Editing Arch (section)

== Shapes ==
[[File:Types of arches.png|thumb|Types of arches]]

The large variety of arch shapes (left) can mostly be classified into three broad categories: [[round arch|rounded]], [[pointed arch|pointed]], and [[parabolic arch|parabolic]].<ref name="Building Structures">{{cite book|last=Ambrose|first=James|title=Building Structures|url=https://archive.org/details/buildingstructur00ambr|url-access=limited|year=2012|publisher=John Wiley & Sons, Inc.|location=Hoboken, NJ|isbn=978-0-470-54260-6|page=[https://archive.org/details/buildingstructur00ambr/page/n48 31]}}</ref>

=== Rounded ===
{{Main|Semicircular arch}}
"Round" [[semicircular arch|semicircular]] arches were commonly used for ancient arches that were constructed of heavy masonry,<ref name="ambrose32">{{cite book|last=Ambrose|first=James|title=Building Structures|url=https://archive.org/details/buildingstructur00ambr|url-access=limited|year=2012|publisher=John Wiley & Sons, Inc.|location=Hoboken, NJ|isbn=978-0-470-54260-6|page=[https://archive.org/details/buildingstructur00ambr/page/n49 32]}}</ref> and were relied heavily on by the [[Ancient Rome|Roman]] builders since the 4th century [[Anno Domini|BC]]. It is considered to be the most common arch form,{{sfn | Woodman | Bloom | 2003 | loc=Round}} characteristic for Roman, [[Romanesque architecture|Romanesque]], and [[Renaissance architecture|Renaissance]] architecture.<ref name=treccani/>

{{Main|Segmental arch}}
A [[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 {{circa}} 2100 BC at [[Beni Hasan]]). Since then it was occasionally used in [[Ancient Greek architecture|Greek temples]],{{sfn | Woodman | Bloom | 2003 | loc=Segmental}} utilized in Roman residential construction,{{sfn|DeLaine|1990|p=417}}  [[Islamic architecture]], and got popular as window [[pediments]] during the Renaissance.{{sfn | Woodman | Bloom | 2003 | loc=Segmental}}

{{Main|Basket-handle arch}}
A [[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 architecture|late Gothic]] and [[Baroque architecture]].{{sfn | Woodman | Bloom | 2003 | loc=Basket}}{{sfn | Woodman | Bloom | 2003 | loc=Depressed}}

{{Main|Horseshoe arch}}
A [[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]], [[Southern France]], [[Italy]]). Occasionally used in Gothics, it briefly enjoyed popularity as the entrance door treatment in the [[interwar]] England.{{sfn | Woodman | Bloom | 2003 | loc=Horseshoe}}

<gallery>
File:InsideGWWatchtower.jpg|Semi-circular arches using [[brick]] and/or [[stone]] block construction at the [[Great Wall]], China
File:Puente de Alconétar, Cáceres Province, Spain. Pic 03.JPG|Segmental arch of the [[Alconétar Bridge]]
File:Fichtelnaab Bahnstrecke Regensburg–Oberkotzau bei Pappenfabrik.jpg|Bridge with a basket handle arch
File:Great Mosque of Cordoba, mihrab area, 10th century (7) (29211135964).jpg|[[Horseshoe arch]] in the [[Great Mosque of Cordoba]]
</gallery>

