Arch

An arch is a curved vertical

A typical true masonry arch consists of the following elements:^[10][11][12]

1. Keystone, the top block in an arch. Portion of the arch around the keystone (including the keystone itself), with no precisely defined boundary, is called a crown
2. Voussoir (a wedge-like construction block). A rowlock arch is formed by multiple concentric layers of voussoirs.^[13]
3. Extrados (an external surface of the arch)
4. dosseret.^[15]
5. Intrados (an underside of the arch, also known as a soffit^[2])
6. Rise (height of the arc, distance from the springing level to the crown)
7. Clear span
8. Abutment^[16] The triangular-shaped portion of the wall between the extrados and the horizontal division above is called spandrel.^[17]

A (left or right) half-segment of an arch is called an arc, the overall line of an arch is arcature^[18] (this term is also used for an arcade).^[19] Archivolt is the exposed (front-facing) part of the arch, sometimes decorated (occasionally also used to designate the intrados).^[20] If the sides of voussoir blocks are not straight, but include angles and curves for interlocking, the arch is called "joggled".^[21]

Arch action

A true arch, due to its rise, resolves the vertical loads into horizontal and vertical reactions at the ends, a so called arch action. The vertical load produces a positive bending moment in the arch, while the inward-directed horizontal reaction from the spandrel/abutment provides a counterbalancing negative moment. As a result, the bending moment in any segment of the arch is much smaller than in a beam with the equivalent load and span.^[22] The diagram on the right shows the difference between a loaded arch and a beam. Elements of the arch are mostly subject to compression (A), while in the beam a bending moment is present, with compression at the top and tension at the bottom (B).

In the past, when arches were made of masonry pieces, the horizontal forces at the ends of an arch caused the need for heavy abutments (cf.

When evaluated from the perspective of an amount of material required to support a given load, the best solid structures are compression-only; with the flexible materials, the same is true for tension-only designs. There is a fundamental symmetry in nature between solid compression-only and flexible tension-only arrangements, noticed by Robert Hooke in 1676: "As hangs the flexible line, so but inverted will stand the rigid arch", thus the study (and terminology) of arch shapes is inextricably linked to the study of hanging chains, the corresponding curves or polygons are called funicular. Just like the shape of a hanging chain will vary depending on the weights attached to it, the shape of an ideal (compression-only) arch will depend on the distribution of the load. ^[23]

• 
  Analogy between an arch and a hanging chain and comparison to the dome of

  Saint Peter's Basilica in Rome (Giovanni Poleni

  , 1748)
• 
  A complex funicular model (

  Gaudi

  , 19th century)

Classifications

There are multiple ways to classify an arch:^[24]

1. by the geometrical shape of its intrados (for example, semicircular, triangular, etc.);^[24][25]
2. for the round arches, by the number of circle segments forming the arch (for example,
   round arch is single-centred, pointed arch is two-centred);^[24]
3. by the material used (stone, brick, concrete, steel) and construction approach.^[24] For example, the wedge-shaped voussoirs of a brick arch can be made by cutting the regular bricks ("axed brick" arch) or manufactured in the wedge shape ("gauged brick" arch);^[26]
4. structurally, by the number of hinges (movable joints) between solid components. For example, voussoirs in a stone arch should not move, so these arches usually have no hinges (are "fixed"). Permitting some movement in a large structure allows to alleviate stresses (caused, for example, by the thermal expansion), so many bridge spans are built with three hinges (one at each support and one at the crown) since the mid-19th century.^[27]

Arrangements

A sequence of arches can be grouped together forming an

Two-tiered arches, with two arches superimposed, were sometimes used in Islamic architecture, mostly for decorative purposes.^[31]

An opening of the arch can be filled, creating a

• 
  Arcades of Pont du Gard (Roman)
• 
  Separating arches in the St. Zeno church [de]
• 
  Two-tiered arches in the

