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The shape of the curve traced by a loose span of chain or rope, the catenary is the structurally ideal shape for a freestanding arch of constant thickness.Types of arches displayed chronologically, roughly in the order in which they were developed: True arches, as opposed to corbel arches, were known by a number of civilizations in the ancient Near East and the Levant, but their use was infrequent and mostly confined to underground structures, such as drains where the problem of lateral thrust is greatly diminished.They also introduced the triumphal arch as a military monument.Vaults began to be used for roofing large interior spaces such as halls and temples, a function that was also assumed by domed structures from the 1st century BC onwards.The semicircular arch was followed in Europe by the pointed Gothic arch or ogive, whose centreline more closely follows the forces of compression and which is therefore stronger.The semicircular arch can be flattened to make an elliptical arch, as in the Ponte Santa Trinita.allowing the structure to move freely and compensate for the thermal expansion and contraction caused by changes in outdoor temperature.However, this can result in additional stresses, so the two-hinged arch is also statically indeterminate, although not to the degree of the fixed arch.
Of all arch types, the parabolic arch produces the most thrust at the base, but can span the largest areas.
This innovation allowed for taller and more closely spaced openings, typical of Gothic architecture.
Vaults are essentially "adjacent arches [that] are assembled side by side." If vaults intersect, complex forms are produced with the intersections.
It is commonly used in bridge design, where long spans are needed.
The catenary arch has a shape different from the parabolic curve.