Catenary arch

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.

A catenary arch (also see pointed arch) is an architectural feature, common in cathedrals, and common in Gothic arches used in Gothic architecture,^[1]

Technically, a catenary arch is an "inverted catenary shape"; see right lower illustration. It is not a parabolic arch.

One note on history

Robert Hooke, engineer, holding a hanging chain, which forms a catenary curve

Catenary arches are old. A 1788 note written by Thomas Jefferson reads, I have lately received from Italy a treatise on the equilibrium of arches, by the Abbé Mascheroni. It appears to be a very scientifical 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. ^[2]

Note on history

The scientist Robert Hooke observed, "Ut pendet continuum flexile, sic stabit contiguum rigidum inversum", or, "As hangs a flexible cable so, inverted, stand the touching pieces of an arch." ^[3]

Ability to withstand weight

What makes the catenary arch important is its ability to withstand weight,^[4][5] For an arch of uniform density and thickness, supporting only its own weight, the catenary is the ideal curve,.^[6]

This is done by a catenary curve: Catenary arches are strong, as 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]

Examples

Cathedrals and churches

St Paul's Cathedral's dome

• King’s College Chapel, in Cambridge, England,^[9]
• St Paul's Dome,^[10]
• Dome of Florence,^[11]
• Casa Batlló has catenary arches,^[12]
• Casa Mila, in Barcelona, Spain,^[13] was designed by Antoni Gaudi, who used many catenary arches,^[14][15]
• Church of Colònia Güell,.^[16]

Natural arches

Landscape Arch, Utah

Utah’s Kolob Arch has a catenary shape,^[17] as does Landscape Arch,.^[18]

Human-made arches

The Gateway Arch in the American city of Saint Louis, Missouri,.^[19]

Due to aspect ratio, the top being thinner than the bottom, its actual shape is technically a "weighted catenary",.^[20]

High-rises

Marquette Plaza in Minneapolis

Marquette Plaza in Minneapolis used catenary arches,.^[21][22]

Kilns

Kilns are often designed with catenary arch cross-section,.^[23]

Igloos

Igloos are designed with catenary arch cross-section,.^[24]

Ancient Egyptians

Saqqara ostracon

The unfinished Saqqara ostracon has a catenary shape,.^[25]

Other architecture

The inside of Budapest’s Keleti Railway Station forms a catenary arch,^[26]

The Nubian ton is a burial vault, of Nubia, For greatest stability, the structure’s cross-section follows a catenary arch,.^[27]

The beehive homes (clocháns) of Ireland’s Skellig Michael have a cross-section that follows the style of a catenary arch,.^[28]

Homes

Rice House

The Rice House has catenary arches,.^[29]

Hotels

The Icehotel in Sweden employs catenary arches,.^[30]

Bridges

A catenary bridge has the form of a catenary arch.

One famous example is the An-Lan Bridge, in China,.^[31]

Monuments

Taq Kasra

In Iraq, the Taq Kasra has the shape of a catenary arch,.^[32]

Airports

The roof of Washington Dulles International Airport is an suspended catenary curve,.^[33]

A catenary steel cable system supports the roof of Denver International Airport,.^[34]

A beehive home (a clochan) on Dingle Peninsula, Kerry, Ireland

Train stations

New York City’s Pennsylvania Station has a roof, in the form of a catenary arch,.^[35]

Banks

On the Federal Reserve Bank of Minneapolis, the building has been remodeled, but still visible is the catenary arch suspending the original building,.^[36]

Mud huts

Cameroon's musgum mud huts have a catenary cross-section,.^[37][38]

Toothpick bridges

Toothpick bridges are catenary arches,.^[39]

Home-made arches

Home-made arches tend to be catenary arches,.^[5]

See also

• Arch bridge
• Catenary
• Catenary bridge
• Catenary lighting
• Cathedral
• Dome
• Gothic arch
• Lancet window
• Mathematics and architecture
• Parabolic arch
• Simple suspension bridge
• Steel catenary riser
• Vault (architecture)

References

1. Richard L. Handy. "The Perfect Dome".
2. Thomas Jefferson. "Jefferson quote". Retrieved 1 May 2016.
3. "The enigma of Robert Hooke". The enigma of Robert Hooke. Retrieved 27 April 2016.
4. "St. Louis Gateway Arch". enchantedlearning.com. Retrieved 27 April 2016.
5. "Building an arch that can stand up by iteself". strath.ac.uk. Retrieved 27 April 2016.
6. "The inverted catenary arch". zonedome.com. Retrieved 27 April 2016.
7. "Build an arch that can stand up by itself" (PDF).
8. Karl Robin Nilsson. "Getting the arch back into architecture" (PDF).
9. "The British Architect". google.com. Retrieved 27 April 2016.
10. "Maths in a minute: St Paul's dome". maths.org. Retrieved 27 April 2016.
11. Nora Hamerman and Claudio Rossi. "Brunelleschi's Dome" (PDF).
12. "Casa Batlló". Retrieved 2 May 2016.
13. "The Catenary Arch". naturalhomes.org. Retrieved 27 April 2016.
14. "The Geometry of Antoni Gaudi". slu.edu. Retrieved 27 April 2016.
15. "Catenary Method" (PDF).
16. "Colònia Güell". barcelonaturisme.com. Retrieved 27 April 2016.
17. Jay H. Wilbur. "The Dimensions of Kolob Arch".
18. Cincinnati Cache Collectors. "Landscape Arch".
19. "Modern Steel Construction" (PDF).
20. Robert Osserman. "How the Gateway arch got its Shape" (PDF).
21. "Marquette Plaza Property Information". Retrieved 2 May 2016.
22. "Platinum Plaza" (PDF). 2 May 2016. Retrieved 2 May 2016.
23. Ken Nagakui (1926). "Kiln Building". Retrieved 30 April 2016.
24. Dan Cruickshank. "What house-builders can learn from igloos". Retrieved 1 May 2016.
25. "An Ancient Egyptian Catenary Construction Curve". 1926.
26. ,"Keleti Railway Station".
27. "Nubian Ton".
28. "Beehive Homes".
29. "Rice House".
30. "Icehotel - facts". ICEHOTEL. Retrieved 27 April 2016.
31. "Suspension Bridge". uoregon.edu. Retrieved 27 April 2016.
32. Chris J K Williams. "Taq Kasra" (PDF).
33. , Jackie Craven. "Dulles Airport".
34. "Denver International Airport".
35. David W. Dunlap (1926). "Penn Station’s 5th Redesign Fails to Charm Some Critics".
36. "100 Years of the Ninth District Fed - Federal Reserve Bank of Minneapolis". minneapolisfed.org. Retrieved 27 April 2016.
37. "musgum earth architecture". Retrieved 2 May 2016.
38. Katy Purviance. "Architecture Addiction, The Official Blog of". Retrieved 2 May 2016.
39. "The Toothpick Bridge". pisymphony.com. Retrieved 27 April 2016.

External links

• The use of the catenary arch in architecture
• Natural arches that are catenary arches
• Twisted Physics reference
• Used in building
• More on the catenary, used in arches
• A few catenary arches
• An experiment
• A youtube, all about catenary arches
• A second youtube
• a youtube on building a catenary arch
• Another youtube

Category:Catenary arches

Category:Catenary

Category:Arches

Category:Naturally occurring catenaries