Catenaria in terra cruda a più corsi di conci

A catenary arch is a type of

architectural Architecture is the art and technique of designing and building, as distinguished from the skills associated with construction. It is both the process and the product of sketching, conceiving, planning, designing, and constructing buildings o ...

arch that follows an inverted catenary curve. The catenary curve has been employed in buildings since ancient times. It forms an underlying principle to the overall system of vaults 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 (s ...

es in stone vaulted

Gothic Gothic or Gothics may refer to: People and languages *Goths or Gothic people, the ethnonym of a group of East Germanic tribes **Gothic language, an extinct East Germanic language spoken by the Goths **Crimean Gothic, the Gothic language spoken b ...

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 denominations ...

s and in

Renaissance The Renaissance ( , ) , from , with the same meanings. is a period in European history marking the transition from the Middle Ages to modernity and covering the 15th and 16th centuries, characterized by an effort to revive and surpass ide ...

dome A dome () is an architectural element similar to the hollow upper half of a sphere. There is significant overlap with the term cupola, which may also refer to a dome or a structure on top of a dome. The precise definition of a dome has been a m ...

s. 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 Robert Hooke FRS (; 18 July 16353 March 1703) was an English polymath active as a scientist, natural philosopher and architect, who is credited to be one of two scientists to discover microorganisms in 1665 using a compound microscope that ...

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 Fathers of the United States, Founding Father who served as the third president of the United States from 18 ...

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 runs through its center. 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. The catenary, spun 180 degrees, forms the structure of simple domed building such as the

beehive home A beehive house is a building made from a circle of stones topped with a domed roof. The name comes from the similarity in shape to a straw beehive. Occurrences The ancient Bantu used this type of house, which was made with mud, poles, and c ...

s of the Dingle Peninsula, 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, ...

designed the pointed, octagonal, Gothic dome on

Florence Cathedral 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 co ...

in a manner that utilised the principle of the catenary arch. In the 17th century,

Christopher Wren Sir Christopher Wren PRS FRS (; – ) was one of the most highly acclaimed English architects in history, as well as an anatomist, astronomer, geometer, and mathematician-physicist. He was accorded responsibility for rebuilding 52 church ...

designed the dome of

St Paul's Cathedral St Paul's Cathedral is an Anglicanism, 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 ...

based directly on a catenary curve. The vaulted roof and buttresses of

Kings College Chapel King's College Chapel is the chapel of King's College in the University of Cambridge. It is considered one of the finest examples of late Perpendicular Gothic English architecture and features the world's largest fan vault. The Chapel was built ...

, Cambridge, have been discovered to comply with the formula of the catenary arch.

Examples

Cathedrals and churches

King’s College Chapel King's College Chapel is the chapel of King's College in the University of Cambridge. It is considered one of the finest examples of late Perpendicular Gothic English architecture and features the world's largest fan vault. The Chapel was built ...

, in Cambridge, England * St Paul's Dome *

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 c ...

The Secrets of the Florentine Dome
The Secrets of the Florentine Dome
accessdate: January 25, 2017 * Casa Batlló has catenary arches * Casa Mila, in

Barcelona, Spain Barcelona ( , , ) is a city on the coast of northeastern Spain. It is the capital and largest city of the autonomous community of Catalonia, as well as the second most populous municipality of Spain. With a population of 1.6 million within ci ...

was designed by Antoni Gaudi, who used many catenary arches *

Church of Colònia Güell Church may refer to: Religion * Church (building), a building for Christian religious activities * Church (congregation), a local congregation of a Christian denomination * Church service, a formalized period of Christian communal worship * Chris ...

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 its ...

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 and

Landscape Arch Landscape Arch is the longest of the many natural rock arches located in Arches National Park, Utah, United States and among the longest natural stone arches in the world. Description The arch is among many in the Devils Garden area in the n ...

, also in Utah, have a catenary shape as well.

Human-made arches

The Gateway Arch in the American city of St. Louis (

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 A weighted catenary is a catenary curve, but of a special form. A "regular" catenary has the equation :y = a \, \cosh \left(\frac\right) = \frac for a given value of ''a''. A ''weighted catenary'' has the equation :y = b \, \cosh \left(\frac\ ...

Ancient Egyptian

The unfinished Saqqara ostracon has a catenary shape.

High-rises

Marquette Plaza in

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 origin ...

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 Cross section may refer to: * Cross section (geometry) ** Cross-sectional views in architecture & engineering 3D *Cross section (geology) * Cross section (electronics) * Radar cross section, measure of detectability * Cross section (physics) **Abs ...

Igloos

Igloos 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 o ...

’s

Keleti Railway Station Budapest Keleti (Eastern) station ( hu, Keleti pályaudvar) is the main international and inter-city railway terminal in Budapest, Hungary. The station stands where Rákóczi út splits to become Kerepesi Avenue and Thököly Avenue. Keleti p� ...

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 Sud ...

, For greatest stability, the structure’s cross-section follows a catenary arch. The beehive homes (clocháns) of Ireland’s Skellig Michael 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 China, officially the People's Republic of China (PRC), is a country in East Asia. It is the world's List of countries and dependencies by population, most populous country, with a Population of China, population exceeding 1.4 billion, slig ...

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 Iraq–Turkey border, the north, Iran to Iran–Iraq ...

, the Taq Kasra 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 F ...

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

Denver International Airport Denver International Airport , locally known as DIA, is an international airport in the Western United States, primarily serving metropolitan Denver, Colorado, as well as the greater Front Range Urban Corridor. At , it is the largest airport i ...

Train stations

New York City New York, often called New York City or NYC, is the List of United States cities by population, most populous city in the United States. With a 2020 population of 8,804,190 distributed over , New York City is also the L ...

’s Pennsylvania Station has a roof in the form of a catenary arch.

Banks

On the Federal Reserve Bank of Minneapolis, 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 ...

's musgum mud huts 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