A catenary arch is a type of architectural 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 buttresses in stone vaulted Gothic cathedrals and in Renaissance domes. [1] It is not a parabolic arch, although the non-circumferential curves used in arch designs (parabola, catenary, and weighted catenary) look similar, and match at shallow profiles, so a catenary is often misclassified as a parabola [2] (per Galileo, "the [hanging] chain fits its parabola almost perfectly" [3] ).
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." [4]
A note written by Thomas Jefferson 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 is in perfect equilibrium". [5]
Architecturally, a catenary arch has the ability to withstand the weight of the material from which it is constructed, without collapsing. [6] [7] For an arch of uniform density and thickness, supporting only its own weight, the catenary is the ideal curve. [8]
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. [9] [10]
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 homes 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 designed the pointed, octagonal, Gothic dome on Florence Cathedral in a manner that utilised the principle of the catenary arch.[ citation needed ] 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.[ citation needed ]
The classification of non-circumferential curves in actual arches is hard. González et al. provide an example of (well-studied) Palau Güell, where researchers do not agree on classification of the arches or claim the prominence of parabolic arches, while the accurate measurements show that just two of the 23 arches designed by Gaudi are actually parabolic. [11]
The curves close in shape to catenary were used in arches of Ramesseum (13th century BC) and Arch of Ctesiphon (6th century AD). [12]
The unfinished Saqqara ostracon has a catenary shape. [13]
Rainbow Natural Bridge in the U.S. state of Utah has a natural catenary shape, possibly produced by weathering in high-stress areas. [23] Kolob Arch and Landscape Arch, also in Utah, have a catenary shape as well. [24] [25]
The Gateway Arch in the American city of St. Louis (Missouri) is a catenary arch [26] Due to more strength needed at the bottom, the bottom of this arch is wider than the top, so the actual shape is technically a "weighted catenary". [27]
Marquette Plaza in Minneapolis used catenary arches. [28] [29]
Kilns are often designed with catenary arch cross-section. [30]
Igloos are designed with a catenary arch cross-section. [31] [23] This shape offers an optimal balance between height and diameter, avoiding the risk of collapsing under the weight of compacted snow. [23]
The inside of Budapest’s Keleti Railway Station forms a catenary arch. [32]
The Nubian ton is a burial vault, of Nubia, For greatest stability, the structure’s cross-section follows a catenary arch. [33]
The beehive homes (clocháns) of Ireland’s Skellig Michael have a cross-section that follows the style of a catenary arch. [34]
The Rice House has catenary arches. [35]
A catenary bridge has the form of a catenary arch.
One famous example is the An-Lan Bridge, in China. [37]
In Iraq, the Taq Kasra has the shape of a catenary arch. [38]
The roof of Washington Dulles International Airport is a suspended catenary curve. [39]
A catenary steel cable system supports the roof of Denver International Airport. [40]
New York City’s Pennsylvania Station has a roof in the form of a catenary arch. [41]
On the Federal Reserve Bank of Minneapolis, the building has been remodeled, but still visible is the catenary arch suspending the original building. [42]
Cameroon's musgum mud huts have a catenary cross-section. [43] [44] [45]
Parc Güell is a privatized complex of parks, gardens and architectural elements in the Gràcia district of Barcelona, Catalonia, Spain. The site is located in the La Salut neighborhood on the southern side of a hill known as the Turó del Carmel, part of the Collserola mountain range. The separate Parc del Carmel is located on the northern side of the hill.
Casa Milà, popularly known as La Pedrera in reference to its unconventional rough-hewn appearance, is a Modernista building in Barcelona, Catalonia, Spain. It was the last private residence designed by architect Antoni Gaudí and was built between 1906 and 1912.
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.
An arch is a curved vertical structure spanning an open space underneath it. 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, but structural load-bearing arches became popular only after their adoption by the Ancient Romans in the 4th century BC.
An igloo, also known as a snow house or snow hut, is a type of shelter built of suitable snow.
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Casa Vicens is a modernist building situated in the Gràcia neighbourhood of Barcelona. It is the work of architect Antoni Gaudí and is considered to be his first major project. It was built between 1883 and 1885, although Gaudí drew up the initial plans between 1878 and 1880. The work belongs to the orientalist style, similar to Neo-Mudéjar architecture, although interpreted in Gaudí’s own personal way, with a uniqueness that only he knew how to add to his projects. In this work, and for the first time, Gaudí outlined some of his constructive resources that would become regular features throughout the emergence of Modernisme. The work was widely discussed when it was built and caused a great sensation among the general public at the time. When the building was constructed, Gràcia was still an independent urban nucleus of Barcelona; it had its own council and was classified as a town, though nowadays it is a district of the city.
Hyperboloid structures are architectural structures designed using a hyperboloid in one sheet. Often these are tall structures, such as towers, where the hyperboloid geometry's structural strength is used to support an object high above the ground. Hyperboloid geometry is often used for decorative effect as well as structural economy. The first hyperboloid structures were built by Russian engineer Vladimir Shukhov (1853–1939), including the Shukhov Tower in Polibino, Dankovsky District, Lipetsk Oblast, Russia.
Eusebi Güell i Bacigalupi, 1st Count of Güell was a Catalan entrepreneur who profited greatly from the industrial revolution in Catalonia in the late 19th century. He married Luisa Isabel Lopez y Bru, daughter of Antonio López y López, 1st Marquis of Comillas and notorious slave trader, in 1871, and the couple had ten children. One of Güell's daughters, Isabel Güell i López, became a noted composer.
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Tāq Kasrā, also transcribed as Taq-i Kisra or Taq-e Kesra or Ayvān-e Kesrā are the remains of a Sasanian-era Persian monument, dated to c. the 3rd to 6th centuries, which is sometimes called the Arch of Ctesiphon. It is located near the modern town of Salman Pak, Iraq. It was the facade of the main palace in Ctesiphon, and is the only visible remaining structure of the ancient capital city. The archway is considered a landmark in the history of architecture, and is the second largest single-span vault of unreinforced brickwork in the world after Gavmishan Bridge.
A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.
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A weighted catenary is a catenary curve, but of a special form: if a catenary is the curve formed by a chain under its own weight, a weighted catenary is the curve formed if the chain's weight is not consistent along its length. Formally, a "regular" catenary has the equation
In architecture, the funicular curve is an approach used to design the compression-only structural forms using an equivalence between the rope with hanging weights and standing arch with its load. This duality was noticed by Robert Hooke in 1675. If the hanging rope carries just its own weight, the resulting curve is a catenary.