# Arch

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Curved structure that spans a space and may support a load

This article is about the architectural construct. For other uses of *arch* or *arches*, see [Arch (disambiguation)](/source/Arch_(disambiguation)).

[Gateway Arch](/source/Gateway_Arch)

An **arch** is a curved vertical [structure](/source/Structure) [spanning](/source/Span_(engineering)) an open space underneath it.[1] Arches may support the load above them, or they may perform a purely decorative role. As a decorative element, the arch dates back to the [4th millennium BC](/source/4th_millennium_BC), but structural load-bearing arches became popular only after their adoption by the [Ancient Romans](/source/Ancient_Romans) in the 4th century [BC](/source/Anno_Domini).[2]

Arch-like structures can be horizontal, like an [arch dam](/source/Arch_dam) that withstands a horizontal [hydrostatic pressure](/source/Hydrostatic_pressure) load.[3] Arches are usually used as supports for many types of [vaults](/source/Vault_(architecture)), with the [barrel vault](/source/Barrel_vault) in particular being a continuous arch.[4] Extensive use of arches and vaults characterizes an **arcuated construction**, as opposed to the [trabeated](/source/Trabeated) system, where, like in the architectures of ancient Greece, China, and Japan (as well as the modern [steel-framed](/source/Steel-framed) technique), [posts and beams](/source/Post_and_lintel) dominate.[5]

The arch had several advantages over the [lintel](/source/Lintel), especially in [masonry](/source/Masonry) construction: with the same amount of material an arch can have larger span, carry more weight, and can be made from smaller and thus more manageable pieces.[6] Its role in construction was diminished in the middle of the 19th century with introduction of [wrought iron](/source/Wrought_iron) (and later [steel](/source/Steel)): the high [tensile strength](/source/Tensile_strength) of these new materials made long lintels possible.

## Basic concepts

### Terminology

"False arch" redirects here. For an arch-like construction that uses offsetting of the stones or bricks, "corbelling", to close the span, see [Corbel arch](/source/Corbel_arch).

A **true arch** is a load-bearing arch with elements held together by compression.[7] In much of the world introduction of the true arch was a result of European influence.[2] The term **false arch** has a few meanings. It is usually used to designate an arch that has no structural purpose, like a [proscenium arch](/source/Proscenium_arch) in theaters used to frame the performance for the spectators, but is also applied to [corbelled](/source/Corbel_arch) and [triangular](/source/Triangular_arch) arches that are not based on compression.[8][9]

Masonry arch elements

A typical true [masonry](/source/Masonry) arch consists of the following elements:[10][11][12]

1. [Keystone](/source/Keystone_(architecture)), 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**

1. [Voussoir](/source/Voussoir) (a wedge-like construction block). A [compound arch](/source/Compound_arch) is formed by multiple concentric layers of voussoirs. The **rowlock arch** is a particular case of the compound arch,[13] where the voussoir faces are formed by the [brick headers](/source/Brick_header).[14]

1. **Extrados** (an external surface of the arch)

1. [Impost](/source/Impost_(architecture)) is block at the base of the arch (the voussoir immediately above the impost is a [springer](/source/Springer_(architecture))). The tops of imposts define the **springing level**. A portion of the arch between the springing level and the crown (centered around the 45° angle[15]) is called a **haunch**. If the arch resides on top of a [column](/source/Column), the impost is formed by an [abacus](/source/Abacus_(architecture)) or its thicker version, [dosseret](/source/Dosseret).[16]

1. **Intrados** (an underside of the arch, also known as a *[soffit](/source/Soffit)*[7])

1. **Rise** (height of the arc, distance from the springing level to the crown)

1. [Clear span](/source/Clear_span)

1. [Abutment](/source/Abutment)[17] The roughly triangular-shaped portion of the wall between the extrados and the [horizontal division](https://en.wikipedia.org/w/index.php?title=Division_(architecture)&action=edit&redlink=1) above is called *[spandrel](/source/Spandrel)*.[18]

A (left or right) half-segment of an arch is called an *arc*, the overall line of an arch is *arcature*[19] (this term is also used for an [arcade](/source/Arcade_(architecture))).[20] [Archivolt](/source/Archivolt) is the exposed (front-facing) part of the arch, sometimes decorated (occasionally also used to designate the intrados).[21] If the sides of voussoir blocks are not straight, but include angles and curves for interlocking, the arch is called "[joggled](/source/Joggle_(architecture))".[22]

### Arch action

Arch (A) action diagram in comparison with a beam (B)

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](/source/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.[23] 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 (so called **thrust**[24]) caused the need for heavy abutments (cf. [Roman triumphal arch](/source/Roman_triumphal_arch)). The other way to counteract the forces, and thus allow thinner supports, was to use the [counter-arches](/source/Counter-arch), as in an [arcade](/source/Arcade_(architecture)) arrangement, where the horizontal thrust of each arch is counterbalanced by its neighbors, and only the end arches need to [buttressed](/source/Buttressed). With new construction materials (steel, concrete, [engineered wood](/source/Engineered_wood)), not only the arches themselves got lighter, but the horizontal thrust can be further relieved by a [tie](/source/Tie_(engineering)) connecting the ends of an arch ([bowstring arch](/source/Bowstring_arch)).[6]

### Funicular shapes

Main article: [Funicular curve](/source/Funicular_curve)

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](/source/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.[25]

		- Analogy between an arch and a hanging chain and comparison to the dome of [Saint Peter's Basilica](/source/Saint_Peter's_Basilica) in Rome ([Giovanni Poleni](/source/Giovanni_Poleni), 1748)

		- A complex funicular model ([Church of Colònia Güell](/source/Church_of_Col%C3%B2nia_G%C3%BCell) by [Gaudi](/source/Gaudi), 19th century)

Arch diagram with pressure polygons drawn. A defect at the R-S portion of the intrados makes the arch susceptible to extra force along the line M-N, where the polygon curve can be pushed out of the envelope of the arch causing a collapse

While building masonry arches in the not very tall buildings of the past, a practical assumption was that the stones can withstand virtually unlimited amount of pressure (up to 100 [N](/source/Newton_(unit)) per mm2), while the tensile strength was very low, even with the mortar added between the stones, and can be effectively assumed to be zero. Under these assumptions the calculations for the arch design are greatly simplified: either a reduced-scale model can be built and tested, or a funicular curve ([pressure polygon](https://en.wikipedia.org/w/index.php?title=Pressure_polygon&action=edit&redlink=1)) can be calculated or modeled, and as long as this curve stays within the confines of the voussoirs, the construction will be stable[26] (a so called "[safe theorem](https://en.wikipedia.org/w/index.php?title=Safe_theorem&action=edit&redlink=1)").

## Classifications

There are multiple ways to classify arches:[27]

1. [by the geometrical shape](#Shapes) of its intrados (for example, [semicircular](/source/Semicircular_arch), [triangular](/source/Triangular_arch), etc.);[27][28]

1. for the arches with rounded intrados, by the number of circle segments forming the arch (for example, [round arch](/source/Round_arch) is single-centred, [pointed arch](/source/Pointed_arch) is two-centred);[27]

1. [by the material used](#Construction) (stone, brick, concrete, steel) and construction approach.[27] 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);[29]

1. [structurally](/source/Structural_analysis), [by the number of *hinges*](#Hinged_arches) (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](/source/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.[30]

## Arrangements

A sequence of arches can be grouped together forming an [arcade](/source/Arcade_(architecture)). [Romans](/source/Roman_architecture) perfected this form, as shown, for example, by arched structures of [Pont du Gard](/source/Pont_du_Gard).[31] In the interior of [hall churches](/source/Hall_church), arcades of [separating arches](/source/Separating_arch) were used to separate the [nave](/source/Nave) of a church from the side aisle,[32] or two adjacent side aisles.[33]

**Two-tiered arches**, with two arches superimposed, were sometimes used in [Islamic architecture](/source/Islamic_architecture), mostly for decorative purposes.[34]

An opening of the arch can be filled, creating a [blind arch](/source/Blind_arch). Blind arches are frequently decorative, and were extensively used in [Early Christian](/source/Early_Christian_architecture), [Romanesque](/source/Romanesque_architecture), and Islamic architecture.[35] Alternatively, the opening can be filled with smaller arches, producing a **containing arch**, common in [Gothic](/source/Gothic_architecture) and Romanesque architecture.[36] Multiple arches can be superimposed with an offset, creating an [interlaced](/source/Interlaced_arch) series of usually (with some exceptions) blind and decorative arches. Most likely of Islamic origin, the interlaced arcades were popular in Romanesque and Gothic architecture.[37] **Rear-arch** (also **rere-arch**) is the one that frames the internal side of an opening in the external wall.[38]

		- Arcades of [Pont du Gard](/source/Pont_du_Gard) (Roman)

		- Separating arches in the [St. Zeno church](https://en.wikipedia.org/w/index.php?title=Kirche_St._Zeno_(Bad_Reichenhall)&action=edit&redlink=1) [[de](https://de.wikipedia.org/wiki/Kirche_St._Zeno_(Bad_Reichenhall))]

		- Two-tiered arches in the [Mosque-Cathedral of Córdoba](/source/Mosque-Cathedral_of_C%C3%B3rdoba) (Islamic)

		- Large blind arch containing three smaller blind arches

		- Interlaced arcade of blind arches at [Castle Acre](/source/Castle_Acre) (Romanesque)

		- Rear arch around three lights at [St Matthew's Church, Langford](/source/St_Matthew's_Church%2C_Langford)

### Structural

Structurally, [relieving arches](/source/Relieving_arch) (often blind or containing) can be used to take off load from some portions of the building (for example, to allow use of thinner exterior walls with larger window openings, or, as in the [Roman Pantheon](/source/Roman_Pantheon), to redirect the weight of the upper structures to particular strong points).[36] [Transverse arches](/source/Transverse_arch), introduced in [Carolingian architecture](/source/Carolingian_architecture), are placed across the [nave](/source/Nave) to compartmentalize (together with longitudinal separating arches) the internal space into [bays](/source/Bay_(architecture)) and support [vaults](/source/Vault_(architecture)).[39] A [diaphragm arch](/source/Diaphragm_arch) similarly goes in the transverse direction, but carries a section of wall on top. It is used to support or divide sections of the high roof.[40] [Strainer arches](/source/Strainer_arch) were built as an afterthought to prevent two adjacent supports from imploding due to miscalculation. Frequently they were made very decorative, with one of the best examples provided by the [Wells Cathedral](/source/Wells_Cathedral). Strainer arches can be "[inverted](/source/Inverted_arch)" (upside-down) while remaining structural.[41][42] When used across railway cuttings to prevent collapse of the walls, strainer arches may be referred to as [flying arches](/source/Flying_arch).[43][44] A [counter-arch](/source/Counter-arch) is built adjacent to another arch to oppose its horizontal action or help to stabilize it, for example, when constructing a [flying buttress](/source/Flying_buttress).[45]

		- Relieving blind arches made of bricks at the Roman Pantheon

		- Transverse arches in [Speyer Cathedral](/source/Speyer_Cathedral)

		- Diaphragm arch in [San Miniato al Monte](/source/San_Miniato_al_Monte)

		- "Scissors" strainer arch arrangement in [Wells Cathedral](/source/Wells_Cathedral) includes an inverted arch

## Shapes

Types of arches

The large variety of arch shapes (left) can mostly be classified into three broad categories: [rounded](/source/Round_arch), [pointed](/source/Pointed_arch), and [parabolic](/source/Parabolic_arch).[46]

### Rounded

"Round" [semicircular arches](/source/Semicircular_arch) were commonly used for ancient arches that were constructed of heavy masonry,[47] and were relied heavily on by the [Roman](/source/Ancient_Rome) builders since the 4th century [BC](/source/Anno_Domini). It is considered to be the most common arch form,[48] characteristic for Roman, [Romanesque](/source/Romanesque_architecture), and [Renaissance](/source/Renaissance_architecture) architecture.[28]