  Mosque-Cathedral of Córdoba

  (Islamic)
• 
  Large blind arch containing three smaller blind arches
• 
  Interlaced arcade of blind arches at Castle Acre (Romanesque)
• 
  Rear arch around three lights at St Matthew's Church, Langford

Structural

Structurally,

• 
  Relieving blind arches made of bricks at the Roman Pantheon
• 
  Transverse arches in Speyer Cathedral
• 
  Diaphragm arch in San Miniato al Monte
• 
  "Scissors" strainer arch arrangement in Wells Cathedral includes an inverted arch
• 
  The Enneüs Heerma Bridge showing a smaller, inverted, counter-arch in the middle

Shapes

The large variety of arch shapes (left) can mostly be classified into three broad categories:

"Round" semicircular arches were commonly used for ancient arches that were constructed of heavy masonry,^[44] and were relied heavily on by the Roman builders since the 4th century BC. It is considered to be the most common arch form,^[45] characteristic for Roman, Romanesque, and Renaissance architecture.^[25]

A

A

A

• 
  Semi-circular arches using

  Great Wall

  , China
• 
  Segmental arch of the Alconétar Bridge
• 
  Bridge with a basket handle arch
• 
  Great Mosque of Cordoba

Pointed

A

The intrados of the

Curtain arch (also known as inflexed arch, and, like the keel arch, usually decorative[25]) uses two (or more) drooping curves that join at the apex. Utilized as a dressing for windows and doors primarily in Saxony in the Late Gothic and early Renaissance buildings (late 15th to early 16th century), associated with Arnold von Westfalen [de].^[67] When the intrados has multiple concave segments, the arch is also called a draped arch or tented arch.^[68] A similar arch that uses a mixture of curved and straight segments^[69] or exhibits sharp turns between segments^[70] is a mixed-line arch.

• 
  Pointed arches of Mosque of Ibn Tulun (9th century AD)
• 
  Cusped arch in Diwan-i-Khas (Red Fort)
• 
  Trefoil arch in the Bayeux Cathedral
• 
  Tudor arch at Layer Marney Tower
• 
  Ogee arch at St Mary the Virgin, Silchester
• 
  Nodding ogee niche at St Peter's Church, Walpole St Peter
• 
  Keel arches at Palazzo Guadagni [it]
• 
  Curtain arches over windows in Hartenfels Castle [de]
• 
  A draped arch at the Government Palace of Tlaxcala [es] (1545)
• 
  Mixed-line arches at Escuelas Menores (Salamanca) [es]

Parabolic

The popularity of the arches using segments of a circle is due to simplicity of layout and construction,

• 
  Palau Güell: Parabolic ^[76]
• 
  Palau Güell: Hyperbolic ^[77]
• 
  Palau Güell:

  Rankine curve^[78] (a.k.a. weighted catenary

  )
• 
  Palau Güell: Elliptical ^[79]

Three parabolic-looking curves in particular are of significance to the arch design: parabola itself, catenary, and weighted catenary. The arches naturally use the inverted (upside-down) versions of these curves.

A parabola represents an ideal (all-compression) shape when the load is equally distributed along the span, while the weight of the arch itself is negligible. A catenary is the best solution for the case where an arch with uniform thickness carries just its own weight with no external load. The practical designs for bridges are somewhere in between, and thus use the curves that represent a compromise that combines both the catenary and the

• 
  A through arch bridge (Tyne Bridge in Newcastle upon Tyne, England): parabolic-looking arches with multiple deck supports distributing the load
• 
  Gateway Arch is stronger at the bottom: weighted catenary curve

Other

Unlike regular arches, the

• 
  Flat arch in the kitchen of

  Pitti Palace
• 
  Triangular arch
• 
  A triangular arch built using masonry
• 
  Mayan corbelled arch

Variations

Few transformations can be applied to arch shapes.

