Catenary arch
A catenary arch is a type of
In history
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
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
Examples
Cathedrals and churches
- Cambridge, England[9]
- St Paul's Dome[10]
- Casa Batlló has catenary arches[13]
- Church of Colònia Güell[17]
Natural arches
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
The unfinished Saqqara ostracon has a catenary shape.[23]
High-rises
Marquette Plaza in Minneapolis used catenary arches.[24][25]
Kilns
Kilns are often designed with catenary arch cross-section.[26]
Igloos
Other architecture
The inside of
The
The
Homes
The Rice House has catenary arches.[31]
Hotels
The Icehotel in Sweden employs catenary arches.[32]
Bridges
A
One famous example is the
Monuments
In Iraq, the Taq Kasra has the shape of a catenary arch.[34]
Airports
The roof of
A catenary steel cable system supports the roof of Denver International Airport.[36]
Train stations
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
See also
- Arch bridge
- Catenary
- Gothic arch
- Lancet window
- Mathematics and architecture
- Parabolic arch
- Simple suspension bridge
- Steel catenary riser
References
- ^ Handy, Richard L. (May 2011). "Letter to the Editors: The Perfect Dome". American Scientist. Archived from the original on 2016-04-23. Retrieved 2016-04-17.
- ^ "The enigma of Robert Hooke". Quantum Frontiers. Institute for Quantum Information and Matter, California Institute of Technology. 31 August 2015.
- ^ Jefferson, Thomas (1830). Memoir, Correspondence, and Miscellanies, from the Papers of Thomas Jefferson, Volume 2. Boston: Gray and Bowen. p. 416.
- ^ "St. Louis Gateway Arch". enchantedlearning.com. Retrieved 27 April 2016.
- ^ "Building an arch that can stand up by itself". strath.ac.uk. Retrieved 27 April 2016.
- ^ "The inverted catenary arch". zonedome.com. Retrieved 27 April 2016.
- ^ "Build an arch that can stand up by itself" (PDF). Archived from the original (PDF) on 2016-04-25.
- ^ Karl Robin Nilsson. "Getting the arch back into architecture" (PDF).
- ^ "The British Architect". google.com. 1887. Retrieved 27 April 2016.
- ^ "Maths in a minute: St Paul's dome". maths.org. Retrieved 27 April 2016.
- ^ Nora Hamerman and Claudio Rossi. "Brunelleschi's Dome" (PDF).
- ^ The Secrets of the Florentine Dome: The Secrets of the Florentine Dome, accessdate: January 25, 2017
- ^ "Casa Batlló". Retrieved 2 May 2016.
- ^ "The Catenary Arch". naturalhomes.org. Retrieved 27 April 2016.
- ^ "The Geometry of Antoni Gaudi". slu.edu. Retrieved 27 April 2016.
- ^ "Catenary Method" (PDF).
- ^ "Colònia Güell". barcelonaturisme.com. Retrieved 27 April 2016.
- ^ doi:10.14430/arctic2926. Archived from the original(PDF) on 2016-03-04. Retrieved 2017-01-15.
- ^ Jay H. Wilbur. "The Dimensions of Kolob Arch".
- ^ Cincinnati Cache Collectors. "Landscape Arch".
- ^ "Modern Steel Construction" (PDF).
- ^ Robert Osserman. "How the Gateway arch got its Shape" (PDF).
- ^ "An Ancient Egyptian Catenary Construction Curve". 1926.
- ^ "Marquette Plaza Property Information". Archived from the original on 23 June 2016. Retrieved 2 May 2016.
- ^ "Platinum Plaza" (PDF). 2 May 2016. Archived from the original (PDF) on 23 June 2016. Retrieved 2 May 2016.
- ^ Ken Nagakui (1926). "Kiln Building". Archived from the original on 24 June 2016. Retrieved 30 April 2016.
- ^ Dan Cruickshank (2 April 2008). "What house-builders can learn from igloos". Retrieved 1 May 2016.
- ^ "Budapest". Retrieved 8 May 2016.
- ^ "Nubian Ton".
- ^ "Beehive Homes".
- ^ "Rice House".
- ^ "Icehotel - facts". ICEHOTEL. Retrieved 27 April 2016.
- ^ "Suspension Bridge". uoregon.edu. Retrieved 27 April 2016.
- ^ Chris J K Williams. "Taq Kasra" (PDF). Archived from the original (PDF) on 2017-01-04.
- ^ , Jackie Craven. "Dulles Airport". Archived from the original on 2016-05-05.
- ^ "Denver International Airport".
- ^ David W. Dunlap (1926). "Penn Station's 5th Redesign Fails to Charm Some Critics". The New York Times.
- ^ "100 Years of the Ninth District Fed - Federal Reserve Bank of Minneapolis". minneapolisfed.org. Archived from the original on 21 November 2019. Retrieved 27 April 2016.
- ^ "musgum earth architecture". 18 February 2010. Retrieved 2 May 2016.
- ^ Katy Purviance. "Architecture Addiction, The Official Blog of". Archived from the original on 4 January 2017. Retrieved 2 May 2016.
- ^ "Masonry Design". 11 May 2010. Retrieved 23 December 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