant. Univariate and bivariate curves are also compared and the former may be not in favor of safety, especially for stronger seismic records. This probabilistic procedure is ideal for applications in earthquake engineering, assessing in stochastic sense the level of improvement obtained with traditional retrofitting solutions.