=== Pointed ===
[[File:Spitzbogen.png|thumb|upright=1.5|Pointed arches, 1 - equilateral with trefoil treatment, 2 - blunt, 3 - lancet, 4 - ogee, 5 - four-centred, 6 - curtain (inflexed), 7 - pointed horseshoe]]
{{main|Pointed arch}}
A [[pointed arch]] consists of two ("''[[two-centred arch]]''"{{sfn | Woodman | Bloom | 2003 | loc=Two-centred}}) or more circle segments culminating in a point at the top. It originated in the Islamic architecture, arrived in Europe in the second half of the 11th century ([[Cluny Abbey]]){{sfn | Woodman | Bloom | 2003 | loc=Pointed}} and later became prominent in the [[Gothic architecture]].<ref>{{cite book|last=Crossley|first=Paul|title=Gothic Architecture|year=2000|publisher=Yale University Press|location=New Haven, CT|isbn=978-0-300-08799-4|page=58|url=https://books.google.com/books?id=LBZ6781vvOwC&q=gothic+architecture|via=[[Google Books]]}}</ref> The advantages of a pointed arch over a semicircular one are flexible ratio of [[Span (engineering)|span]] to [[Rise (arch)|rise]]{{sfn | Bond | 1905 | p=265}} and lower horizontal reaction at the base. This innovation allowed for taller and more closely spaced openings, which are typical of Gothic architecture.<ref>{{cite book|last=Hadrovic|first=Ahmet|title=Structural Systems in Architecture|year=2009|publisher=On Demand Publishing|isbn=978-1-4392-5944-3|page=289}}</ref><ref>{{cite web|last=MHHE |title=Structural Systems in Architecture |url=http://dev5.mhhe.com/textflowdev/genhtml/0073379204/13.1.htm |publisher=MHHE.com |access-date=3 February 2013 |url-status=dead |archive-url=https://web.archive.org/web/20130313101430/http://dev5.mhhe.com/textflowdev/genhtml/0073379204/13.1.htm |archive-date=13 March 2013 }}</ref> [[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 (geometry)|apex]] point, they form an [[equilateral triangle]], thus the name.{{sfn | Woodman | Bloom | 2003 | loc=Equilateral}} If the centers of circles are farther apart, the arch becomes a narrower and sharper [[lancet arch]] that appeared in France in the [[Early Gothic architecture]] ([[Saint-Denis Abbey]]) and became prominent in England in the late 12th and early 13th centuries ([[Salisbury Cathedral]]).{{sfn | Woodman | Bloom | 2003 | loc=Lancet}} If the centers are closer to another, the result is a wider [[blunt arch]].

The intrados of the [[cusped arch]] (also known as ''multifoil arch'', ''polyfoil arch'', ''polylobed arch'', and ''scalloped arch'') includes several independent circle segments in a [[scalloped]] arrangement. These primarily decorative arches are common in Islamic architecture and Northern European Late Gothic, can be found in [[Romanesque architecture]].{{sfn | Woodman | Bloom | 2003 | loc=Cusped}} A similar [[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.{{sfn | Woodman | Bloom | 2003 | loc=Trefoil}}

Each arc of an [[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]], the arch became a fixture of the [[English Gothic architecture#Decorated Gothic (late 13th–late 14th centuries)|English Decorated style]], French [[Flamboyant]], [[Venetian Gothic|Venetian]], and other Late Gothic styles.{{sfn | Woodman | Bloom | 2003 | loc=Ogee}} Ogee arch is also known as ''reversed curve arch'', occasionally also called an ''inverted arch''.{{sfn | Woodman | Bloom | 2003 | loc=Inverted}} The top of an ogee arch sometimes projects beyond the wall, forming the so-called ''nodding ogee'' popular in 14th century England ([[pulpitum]] in [[Southwell Minster]]).{{sfn | Woodman | Bloom | 2003 | loc=Nodding}}

Each arc of a [[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]]), and, with upper portion flattened  almost to straight lines ([[Tudor arch]]{{sfn | Woodman | Bloom | 2003 | loc=Tudor}}), in the English [[Perpendicular Gothic]].{{sfn | Woodman | Bloom | 2003 | loc=Four-centred}}A [[keel arch]] is a variant of four-centred arch with haunches almost straight, resembling a section view of a [[capsized]] ship. Popular in Islamic architecture, it can be also found in Europe, occasionally with a small ogee element at the top,{{sfn | Woodman | Bloom | 2003 | loc=Keel}} so it is sometimes considered to be a variation of an ogee arch.{{sfn |Curl|2006|loc=ogee arch p=37}} 
 