A [segmental arch](/source/Segmental_arch), with a rounded shape that is less than a semicircle, is very old (the versions were cut in the rock in Ancient Egypt c. 2100 BC at [Beni Hasan](/source/Beni_Hasan)). Since then it was occasionally used in [Greek temples](/source/Ancient_Greek_architecture),[49] utilized in Roman residential construction,[50] [Islamic architecture](/source/Islamic_architecture), and got popular as window [pediments](/source/Pediments) during the Renaissance.[49]

A [basket-handle arch](/source/Basket-handle_arch) (also known as *depressed arch*, *three-centred arch*, *basket arch*) consists of segments of three circles with origins at three different centers (sometimes uses five or seven segments, so can also be *five-centred*, etc.). Was used in [late Gothic](/source/Late_Gothic_architecture) and [Baroque architecture](/source/Baroque_architecture).[51][52]

A [horseshoe arch](/source/Horseshoe_arch) (also known as *keyhole arch*) has a rounded shape that includes more than a semicircle, is associated with Islamic architecture and was known in areas of Europe with Islamic influence ([Spain](/source/Spain), [Southern France](/source/Southern_France), [Italy](/source/Italy)). Occasionally used in Gothics, it briefly enjoyed popularity as the entrance door treatment in the [interwar](/source/Interwar) England.[53]

In a [Florentine arch](/source/Florentine_arch) (also known as "Venetian", "Italian" on the illustration), the distance between intrados and extrados grows closer to the apex. It can combine rounded intrados with pointed extrados.[54][55]

		- Semi-circular arches using [brick](/source/Brick) and/or [stone](/source/Stone) block construction at the [Great Wall](/source/Great_Wall), China

		- Segmental arch of the [Alconétar Bridge](/source/Alcon%C3%A9tar_Bridge)

		- Bridge with a basket handle arch

		- [Horseshoe arch](/source/Horseshoe_arch) in the [Great Mosque of Cordoba](/source/Great_Mosque_of_Cordoba)

### Pointed

Pointed arches, 1 - equilateral with trefoil treatment, 2 - blunt, 3 - lancet, 4 - ogee, 5 - four-centred, 6 - curtain (inflexed), 7 - pointed horseshoe

Main article: [Pointed arch](/source/Pointed_arch)

A [pointed arch](/source/Pointed_arch) consists of two ("*[two-centred arch](/source/Two-centred_arch)*"[56]) or more circle segments culminating in a point at the top. It originated in the Islamic architecture (there are other opinions, cf. Warren 1991[57]), arrived in Europe in the second half of the 11th century ([Cluny Abbey](/source/Cluny_Abbey))[58] and later became prominent in the [Gothic architecture](/source/Gothic_architecture).[59] The advantages of a pointed arch over a semicircular one are flexible ratio of [span](/source/Span_(engineering)) to [rise](/source/Rise_(arch))[60] and lower horizontal reaction at the base. This innovation allowed for taller and more closely spaced openings, which are typical of Gothic architecture.[61][62] [Equilateral arch](/source/Equilateral_arch) is the most common form of the pointed arch, with the centers of two circles forming the intrados coinciding with the springing points of the opposite segment. Together with the [apex](/source/Apex_(geometry)) point, they form an [equilateral triangle](/source/Equilateral_triangle), thus the name.[63] If the centers of circles are farther apart, the arch becomes a narrower and sharper [lancet arch](/source/Lancet_arch) that appeared in France in the [Early Gothic architecture](/source/Early_Gothic_architecture) ([Saint-Denis Abbey](/source/Saint-Denis_Abbey)) and became prominent in England in the late 12th and early 13th centuries ([Salisbury Cathedral](/source/Salisbury_Cathedral)).[64] If the centers are closer to another, the result is a wider [blunt arch](/source/Blunt_arch).

The intrados of the [cusped arch](/source/Cusped_arch) (also known as *multifoil arch*, *polyfoil arch*, *polylobed arch*, and *scalloped arch*) includes several independent circle segments in a [scalloped](/source/Scalloped) arrangement. These primarily decorative arches are common in Islamic architecture and Northern European Late Gothic, can be found in [Romanesque architecture](/source/Romanesque_architecture).[65] A similar [trefoil arch](/source/Trefoil_arch) includes only three segments and sometimes has a rounded, not pointed, top. Common in Islamic architecture and Romanesque buildings influenced by it, it later became popular in the decorative motifs of the Late Gothic designs of Northern Europe.[66]

Each arc of an [ogee arch](/source/Ogee_arch) consists of at least two circle segments (for a total of at least four), with the center of an upper circle being outside the extrados. After European appearance in the 13th century on the facade of the [St Mark's Basilica](/source/St_Mark's_Basilica), the arch became a fixture of the [English Decorated style](/source/English_Gothic_architecture#Decorated_Gothic_(late_13th–late_14th_centuries)), French [Flamboyant](/source/Flamboyant), [Venetian](/source/Venetian_Gothic), and other Late Gothic styles.[67] Ogee arch is also known as *reversed curve arch*, occasionally also called an *inverted arch*.[41] The top of an ogee arch sometimes projects beyond the wall, forming the so-called *nodding ogee* popular in 14th century England ([pulpitum](/source/Pulpitum) in [Southwell Minster](/source/Southwell_Minster)).[68]

Each arc of a [four-centred arch](/source/Four-centred_arch) is made of two circle segments with distinct centers; usually the radius used closer to the springing point is smaller with a more pronounced curvature. Common in Islamic architecture ([Persian arch](/source/Persian_arch)), and, with upper portion flattened almost to straight lines ([Tudor arch](/source/Tudor_arch)[69]), in the English [Perpendicular Gothic](/source/Perpendicular_Gothic).[70]A [keel arch](/source/Keel_arch) is a variant of four-centred arch with haunches almost straight, resembling a section view of a [capsized](/source/Capsized) ship. Popular in Islamic architecture, it can be also found in Europe, occasionally with a small ogee element at the top,[71] so it is sometimes considered to be a variation of an ogee arch.[72]

**Curtain arch** (also known as **inflexed arch**, and, like the keel arch, usually decorative[28]) uses two (or more) drooping curves that join at the apex. Utilized as a dressing for windows and doors primarily in [Saxony](/source/Saxony) in the Late Gothic and early Renaissance buildings (late 15th to early 16th century), associated with [Arnold von Westfalen](https://en.wikipedia.org/w/index.php?title=Arnold_von_Westfalen&action=edit&redlink=1) [[de](https://de.wikipedia.org/wiki/Arnold_von_Westfalen)].[73] When the intrados has multiple concave segments, the arch is also called a **draped arch** or **tented arch**.[74] A similar arch that uses a mixture of curved and straight segments[75] or exhibits sharp turns between segments[76] is a [mixed-line arch](/source/Mixed-line_arch) (or *mixtilinear arch*). In [Moorish architecture](/source/Moorish_architecture) the mixed-line arch evolved into an ornate [lambrequin arch](/source/Lambrequin_arch),[77] also known as *[muqarnas](/source/Muqarnas) arch*.

		- Pointed arches of [Mosque of Ibn Tulun](/source/Mosque_of_Ibn_Tulun) (9th century [AD](/source/Anno_Domini))

		- Cusped arch in [Diwan-i-Khas (Red Fort)](/source/Diwan-i-Khas_(Red_Fort))

		- Trefoil arch in the [Bayeux Cathedral](/source/Bayeux_Cathedral)

		- Tudor arch at [Layer Marney Tower](/source/Layer_Marney_Tower)

		- Ogee arch at [St Mary the Virgin, Silchester](https://en.wikipedia.org/w/index.php?title=St_Mary_the_Virgin,_Silchester&action=edit&redlink=1)

		- Nodding ogee niche at [St Peter's Church, Walpole St Peter](/source/St_Peter's_Church%2C_Walpole_St_Peter)

		- Keel arches at [Palazzo Guadagni](https://en.wikipedia.org/w/index.php?title=Palazzo_Guadagni&action=edit&redlink=1) [[it](https://it.wikipedia.org/wiki/Palazzo_Guadagni)]

		- Curtain arches over windows in [Hartenfels Castle](https://en.wikipedia.org/w/index.php?title=Hartenfels_Castle&action=edit&redlink=1) [[de](https://de.wikipedia.org/wiki/Schloss_Hartenfels)]

		- A draped arch at the [Government Palace of Tlaxcala](https://en.wikipedia.org/w/index.php?title=Palacio_de_Gobierno_de_Tlaxcala&action=edit&redlink=1) [[es](https://es.wikipedia.org/wiki/Palacio_de_Gobierno_de_Tlaxcala)] (1545)

		- Mixed-line arches at [Escuelas Menores (Salamanca)](https://en.wikipedia.org/w/index.php?title=Escuelas_Menores_(Salamanca)&action=edit&redlink=1) [[es](https://es.wikipedia.org/wiki/Escuelas_Menores_(Salamanca))]

		- Lambrequin arch at [Bahia Palace](/source/Bahia_Palace) in [Morocco](/source/Morocco)

### Parabolic

The popularity of the arches using segments of a circle is due to simplicity of layout and construction,[78] not their structural properties. Consequently, the architects historically used a variety of other curves in their designs: [elliptical curves](/source/Elliptical_curve), [hyperbolic cosine](/source/Hyperbolic_cosine) curves (including [catenary](/source/Catenary)), and [parabolic curves](/source/Parabolic_curve). There are two reasons behind the selection of these curves:[79]

1. they are still relatively easy to trace with common tools prior to construction;

1. depending on a situation, they can have superior structural properties and/or appearance.

The [hyperbolic curve](/source/Hyperbolic_curve) is not easy to trace, but there are known cases of its use.[79] The non-[circumferential](/source/Circumference) curves look similar, and match at shallow profiles, so a catenary is often misclassified as a parabola[80] (per [Galileo](/source/Galileo), "the [hanging] chain fits its parabola almost perfectly"[81]). González et al. provide an example of [Palau Güell](/source/Palau_G%C3%BCell), where researchers do not agree on classification of the arches or claim the prominence of parabolic arches, while the measurements show that just two of the 23 arches designed by [Gaudi](/source/Gaudi) are actually parabolic.[82]

		- Palau Güell: Parabolic[83]

		- Palau Güell: Hyperbolic[84]

		- Palau Güell: [Rankine curve](/source/Rankine_curve)[85] (a.k.a. [weighted catenary](/source/Weighted_catenary))

		- Palau Güell: Elliptical[86]

Three parabolic-looking curves in particular are of significance to the arch design: [parabola](/source/Parabola) itself, [catenary](/source/Catenary), and [weighted catenary](/source/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 [funicular curve](/source/Funicular_curve) for particular non-uniform distribution of load.[87] The practical free-standing arches are stronger and thus heavier at the bottom, so a weighted catenary curve is utilized for them. The same curve also fits well an application where a bridge consists of an arch with a roadway of packed dirt above it, as the [dead load](/source/Dead_load) increases with a distance from the center.[88]

		- A [through arch bridge](/source/Through_arch_bridge) ([Tyne Bridge](/source/Tyne_Bridge) in [Newcastle upon Tyne](/source/Newcastle_upon_Tyne), [England](/source/England)): parabolic-looking arches with multiple deck supports distributing the load

		- [Gateway Arch](/source/Gateway_Arch) is stronger at the bottom: weighted catenary curve

### Other

Unlike regular arches, the [flat arch](/source/Flat_arch) (also known as *jack arch*, *lintel arch*, *straight arch*, *plate-bande*[89]) is not curved. Instead, the arch is flat in profile and can be used under the same circumstances as [lintel](/source/Lintel). However, lintels are subject to bending stress, while the flat arches are true arches, composed of irregular voussoir shapes (the keystone is the only one of the symmetric wedge shape),[90] and that efficiently uses the compressive strength of the masonry in the same manner as a curved arch and thus requires a mass of masonry on both sides to absorb the considerable lateral thrust. Used in the Roman architecture to imitate the Greek lintels, Islamic architecture, European [medieval](/source/Medieval_architecture) and Renaissance architecture. The flat arch is still being used as a decorative pattern, primarily at the top of window openings.[90]

#### False arches

The corbel (also *corbelled*) arch, made of two [corbels](/source/Corbel) meeting in the middle of the span, is a true arch in a sense of being able to carry a load, but it is false in a structural sense, as its components are subject to bending stress. The typical profile is not curved, but has triangular shape. Invented prior to the semicircular arch, the corbel arch was used already in the [Egyptian](/source/Ancient_Egyptian_architecture) and [Mycenaean](/source/Mycenaean_architecture) architecture in the [3rd](/source/3rd_millennium_BC) and [2nd millennium BC](/source/2nd_millennium_BC).[91]

Like a corbel arch, the [triangular arch](/source/Triangular_arch) is not a true arch in a structural sense. Its intrados is formed by two slabs leaning against each other.[9] Brick builders would call triangular any arch with straight inclined sides.[92] The design was common in [Anglo-Saxon England](/source/Anglo-Saxon_England) until the late 11th century ([St Mary Coslany](/source/St_Mary_Coslany)).[9] [Mayan](/source/Maya_civilization) corbel arches are sometimes called triangular due to their shape.[93]

		- Flat arch in the kitchen of [Pitti Palace](/source/Pitti_Palace)

		- Triangular arch

		- A triangular arch built using masonry

		- Mayan corbelled arch

### Variations

Few transformations can be applied to arch shapes.

