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

The mathematics

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.

The Line of Thrust, why such arches are used

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]

Compared to catenary arches

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]

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

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
The Bixby Creek Bridge's parabolic arch

See also

An unusual combination of parabolic and Perpendicular Gothic arches in St Mark's Church, Bromley, London

References

  1. ↑ Article about parabolic arch by The Free Dictionary: Parabolic arch | Article about parabolic arch by The Free Dictionary, accessdate: March 2, 2017
  2. ↑ "Developments in Mechanics of Structures & Materials".
  3. 1 2 The Design of Prestressed Concrete Bridges/Chapter 17 The Design And Construction Of Arches
  4. ↑ ""Characterizing the Shape of a Hen's Egg"" (PDF). Retrieved 22 March 2017.
  5. ↑ 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
  6. ↑ TripAdvisor: Parabolic arch supporting roof of Casa Mila - Picture of La Pedrera, Barcelona - TripAdvisor, accessdate: March 2, 2017
  7. ↑ RIBA: Llandaff Cathedral, Cardiff: the nave with the Majestas by Jacob Epstein supported on concrete parabolic arches | RIBA Archived 2016-05-09 at the Wayback Machine., accessdate: March 2, 2017
  8. ↑ 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
  9. ↑ Organ, St Leonard's Parish Church (C) Julian P Guffogg :: Geograph Ireland: para, accessdate: March 3, 2017
  10. ↑ Queensland Government: St Paul's Anglican Church | Environment, land and water | Queensland Government, accessdate: March 2, 2017
  11. ↑ "Art, culture and society from Far East". Modello Fantastico. Retrieved 8 Dec 2016.
  12. ↑ Bisbort, Alan (April 10, 1992). "The Draw of Bridges". The Washington Post. pp. A8–A9.
  13. ↑ Heritage New Zealand: www.heritage.org.nz/the-list/details/5180, accessdate: March 3, 2017
  14. ↑ The New York Times: parab, accessdate: March 3, 2017
  15. ↑ Berlin Iron Bridge Company: Berlin Iron Bridge Company, accessdate: March 4, 2017
  16. ↑ 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
  17. ↑ 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.
  18. ↑ Alamy: para, accessdate: March 4, 2017
  19. ↑ Golden Gate Bridge Parabola by Silvia Stagno on Prezi: Golden Gate Bridge Parabola by Silvia Stagno on Prezi, accessdate: March 4, 2017
  20. ↑ Mathematics Stack Exchange: berli, accessdate: March 4, 2017
  21. ↑ "Hulme Arch Bridge project". Arup. Archived from the original on March 23, 2006. Retrieved 3 March 2017.
  22. ↑ Krasnoyarsk Bridge: parab, accessdate: March 4, 2017
  23. ↑ Jean McConochie photos at pbase.com: para, accessdate: March 3, 2017
  24. ↑ Arch Bridges on Waymarking.com: Memorial Bridge - Springfield/West Springfield, MA - Arch Bridges on Waymarking.com, accessdate: March 4, 2017
  25. ↑ Smith 2001, p. 38
  26. ↑ Gimeno and Gutierrez. pag.122
  27. ↑ Parabolas in Suspension Bridges! Oh, my!: parab, accessdate: March 4, 2017
  28. ↑ 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
  29. ↑ "Tyne Bridge". BBC Inside Out. 24 September 2014. Retrieved 3 March 2017.
  30. ↑ The Victoria Falls Bridge: To the Victoria Falls - The Victoria Falls Bridge, accessdate: March 2, 2017
  31. ↑ Livingstone News: central, accessdate: March 2, 2017
  32. ↑ Best Bridge Africa Victoria Falls Bridge: Best Bridge Africa Victoria Falls Bridge, accessdate: March 2, 2017

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
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.