If one

• 
  Ramping arches at Palau Dalmases [ca] in Barcelona
• 
  Shouldered arch around the door of Lorenziberg church [de]. The raised portion is a flat arch.
• 
  Shouldered arch above the main entrance of Doge's Palace in Venice. The vertical supports separate the segments of an ogee arch.
• 
  The smaller arches at the lower level are stilted to match the wider arches on the left (St John's Chapel, London)
• 
  Stilted pointed arches at the Monreale Cathedral)
• 
  Skew arch (Sickergill Bridge) with

  masonry courses
• 
  Splayed arch over a window opening in the All Saints Church in Chedgrave

A wide arch with its rise less than 1⁄2 of the span (and thus the geometric circle of at least one segment is below the springing line) is called a surbased arch^[96] (sometimes also a depressed arch^[97]). A drop arch is either a basket handle arch^[98] or a blunt arch.^[99]

Hinged arches

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The practical arch bridges are built either as a fixed arch, a two-hinged arch, or a three-hinged arch.^[100] The fixed arch is most often used in reinforced concrete bridges and tunnels, which have short spans. Because it is subject to additional internal stress from thermal expansion and contraction, this kind of arch is statically indeterminate (the internal state is impossible to determine based on the external forces alone).^[43]

The two-hinged arch is most often used to bridge long spans.

The three-hinged arch is not only hinged at its base, like the two-hinged arch, yet also at its apex. The additional apical connection allows the three-hinged arch to move in two opposite directions and compensate for any expansion and contraction. This kind of arch is thus not subject to additional stress from thermal change. Unlike the other two kinds of arch, the three-hinged arch is therefore statically determinate.[100] It is most often used for spans of medial length, such as those of roofs of large buildings. Another advantage of the three-hinged arch is that the reaction of the pinned bases is more predictable than the one for the fixed arch, allowing shallow, bearing-type foundations in spans of medial length. In the three-hinged arch "thermal expansion and contraction of the arch will cause vertical movements at the peak pin joint but will have no appreciable effect on the bases," which further simplifies foundational design.^[43]

History

The arch became popular in the

True arches, as opposed to corbel arches, were known by a number of civilizations in the ancient Near East including 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.^[102] An example of the latter would be the

As evidenced by their imitations of the parabolic arches, Hittites most likely were exposed to the Egyptian designs, but used the corbelled technique to build them.^[109]

• 
  Vaulted building using a decorative segmented arch at the

  Heb-sed court in Saqqara (restored, c. 2650 BC

  )
• 
  A true arch (catenary) at the Ramesseum

  granaries

  (c. 1300 BC)
• 
  Ruins of the Kazarma tholos tomb [de] (c.1500 BC) showing the Mycenaean beehive technique
• 
  Arkadiko Bridge (c. 1300-1190 BC): corbel arch, cyclopean masonry
• 
  King's Gate (Hattusa) [de] (c.1400-1200 BC), an imitation of the parabolic arch by Hittites

Classical Persia and Greece

The Assyrians, also apparently under the Egyptian influence, adopted the true arch (with a slightly pointed profile) early in the 8th century.^[109] In ancient Persia, the Achaemenid Empire (550 BC–330 BC) built small barrel vaults (essentially a series of arches built together to form a hall) known as iwan, which became massive, monumental structures during the later Parthian Empire (247 BC–AD 224).^{[110][111][112]} This architectural tradition was continued by the Sasanian Empire (224–651), which built the Taq Kasra at Ctesiphon in the 6th century AD, the largest free-standing vault until modern times.^[113]

An early European example of a

.

• 
  Arch at the excavation in

  Assyrian architecture

  , end of 8th century BC, photo taken in 1853)
• 
  Vault underneath the temple of Apollo in Didyma, Turkey (4th century BC)
• 
  Arch at the stadium of Olympia (4th century BC)

Ancient Rome

The ancient

Etruscans (both cultures apparently adopted the design in the 4th century BC^[28]

), refined it and were the first builders in Europe to tap its full potential for above ground buildings:

The Romans were the first builders in Europe, perhaps the first in the world, to fully appreciate the advantages of the arch, the vault and the dome.[116]

