Catenaria in terra cruda a più corsi di conci

A catenary arch is a type of architectural arch that follows an inverted

catenary curve In physics and geometry, a catenary (, ) is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends in a uniform gravitational field. The catenary curve has a U-like shape, superficial ...

. The catenary curve has been employed in buildings since ancient times. It forms an underlying principle to the overall system of

vault Vault may refer to: * Jumping, the act of propelling oneself upwards Architecture * Vault (architecture), an arched form above an enclosed space * Bank vault, a reinforced room or compartment where valuables are stored * Burial vault (enclosure ...

s and

buttress A buttress is an architectural structure built against or projecting from a wall which serves to support or reinforce the wall. Buttresses are fairly common on more ancient buildings, as a means of providing support to act against the lateral ( ...

es in stone vaulted Gothic

cathedral A cathedral is a church that contains the '' cathedra'' () of a bishop, thus serving as the central church of a diocese, conference, or episcopate. Churches with the function of "cathedral" are usually specific to those Christian denominatio ...

s and in

Renaissance The Renaissance ( , ) , from , with the same meanings. is a period in European history The history of Europe is traditionally divided into four time periods: prehistoric Europe (prior to about 800 BC), classical antiquity (800 BC to AD ...

domes. It is not a

parabolic arch A parabolic arch is an arch in the shape of a parabola.Article about parabolic arch by The Free DictionaryParabolic arch , Article about parabolic arch by The Free Dictionary accessdate: March 2, 2017 In structures, their curve represents an effi ...

In history

The 17th-century scientist Robert Hooke wrote: "''Ut pendet continuum flexile, sic stabit contiguum rigidum inversum''", or, "As hangs a flexible cable so, inverted, stand the touching pieces of an arch." A note written by

Thomas Jefferson Thomas Jefferson (April 13, 1743 – July 4, 1826) was an American statesman, diplomat, lawyer, architect, philosopher, and Founding Father who served as the third president of the United States from 1801 to 1809. He was previously the natio ...

in 1788 reads, "I have lately received from Italy a treatise on the equilibrium of arches, by the Abbé Mascheroni. It appears to be a very scientific work. I have not yet had time to engage in it; but I find that the conclusions of his demonstrations are, that every part of the

catenary In physics and geometry, a catenary (, ) is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends in a uniform gravitational field. The catenary curve has a U-like shape, superfici ...

is in perfect equilibrium".

Structural properties

Architecturally, a catenary arch has the ability to withstand the weight of the material from which it is constructed, without collapsing. For an arch of uniform density and thickness, supporting only its own weight, the catenary is the ideal curve. Catenary arches are strong because they redirect the vertical force of gravity into compression forces pressing along the arch's curve. In a uniformly loaded catenary arch, the

line of thrust The line of thrust is the locus of the points, through which forces pass in a retaining wall or an arch. It is the line, along which internal forces flow This principle has been employed architecturally to create arched structures that follow exactly, and in a visibly apparent way, the form of an inverted catenary. A significant early example of this is the arch of

Taq Kasra Tāq Kasrā ( ar, طاق كسرى, translit=ṭāq kisrā), also transcribed as ''Taq-i Kisra'' or ''Taq-e Kesra'' ( fa, طاق کسری, romanized: ''tâğe kasrâ'') or Ayvān-e Kesrā ( fa, ایوان خسرو, translit=Eivâne Xosrow, links=, ...

. The catenary, spun 180 degrees, forms the structure of simple domed building such as the beehive homes of the

Dingle Peninsula The Dingle Peninsula ( ga, Corca Dhuibhne; anglicised as Corkaguiny, the name of the corresponding barony) is the northernmost of the major peninsulas in County Kerry. It ends beyond the town of Dingle at Dunmore Head, the westernmost point ...

, Ireland. The principle of the catenary is also the underlying factor in the much more complex architectural systems of the Medieval and Renaissance architecture. Buildings that have heavy roofs that are arched in shape and deliver a strong outward thrust must comply with the form of the catenary curve in order not to collapse. This does not imply that the arches themselves are catenary in form, but that the total system of walls or buttresses that support the roof or dome contain a catenary curve, which delivers the downward thrust. In the 15th century

Brunelleschi Filippo Brunelleschi ( , , also known as Pippo; 1377 – 15 April 1446), considered to be a founding father of Renaissance architecture, was an Italian architect, designer, and sculptor, and is now recognized to be the first modern engineer, p ...

designed the pointed, octagonal, Gothic dome on Florence Cathedral in a manner that utilised the principle of the catenary arch. In the 17th century, Christopher Wren designed the dome of St Paul's Cathedral based directly on a catenary curve. The vaulted roof and buttresses of Kings College Chapel, Cambridge, have been discovered to comply with the formula of the catenary arch.