If one [impost](/source/Impost_(architecture)) is much higher than another, the arch (frequently [pointed](/source/Pointed_arch)) is known as *[ramping arch](/source/Ramping_arch)*, *raking arch*,[94] or *rampant arch* (from [French](/source/French_language): *arc rampant*).[95] Originally used to support inclined structures, like stairs, in the 13th-14th centuries they appeared as parts of [flying buttresses](/source/Flying_buttress) used to counteract the thrust of Gothic [ribbed vaults](/source/Ribbed_vault).[96]

A central part of an arch can be raised on short vertical supports, creating a [trefoil](/source/Trefoil_arch)-like **shouldered arch**. The raised central part can vary all the way from a flat arch to ogee. The shouldered arches were used to decorate openings in Europe from medieval times to [Late Gothic architecture](/source/Late_Gothic_architecture), became common in [Iranian architecture](/source/Iranian_architecture) from the 14th century, and were later adopted in the [Ottoman Turkey](/source/Ottoman_Turkey).[97]

In a [stilted arch](/source/Stilted_arch) (also *surmounted*[98]), the springing line is located above the imposts (on "stilts"). Known to Islamic architects by the 8th century, the technique was utilized to vertically align the apexes of arches of different dimensions in Romanesque and Gothic architecture.[99] Stilting was useful for semicircular arches, where the ratio of the rise fixed at 1⁄2 of the span, but was applied to the pointed arches, too.

The [skew arch](/source/Skew_arch) (also known as an *oblique arch*) is used when the arch needs to form an oblique angle in the horizontal plane with respect to the (parallel) springings,[100][101] for example, when a bridge crosses the river at an angle different than 90°. A [splayed arch](/source/Splayed_arch) is used for the case of unequal spans on the sides of the arch (when, for example, an interior opening in the wall is larger than the exterior one), the intrados of a round splayed arch is not cylindrical, but has a [conical](/source/Conical) shape.[102][101]

		- Ramping arches at [Palau Dalmases](https://en.wikipedia.org/w/index.php?title=Palau_Dalmases&action=edit&redlink=1) [[ca](https://ca.wikipedia.org/wiki/Palau_Dalmases)] in [Barcelona](/source/Barcelona)

		- Shouldered arch around the door of [Lorenziberg church](https://en.wikipedia.org/w/index.php?title=Filialkirche_Lorenziberg&action=edit&redlink=1) [[de](https://de.wikipedia.org/wiki/Filialkirche_Lorenziberg)]. The raised portion is a flat arch.

		- Shouldered arch above the main entrance of [Doge's Palace](/source/Doge's_Palace) in [Venice](/source/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](/source/St_John's_Chapel%2C_London))

		- Stilted pointed arches at the [Monreale Cathedral](/source/Monreale_Cathedral))

		- Skew arch (Sickergill Bridge) with [helicoidal](/source/Helicoidal) [masonry courses](/source/Masonry_course)

		- Splayed arch over a window opening in the All Saints Church in [Chedgrave](/source/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**[103] (sometimes also a *depressed arch*[104]). A **drop arch** is either a [basket handle arch](/source/Basket-handle_arch)[105] or a blunt arch.[106]

## Hinged arches

Main article: [Hinged arch bridge](/source/Hinged_arch_bridge)

Rossgraben bridge ([Rüeggisberg](/source/R%C3%BCeggisberg)) near Bern, Switzerland, showing the [hinge](/source/Concrete_hinge) at mid-span of this three-hinged arch.

Practical [arch bridges](/source/Arch_bridge) are built either as a fixed arch, a two-hinged arch, or a three-hinged arch.[107] 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](/source/Statically_indeterminate) (the internal state is impossible to determine based on the external forces alone).[46]

The two-hinged arch is most often used to bridge long spans.[46] This kind of arch has pinned connections at its base. Unlike that of the fixed arch, the pinned base can rotate,[108] thus allowing the structure to move freely and compensate for the [thermal expansion](/source/Thermal_expansion) and [contraction](/source/Thermal_contraction) that changes in outdoor temperature cause. However, this can result in additional stresses, and therefore the two-hinged arch is also statically indeterminate, although not as much as the fixed arch.[46]

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.[107] 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.[46]

## History

The arch became popular in the [Roman times](/source/Ancient_Rome) and mostly spread alongside the European influence, although it was known and occasionally used much earlier. Many ancient architectures avoided the use of arches, including the [Viking](/source/Viking_architecture) and [Hindu](/source/Hindu_architecture) ones.[2]

### Bronze Age: ancient Near East

True arches, as opposed to [corbel arches](/source/Corbel_arch), were known by a number of civilizations in the [ancient Near East](/source/Ancient_Near_East) including the [Levant](/source/Levant), but their use was infrequent and mostly confined to underground structures, such as drains where the problem of lateral thrust is greatly diminished.[109] An example of the latter would be the [Nippur](/source/Nippur) arch, built before 3800 BC,[110] and dated by [H. V. Hilprecht](/source/Hermann_Volrath_Hilprecht) (1859–1925) to even before 4000 BC.[111] Rare exceptions are an arched mudbrick home doorway dated to c. 2000 BC from [Tell Taya](/source/Tell_Taya) in [Iraq](/source/Iraq)[112] and two [Bronze Age](/source/Bronze_Age) arched [Canaanite](/source/Canaan) city gates, one at [Ashkelon](/source/Ashkelon) (dated to c. 1850 BC),[113] and one at [Tel Dan](/source/Tel_Dan) (dated to c. 1750 BC), both in modern-day [Israel](/source/Israel).[114][115] An Elamite tomb dated 1500 BC from [Haft Teppe](/source/Haft_Tepe) contains a parabolic vault which is considered one of the earliest evidences of arches in Iran.

The use of true arches in Egypt also originated in the [4th millennium BC](/source/4th_millennium_BC) (underground barrel vaults at the [Dendera](/source/Dendera) cemetery). Standing arches were known since at least the [Third Dynasty](/source/Third_Dynasty), but very few examples survived, since the arches were mostly used in non-durable secular buildings and made of [mud brick](/source/Mud_brick) voussoirs that were not wedge-shaped, but simply held in place by [mortar](/source/Mortar_(masonry)), and thus susceptible to a collapse (the oldest arch still standing is at [Ramesseum](/source/Ramesseum)). Sacred buildings exhibited either lintel design or corbelled arches. Arches were mostly missing in Egypt temples even after the [Roman conquest](/source/Roman_conquest_of_Egypt), even though Egyptians thought of the arch as a spiritual shape and used it in the rock-cut tombs and portable shrines.[116] [Auguste Mariette](/source/Auguste_Mariette) suggested that this choice was based on a relative fragility of a vault: "what would remain of the tombs and temples of Egyptians today, if they had preferred the vault?"[28]

[Mycenaean architecture](/source/Mycenaean_architecture) utilized only the corbel arches in their [beehive tombs](/source/Beehive_tombs) with triangular openings.[116] [Mycenaeans](/source/Mycenaeans) had also built probably the oldest still standing[117] stone-arch bridge in the world, [Arkadiko Bridge](/source/Arkadiko_Bridge), in Greece.

As evidenced by their imitations of the parabolic arches, [Hittites](/source/Hittites) most likely were exposed to the Egyptian designs, but used the corbelled technique to build them.[116]

		- Vaulted building using a decorative segmented arch at the [Heb-sed court](/source/Heb-sed_court) in [Saqqara](/source/Saqqara) (restored, c. 2650 [BC](/source/Anno_Domini))

		- A true arch (catenary) at the Ramesseum [granaries](/source/Granaries) (c. 1300 BC)

		- Ruins of the [Kazarma tholos tomb](/source/Kazarma_tholos_tomb) (c.1500 BC) showing the Mycenaean beehive technique

		- Arkadiko Bridge (c. 1300-1190 BC): corbel arch, [cyclopean masonry](/source/Cyclopean_masonry)

		- [King's Gate (Hattusa)](https://en.wikipedia.org/w/index.php?title=K%C3%B6nigstor_(%E1%B8%AAattu%C5%A1a)&action=edit&redlink=1) [[de](https://de.wikipedia.org/wiki/K%C3%B6nigstor_(%E1%B8%AAattu%C5%A1a))] (c.1400-1200 BC), an imitation of the parabolic arch by [Hittites](/source/Hittites)

### Classical Persia and Greece

The [Assyrians](/source/Assyria), also apparently under the Egyptian influence, adopted the true arch (with a slightly pointed profile) early in the 8th century.[116] In [ancient Persia](/source/History_of_Iran), the [Achaemenid Empire](/source/Achaemenid_Empire) (550 BC–330 BC) built small [barrel vaults](/source/Barrel_vault) (essentially a series of arches built together to form a hall) known as *[iwan](/source/Iwan)*, which became massive, monumental structures during the later [Parthian Empire](/source/Parthian_Empire) (247 BC–AD 224).[118][119][120] This architectural tradition was continued by the [Sasanian Empire](/source/Sasanian_Empire) (224–651), which built the [Taq Kasra](/source/Taq_Kasra) at [Ctesiphon](/source/Ctesiphon) in the 6th century AD, the largest free-standing vault until modern times.[121]

An early European example of a *[voussoir](/source/Voussoir)* arch appears in the 4th century BC [Greek](/source/Ancient_Greece) [Rhodes Footbridge](/source/Rhodes_Footbridge).[122][123] Proto-true arches can also be found under the stairs of the [temple of Apollo at Didyma](/source/Temple_of_Apollo_at_Didyma) and the [stadium at Olympia](/source/Stadium_at_Olympia).[31] .

