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 is a type of architectural pointed arch that follows an inverted catenary curve. It is common in cathedrals and in Gothic arches used in Gothic architecture.[1] It is not a parabolic arch.


In historyEdit

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 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".[3]

Structural propertiesEdit

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]


Cathedrals and churchesEdit

St Paul's Cathedral's dome

Natural archesEdit

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 archesEdit

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

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


Marquette Plaza in Minneapolis used catenary arches.[23][24]


Kilns are often designed with catenary arch cross-section.[25]


Igloos are designed with a catenary arch cross-section.[26][18] This shape offers an optimal balance between height and diameter, avoiding the risk of collapsing under the weight of compacted snow.[18]

Ancient EgyptiansEdit

The unfinished Saqqara ostracon has a catenary shape.[27]

Other architectureEdit

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]


The Rice House has catenary arches.[31]


The Icehotel in Sweden employs catenary arches.[32]


A catenary bridge has the form of a catenary arch.

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


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


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 stationsEdit

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


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 hutsEdit

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

See alsoEdit


  1. ^ Handy, Richard L. (May 2011). "Letter to the Editors: The Perfect Dome". American Scientist.
  2. ^ "The enigma of Robert Hooke". Quantum Frontiers. Institute for Quantum Information and Matter, California Institute of Technology. 31 August 2015.
  3. ^ Jefferson, Thomas (1830). Memoir, Correspondence, and Miscellanies, from the Papers of Thomas Jefferson, Volume 2. Boston: Gray and Bowen. p. 416.
  4. ^ "St. Louis Gateway Arch". enchantedlearning.com. Retrieved 27 April 2016.
  5. ^ "Building an arch that can stand up by itself". 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. 1887. 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. ^ The Secrets of the Florentine Dome: The Secrets of the Florentine Dome, accessdate: January 25, 2017
  13. ^ "Casa Batlló". Retrieved 2 May 2016.
  14. ^ "The Catenary Arch". naturalhomes.org. Retrieved 27 April 2016.
  15. ^ "The Geometry of Antoni Gaudi". slu.edu. Retrieved 27 April 2016.
  16. ^ "Catenary Method" (PDF).
  17. ^ "Colònia Güell". barcelonaturisme.com. Retrieved 27 April 2016.
  18. ^ a b c Handy, Richard L. (Dec 1973). "The Igloo and the Natural Bridge as Ultimate Structures" (PDF). Arctic. 26 (4): 276–281. doi:10.14430/arctic2926.
  19. ^ Jay H. Wilbur. "The Dimensions of Kolob Arch".
  20. ^ Cincinnati Cache Collectors. "Landscape Arch".
  21. ^ "Modern Steel Construction" (PDF).
  22. ^ Robert Osserman. "How the Gateway arch got its Shape" (PDF).
  23. ^ "Marquette Plaza Property Information". Retrieved 2 May 2016.
  24. ^ "Platinum Plaza" (PDF). 2 May 2016. Retrieved 2 May 2016.
  25. ^ Ken Nagakui (1926). "Kiln Building". Retrieved 30 April 2016.
  26. ^ Dan Cruickshank. "What house-builders can learn from igloos". Retrieved 1 May 2016.
  27. ^ "An Ancient Egyptian Catenary Construction Curve". 1926.
  28. ^ "Budapest". Retrieved 8 May 2016.
  29. ^ "Nubian Ton".
  30. ^ "Beehive Homes".
  31. ^ "Rice House".
  32. ^ "Icehotel - facts". ICEHOTEL. Retrieved 27 April 2016.
  33. ^ "Suspension Bridge". uoregon.edu. Retrieved 27 April 2016.
  34. ^ Chris J K Williams. "Taq Kasra" (PDF).
  35. ^ , Jackie Craven. "Dulles Airport".
  36. ^ "Denver International Airport".
  37. ^ David W. Dunlap (1926). "Penn Station's 5th Redesign Fails to Charm Some Critics".
  38. ^ "100 Years of the Ninth District Fed - Federal Reserve Bank of Minneapolis". minneapolisfed.org. Retrieved 27 April 2016.
  39. ^ "musgum earth architecture". Retrieved 2 May 2016.
  40. ^ Katy Purviance. "Architecture Addiction, The Official Blog of". Retrieved 2 May 2016.
  41. ^ "Masonry Design". 11 May 2010. Retrieved 23 December 2016.

External linksEdit