# Parabolic arch

(Redirected from Parabolic vault)
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]

## 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

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. ^
3. ^ a b 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. ^
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