		- Arch at the excavation in [Dur-Sharrukin](/source/Dur-Sharrukin) ([Assyrian architecture](/source/Assyrian_architecture), end of 8th century BC, photo taken in 1853)

		- Vault underneath the temple of Apollo in [Didyma](/source/Didyma), [Turkey](/source/Turkey) (4th century BC)

		- Arch at the stadium of Olympia (4th century BC)

### Ancient Rome

The ancient [Romans](/source/Roman_architecture) learned the [semicircular arch](/source/Semicircular_arch) from the [Etruscans](/source/Etruscans) (both cultures apparently adopted the design in the 4th century BC[31]), 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.[124]

Throughout the [Roman Empire](/source/Roman_Empire), from [Syria](/source/Syria) to [Scotland](/source/Scotland), engineers erected arch structures. The first use of arches was for civic structures, like drains and city gates. Later the arches were utilized for major civic buildings [bridges](/source/Roman_bridge) and [aqueducts](/source/Roman_aqueduct), with the outstanding 1st century [AD](/source/Anno_Domini) examples provided by the [Colosseum](/source/Colosseum), [Pont Du Gard](/source/Pont_Du_Gard), and the [aqueduct of Segovia](/source/Aqueduct_of_Segovia).[31] The introduction of the ceremonial [triumphal arch](/source/Triumphal_arch) dates back to [Roman Republic](/source/Roman_Republic), although the best examples are from the imperial times ([Arch of Augustus](/source/Arch_of_Augustus_(Susa)) at Susa, [Arch of Titus](/source/Arch_of_Titus)).[31]

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 [Pantheon](/source/Roman_Pantheon) and the ["temple of Minerva Medica"](/source/Temple_of_Minerva_Medica_(nymphaeum))[*[verification needed](https://en.wikipedia.org/wiki/Wikipedia:Verifiability)*]). Away from the capital, arched temples were more common ([temple of Hadrian at Ephesus](https://en.wikipedia.org/w/index.php?title=Hadrianstempel_(Ephesos)&action=edit&redlink=1) [[de](https://de.wikipedia.org/wiki/Hadrianstempel_(Ephesos))], [temple of Jupiter at Sbeitla](/source/Archaeological_site_of_Sbeitla), Severan temple at [Djemila](/source/Djemila)).[31] Arrival of Christianity prompted creation of the new type of temple, a [Christian basilica](https://en.wikipedia.org/w/index.php?title=Christian_basilica&action=edit&redlink=1), that made a thorough break with the pagan tradition with arches as one of the main elements of the design, along with the exposed brick walls ([Santa Sabina](/source/Santa_Sabina) in Rome, [Sant'Apollinare in Classe](/source/Sant'Apollinare_in_Classe)). For a long period, from the late 5th century to the 20th century, [arcades](/source/Arcade_(architecture)) were a standard staple for the Western [Christian architecture](/source/Christian_architecture).[31]

Vaults began to be used for roofing large interior spaces such as halls and temples, a function that was also assumed by [domed structures](/source/List_of_Roman_domes) 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,[125][126] such as in [Alconétar Bridge](/source/Alcon%C3%A9tar_Bridge) or [Ponte San Lorenzo](/source/Ponte_San_Lorenzo). The utilitarian and mass residential ([insulae](/source/Insula_(Roman_city))) buildings, as found in [Ostia Antica](/source/Ostia_Antica) and [Pompeii](/source/Pompeii), mostly used low [segmental arches](/source/Segmental_arch) made of bricks and [architraves](/source/Architrave) made of wood, while the concrete [lintel arches](/source/Lintel_arch) can be found in [villas](/source/Roman_villa) and palaces.[50]

		- The Jupiter gate at [Falerii Novi](/source/Falerii_Novi) (c. 300 BC)

		- Arches of the aqueduct at Segovia

		- Arches of the Colosseum

		- Arch of Augustus, [Susa, Piedmont](/source/Susa%2C_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](/source/Sbeitla) (c. 150 AD)

		- Arches in the [narthex](/source/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

[Ancient architecture of China](/source/Chinese_architecture) (and Japan) used mostly [timber-framed](/source/Timber-framed) construction and [trabeated](/source/Trabeated) system.[5] Arches were little-used, although there are few [arch bridges](/source/Arch_bridge) known from literature and one artistic depiction in stone-carved [relief](/source/Relief).[127][128][129] Since the only surviving artefacts of architecture from the [Han dynasty](/source/Han_dynasty) (202 BC – 220 AD) are [rammed earth](/source/Rammed_earth) defensive walls and towers, [ceramic roof tiles](/source/Chinese_glazed_roof_tile) from no longer existent wooden buildings,[130][131][132] [stone gate towers](/source/Que_(tower)),[133][134] and underground brick tombs, the known vaults, domes, and archways were built with the support of the earth and were not free-standing.[135][136]

China's oldest surviving stone [arch bridge](/source/Arch_bridge) is the [Anji Bridge](/source/Anji_Bridge). Still in use, it was built between 595 CE and 605 CE during the [Sui dynasty](/source/Sui_dynasty).[137][138]

		- Anji Bridge: segmental arch, open-[spandrel](/source/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 [Umayyad architecture](/source/Umayyad_architecture) notwithstanding (cf. the [Great Mosque of Damascus](/source/Great_Mosque_of_Damascus), 706–715 CE). The first [pointed arches](/source/Pointed_arch) appear already at the end of the 7th century AD ([Al-Aqsa Mosque](/source/Al-Aqsa_Mosque), [Palace of Ukhaidhir](/source/Palace_of_Ukhaidhir), [cisterns](/source/Cisterns) at the [White Mosque of Ramle](/source/White_Mosque_of_Ramle)[139][140]). Their variations spread fast and wide: [Mosque of Ibn Tulun](/source/Mosque_of_Ibn_Tulun) in Cairo (876-879 AD), Nizamiyya Madrasa at [Khar Gerd](/source/Khar_Gerd) (now [Iran](/source/Iran), 11th century), Kongo Mosque in [Diani Beach](/source/Diani_Beach) ([Kenya](/source/Kenya), 16th century).[76][140]

Islamic architecture brought to life a large amount of arch forms: the round [horseshoe arch](/source/Horseshoe_arch) that became a characteristic trait of the Islamic buildings, the [keel arch](/source/Keel_arch), the [cusped arch](/source/Cusped_arch), and the [mixed-line arch](/source/Mixed-line_arch) (where the curved "ogee swell" is interspersed with abrupt bends).[140] The [Great Mosque of Cordoba](/source/Great_Mosque_of_Cordoba), that can be considered a catalogue of Islamic arches, contains also the arches with almost straight sides, [trefoil](/source/Trefoil_arch), [interlaced](/source/Interlaced_arches), and [joggled](/source/Joggled_arch). Mosque of Ibn Tulun adds [four-centred](/source/Four-centred_arch) and [stilted](/source/Stilted_arch) version of the pointed arch.[76]

It is quite likely that the appearance of the pointed arch, an essential element of the [Gothic style](/source/Gothic_style), in Europe ([Monte Cassino](/source/Monte_Cassino), 1066–1071 AD, and the [Cluny Abbey](/source/Cluny_Abbey) five years later) and the [ogee arch](/source/Ogee_arch) in Venice (c. 1250) is a result of the Islamic influence,[76] possibly through [Sicily](/source/Sicily).[141] [John Ruskin](/source/John_Ruskin), however, traces the development of the Gothic [ogee arch](/source/Ogee_arch) as an indigenous evolution of the different shapes ("orders") of the [Florentine arch](/source/Florentine_arch).[142]

Saoud[143] also credits to Islamic architects the spread of the [transverse arch](/source/Transverse_arch). Mixed-line arch became popular in the [Mudéjar style](/source/Mud%C3%A9jar_style) and subsequently spread around the Spanish-speaking world.[75]

		- Semicircular arches at the Umayyad mosque

		- Pointed arches in the cisterns of the White Mosque in [Ramla](/source/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](/source/Palacio_de_Torre_Tagle), Lima, Peru (1735)

### Western Europe

The collapse of the [Western Roman Empire](/source/Western_Roman_Empire) left the church as the only client of major construction; with all [pre-Romanesque](/source/Pre-Romanesque) architectural styles borrowing from Roman construction with its semicircular arch. Due to the decline in the construction quality, the walls were thicker, and the arches thus heavier, than their Roman prototypes. Eventually the architects started to use the depth of the arches for decoration, turning the deep opening into [recessed orders](/source/Recessed_orders) (or *rebated arch*, a sequence of progressively smaller concentric arches, each inset with a [rebate](/source/Rebate_(architecture))).[144]

[Romanesque style](/source/Romanesque_style) started experiments with the [pointed arch](/source/Pointed_arch) late in the 11th century ([Cluny Abbey](/source/Cluny_Abbey)). In few decades, the practice spread ([Durham Cathedral](/source/Durham_Cathedral), [Basilica of Saint-Denis](/source/Basilica_of_Saint-Denis)). [Early Gothic](/source/Early_Gothic) utilized the flexibility of the pointed arch by grouping together arches of different [spans](/source/Span_(engineering)) but with the same height.[144]

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](/source/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](/source/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.[144]

### India

The history of arch in India is very long (some arches were apparently found in excavations of [Kosambi](/source/Kosambi), [2nd millennium BC](/source/2nd_millennium_BC). However, the continuous history begins with rock-cut arches in the [Lomas Rishi](/source/Lomas_Rishi) cave (3rd century BC).[76] Vaulted roof of an early [Harappan](/source/Harappan_architecture) burial chamber has been noted at [Rakhigarhi](/source/Rakhigarhi).[145] [S.R Rao](/source/Shikaripura_Ranganatha_Rao) reports vaulted roof of a small chamber in a house from [Lothal](/source/Lothal).[146] Barrel vaults were also used in the Late Harappan [Cemetery H culture](/source/Cemetery_H_culture) dated 1900 BC-1300 BC which formed the roof of the metal working furnace, the discovery was made by [Vats](/source/Madho_Sarup_Vats) in 1940 during excavation at Harappa.[147][148][149]

The use of arches until the [Islamic conquest of India](/source/Islamic_conquest_of_India) in the 12th century [AD](/source/Anno_Domini) was sporadic, with [ogee arches](/source/Ogee_arch) and barrel vaults in rock-cut temples ([Karla Caves](/source/Karla_Caves), from the 1st century BC) and decorative pointed [gavaksha](/source/Gavaksha) arches. By the 5th century AD voussoir vaults were used structurally in the brick construction. Surviving examples include the temple at [Bhitargaon](/source/Bhitargaon) (5th century AD) and [Mahabodhi Temple](/source/Mahabodhi_Temple) (7th century AD), the latter has both [pointed arches](/source/Pointed_arch) and [semicircular arches](/source/Semicircular_arch).[76][150] These [Gupta era](/source/Gupta_era) arch vault system was later used extensively in Burmese Buddhist temples in [Pyu](/source/Pyu_city-states) and [Bagan](/source/Bagan) in 11th and 12th centuries.[151]

With the arrival of Islamic and other [Western Asia](/source/Western_Asia) influence, the arches became prominent in the Indian architecture, although the [post and lintel](/source/Post_and_lintel) construction was still preferred. A variety of pointed and lobed arches was characteristic for the [Indo-Islamic architecture](/source/Indo-Islamic_architecture), with the monumental example of [Buland Darwaza](/source/Buland_Darwaza), that has pointed arch decorated with small [cusped arches](/source/Cusped_arch).[76]

		- The insides of the Lomas Rishi cave

		- Arches at Karle ([Great Chaitya](/source/Karla_Caves), 1st century AD)

		- Decorative ogee arches (gavaksha) in [Ajanta Caves](/source/Ajanta_Caves)

		- Pointed vault at the Mahabodhi temple

		- Arches at Buland Darwaza (16th century AD)

### Pre-Columbian America

[Mayan architecture](/source/Mayan_architecture) utilized the corbel arches. The other [Mesoamerican cultures](/source/Mesoamerican_cultures) used only the flat roofs with no arches whatsoever,[152] although some researchers had suggested that both Maya and [Aztec](/source/Aztec_architecture) architects understood the concept of a true arch.[153][154]

### Revival of the trabeated system

The 19th-century introduction of the [wrought iron](/source/Wrought_iron) (and later [steel](/source/Steel)) into construction changed the role of the arch. Due to the high [tensile strength](/source/Tensile_strength) of new materials, relatively long lintels became possible, as was demonstrated by the [tubular](/source/Tubular_bridge) [Britannia Bridge](/source/Britannia_Bridge) ([Robert Stephenson](/source/Robert_Stephenson), 1846-1850). A fervent proponent of the [trabeated](/source/Trabeated) system, [Alexander "Greek" Thomson](/source/Alexander_%22Greek%22_Thomson), whose preference for [lintels](/source/Lintel) was originally based on aesthetic criteria, observed that the [spans](/source/Span_(engineering)) of this bridge are longer than that of any arch ever built, thus "the simple, unsophisticated stone lintel contains in its structure all the scientific appliances [...] used in the great tubular bridge. [...] [Stonehenge](/source/Stonehenge) is more scientifically constructed than [York Minster](/source/York_Minster)."[155] Use of arches in bridge construction continued (the Britannia Bridge was rebuilt in 1972 as a [truss arch bridge](/source/Truss_arch_bridge)), yet the [steel frames](/source/Steel_frame) and [reinforced concrete frames](/source/Reinforced_concrete_frame) mostly replaced the arches as the load-bearing elements in buildings.