Throughout the

Roman republic, although the best examples are from the imperial times (Arch of Augustus at Susa, Arch of Titus).^[28]

Romans initially avoided using the arch in the religious buildings and, in Rome, arched temples were quite rare until the recognition of Christianity in 313 AD (with the exceptions provided by the

Christian architecture.^[28]

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 segmental arch was first built by the Romans who realized that an arch in a bridge did not have to be a semicircle,

lintel arches can be found in villas and palaces.^[47]

• 
  The Jupiter gate at Falerii Novi (c. 300 BC)
• 
  Arches of the aqueduct at Segovia
• 
  Arches of the Colosseum
• 
  Arch of Augustus, Susa, Piedmont (c. 8 BC)
• 
  Arches at the "temple of Minerva Medica" in Rome
• 
  Temple of Hadrian at Ephesus combines a semicircular arch with the lintels (117 AD)
• 
  Temple of Jupiter at Sbeitla (c. 150 AD)
• 
  Arches in the narthex of Santa Sabina, Rome (c. 425 AD)
• 
  Arches and dome in Sant'Apollinare in Classe (534-536 AD)
• 
  Segmental arches in an Ostian insula

Ancient China

trabeated system.^[6] Arches were little-used, although there are few arch bridges known from literature and one artistic depiction in stone-carved relief.^{[119][120][121]} Since the only surviving artefacts of architecture from the Han dynasty (202 BC – 220 AD) are rammed earth defensive walls and towers, ceramic roof tiles from no longer existent wooden buildings,^{[122][123][124]} stone gate towers,^[125][126] and underground brick tombs, the known vaults, domes, and archways were built with the support of the earth and were not free-standing.^[127][128]

China's oldest surviving stone arch bridge is the Anji Bridge. Still in use, it was built between 595 CE and 605 CE during the Sui dynasty.^[129][130]

• 
  Anji Bridge: segmental arch, open-spandrel design

Islamic

Islamic architects adopted the Roman arches, but had quickly shown their resourcefulness: by the 8th century the simple semicircular arch was almost entirely replaced with fancier shapes, few fine examples of the former in the

cisterns at the White Mosque of Ramle^[131][132]). Their variations spread fast and wide: Mosque of Ibn Tulun in Cairo (876-879 AD), Nizamiyya Madrasa at Khar Gerd (now Iran, 11th century), Kongo Mosque in Diani Beach (Kenya, 16th century).^[70][132]

Islamic architecture brought to life a large amount of arch forms: the round

stilted version of the pointed arch.^[70]

It is quite likely that the appearance of the pointed arch, an essential element of the

Mudéjar style and subsequently spread around the Spanish-speaking world.^[69]

• 
  Semicircular arches at the Umayyad mosque
• 
  Pointed arches in the cisterns of the White Mosque in Ramla
• 
  Trefoil arches at the Cordoba Mosque
• 
  Interlaced arches at the Cordoba Mosque
• 
  Horseshoe arches at the Cordoba Mosque
• 
  Ogee arch at the Cordoba Mosque
• 
  Cusped arhes at the Cordoba Mosque
• 
  Mixed line arches at Palacio de Torre Tagle, Lima, Peru (1735)

Western Europe

The collapse of the

rebate).^[135]

Early Gothic utilized the flexibility of the pointed arch by grouping together arches of different spans but with the same height.^[135]

While the arches used in the mediaeval Europe were borrowed from the Roman and Islamic architecture, the use of pointed arch to form the rib vault was novel and became the defining characteristic of Gothic construction. At about 1400 AD, the city-states of Italy, where the pointed arch had never gotten much traction, initiated the revival of the Roman style with its round arches, Renaissance. By the 16th century the new style spread across Europe and, through the influence of empires, to the rest of the world. Arch became a dominant architectural form until the introduction of the new construction materials, like steel and concrete.^[135]

India

The history of arch in India is very long (some arches were apparently found in excavations of

