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This thesis presents a simplified methodology for the assessment of Catalan double curvature masonry vaults. The methodology consists on discretize the vault in a series of arches capable of representing the structural behavior of the vault. This network of hanging cables catenaries that represents the thrust lines of the structure in an inverted model are handled with the application of the limit theorems of plasticity. An optimization on the analysis process allows us to efficiently apply this methodology to assess the safety of thin tile vaulted structures and estimate the ultimate capacity load.