		- Original Britannia bridge (a colored postcard)

		- Britannia bridge (2008)

## Construction

A series of parabolic arches on the [Móra d'Ebre](/source/M%C3%B3ra_d'Ebre) bridge, [Catalonia](/source/Catalonia), Spain (2005)

As a pure compression form, the utility of the arch is due to many building materials, including [stone](/source/Rock_(geology)) and unreinforced [concrete](/source/Concrete), being strong under [compression](/source/Compression_(physical)), but brittle when [tensile stress](/source/Tensile_stress) is applied to them.[156]

### Masonry

Main article: [Centering (Masonry)](/source/Centering_(Masonry))

The [voussoirs](/source/Voussoir) may be wedge-shaped or rectangular; in the latter case, the wedge action is provided by the [mortar](/source/Mortar_(masonry)).[96] During construction, the ring is supported on temporary timber or framed work called [centering](/source/Centering_(Masonry)) (a form of [falsework](/source/Falsework)), which follows the intrados profile of the arch.[157] For arches higher than head height, the centering may be combined with [scaffolding](/source/Scaffolding) or staging to provide working access.[158] For key parts of an arch, see [arch terminology](#Terminology).

After the [keystone](/source/Keystone_(architecture)) is set and the ring is seated, the centering is *struck* (lowered and removed). In mortared construction, removal is deferred until the mortar has gained adequate strength; modern guidance often recommends a minimum of seven days, with longer periods recommended in cold weather or when analysis requires it.[159][160] To avoid shock and uneven load transfer, larger works are lowered uniformly using paired wedges, long compound wedges, or sand-boxes (sand jacks).[161] Insufficient stiffness of the centering, premature striking, or construction faults can produce settlement or local failure as reactions shift toward the haunches and abutments.[162]

### 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](/source/Rebar) or fibres.[163]

## Architectural styles

The type of arches (or absence of them) is one of the most prominent characteristics of an [architectural style](/source/Architectural_style). For example, when [Heinrich Hübsch](/source/Heinrich_H%C3%BCbsch), in the 19th century, tried to classify the architectural style, his "primary elements" were roof and supports, with the top-level basic types: [trabeated](/source/Trabeated) (no arches) and [arcuated](/source/Arcuated) (arch-based). His next division for the arcuated styles was based on the use of round and pointed arch shapes.[164]

## 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 [Hindu](/source/Hindu)[165] to [Arabs](/source/Arabs).[28] This [adage](/source/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.[28] The plot of [The Nebuly Coat](/source/The_Nebuly_Coat) by [J. Meade Falkner](/source/J._Meade_Falkner), inspired by a collapse of a tower at the [Chichester Cathedral](/source/Chichester_Cathedral) plays with the idea while dealing with the slow disintegration of a church building.[165] Saoud[166] explains the proverb by chain-like self-balancing of the horizontal and vertical forces in the arch and its "universal adaptability".[167]

The metaphoric term **bald arch** has been used since at least the 19th century to designate a decaying arch[168] or a plain, unadorned, arch.[169] The former meaning is still used in the 21st century.[170]

## See also

- [Buttress](/source/Buttress)

- [Dome](/source/Dome)

- [Flying arch](/source/Flying_arch)

- [Flying buttress](/source/Flying_buttress)

- [Order moulding](/source/Order_(mouldings))

- [Squinch](/source/Squinch), [Trumpet arch](/source/Trumpet_arch)

- [Suspension bridge](/source/Suspension_bridge)

## References

1. **[^](#cite_ref-FOOTNOTEGorseJohnstonPritchard2020arch_1-0)** [Gorse, Johnston & Pritchard 2020](#CITEREFGorseJohnstonPritchard2020), arch.

1. ^ [***a***](#cite_ref-FOOTNOTEWoodmanBloom2003History_2-0) [***b***](#cite_ref-FOOTNOTEWoodmanBloom2003History_2-1) [***c***](#cite_ref-FOOTNOTEWoodmanBloom2003History_2-2) [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), History.

1. **[^](#cite_ref-FOOTNOTEGorseJohnstonPritchard2020arch_dam_3-0)** [Gorse, Johnston & Pritchard 2020](#CITEREFGorseJohnstonPritchard2020), arch dam.

1. **[^](#cite_ref-FOOTNOTEClarkeClarke2010vault_4-0)** [Clarke & Clarke 2010](#CITEREFClarkeClarke2010), vault.

1. ^ [***a***](#cite_ref-FOOTNOTELyttleton2003_5-0) [***b***](#cite_ref-FOOTNOTELyttleton2003_5-1) [Lyttleton 2003](#CITEREFLyttleton2003).

1. ^ [***a***](#cite_ref-britannica_6-0) [***b***](#cite_ref-britannica_6-1) [Arch](https://www.britannica.com/EBchecked/topic/32510) at the *[Encyclopædia Britannica](/source/Encyclop%C3%A6dia_Britannica)*

1. ^ [***a***](#cite_ref-FOOTNOTEWoodmanBloom2003_7-0) [***b***](#cite_ref-FOOTNOTEWoodmanBloom2003_7-1) [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003).

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003False_8-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), False.

1. ^ [***a***](#cite_ref-FOOTNOTEWoodmanBloom2003Triangular_9-0) [***b***](#cite_ref-FOOTNOTEWoodmanBloom2003Triangular_9-1) [***c***](#cite_ref-FOOTNOTEWoodmanBloom2003Triangular_9-2) [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Triangular.

1. **[^](#cite_ref-FOOTNOTEBoyd197890_10-0)** [Boyd 1978](#CITEREFBoyd1978), p. 90.

1. **[^](#cite_ref-FOOTNOTEWilkins1879291–293_11-0)** [Wilkins 1879](#CITEREFWilkins1879), pp. 291–293.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Structure_12-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Structure.

1. **[^](#cite_ref-13)** ["rowlock arch"](https://www.merriam-webster.com/dictionary/rowlock%20arch). *[Merriam-Webster.com Dictionary](/source/Merriam-Webster)*. Merriam-Webster. [OCLC](/source/OCLC_(identifier)) [1032680871](https://search.worldcat.org/oclc/1032680871).

1. **[^](#cite_ref-FOOTNOTEAmerican_Technical_Society1908111_14-0)** [American Technical Society 1908](#CITEREFAmerican_Technical_Society1908), p. 111.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Haunch_15-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Haunch.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Dosseret_16-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Dosseret.

1. **[^](#cite_ref-FOOTNOTEBeall1987301_17-0)** [Beall 1987](#CITEREFBeall1987), p. 301.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Intrados_18-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Intrados.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Arc_19-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Arc.

1. **[^](#cite_ref-20)** ["arcature"](https://www.merriam-webster.com/dictionary/arcature). *[Merriam-Webster.com Dictionary](/source/Merriam-Webster)*. Merriam-Webster. [OCLC](/source/OCLC_(identifier)) [1032680871](https://search.worldcat.org/oclc/1032680871).

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Archivolt_21-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Archivolt.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Joggled_22-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Joggled.

1. **[^](#cite_ref-FOOTNOTEAu1960169_23-0)** [Au 1960](#CITEREFAu1960), p. 169.

1. **[^](#cite_ref-FOOTNOTECalvo-López20208_24-0)** [Calvo-López 2020](#CITEREFCalvo-López2020), p. 8.

1. **[^](#cite_ref-FOOTNOTEAllenOchsendorfWest201640_25-0)** [Allen, Ochsendorf & West 2016](#CITEREFAllenOchsendorfWest2016), p. 40.

1. **[^](#cite_ref-FOOTNOTECalvo-López20208–9_26-0)** [Calvo-López 2020](#CITEREFCalvo-López2020), pp. 8–9.

1. ^ [***a***](#cite_ref-FOOTNOTEPunmiaJainJain2005425_27-0) [***b***](#cite_ref-FOOTNOTEPunmiaJainJain2005425_27-1) [***c***](#cite_ref-FOOTNOTEPunmiaJainJain2005425_27-2) [***d***](#cite_ref-FOOTNOTEPunmiaJainJain2005425_27-3) [Punmia, Jain & Jain 2005](#CITEREFPunmiaJainJain2005), p. 425.

1. ^ [***a***](#cite_ref-treccani_28-0) [***b***](#cite_ref-treccani_28-1) [***c***](#cite_ref-treccani_28-2) [***d***](#cite_ref-treccani_28-3) [***e***](#cite_ref-treccani_28-4) [***f***](#cite_ref-treccani_28-5) [Arco](http://www.treccani.it/enciclopedia/arco_(Enciclopedia-Italiana)/) entry (in Italian) in the *[Enciclopedia Treccani](/source/Treccani)*, 1929

1. **[^](#cite_ref-FOOTNOTEPunmiaJainJain2005431–432_29-0)** [Punmia, Jain & Jain 2005](#CITEREFPunmiaJainJain2005), pp. 431–432.

1. **[^](#cite_ref-FOOTNOTESlivnik20131089_30-0)** [Slivnik 2013](#CITEREFSlivnik2013), p. 1089.

1. ^ [***a***](#cite_ref-FOOTNOTEWoodmanBloom2003Ancient_Greece_and_Rome_31-0) [***b***](#cite_ref-FOOTNOTEWoodmanBloom2003Ancient_Greece_and_Rome_31-1) [***c***](#cite_ref-FOOTNOTEWoodmanBloom2003Ancient_Greece_and_Rome_31-2) [***d***](#cite_ref-FOOTNOTEWoodmanBloom2003Ancient_Greece_and_Rome_31-3) [***e***](#cite_ref-FOOTNOTEWoodmanBloom2003Ancient_Greece_and_Rome_31-4) [***f***](#cite_ref-FOOTNOTEWoodmanBloom2003Ancient_Greece_and_Rome_31-5) [***g***](#cite_ref-FOOTNOTEWoodmanBloom2003Ancient_Greece_and_Rome_31-6) [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Ancient Greece and Rome.

1. **[^](#cite_ref-32)** Günther Wasmuth (ed.): *Wasmuths Lexikon der Baukunst*, vol. 4: *P - Zyp*. Wasmuth, Berlin 1932, p. 293.

1. **[^](#cite_ref-33)** [Wilfried Koch](https://en.wikipedia.org/w/index.php?title=Wilfried_Koch&action=edit&redlink=1) [[de](https://de.wikipedia.org/wiki/Wilfried_Koch)]: *Baustilkunde - Europäische Baukunst von der Antike bis zur Gegenwart*. Sonderausgabe, Orbis Verlag, München 1988, [ISBN](/source/ISBN_(identifier)) [3-572-05927-5](https://en.wikipedia.org/wiki/Special:BookSources/3-572-05927-5), p. 447.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Two-tiered_34-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Two-tiered.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Blind_35-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Blind.