'''Curtain arch''' (also known as '''inflexed arch''', and, like the keel arch, usually decorative<ref name=treccani/>) uses two (or more) drooping curves that join at the apex. Utilized as a dressing for windows and doors primarily in [[Saxony]] in the Late Gothic and early Renaissance buildings (late 15th to early 16th century), associated with {{ill|Arnold von Westfalen|de}}.{{sfn | Woodman | Bloom | 2003 | loc=Curtain}} When the intrados has multiple concave segments, the arch is also called a '''draped arch''' or '''tented arch'''.{{sfn | Davies | Jokiniemi | 2012 | p=153}} A similar arch that uses a mixture of curved and straight segments{{sfn | Martinez Nespral | 2023 | p=15}} or exhibits sharp turns between segments{{sfn | Woodman | Bloom | 2003 | loc= Indian subcontinent and Islamic lands }} is a [[mixed-line arch]] (or ''mixtilinear arch''). In [[Moorish architecture]] the mixed-line arch evolved into an ornate [[lambrequin arch]],<ref>{{Cite book | first1=Marianne |last1 = Barrucand | first2=Achim |last2 = Bednorz | title=Architecture maure en Andalousie | publisher=PML Éditions | date =1995 | page=162 | isbn= | language=fr}}</ref>  also known as ''[[muqarnas]] arch''.

<gallery>
File:Flickr - Gaspa - Cairo, Moschea di Ibn-Tulun (24).jpg|Pointed arches of [[Mosque of Ibn Tulun]] (9th century [[Anno Domini|AD]])
File:20191203 Diwan-i-Khas, Red Fort, Delhi 0507 6368 DxO.jpg|Cusped arch in [[Diwan-i-Khas (Red Fort)]] 
File:Normandie Calvados Bayeux4 tango7174.jpg|Trefoil arch in the [[Bayeux Cathedral]]
File:N2 layer marney3.jpg|Tudor arch at [[Layer Marney Tower]]
File:A 14th century lady - geograph.org.uk - 1341596.jpg|Ogee arch at [[St Mary the Virgin, Silchester]]
File:Nodding ogee niche.jpg|Nodding ogee niche at [[St Peter's Church, Walpole St Peter]]
File:Keel_arches.jpg|Keel arches at {{ill|Palazzo Guadagni|it}}
File:Schloss Hartenfels, Torgau 2H1A5753WI.jpg|Curtain arches over windows in {{ill|Hartenfels Castle|de|Schloss Hartenfels}}
File:Draped arch.png|A draped arch at the {{ill|Palacio de Gobierno de Tlaxcala|es|lt=Government Palace of Tlaxcala}} (1545)
File:Salamanca Escuelas Menores 494.jpg|Mixed-line arches at {{ill|Escuelas Menores (Salamanca)|es}}
File:Lambrequin arch.jpg|Lambrequin arch at [[Bahia Palace]] in [[Morocco]]
</gallery>

=== Parabolic ===
The popularity of the arches using segments of a circle is due to simplicity of layout and construction,{{sfn|Mark|1996|p=387}} not their structural properties. Consequently, the architects historically used a variety of other curves in their designs: [[elliptical curve]]s, [[hyperbolic cosine]] curves (including [[catenary]]), and [[parabolic curve]]s. There are two reasons behind the selection of these curves:{{sfn | González | Samper | Herrera | 2018 | p=185}}
# they are still relatively easy to trace with common tools prior to construction;
# depending on a situation, they can have superior structural properties and/or appearance.
The [[hyperbolic curve]] is not easy to trace, but there are known cases of its use.{{sfn | González | Samper | Herrera | 2018 | p=185}} The non-[[circumference|circumferential]] curves look similar, and match at shallow profiles, so a catenary is often misclassified as a parabola{{sfn | Bradley | Gohnert | 2022 }} (per [[Galileo]], "the [hanging] chain fits its parabola almost perfectly"{{sfn|Osserman|2010|p=220}}). González et al. provide an example of [[Palau Güell]], 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]] are actually parabolic.{{sfn | González | Samper | Herrera | 2018 | pp=174, 184}}