Examples

Cathedrals and churches

* King’s College Chapel, in

Cambridge, England Cambridge ( ) is a university city and the county town in Cambridgeshire, England. It is located on the River Cam approximately north of London. As of the 2021 United Kingdom census, the population of Cambridge was 145,700. Cambridge became ...

St Paul's Dome St Paul's Cathedral is an Anglican cathedral in London and is the seat of the Bishop of London. The cathedral serves as the mother church of the Diocese of London. It is on Ludgate Hill at the highest point of the City of London and is a Gr ...

Brunelleschi's Dome Florence Cathedral, formally the (; in English Cathedral of Saint Mary of the Flower), is the cathedral of Florence, Italy ( it, Duomo di Firenze). It was begun in 1296 in the Gothic style to a design of Arnolfo di Cambio and was structurally ...

The Secrets of the Florentine Dome
The Secrets of the Florentine Dome
accessdate: January 25, 2017 *

Casa Batlló () is a building in the center of Barcelona. It was designed by Antoni Gaudí, and is considered one of his masterpieces. A remodel of a previously built house, it was redesigned in 1904 by Gaudí and has been refurbished several times after th ...

has catenary arches * Casa Mila, in Barcelona, Spain was designed by

Antoni Gaudi Antoni is a Catalan, Polish, and Slovene given name and a surname used in the eastern part of Spain, Poland and Slovenia. As a Catalan given name it is a variant of the male names Anton and Antonio. As a Polish given name it is a variant of the fe ...

, who used many catenary arches * Church of Colònia Güell

Natural arches

Rainbow Natural Bridge in the U.S. state of

Utah Utah ( , ) is a state in the Mountain West subregion of the Western United States. Utah is a landlocked U.S. state bordered to its east by Colorado, to its northeast by Wyoming, to its north by Idaho, to its south by Arizona, and to it ...

has a natural catenary shape, possibly produced by

weathering Weathering is the deterioration of rocks, soils and minerals as well as wood and artificial materials through contact with water, atmospheric gases, and biological organisms. Weathering occurs ''in situ'' (on site, with little or no movement) ...

in high-stress areas.

Kolob Arch Kolob Arch is a natural arch in Zion National Park, Utah, United States. According to the Natural Arch and Bridge Society (NABS), it is the sixth-longest natural arch in the world. In 2006, the Society measured the span at 287.4 ± 2 feet (87.6 m ...

and Landscape Arch, also in Utah, have a catenary shape as well.

Human-made arches

The

Gateway Arch The Gateway Arch is a monument in St. Louis, Missouri, United States. Clad in stainless steel and built in the form of a weighted catenary arch, it is the world's tallest arch and Missouri's tallest accessible building. Some sources consider ...

in the American city of

St. Louis St. Louis () is the second-largest city in Missouri, United States. It sits near the confluence of the Mississippi and the Missouri Rivers. In 2020, the city proper had a population of 301,578, while the bi-state metropolitan area, which e ...

(

Missouri Missouri is a state in the Midwestern region of the United States. Ranking 21st in land area, it is bordered by eight states (tied for the most with Tennessee): Iowa to the north, Illinois, Kentucky and Tennessee to the east, Arkansas t ...

) is an inverted catenary arch. Due to aspect ratio, the top being thinner than the bottom, its actual shape is technically a " weighted catenary".

Ancient Egyptian

The unfinished Saqqara ostracon has a catenary shape.

High-rises

Marquette Plaza Marquette Plaza is a highrise in downtown Minneapolis, Minnesota, United States, located at 250 Marquette Avenue. Design Designed by Gunnar Birkerts, it was home to the Federal Reserve Bank of Minneapolis from 1973 to 1997 (hence, many people re ...