1. ^ [***a***](#cite_ref-FOOTNOTEWoodmanBloom2003Containing_36-0) [***b***](#cite_ref-FOOTNOTEWoodmanBloom2003Containing_36-1) [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Containing.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Interlace_37-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Interlace.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Rear-arch_[rere-arch]_38-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Rear-arch [rere-arch].

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Transverse_39-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Transverse.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Diaphragm_40-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Diaphragm.

1. ^ [***a***](#cite_ref-FOOTNOTEWoodmanBloom2003Inverted_41-0) [***b***](#cite_ref-FOOTNOTEWoodmanBloom2003Inverted_41-1) [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Inverted.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Strainer_42-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Strainer.

1. **[^](#cite_ref-43)** ["Rare Victorian Railway Arches Saved"](https://historicengland.org.uk/whats-new/news/rare-victorian-railway-arches-saved/). *historicengland.org.uk*. Historic England. 18 August 2014. Retrieved 21 April 2024.

1. **[^](#cite_ref-44)** [Historic England](/source/Historic_England). ["Series of 16 strainer arches in railway cutting at SD 581 192 (1072648)"](https://HistoricEngland.org.uk/listing/the-list/list-entry/1072648?section=official-list-entry). *[National Heritage List for England](/source/National_Heritage_List_for_England)*. Retrieved 21 April 2024.

1. **[^](#cite_ref-FOOTNOTECurl2006207counter-arch_45-0)** [Curl 2006](#CITEREFCurl2006), p. 207, counter-arch.

1. ^ [***a***](#cite_ref-Building_Structures_46-0) [***b***](#cite_ref-Building_Structures_46-1) [***c***](#cite_ref-Building_Structures_46-2) [***d***](#cite_ref-Building_Structures_46-3) [***e***](#cite_ref-Building_Structures_46-4) Ambrose, James (2012). [*Building Structures*](https://archive.org/details/buildingstructur00ambr). Hoboken, NJ: John Wiley & Sons, Inc. p. [31](https://archive.org/details/buildingstructur00ambr/page/n48). [ISBN](/source/ISBN_(identifier)) [978-0-470-54260-6](https://en.wikipedia.org/wiki/Special:BookSources/978-0-470-54260-6).

1. **[^](#cite_ref-ambrose32_47-0)** Ambrose, James (2012). [*Building Structures*](https://archive.org/details/buildingstructur00ambr). Hoboken, NJ: John Wiley & Sons, Inc. p. [32](https://archive.org/details/buildingstructur00ambr/page/n49). [ISBN](/source/ISBN_(identifier)) [978-0-470-54260-6](https://en.wikipedia.org/wiki/Special:BookSources/978-0-470-54260-6).

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Round_48-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Round.

1. ^ [***a***](#cite_ref-FOOTNOTEWoodmanBloom2003Segmental_49-0) [***b***](#cite_ref-FOOTNOTEWoodmanBloom2003Segmental_49-1) [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Segmental.

1. ^ [***a***](#cite_ref-FOOTNOTEDeLaine1990417_50-0) [***b***](#cite_ref-FOOTNOTEDeLaine1990417_50-1) [DeLaine 1990](#CITEREFDeLaine1990), p. 417.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Basket_51-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Basket.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Depressed_52-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Depressed.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Horseshoe_53-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Horseshoe.

1. **[^](#cite_ref-FOOTNOTEDaviesJokiniemi2012198_54-0)** [Davies & Jokiniemi 2012](#CITEREFDaviesJokiniemi2012), p. 198.

1. **[^](#cite_ref-FOOTNOTEHarris2013217_55-0)** [Harris 2013](#CITEREFHarris2013), p. 217.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Two-centred_56-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Two-centred.

1. **[^](#cite_ref-FOOTNOTEWarren1991_57-0)** [Warren 1991](#CITEREFWarren1991).

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Pointed_58-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Pointed.

1. **[^](#cite_ref-59)** Crossley, Paul (2000). [*Gothic Architecture*](https://books.google.com/books?id=LBZ6781vvOwC&q=gothic+architecture). New Haven, CT: Yale University Press. p. 58. [ISBN](/source/ISBN_(identifier)) [978-0-300-08799-4](https://en.wikipedia.org/wiki/Special:BookSources/978-0-300-08799-4) – via [Google Books](/source/Google_Books).

1. **[^](#cite_ref-FOOTNOTEBond1905265_60-0)** [Bond 1905](#CITEREFBond1905), p. 265.

1. **[^](#cite_ref-61)** Hadrovic, Ahmet (2009). *Structural Systems in Architecture*. On Demand Publishing. p. 289. [ISBN](/source/ISBN_(identifier)) [978-1-4392-5944-3](https://en.wikipedia.org/wiki/Special:BookSources/978-1-4392-5944-3).

1. **[^](#cite_ref-62)** MHHE. ["Structural Systems in Architecture"](https://web.archive.org/web/20130313101430/http://dev5.mhhe.com/textflowdev/genhtml/0073379204/13.1.htm). MHHE.com. Archived from [the original](http://dev5.mhhe.com/textflowdev/genhtml/0073379204/13.1.htm) on 13 March 2013. Retrieved 3 February 2013.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Equilateral_63-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Equilateral.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Lancet_64-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Lancet.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Cusped_65-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Cusped.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Trefoil_66-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Trefoil.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Ogee_67-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Ogee.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Nodding_68-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Nodding.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Tudor_69-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Tudor.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Four-centred_70-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Four-centred.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Keel_71-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Keel.

1. **[^](#cite_ref-FOOTNOTECurl2006ogee_arch_p=37_72-0)** [Curl 2006](#CITEREFCurl2006), ogee arch p=37.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Curtain_73-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Curtain.

1. **[^](#cite_ref-FOOTNOTEDaviesJokiniemi2012153_74-0)** [Davies & Jokiniemi 2012](#CITEREFDaviesJokiniemi2012), p. 153.

1. ^ [***a***](#cite_ref-FOOTNOTEMartinez_Nespral202315_75-0) [***b***](#cite_ref-FOOTNOTEMartinez_Nespral202315_75-1) [Martinez Nespral 2023](#CITEREFMartinez_Nespral2023), p. 15.

1. ^ [***a***](#cite_ref-FOOTNOTEWoodmanBloom2003Indian_subcontinent_and_Islamic_lands_76-0) [***b***](#cite_ref-FOOTNOTEWoodmanBloom2003Indian_subcontinent_and_Islamic_lands_76-1) [***c***](#cite_ref-FOOTNOTEWoodmanBloom2003Indian_subcontinent_and_Islamic_lands_76-2) [***d***](#cite_ref-FOOTNOTEWoodmanBloom2003Indian_subcontinent_and_Islamic_lands_76-3) [***e***](#cite_ref-FOOTNOTEWoodmanBloom2003Indian_subcontinent_and_Islamic_lands_76-4) [***f***](#cite_ref-FOOTNOTEWoodmanBloom2003Indian_subcontinent_and_Islamic_lands_76-5) [***g***](#cite_ref-FOOTNOTEWoodmanBloom2003Indian_subcontinent_and_Islamic_lands_76-6) [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Indian subcontinent and Islamic lands.

1. **[^](#cite_ref-77)** Barrucand, Marianne; Bednorz, Achim (1995). *Architecture maure en Andalousie* (in French). PML Éditions. p. 162.

1. **[^](#cite_ref-FOOTNOTEMark1996387_78-0)** [Mark 1996](#CITEREFMark1996), p. 387.

1. ^ [***a***](#cite_ref-FOOTNOTEGonzálezSamperHerrera2018185_79-0) [***b***](#cite_ref-FOOTNOTEGonzálezSamperHerrera2018185_79-1) [González, Samper & Herrera 2018](#CITEREFGonzálezSamperHerrera2018), p. 185.

1. **[^](#cite_ref-FOOTNOTEBradleyGohnert2022_80-0)** [Bradley & Gohnert 2022](#CITEREFBradleyGohnert2022).

1. **[^](#cite_ref-FOOTNOTEOsserman2010220_81-0)** [Osserman 2010](#CITEREFOsserman2010), p. 220.

1. **[^](#cite_ref-FOOTNOTEGonzálezSamperHerrera2018174,_184_82-0)** [González, Samper & Herrera 2018](#CITEREFGonzálezSamperHerrera2018), pp. 174, 184.

1. **[^](#cite_ref-FOOTNOTEGonzálezSamperHerrera2018183#14_83-0)** [González, Samper & Herrera 2018](#CITEREFGonzálezSamperHerrera2018), p. 183, #14.

1. **[^](#cite_ref-FOOTNOTEGonzálezSamperHerrera2018182#9_84-0)** [González, Samper & Herrera 2018](#CITEREFGonzálezSamperHerrera2018), p. 182, #9.

1. **[^](#cite_ref-FOOTNOTEGonzálezSamperHerrera2018183#18_85-0)** [González, Samper & Herrera 2018](#CITEREFGonzálezSamperHerrera2018), p. 183, #18.

1. **[^](#cite_ref-FOOTNOTEGonzálezSamperHerrera2018183#19_86-0)** [González, Samper & Herrera 2018](#CITEREFGonzálezSamperHerrera2018), p. 183, #19.

1. **[^](#cite_ref-FOOTNOTEBenaim2019501_87-0)** [Benaim 2019](#CITEREFBenaim2019), p. 501.

1. **[^](#cite_ref-FOOTNOTEOsserman2010224_88-0)** [Osserman 2010](#CITEREFOsserman2010), p. 224.

1. **[^](#cite_ref-89)** Mahan, D.H. (1873). [*A Treatise on Civil Engineering*](https://books.google.com/books?id=ANY5AAAAMAAJ&pg=PA247). J. Wiley & Son. p. 247. Retrieved 13 January 2024.

1. ^ [***a***](#cite_ref-FOOTNOTEWoodmanBloom2003Flat_90-0) [***b***](#cite_ref-FOOTNOTEWoodmanBloom2003Flat_90-1) [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Flat.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Corbelled_91-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Corbelled.

1. **[^](#cite_ref-92)** Brick Industry Association] (January 1995). [*Brick Masonry Arches: Introduction*](https://faculty-legacy.arch.tamu.edu/anichols/index_files/courses/arch631/NS6-1brickarch.pdf) (PDF). Technical Notes on Brick Construction. Brick Industry Association. p. 2.

1. **[^](#cite_ref-FOOTNOTESturgisDavis2013121Triangular_Arch_93-0)** [Sturgis & Davis 2013](#CITEREFSturgisDavis2013), p. 121, Triangular Arch.

1. **[^](#cite_ref-FOOTNOTEDaviesJokiniemi2008305_94-0)** [Davies & Jokiniemi 2008](#CITEREFDaviesJokiniemi2008), p. 305.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Ramping_95-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Ramping.

1. ^ [***a***](#cite_ref-treccani1991_96-0) [***b***](#cite_ref-treccani1991_96-1) [arco](http://www.treccani.it/enciclopedia/arco_(Enciclopedia-dell'-Arte-Medievale)/) entry (in Italian) by C. Ewert in the *[Enciclopedia Treccani](/source/Treccani)*, 1991

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Shouldered_97-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Shouldered.

1. **[^](#cite_ref-98)** ["surmounted arch"](https://www.merriam-webster.com/dictionary/surmounted%20arch). *[Merriam-Webster.com Dictionary](/source/Merriam-Webster)*. Merriam-Webster. [OCLC](/source/OCLC_(identifier)) [1032680871](https://search.worldcat.org/oclc/1032680871).

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Stilted_99-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Stilted.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Skew_100-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Skew.

1. ^ [***a***](#cite_ref-FOOTNOTECalvo-López2020265_101-0) [***b***](#cite_ref-FOOTNOTECalvo-López2020265_101-1) [Calvo-López 2020](#CITEREFCalvo-López2020), p. 265.

