Nineteenth-century builders who used new materials were able to build large iron skeletons as frames for vaults made of light materials – for example, the glass crystal palace of the Great Exhibition of 1851 in London. As the new materials eliminated weight and shear problems, the simple barrel vault was again preferred for structures such as railway terminals and exhibition halls. In many modern framing systems, the vault has lost its functional significance and has become a thin skin placed on a series of arches. The reinforced concrete vault, a curved or shaped slab, is an important innovation. The steel-reinforced shell does not exert lateral thrust and can be supported as a beam. A barrel vault that is curved in the plane to form a circular passage is called a ring-shaped vault. The fan-shaped vault seems to owe its origin to the use of centering of a curve for all ribs, rather than having separate centering for the transverse, diagonal and intermediate ribs; It was also facilitated by the introduction of the four-centric arch, since the lower part of the arch was part of the fan or coroid, and the upper part could be extended at will with a greater radius above the vault. These ribs were often carved from the same stones as the walkways, the entire vault being treated as a single joint surface covered with interlocking interlacing.  One of the earliest examples of the introduction of the interrib is found in the nave of Lincoln Cathedral, where the rib of the comb is not worn at the rib of the wall. However, it soon became apparent that the construction of the net was greatly facilitated by additional ribs, and consequently there was a tendency to increase their number, so that in the nave of Exeter Cathedral, three intermediate ribs were provided between the rib of the wall and the diagonal rib. To hide the connection of the different ribs, their crosses were decorated with richly carved bosses, and this practice intensified with the introduction of another short rib, known as lierne, a term given in France to the comb rib. The ribs of Lierne are short ribs that intersect between the main ribs and have been mainly used as decorative elements, as in the Church of Our Lady (1482) in Mühlacker, Germany.
One of the best examples of Lierne ribs is found in the vault of the bay window of Crosby Hall, London. The tendency to increase the number of ribs has led in some cases to singular results, as in the choir of Gloucester Cathedral, where ordinary diagonal ribs become mere ornamental mouldings on the surface of a cut pointed barrel vault, and again in cloisters, where the introduction of the fan vault, which forms a conoid with concave sides, has returned to the principles of the Roman geometric vault. This is also evident in the construction of these fan vaults, because although in the early examples each of the ribs above the heap was an independent feature, it was eventually found easier to carve them and the net in solid stone, so that the rib and net were purely decorative and had no constructive or independent function.  There is another remarkable vault, also built by Justinian in the Church of Saints Sergius and Bacchus in Constantinople. The central area of this church was octagonal on the ground plane, and the dome is divided into sixteen sections; Of these, eight consist of broad flat strips rising from the center of each of the walls, and the eight alternate are concave cells above the corners of the octagon, giving the roof the appearance of an umbrella outside and inside.  A cross vault is a vault in which all cornices are covered by ribs or diagonal ribs in the form of segmental arches. Their curvatures are defined by boundary arcs. While the transverse arches retain the same semicircular profile as their edge vaults, the longitudinal arches are pointed, with both arches having their centers on the transom line.
As a result, the latter can better match the curvatures of the diagonal ribs, creating a straight tunnel that runs from east to west.  In these cases, the continuous thrust of the barrel vault collided with semicircular or pointed barrel vaults on the side aisles, which had only half the span of the nave; An interesting example of this can be found in the Chapel of St. John in the Tower of London – and sometimes by half-barrel vaults. However, the great thickness of the walls required in such constructions seems to have led to another solution to the problem of churches covered with non-combustible material, namely. The one found throughout the Périgord and Charente, where a series of domes are covered with pendants above the nave, the main peculiarities of these domes being the fact that the arches that support them are part of the pendants, all built in horizontal ways.  Due to structural advantages, the vault was retained as a standard construction. Because of its links to the official architecture of ancient Rome, the vault is often used for public buildings such as state capitals. The cross and cross vault of the Romans was used in the early Christian churches of Rome, but only above the aisles, which were comparatively small in scope, but in these there was a tendency to raise the centers of these vaults, which became slightly dominant; In all these cases, centering was used.  The cathedral`s vaults crown Italian Gothic churches such as Siena Cathedral, whose dome rises from a hexagonal base, and Florence Cathedral, whose dome rises from an octagonal base.
Although dome vaults are not true domes that have a continuous and uninterrupted contour, vaults like these are commonly referred to as domes. A good example of the fan vault is the one above the staircase leading to Christ Church, Oxford, where the entire conoid is supported in its centre on a central column. This vault, built as recently as 1640, is an example of traditional craftsmanship, probably passed down to Oxford as a result of the late vaulting of the college entrance doors. The fan vault is a peculiarity of England, the only example that comes close to it in France is the pendant of the Marienkapelle in Caudebec-en-Caux in Normandy.  The first barrel vaults of ancient Egypt are probably those of the granaries built by Pharaoh Ramses II of the 19th dynasty, whose ruins are behind the Ramesseum of Thebes.    The range was 12 feet (3.7 m) and the lower part of the arch was built in horizontal orbits, up to about one-third of the height, and the rings above were tilted backwards at a slight angle, so that the bricks of each ring, laid flat until the ring was completed, without the need for centering; The vault thus formed was elliptical in section, which resulted from the nature of its construction. A similar building system was used for the vault above the great hall of Ctesiphon, where the material used was baked bricks or tiles of large dimensions, cemented with mortar; But the span was close to 83 feet (25 m), and the thickness of the vault was nearly 5 feet (1.5 m) at the top, there were four masonry rings. The first example is thought to be above a small hall in Pergamon in Asia Minor, but its first use on large rooms was due to the Romans. When two semicircular barrel vaults of the same diameter intersect, their intersection (a true ellipse) is called the ridge vault, through which the thrust of the vault is carried to the transverse walls; When a row of two or more barrel vaults intersects, the weight is transferred to the pillars at their intersection and the thrust is transferred to the outer transverse walls; Thus, in the Roman reservoir of Baiae, known as Piscina Mirabilis, a series of five corridors with semicircular barrel vaults is intersected by twelve transepts, with the vaults supported by 48 pillars and thick outer walls.
The width of these corridors was only about 13 feet (4.0 m) and there were no great difficulties in building these vaults, but in the Roman baths of Caracalla, the tepidarium had a span of 80 feet (24 m), more than twice the height of an English cathedral, so its construction was of paramount importance from a static and economic point of view.   The research of M. Choisy (L`Art de construire chez les Romains), based on a careful examination of the parts of the vaults still preserved in situ, has shown that on a relatively light centering, consisting of trusses spaced about 10 feet (3.0 m) apart and covered with planks laid half-timbered, First, two layers of Roman bricks (nearly 2 feet (0.61 m) square and 2 in. thick); On these and on the lattice beams, transverse brick rings with longitudinal cross-members were constructed at regular intervals; On the brick layers and the embedding of the rings and transverse trusses, the concrete was cast in horizontal layers, with the rear parts massively filled and the surface inclined on both sides and covered with a low-pitched tile roof, which was placed directly on the concrete.