Lomas Rishi cave (3rd century BC).^[70] Vaulted roof of an early Harappan burial chamber has been noted at Rakhigarhi.^[136] S.R Rao reports vaulted roof of a small chamber in a house from Lothal.^[137] Barrel vaults were also used in the Late Harappan Cemetery H culture dated 1900 BC-1300 BC which formed the roof of the metal working furnace, the discovery was made by Vats in 1940 during excavation at Harappa.^{[138][139][140]}

The use of arches until the

Mahabodhi temple (7th century AD), the latter has both pointed arches and semicircular arches.^[70][141] These Gupta era arch vault system was later used extensively in Burmese Buddhist temples in Pyu and Bagan in 11th and 12th centuries.^[142]

With the arrival of Islamic and other

cusped arches.^[70]

• 
  The insides of the Lomas Rishi cave
• 
  Arches at Karle (Great Chaitya, 1st century AD)
• 
  Decorative ogee arches (gavaksha) in Ajanta Caves
• 
  Pointed vault at the Mahabodhi temple
• 
  Arches at Buland Darwaza (16th century AD)

Pre-Columbian America

Mesoamerican cultures used only the flat roofs with no arches whatsoever,^[143] although some researchers had suggested that both Maya and Aztec architects understood the concept of a true arch.^[144][145]

Revival of the trabeated system

The 19th-century introduction of the

reinforced concrete frames

mostly replaced the arches as the load-bearing elements in buildings.

• 
  Original Britannia bridge (a colored postcard)
• 
  Britannia bridge (2008)

Construction

As a pure compression form, the utility of the arch is due to many building materials, including

tensile stress is applied to them.^[147]

Masonry

The voussoirs can be wedge-shaped or have a form of a rectangular cuboid, in the latter case the wedge-like shape is provided by the mortar.^[89]

An arch is held in place by the weight of all of its members, making construction problematic. One answer is to build a frame (historically, of wood) which exactly follows the form of the underside of the arch. This is known as a centre or centring. Voussoirs are laid on it until the arch is complete and self-supporting. For an arch higher than head height, scaffolding would be required, so it could be combined with the arch support. Arches may fall when the frame is removed if design or construction has been faulty.^{[citation needed]}

Old arches sometimes need reinforcement due to decay of the keystones, forming what is known as bald arch.

Reinforced concrete

In reinforced concrete construction, the principle of the arch is used so as to benefit from the concrete's strength in resisting compressive stress. Where any other form of stress is raised, such as tensile or torsional stress, it has to be resisted by carefully placed reinforcement rods or fibres.^[148]

Architectural styles

The type of arches (or absence of them) is one of the most prominent characteristics of an

arcuated (arch-based). His next division for the arcuated styles was based on the use of round and pointed arch shapes.^[149]

Cultural references

The steady horizontal push of an arch against the abutments gave rise to a saying "the arch never sleeps", attributed to many sources, from

adage stresses that the arch carries "a seed of death" for itself and the structure containing it, a statement that can be made upon observation of the Roman ruins.^[25] The plot of The Nebuly Coat by J. Meade Falkner, inspired by a collapse of a tower at the Chichester Cathedral plays with the idea while dealing with the slow disintegration of a church building.^[150] Saoud^[151] explains the proverb by chain-like self-balancing of the horizontal and vertical forces in the arch and its "universal adaptability".^[152]

See also

• Buttress
• Dome
• Flying arch
• Flying buttress
• Order moulding
• Suspension bridge

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132. ^ ^{a b c} Graves 2009.
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134. ^ Saoud 2002, p. 4.
135. ^ ^{a b c} Woodman & Bloom 2003, Western Europe and its influence.
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146. JSTOR 991404
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External links

Wikiquote has quotations related to Arch.

Wikimedia Commons has media related to:
Arch (category)

• Physics of Stone Arches by
  Nova
  : a model to build an arch without it collapsing
• InteractiveTHRUST: interactive applets, tutorials
• Paper about the three-hinged arch of the Galerie des Machines of 1889 Whitten by Javier Estévez Cimadevila & Isaac López César.