1. **[^](#cite_ref-102)** ["splayed arch"](https://www.merriam-webster.com/dictionary/splayed%20arch). *[Merriam-Webster.com Dictionary](/source/Merriam-Webster)*. Merriam-Webster. [OCLC](/source/OCLC_(identifier)) [1032680871](https://search.worldcat.org/oclc/1032680871).

1. **[^](#cite_ref-103)** ["surbased"](https://www.merriam-webster.com/dictionary/surbased). *[Merriam-Webster.com Dictionary](/source/Merriam-Webster)*. Merriam-Webster. [OCLC](/source/OCLC_(identifier)) [1032680871](https://search.worldcat.org/oclc/1032680871).

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Surbased_104-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Surbased.

1. **[^](#cite_ref-FOOTNOTEWoodmanBloom2003Drop_105-0)** [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Drop.

1. **[^](#cite_ref-106)** ["drop arch"](https://www.merriam-webster.com/dictionary/drop%20arch). *[Merriam-Webster.com Dictionary](/source/Merriam-Webster)*. Merriam-Webster. [OCLC](/source/OCLC_(identifier)) [1032680871](https://search.worldcat.org/oclc/1032680871).

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1. ^ [***a***](#cite_ref-FOOTNOTEWoodmanBloom2003Ancient_Egypt,_the_Near_East_and_the_eastern_Mediterranean_116-0) [***b***](#cite_ref-FOOTNOTEWoodmanBloom2003Ancient_Egypt,_the_Near_East_and_the_eastern_Mediterranean_116-1) [***c***](#cite_ref-FOOTNOTEWoodmanBloom2003Ancient_Egypt,_the_Near_East_and_the_eastern_Mediterranean_116-2) [***d***](#cite_ref-FOOTNOTEWoodmanBloom2003Ancient_Egypt,_the_Near_East_and_the_eastern_Mediterranean_116-3) [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Ancient Egypt, the Near East and the eastern Mediterranean.

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1. **[^](#cite_ref-121)** Wright, G. R. H., *Ancient building technology vol. 3*. Leiden, Netherlands. Koninklijke Brill NV. 2009. p. 237. Print.

1. **[^](#cite_ref-FOOTNOTEGalliazzo199536_122-0)** [Galliazzo 1995](#CITEREFGalliazzo1995), p. 36.

1. **[^](#cite_ref-FOOTNOTEBoyd197891_123-0)** [Boyd 1978](#CITEREFBoyd1978), p. 91.

1. **[^](#cite_ref-Robertson_124-0)** Robertson, D.S. (1969). ["Chapter Fifteen: Roman Construction. Arches, Vaults, and Domes"](https://archive.org/details/greekromanarchit0000robe/page/231/mode/1up). [*Greek and Roman Architecture*](https://archive.org/details/greekromanarchit0000robe/page/n4/mode/1up) (2nd ed.). [Cambridge, England](/source/Cambridge): [Cambridge University Press](/source/Cambridge_University_Press). p. 231. [ISBN](/source/ISBN_(identifier)) [0521061040](https://en.wikipedia.org/wiki/Special:BookSources/0521061040). [OCLC](/source/OCLC_(identifier)) [1149316661](https://search.worldcat.org/oclc/1149316661). Retrieved 31 December 2020 – via [Internet Archive](/source/Internet_Archive).

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1. **[^](#cite_ref-133)** Liu, Xujie (2002), "The Qin and Han dynasties", in Steinhardt, Nancy S., *Chinese Architecture*, New Haven: Yale University Press, p. 55, [ISBN](/source/ISBN_(identifier)) [0-300-09559-7](https://en.wikipedia.org/wiki/Special:BookSources/0-300-09559-7).

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1. **[^](#cite_ref-FOOTNOTESaoud20025_139-0)** [Saoud 2002](#CITEREFSaoud2002), p. 5.

1. ^ [***a***](#cite_ref-FOOTNOTEGraves2009_140-0) [***b***](#cite_ref-FOOTNOTEGraves2009_140-1) [***c***](#cite_ref-FOOTNOTEGraves2009_140-2) [Graves 2009](#CITEREFGraves2009).

1. **[^](#cite_ref-FOOTNOTESaoud20027_141-0)** [Saoud 2002](#CITEREFSaoud2002), p. 7.

1. **[^](#cite_ref-FOOTNOTEBalchin2022_142-0)** [Balchin 2022](#CITEREFBalchin2022).

1. **[^](#cite_ref-FOOTNOTESaoud20024_143-0)** [Saoud 2002](#CITEREFSaoud2002), p. 4.

1. ^ [***a***](#cite_ref-FOOTNOTEWoodmanBloom2003Western_Europe_and_its_influence_144-0) [***b***](#cite_ref-FOOTNOTEWoodmanBloom2003Western_Europe_and_its_influence_144-1) [***c***](#cite_ref-FOOTNOTEWoodmanBloom2003Western_Europe_and_its_influence_144-2) [Woodman & Bloom 2003](#CITEREFWoodmanBloom2003), Western Europe and its influence.

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1. **[^](#cite_ref-149)** Kenoyer, J.M.; Miller, Heather M..L. [*Metal Technologies of the Indus Valley Tradition in Pakistan and Western India*](https://www.harappa.com/sites/default/files/pdf/Kenoyer1999_Metal%20Technologies%20of%20the%20Indus%20Valley%20Tradition.pdf) (PDF). p. 124.

1. **[^](#cite_ref-150)** Chihara, Daigorō (1996). [*Hindu-Buddhist Architecture in Southeast Asia*](https://web.archive.org/web/20180702133648/https://books.google.com/books?id=wiUTOanLClcC&pg=PA9&lpg=PA9#v=onepage&f=false). Brill. [ISBN](/source/ISBN_(identifier)) [978-90-04-10512-6](https://en.wikipedia.org/wiki/Special:BookSources/978-90-04-10512-6). Archived from [the original](https://books.google.com/books?id=wiUTOanLClcC&pg=PA9) on 2 July 2018. Retrieved 1 April 2018 – via [Google Books](/source/Google_Books).

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1. **[^](#cite_ref-153)** Befu, Harumi; Ekholm, Gordon F. (1964). ["The True Arch in Pre-Columbian America?"](https://www.journals.uchicago.edu/doi/abs/10.1086/200506?journalCode=ca). *Current Anthropology*. **5** (4): 328–329. [doi](/source/Doi_(identifier)):[10.1086/200506](https://doi.org/10.1086%2F200506). [ISSN](/source/ISSN_(identifier)) [0011-3204](https://search.worldcat.org/issn/0011-3204). [S2CID](/source/S2CID_(identifier)) [145134147](https://api.semanticscholar.org/CorpusID:145134147).

1. **[^](#cite_ref-154)** Schwerin, Karl H.; Ekholm, Gordon F. (1966). ["On the Arch in Pre-Columbian Mesoamerica"](https://www.journals.uchicago.edu/doi/abs/10.1086/200668?journalCode=ca). *Current Anthropology*. **7** (1): 89–90. [doi](/source/Doi_(identifier)):[10.1086/200668](https://doi.org/10.1086%2F200668). [ISSN](/source/ISSN_(identifier)) [0011-3204](https://search.worldcat.org/issn/0011-3204). [S2CID](/source/S2CID_(identifier)) [144301211](https://api.semanticscholar.org/CorpusID:144301211).

1. **[^](#cite_ref-155)** Stamp, Gavin (March 1998). ""At Once Classic and Picturesque...": Alexander Thomson's Holmwood". *The Journal of the Society of Architectural Historians*. **57** (1): 46–58. [doi](/source/Doi_(identifier)):[10.2307/991404](https://doi.org/10.2307%2F991404). [JSTOR](/source/JSTOR_(identifier)) [991404](https://www.jstor.org/stable/991404).

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1. **[^](#cite_ref-157)** Baker, Ira O. (1889). [*A Treatise on Masonry Construction*](https://books.google.com/books?id=B69IAAAAMAAJ) (7th ed.). New York: J. Wiley & Sons. pp. 515–516. Retrieved 30 October 2025.

1. **[^](#cite_ref-158)** Kidder, Frank E. (1905). [*The Architect's and Builder's Pocket-Book*](https://archive.org/details/architectsbuilde00kiddrich). New York: J. Wiley. Retrieved 30 October 2025.

1. **[^](#cite_ref-159)** Baker, Ira O. (1889). [*A Treatise on Masonry Construction*](https://books.google.com/books?id=B69IAAAAMAAJ) (7th ed.). New York: J. Wiley & Sons. pp. 526–527. Retrieved 30 October 2025.

1. **[^](#cite_ref-160)** ["Technical Notes 31: Brick Masonry Arches"](https://www.gobrick.com/media/file/31-brick-masonry-arches.pdf) (PDF). *Brick Industry Association*. January 1995. p. 19. Retrieved 30 October 2025.

1. **[^](#cite_ref-161)** Baker, Ira O. (1889). [*A Treatise on Masonry Construction*](https://books.google.com/books?id=B69IAAAAMAAJ) (7th ed.). New York: J. Wiley & Sons. pp. 522–525, 526–527. Retrieved 30 October 2025.

1. **[^](#cite_ref-162)** Baker, Ira O. (1889). [*A Treatise on Masonry Construction*](https://books.google.com/books?id=B69IAAAAMAAJ) (7th ed.). New York: J. Wiley & Sons. pp. 517–518, 526–527. Retrieved 30 October 2025.

1. **[^](#cite_ref-163)** Allen, Edward (2009). [*Fundamentals of Building Construction*](https://archive.org/details/fundamentalsbuil00alle). Hoboken, NJ: John Wiley & Sons. p. [529](https://archive.org/details/fundamentalsbuil00alle/page/n542). [ISBN](/source/ISBN_(identifier)) [978-0-470-07468-8](https://en.wikipedia.org/wiki/Special:BookSources/978-0-470-07468-8).

1. **[^](#cite_ref-FOOTNOTEMallgrave198814–15_164-0)** [Mallgrave 1988](#CITEREFMallgrave1988), pp. 14–15.

1. ^ [***a***](#cite_ref-FOOTNOTEHeyman20151_165-0) [***b***](#cite_ref-FOOTNOTEHeyman20151_165-1) [Heyman 2015](#CITEREFHeyman2015), p. 1.

1. **[^](#cite_ref-FOOTNOTESaoud2002_166-0)** [Saoud 2002](#CITEREFSaoud2002).

1. **[^](#cite_ref-FOOTNOTERoyster202162_167-0)** [Royster 2021](#CITEREFRoyster2021), p. 62.

1. **[^](#cite_ref-FOOTNOTEAuld192945_168-0)** [Auld 1929](#CITEREFAuld1929), p. 45.

1. **[^](#cite_ref-FOOTNOTEBritish_Architect1893313_169-0)** [British Architect 1893](#CITEREFBritish_Architect1893), p. 313.

1. **[^](#cite_ref-FOOTNOTELaunaro2024249_170-0)** [Launaro 2024](#CITEREFLaunaro2024), p. 249.

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- Davies, N.; Jokiniemi, E. (2012). [*Architect's Illustrated Pocket Dictionary*](https://books.google.com/books?id=7PXEeoS88lQC&pg=PA153). Taylor & Francis. [ISBN](/source/ISBN_(identifier)) [978-1-136-44406-7](https://en.wikipedia.org/wiki/Special:BookSources/978-1-136-44406-7). Retrieved 20 February 2024.

- DeLaine, Janet (1990). "Structural experimentation: The lintel arch, corbel and tie in western Roman architecture". *World Archaeology*. **21** (3): 407–424. [doi](/source/Doi_(identifier)):[10.1080/00438243.1990.9980116](https://doi.org/10.1080%2F00438243.1990.9980116). [ISSN](/source/ISSN_(identifier)) [0043-8243](https://search.worldcat.org/issn/0043-8243). [JSTOR](/source/JSTOR_(identifier)) [124838](https://www.jstor.org/stable/124838).

