Parabolic arch
Parabolic arches in Celler de Sant Cugat
A parabolic arch is an arch shaped like a parabola.[1] Such arches are used in bridges, cathedrals, and elsewhere in architecture and engineering.
Description
While a parabolic arch may resemble a catenary arch, a parabola is a quadratic function while a catenary is the hyperbolic cosine, cosh(x), a sum of two exponential functions.
Unlike a catenary arch, the parabolic arch employs the principle that when weight is uniformly applied above, the internal compression (see line of thrust) resulting from that weight will follow a parabolic curve. Of all arch types, the parabolic arch produces the most thrust at the base. Also, it can span the widest area. It is commonly used in bridge design, where long spans are needed.[2][3]
When an arch carries a uniformly distributed vertical load, the correct shape is a parabola. When an arch carries only its own weight, the best shape is a catenary.[3]
- A catenary, in blue, graphed against a parabola, in red
Parabola (red) graphed against a catenary (blue), view to simulate an arch.
Parabola (red) graphed against a catenary (blue), view to simulate an arch. Zoomed out.
Uses
A hen's egg can be fairly well described as two different paraboloids connected by part of an ellipse.[4][5]
Cathedrals and churches
A few examples of parabolic arches.:
The Memorial Cenotaph in the Hiroshima Peace Memorial Park
- Casa Milà[6] is a famous example, and
- Llandaff Cathedral[7]
- St Leonard's Church[8][9]
- St Paul's Anglican Church[10]
- The Memorial Cenotaph in the Hiroshima Peace Memorial Park is in the form of a parabolic arch.[11]
Architects
Parabolic arches were used by architects Oscar Niemeyer, and Antoni Gaudí, who also used catenary arches.
Bridges and their technology
The Golden Gate Bridge's parabolic arches
- 16th Street Bridge (Washington, D.C.)[12]
- Balclutha Road Bridge[13]
- Bayonne Bridge[14]
- Berlin Iron Bridge Co.[15]
- Bixby Creek Bridge[16]
- Cape Creek Bridge[17]
- Dell Bridge[18]
- Golden Gate Bridge[19][20]
- Hulme Arch Bridge[21]
The Bixby Creek Bridge's parabolic arch
- Krasnoyarsk Bridge[22]
- L'Umbracle[23]
- Memorial Bridge (Massachusetts)[24]
- Ordish–Lefeuvre system[25]
- Puente Nuevo (Murcia)[26]
- Simple suspension bridge
- Suspension bridge[27][28]
- Tyne Bridge[29]
- Victoria Falls Bridge[30][31][32]
See also
An unusual combination of parabolic and Perpendicular Gothic arches in St Mark's Church, Bromley, London
- Arch bridge
- catenary arch
- Catenary
- Catenary bridge
- Catenary lighting
- Catenoid
- Cathedral
- Dome
- Gothic arch
- Gothic architecture
- Lancet arch
- Lancet window
- Mathematics and architecture
- Musgum mud huts
- Natural arch, some of whom are catenary arches
- Nubian vault
- Overhead line
- Simple suspension bridge
- Steel catenary riser
- Suspension bridge
- Toothpick bridge
- Truss arch bridge
- Vault (architecture)
- Voussoir
References
- ↑ Article about parabolic arch by The Free Dictionary: Parabolic arch | Article about parabolic arch by The Free Dictionary, accessdate: March 2, 2017
- ↑ "Developments in Mechanics of Structures & Materials".
- 1 2 The Design of Prestressed Concrete Bridges/Chapter 17 The Design And Construction Of Arches
- ↑ ""Characterizing the Shape of a Hen's Egg"" (PDF). Retrieved 22 March 2017.