<gallery>
File:Palau Güell, Barcelona 07.jpg|Palau Güell: Parabolic{{sfn| González | Samper | Herrera | 2018 | p=183 | loc = #14}}
File:Palau Güell, Barcelona 114.jpg|Palau Güell: Hyperbolic{{sfn| González | Samper | Herrera | 2018 | p=182 | loc = #9}}
File:043 Palau Güell, c. Nou de la Rambla 3-5 (Barcelona), baixos.jpg|Palau Güell: [[Rankine curve]]{{sfn | González | Samper | Herrera | 2018 | p=183 | loc = #18}} (a.k.a. [[weighted catenary]])
File:Barcelona Palau Güell Orgel (1).jpg|Palau Güell: Elliptical{{sfn| González | Samper | Herrera | 2018 | p=183 | loc = #19}}
</gallery>

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

A parabola represents an ideal (all-compression) shape when the load is equally distributed along the span, while the weight of the arch itself is negligible. A catenary is the best solution for the case where an arch with uniform thickness carries just its own weight with no external load. The practical designs for bridges are somewhere in between, and thus use the curves that represent a compromise that combines both the catenary and the [[funicular curve]] for particular non-uniform distribution of load.{{sfn | Benaim | 2019 | p=501}} 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]] increases with a distance from the center.{{sfn|Osserman|2010|p=224}}

<gallery>
File:Tyne Bridge - Newcastle Upon Tyne - England - 2004-08-14.jpg|A [[through arch bridge]] ([[Tyne Bridge]] in [[Newcastle upon Tyne]], [[England]]): parabolic-looking arches with multiple deck supports distributing the load
File:Arch Reflection 1 (5263608871).jpg|[[Gateway Arch]] is stronger at the bottom: weighted catenary curve
</gallery>

=== Other ===
Unlike regular arches, the [[flat arch]] (also known as ''jack arch'', ''lintel arch'', ''straight arch'', ''plate-bande''<ref>{{cite book | last=Mahan | first=D.H. | title=A Treatise on Civil Engineering | publisher=J. Wiley & Son | year=1873 | url=https://books.google.com/books?id=ANY5AAAAMAAJ&pg=PA247 | access-date=2024-01-13 | page=247}}</ref>)  is not curved. Instead, the arch is flat in profile and can be used under the same circumstances as [[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),{{sfn | Woodman | Bloom | 2003 | loc=Flat}} 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 architecture|medieval]] and Renaissance architecture. The flat arch is still being used as a decorative pattern, primarily at the top of window openings.{{sfn | Woodman | Bloom | 2003 | loc=Flat}}

==== False arches ====
The corbel (also ''corbelled'') arch, made of two [[corbel]]s 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 [[Ancient Egyptian architecture|Egyptian]] and [[Mycenaean architecture|Mycenaean]] architecture in the [[3rd millennium BC|3rd]] and [[2nd millennium BC]].{{sfn | Woodman | Bloom | 2003 | loc=Corbelled}}

Like a corbel arch, the [[triangular arch]] is not a true arch in a structural sense. Its intrados is formed by two slabs leaning against each other.{{sfn | Woodman | Bloom | 2003 | loc=Triangular}} Brick builders would call triangular any arch with straight inclined sides.<ref>{{cite book |last1=Brick Industry Association] |series=Technical Notes on Brick Construction |title=Brick Masonry Arches: Introduction |date=January 1995 |publisher=Brick Industry Association |page=2 |url=https://faculty-legacy.arch.tamu.edu/anichols/index_files/courses/arch631/NS6-1brickarch.pdf}}</ref> The design was common in [[Anglo-Saxon England]] until the late 11th century ([[St Mary Goslany]]).{{sfn | Woodman | Bloom | 2003 | loc=Triangular}} [[Maya civilization|Mayan]] corbel arches are sometimes called triangular due to their shape.{{sfn|Sturgis|Davis|2013|p=121|loc=Triangular Arch}}
<gallery>
File:Cucinone di palazzo pitti, cappa con piattabanda attr. al dis. del buontalenti 02.jpg|Flat arch in the kitchen of [[Pitti Palace]]
File:Refugi pedra Tales.jpg|Triangular arch
File:White Castle, arrow slit.jpg|A triangular arch built using masonry
File:Kabah Arch 2002.12.29 27.jpg|Mayan corbelled arch
</gallery>

