The structural action of vaults depends on their final shape rather than on their method of construction. Intersecting semicircular barrel vaults evolved into pointed Gothic vaults which remain stable but need much less material. The vaults between the groins can be slightly domed, so they can be analysed much like fuller domes, by both membrane and slicing techniques. The ribs at the groins carry severe stresses; this is their structural purpose. The lines of thrust escape from the ribs into vaulting pockets filled with rubble, whence they pass through the walls into the buttresses. Ungewitter’s tables show how thrusts vary with vault materials and rise-to-span ratios. Vaults develop cracks of different types (as do arches); these can respond differently to unexpected loads, such as those due to fires and firefighting. Technical analyses of vaults can illuminate historical debates, about the original presence and purpose of flying buttresses, for example. Fan vaults are more demanding technically than other vaults but can still be analysed using membrane techniques to obtain profiles and lines of thrust. Henry VII Chapel at Westminster provides a case study of cracks.