- ↑ Google Books: https://books.google.co.uk/books?id=CIAAAAAAMAAJ&pg=PA264&lpg=PA264&dq="hen's+egg"+"parabolic+arch"&source=bl&ots=uOzbRBeDwm&sig=ohyUSTlHvU8sNUqTahR_BjU6gp4&hl=en&sa=X&redir_esc=y#v=onepage&q="hen's egg" "parabolic arch"&f=false, accessdate: March 22, 2017
- ↑ TripAdvisor: Parabolic arch supporting roof of Casa Mila - Picture of La Pedrera, Barcelona - TripAdvisor, accessdate: March 2, 2017
- ↑ RIBA: Llandaff Cathedral, Cardiff: the nave with the Majestas by Jacob Epstein supported on concrete parabolic arches | RIBA, accessdate: March 2, 2017
- ↑ Interior of St Leonard's church, St... (C) Julian P Guffogg :: Geograph Britain and Ireland: Interior of St Leonard's church, St... (C) Julian P Guffogg :: Geograph Britain and Ireland, accessdate: March 2, 2017
- ↑ Organ, St Leonard's Parish Church (C) Julian P Guffogg :: Geograph Ireland: para, accessdate: March 3, 2017
- ↑ Queensland Government: St Paul's Anglican Church | Environment, land and water | Queensland Government, accessdate: March 2, 2017
- ↑ "Art, culture and society from Far East". Modello Fantastico. Retrieved 8 Dec 2016.
- ↑ Bisbort, Alan (April 10, 1992). "The Draw of Bridges". The Washington Post. pp. A8–A9.
- ↑ Heritage New Zealand: www.heritage.org.nz/the-list/details/5180, accessdate: March 3, 2017
- ↑ The New York Times: parab, accessdate: March 3, 2017
- ↑ Berlin Iron Bridge Company: Berlin Iron Bridge Company, accessdate: March 4, 2017
- ↑ Bixby Creek Bridge on Highway One from the Pat Hathaway Photo Collection: Bixby Creek Bridge on Highway One from the Pat Hathaway Photo Collection, accessdate: March 6, 2017
- ↑ Style & Vernacular: A Guide to the Architecture of Lane County, Oregon. Western Imprints, The Press of the Oregon Historical Society. 1983. p. 151. ISBN 0-87595-085-X.
- ↑ Alamy: para, accessdate: March 4, 2017
- ↑ Golden Gate Bridge Parabola by Silvia Stagno on Prezi: Golden Gate Bridge Parabola by Silvia Stagno on Prezi, accessdate: March 4, 2017
- ↑ Mathematics Stack Exchange: berli, accessdate: March 4, 2017
- ↑ "Hulme Arch Bridge project". Arup. Archived from the original on March 23, 2006. Retrieved 3 March 2017.
- ↑ Krasnoyarsk Bridge: parab, accessdate: March 4, 2017
- ↑ Jean McConochie photos at pbase.com: para, accessdate: March 3, 2017
- ↑ Arch Bridges on Waymarking.com: Memorial Bridge - Springfield/West Springfield, MA - Arch Bridges on Waymarking.com, accessdate: March 4, 2017
- ↑ Smith 2001, p. 38
- ↑ Gimeno and Gutierrez. pag.122
- ↑ Parabolas in Suspension Bridges! Oh, my!: parab, accessdate: March 4, 2017
- ↑ Why are cables connecting towers in a suspension bridge in the form of a parabola? Is this better from a structural standpoint or is it purely aesthetic? : askscience: Why are cables connecting towers in a suspension bridge in the form of a parabola? Is this better from a structural standpoint or is it purely aesthetic? : askscience, accessdate: March 4, 2017
- ↑ "Tyne Bridge". BBC Inside Out. 24 September 2014. Retrieved 3 March 2017.
- ↑ The Victoria Falls Bridge: To the Victoria Falls - The Victoria Falls Bridge, accessdate: March 2, 2017
- ↑ Livingstone News: central, accessdate: March 2, 2017
- ↑ Best Bridge Africa Victoria Falls Bridge: Best Bridge Africa Victoria Falls Bridge, accessdate: March 2, 2017
External links
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Wikimedia Commons has media related to |
- On why suspension bridges are parabolic
- Many parabolic arches
- One the difference between a parabola and a catenary
- On parabolic versus catenary arches
- On a variety of curves, parabolas, catenaries, hyperbolas, and ellipses
- YouTube video
- Another Youtube video
Bibliography
- Gimeno Díaz de Atauri, Jorge; Gutiérrez Andrés, Juan (2001), El Puente de la Pólvora y otros puentes, Murcia: Colegio de Ingenieros de Caminos, Canales y Puentes. Demarcación Murcia, ISBN 978-84-607-3209-9
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