=== Variations ===
Few transformations can be applied to arch shapes.

If one [[Impost (architecture)|impost]] is much higher than another, the arch (frequently [[pointed arch|pointed]]) is known as ''[[ramping arch]]'', ''raking arch'',{{sfn | Davies | Jokiniemi | 2008 | p=305}} or ''rampant arch'' (from {{langx|fr|arc rampant}}).{{sfn | Woodman | Bloom | 2003 | loc=Ramping}} Originally used to support inclined structures, like stairs, in the 13th-14th centuries they appeared as parts of [[flying buttress]]es used to counteract the thrust of Gothic [[ribbed vault]]s.<ref name=treccani1991/> 

A central part of an arch can be raised on short vertical supports, creating a [[trefoil arch|trefoil]]-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]], became common in [[Iranian architecture]] from the 14th century, and were later adopted in the [[Ottoman Turkey]].{{sfn | Woodman | Bloom | 2003 | loc=Shouldered}}

In a [[stilted arch]] (also ''surmounted''<ref>{{M-W|surmounted arch}}</ref>), 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.{{sfn | Woodman | Bloom | 2003 | loc=Stilted}} Stilting was useful for semicircular arches, where the ratio of the rise fixed at {{frac|1|2}} of the span, but was applied to the pointed arches, too.

The [[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,{{sfn | Woodman | Bloom | 2003 | loc=Skew}}{{sfn | Calvo-López | 2020 | p=265}} for example, when a bridge crosses the river at an angle different than 90°. A [[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]] shape.<ref>{{MW|splayed arch}}</ref>{{sfn | Calvo-López | 2020 | p=265}}

<gallery>
File:Palau Dalmases.jpg|Ramping arches at {{ill|Palau Dalmases|ca}} in [[Barcelona]]
File:Frauenstein Lorenziberg Filialkirche hl Laurentius Vorlaube Schulterbogenportal 25042017 7964.jpg|Shouldered arch around the door of {{ill|Filialkirche Lorenziberg|de|lt=Lorenziberg church}}. The raised portion is a flat arch.
File:Doges Palace 5 (7243239310).jpg|Shouldered arch above the main entrance of [[Doge's Palace]] in [[Venice]]. The vertical supports separate the segments of an ogee arch.
File:St John's Chapel, Tower of London.jpg|The smaller arches at the lower level are stilted to match the wider arches on the left ([[St John's Chapel, London]])
File:Nave and left aisle - Cathedral of Monreale - Italy 2015.JPG|Stilted pointed arches at the [[Monreale Cathedral]])
File:Sickergill Skew Bridge in 1898.jpg|Skew arch (Sickergill Bridge) with [[helicoidal]] [[masonry course]]s
File:All Saints Church - splayed tower window - geograph.org.uk - 1361830.jpg|Splayed arch over a window opening in the All Saints Church in [[Chedgrave]]
</gallery>

A wide arch with its rise less than {{frac|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'''<ref>{{M-W|surbased}}</ref> (sometimes also a ''depressed arch''{{sfn | Woodman | Bloom | 2003 | loc=Surbased}}). A '''drop arch''' is either a [[Basket-handle arch|basket handle arch]]{{sfn | Woodman | Bloom | 2003 | loc=Drop}} or a blunt arch.<ref>{{M-W|drop arch}}</ref>