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- González, Genaro; Samper, Albert; Herrera, Blas (2018). "Classification by Type of the Arches in Gaudí's Palau Güell". *Nexus Network Journal*. **20** (1): 173–186. [doi](/source/Doi_(identifier)):[10.1007/s00004-017-0355-7](https://doi.org/10.1007%2Fs00004-017-0355-7). [ISSN](/source/ISSN_(identifier)) [1590-5896](https://search.worldcat.org/issn/1590-5896).

- Gorse, Christopher; Johnston, David; Pritchard, Martin, eds. (2020). *A Dictionary of Construction, Surveying and Civil Engineering*. Oxford University Press. [doi](/source/Doi_(identifier)):[10.1093/acref/9780198832485.001.0001](https://doi.org/10.1093%2Facref%2F9780198832485.001.0001). [ISBN](/source/ISBN_(identifier)) [978-0-19-883248-5](https://en.wikipedia.org/wiki/Special:BookSources/978-0-19-883248-5).

- Graves, Margaret (2 July 2009). "Arches in Islamic architecture". *Oxford Art Online*. Oxford University Press. [doi](/source/Doi_(identifier)):[10.1093/gao/9781884446054.article.t2082057](https://doi.org/10.1093%2Fgao%2F9781884446054.article.t2082057). [ISBN](/source/ISBN_(identifier)) [978-1-884446-05-4](https://en.wikipedia.org/wiki/Special:BookSources/978-1-884446-05-4).

- Harris, Cyril M. (28 February 2013). ["Florentine arch"](https://books.google.com/books?id=kp_DAgAAQBAJ&pg=PA217). *Illustrated Dictionary of Historic Architecture*. Courier Corporation. [ISBN](/source/ISBN_(identifier)) [978-0-486-13211-2](https://en.wikipedia.org/wiki/Special:BookSources/978-0-486-13211-2). Retrieved 14 November 2025.

- Heyman, Jacques (2015). ["Strainer arches"](http://www.jstor.org/stable/44215905). *Construction History*. **30** (2). The Construction History Society: 1–14. [ISSN](/source/ISSN_(identifier)) [0267-7768](https://search.worldcat.org/issn/0267-7768). [JSTOR](/source/JSTOR_(identifier)) [44215905](https://www.jstor.org/stable/44215905). Retrieved 25 January 2024.

- Hourihane, C. (2012). ["Arch"](https://books.google.com/books?id=FtlMAgAAQBAJ&pg=PA131). *The Grove Encyclopedia of Medieval Art and Architecture*. Vol. 1. Oxford University Press. pp. 129–134. [ISBN](/source/ISBN_(identifier)) [978-0-19-539536-5](https://en.wikipedia.org/wiki/Special:BookSources/978-0-19-539536-5). Retrieved 24 December 2024.

- Launaro, Alessandro (15 February 2024). [*Roman Urbanism in Italy: Recent Discoveries and New Directions*](https://books.google.com/books?id=ogHkEAAAQBAJ&pg=PA249). Oxbow Books. [ISBN](/source/ISBN_(identifier)) [979-8-88857-037-1](https://en.wikipedia.org/wiki/Special:BookSources/979-8-88857-037-1). Retrieved 14 November 2025.

- Lyttleton, Margaret (2003). "Trabeated construction". *Grove Art Online*. Oxford University Press. [doi](/source/Doi_(identifier)):[10.1093/gao/9781884446054.article.t085978](https://doi.org/10.1093%2Fgao%2F9781884446054.article.t085978). [ISBN](/source/ISBN_(identifier)) [978-1-884446-05-4](https://en.wikipedia.org/wiki/Special:BookSources/978-1-884446-05-4).

- Mallgrave, Harry Francis (1988). "Introduction". [*Modern Architecture: A Guidebook for His Students to this Field of Art*](https://books.google.com/books?id=-LNDAgAAQBAJ). Texts & Documents. Getty Center for the History of Art and the Humanities. pp. 1–54. [ISBN](/source/ISBN_(identifier)) [978-0-226-86939-1](https://en.wikipedia.org/wiki/Special:BookSources/978-0-226-86939-1). Retrieved 7 February 2024.

- Mark, Robert (July–August 1996). ["Architecture and Evolution"](https://www.uv.mx/personal/tcarmona/files/2010/08/Mark-1996.pdf) (PDF). *[American Scientist](/source/American_Scientist)*. **84** (4). [Sigma Xi](/source/Sigma_Xi), The Scientific Research Honor Society: 383–389. [Bibcode](/source/Bibcode_(identifier)):[1996AmSci..84..383M](https://ui.adsabs.harvard.edu/abs/1996AmSci..84..383M). [JSTOR](/source/JSTOR_(identifier)) [29775710](https://www.jstor.org/stable/29775710).

- Martinez Nespral, Fernando Luis (2023). ["Islamic Presence in Latin American Architecture. Three Periods - Three Ways"](https://books.google.com/books?id=tqzPEAAAQBAJ&pg=PA15). In Rashid, H.; Petersen, K. (eds.). *The Bloomsbury Handbook of Muslims and Popular Culture*. Bloomsbury Handbooks. Bloomsbury Publishing. pp. 13–24. [ISBN](/source/ISBN_(identifier)) [978-1-350-14541-2](https://en.wikipedia.org/wiki/Special:BookSources/978-1-350-14541-2). Retrieved 20 February 2024.

- O'Connor, Colin (1993), *Roman Bridges*, Cambridge University Press, [ISBN](/source/ISBN_(identifier)) [978-0-521-39326-3](https://en.wikipedia.org/wiki/Special:BookSources/978-0-521-39326-3)

- Osserman, Robert (February 2010). ["Mathematics of the Gateway Arch"](https://www.ams.org/notices/201002/rtx100200220p.pdf) (PDF). *[Notices of the American Mathematical Society](/source/Notices_of_the_American_Mathematical_Society)*. **57** (2): 220–229. [ISSN](/source/ISSN_(identifier)) [0002-9920](https://search.worldcat.org/issn/0002-9920).

- Punmia, B.C.; Jain, Ashok Kumar; Jain, Arun Kumar (2005). [*Building Construction*](https://books.google.com/books?id=_kAvTMzKGhAC&pg=PA425). Laxmi Publications. [ISBN](/source/ISBN_(identifier)) [978-81-7008-053-4](https://en.wikipedia.org/wiki/Special:BookSources/978-81-7008-053-4). Retrieved 23 January 2024.

- Quirarte, Jacinto (1989). "The Art and Architecture of Mesoamerica: An Overview". [*Latin American Art and Music: A Handbook for Teaching*](https://files.eric.ed.gov/fulltext/ED342705.pdf) (PDF). Austin, TX: Texas Univ., Austin. Inst. of Latin American Studies. pp. 27–. [ISBN](/source/ISBN_(identifier)) [0-86728-012-3](https://en.wikipedia.org/wiki/Special:BookSources/0-86728-012-3).

- Rasch, Jürgen (1985), "Die Kuppel in der römischen Architektur. Entwicklung, Formgebung, Konstruktion", *Architectura*, vol. 15, pp. 117–139

- Roth, Leland M (1993). [*Understanding Architecture: Its Elements History and Meaning*](https://archive.org/details/understandingarc00roth/page/27). Oxford, UK: Westview Press. pp. [27–28](https://archive.org/details/understandingarc00roth/page/27). [ISBN](/source/ISBN_(identifier)) [978-0-06-430158-9](https://en.wikipedia.org/wiki/Special:BookSources/978-0-06-430158-9).

- Royster, Paula D. (1 January 2021). *Decolonizing Arts-Based Methodologies: Researching the African Diaspora*. BRILL. [doi](/source/Doi_(identifier)):[10.1163/9789004446120_004](https://doi.org/10.1163%2F9789004446120_004). [ISBN](/source/ISBN_(identifier)) [978-90-04-44612-0](https://en.wikipedia.org/wiki/Special:BookSources/978-90-04-44612-0).* Saoud, Rabah (17 January 2002). ["The Arch That Never Sleeps"](https://www.muslimheritage.com/uploads/ACF4FB.pdf) (PDF). *Muslim Heritage*. Retrieved 25 January 2024.

- Slivnik, L. (27 June 2013). ["Three–hinged structures in a historical perspective"](https://books.google.com/books?id=in3OBQAAQBAJ&pg=PA1089). *Structures and Architecture*. [CRC Press](/source/CRC_Press). pp. 1129–1136. [doi](/source/Doi_(identifier)):[10.1201/b15267-153](https://doi.org/10.1201%2Fb15267-153). [ISBN](/source/ISBN_(identifier)) [978-0-429-15935-0](https://en.wikipedia.org/wiki/Special:BookSources/978-0-429-15935-0).

- Sturgis, Russell; Davis, Francis A. (2013). ["Triangular Arch"](https://books.google.com/books?id=j9wAW2YleywC&pg=PA116). *Sturgis' Illustrated Dictionary of Architecture and Building: An Unabridged Reprint of the 1901-2 Edition*. Dover Architecture. Dover Publications. [ISBN](/source/ISBN_(identifier)) [978-0-486-14840-3](https://en.wikipedia.org/wiki/Special:BookSources/978-0-486-14840-3). Retrieved 15 December 2023.

- Vieitez, Fátima Otero (2020). "Past and Present for Arch Executions". *Proceedings of ARCH 2019*. Structural Integrity. Vol. 11. Cham: Springer International Publishing. pp. 604–611. [doi](/source/Doi_(identifier)):[10.1007/978-3-030-29227-0_65](https://doi.org/10.1007%2F978-3-030-29227-0_65). [ISBN](/source/ISBN_(identifier)) [978-3-030-29226-3](https://en.wikipedia.org/wiki/Special:BookSources/978-3-030-29226-3). [S2CID](/source/S2CID_(identifier)) [211581407](https://api.semanticscholar.org/CorpusID:211581407).

- Warren, John (1991). ["Creswell's Use of the Theory of Dating by the Acuteness of the Pointed Arches in Early Muslim Architecture"](https://www.archnet.org/publications/4180). *Muqarnas*. **8**: 59–65. [doi](/source/Doi_(identifier)):[10.2307/1523154](https://doi.org/10.2307%2F1523154). [JSTOR](/source/JSTOR_(identifier)) [1523154](https://www.jstor.org/stable/1523154). Retrieved 7 August 2025.

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- Woodman, Francis; Bloom, Jonathan M. (2003). "Arch". *Oxford Art Online*. Oxford University Press. [doi](/source/Doi_(identifier)):[10.1093/gao/9781884446054.article.t003657](https://doi.org/10.1093%2Fgao%2F9781884446054.article.t003657). [ISBN](/source/ISBN_(identifier)) [978-1-884446-05-4](https://en.wikipedia.org/wiki/Special:BookSources/978-1-884446-05-4).

## External links

Wikiquote has quotations related to ***[Arch](https://en.wikiquote.org/wiki/Special:Search/Arch)***.

[Wikimedia Commons](/source/Wikimedia_Commons) has media related to:

[Arch](https://commons.wikimedia.org/wiki/Arch) ([category](https://commons.wikimedia.org/wiki/Category:Arches))

- [Physics of Stone Arches](https://www.pbs.org/wgbh/nova/physics/arch-physics.html) by [*Nova*](/source/Nova_(American_TV_series)): a model to build an arch without it collapsing

- [InteractiveTHRUST](https://web.mit.edu/masonry/interactiveThrust/index.html): interactive applets, tutorials

- [Paper about the three-hinged arch of the Galerie des Machines of 1889](https://dx.doi.org/10.4995/vlc.2015.3598) Whitten by Javier Estévez Cimadevila & Isaac López César.

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Adapted from the Wikipedia article [Arch](https://en.wikipedia.org/wiki/Arch) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Arch?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.