Minneapolis Minneapolis () is the largest city in Minnesota, United States, and the county seat of Hennepin County. The city is abundant in water, with thirteen lakes, wetlands, the Mississippi River, creeks and waterfalls. Minneapolis has its origins ...

used catenary arches.

Kilns

Kiln A kiln is a thermally insulated chamber, a type of oven, that produces temperatures sufficient to complete some process, such as hardening, drying, or chemical changes. Kilns have been used for millennia to turn objects made from clay int ...

s are often designed with catenary arch cross-section.

Igloos

Igloos An igloo (Inuit languages: , Inuktitut syllabics (plural: )), also known as a snow house or snow hut, is a type of shelter built of suitable snow. Although igloos are often associated with all Inuit, they were traditionally used only b ...

are designed with a catenary arch cross-section. This shape offers an optimal balance between height and diameter, avoiding the risk of collapsing under the weight of compacted snow.

Other architecture

The inside of

Budapest Budapest (, ; ) is the capital and most populous city of Hungary. It is the ninth-largest city in the European Union by population within city limits and the second-largest city on the Danube river; the city has an estimated population ...

’s Keleti Railway Station forms a catenary arch. The Nubian ton is a burial vault, of

Nubia Nubia () (Nobiin: Nobīn, ) is a region along the Nile river encompassing the area between the first cataract of the Nile (just south of Aswan in southern Egypt) and the confluence of the Blue and White Niles (in Khartoum in central Sudan), or ...

, For greatest stability, the structure’s cross-section follows a catenary arch. The beehive homes (clocháns) of Ireland’s

Skellig Michael Skellig Michael ( ga, Sceilg Mhichíl ), also called Great Skellig ( ga, link=no, Sceilig Mhór ), is a twin-pinnacled crag west of the Iveragh Peninsula in County Kerry, Ireland. The island is named after the archangel Michael, with "Skellig ...

have a cross-section that follows the style of a catenary arch.

Homes

The Rice House has catenary arches.

Hotels

The Icehotel in Sweden employs catenary arches.

Bridges

A catenary bridge has the form of a catenary arch. One famous example is the An-Lan Bridge, in China.

Monuments

Iraq Iraq,; ku, عێراق, translit=Êraq officially the Republic of Iraq, '; ku, کۆماری عێراق, translit=Komarî Êraq is a country in Western Asia. It is bordered by Turkey to the north, Iran to the east, the Persian Gulf and K ...

, the

has the shape of a catenary arch.

Airports

The roof of

Washington Dulles International Airport Washington Dulles International Airport , typically referred to as Dulles International Airport, Dulles Airport, Washington Dulles, or simply Dulles ( ), is an international airport in the Eastern United States, located in Loudoun County and Fa ...

is a suspended catenary curve., A catenary steel cable system supports the roof of Denver International Airport.

Train stations

New York City New York, often called New York City or NYC, is the most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the most densely populated major city in the Un ...

’s

Pennsylvania Station Pennsylvania Station (often abbreviated Penn Station) is a name applied by the Pennsylvania Railroad (PRR) to several of its grand passenger terminals. Several are still in active use by Amtrak and other transportation services; others have been ...

has a roof in the form of a catenary arch.

Banks

On the

Federal Reserve Bank of Minneapolis Federal or foederal (archaic) may refer to: Politics General *Federal monarchy, a federation of monarchies *Federation, or ''Federal state'' (federal system), a type of government characterized by both a central (federal) government and states or ...

, the building has been remodeled, but still visible is the catenary arch suspending the original building.

Mud huts

Cameroon Cameroon (; french: Cameroun, ff, Kamerun), officially the Republic of Cameroon (french: République du Cameroun, links=no), is a country in west-central Africa. It is bordered by Nigeria to the west and north; Chad to the northeast; the C ...

musgum mud huts Musgum mud huts or Musgum dwelling units are traditional domestic structures built of mud by the ethnic Musgum people in the Maga sub-division, Mayo-Danay division, Far North Province in Cameroon. (Musgum also is spelled as Moosgoum.) Referred to ...

have a catenary cross-section.

References

{{Reflist, 30em

External links

The use of the catenary arch in architecture

A few catenary arches

An experiment

A youtube, all about catenary arches

A second youtube

a youtube on building a catenary arch

Another youtube
Arches and vaults Architectural history Catholic architecture