Catenary arch

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A mudbrick catenary arch Catenaria in terra cruda a piu corsi di conci.jpeg
A mudbrick catenary arch
A catenary curve (left) and a catenary arch, also a catenary curve (right). One points up, and one points down, but the curves are the same. Hanging chain and arch.svg
A catenary curve (left) and a catenary arch, also a catenary curve (right). One points up, and one points down, but the curves are the same.

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.

Contents

In history

Robert Hooke, holding a hanging chain, which forms a catenary curve 17 Robert Hooke Engineer.JPG
Robert Hooke, holding a hanging chain, which forms a catenary curve

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." [2]

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". [3]

Structural properties

Architecturally, a catenary arch has the ability to withstand the weight of the material from which it is constructed, without collapsing. [4] [5] For an arch of uniform density and thickness, supporting only its own weight, the catenary is the ideal curve. [6]

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. [7] [8]

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 ]

Examples

Cathedrals and churches

St Paul's Cathedral's dome St Paul's Cathedral's dome.jpg
St Paul's Cathedral's dome

Natural arches

Landscape Arch, Utah Landscape Arch Utah.jpg
Landscape Arch, Utah

Rainbow Natural Bridge in the U.S. state of Utah has a natural catenary shape, possibly produced by weathering in high-stress areas. [18] Kolob Arch and Landscape Arch, also in Utah, have a catenary shape as well. [19] [20]

Human-made arches

The Gateway Arch in the American city of St. Louis (Missouri) is a catenary arch. [21]

Due to aspect ratio, the top being thinner than the bottom, its actual shape is technically a "weighted catenary". [22]

Ancient Egyptian

Saqqara ostracon Saqqara ostracon.jpg
Saqqara ostracon

The unfinished Saqqara ostracon has a catenary shape. [23]

High-rises

Marquette Plaza in Minneapolis Marquette Plaza.jpg
Marquette Plaza in Minneapolis

Marquette Plaza in Minneapolis used catenary arches. [24] [25]

Kilns

Kilns are often designed with catenary arch cross-section. [26]

Igloos

Igloos are designed with a catenary arch cross-section. [27] [18] This shape offers an optimal balance between height and diameter, avoiding the risk of collapsing under the weight of compacted snow. [18]

Other architecture

The inside of Budapest’s Keleti Railway Station forms a catenary arch. [28]

The Nubian ton is a burial vault, of Nubia, For greatest stability, the structure’s cross-section follows a catenary arch. [29]

The beehive homes (clocháns) of Ireland’s Skellig Michael have a cross-section that follows the style of a catenary arch. [30]

Homes

A beehive home (a clochan) on Dingle Peninsula, Kerry, Ireland Dingle beehive hut.JPG
A beehive home (a clochan) on Dingle Peninsula, Kerry, Ireland
Rice House K borland-3.jpg
Rice House

The Rice House has catenary arches. [31]

Hotels

The Icehotel in Sweden employs catenary arches. [32]

Bridges

A catenary bridge has the form of a catenary arch.

One famous example is the An-Lan Bridge, in China. [33]

Monuments

Taq Kasra Ctesiphon, Iraq, 1932.jpg
Taq Kasra

In Iraq, the Taq Kasra has the shape of a catenary arch. [34]

Airports

The roof of Washington Dulles International Airport is a suspended catenary curve. [35]

A catenary steel cable system supports the roof of Denver International Airport. [36]

Train stations

New York City’s Pennsylvania Station has a roof in the form of a catenary arch. [37]

Banks

On the Federal Reserve Bank of Minneapolis, the building has been remodeled, but still visible is the catenary arch suspending the original building. [38]

Mud huts

Cameroon's musgum mud huts have a catenary cross-section. [39] [40] [41]

See also

Related Research Articles

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