Parabolic Arch

A parabolic arch is a very complex, yet extremely simple arch all at the same time. It is also referred to as a catenary arch. It was developed fairly recently and is used around the world. This arch consists of a relatively simple equation, and one can discover many of its characteristics from its equation if he or she makes use of it. Perhaps the most interesting aspect of this equation is that one of the landmarks in the United States is a catenary arch.

               

A parabolic arch utilizes the principle that if a weight is uniformly applied to an arch, the internal compression deriving from that weight will follow a parabolic profile. Among all the basic arch types, parabolic arches produce the most thrust at the base, but can span the largest areas. This type of arch is usually used in designs for bridges where long span is needed like between valleys or high areas.

  The Arch of Saint Louis

Navajo Bridge– It spans the two sides of the humungous Grand Canyon.

A very strong arch shape defined by the intersection of a cone and a plane parallel to the plane tangent of the cone. For uniform loads a parabola is theoretically an ideal arch shape because the line of thrust coincides with the centre-line of the arch ring.

Sources: www.studymode.com/essays/Parabolic–Arch-152166.html

https://sites.google.com/site/furerplox/re/archarchesoftheromanempireandmodernsociety

History of Parabolic Arches

The parabola was studied by Menaechmus who was a pupil of Plato and Eudoxus. He attempted to duplicate the cube, namely to find side of a cube that has a volume double that of a given cube. Hence he attempted to solve x3 = 2 by geometrical methods.

In fact the geometrical methods of ruler and compass constructions cannot solve this (but Menaechmus did not know this). Menaechmus solved it by finding the intersection of the two parabolas x2 = y and y2 = 2x.

Euclid wrote about the parabola and it was given its present name by Apollonius. The focus and directrix of a parabola were considered by Pappus.

Pascal considered the parabola as a projection of a circle and Galileo showed that projectiles follow parabolic paths.

Gregory and Newton considered the properties of a parabola which bring parallel rays of light to a focus.

The pedal of the parabola with its vertex as pedal point is a cissoid. The pedal of the parabola with its focus as pedal point is a straight line. With the foot of the directrix as pedal point it is a right strophoid (an oblique strophoid for any other point of the directrix). The pedal curve when the pedal point is the image of the focus in the directrix is a Trisectrix of Maclaurin.

The evolute of the parabola is Neile’s parabola. From a point above the evolute three normals can be drawn to the parabola, while only one normal can be drawn to the parabola from a point below the evolute.

If the focus of the parabola is taken as the centre of inversion, the parabola inverts to a cardioid. If the vertex of the parabola is taken as the centre of inversion, the parabola inverts to a Cissoid of Diocles.

Source: http://www-history.mcs.st-and.ac.uk/Curves/Parabola.html

Purpose of Parabolic Arches

The purpose of this experiment is to determine experimental values for the reactions in 2-hinged and fixed parabolic arches.

The catenary and parabolic arch were introduced into construction by a Spanish architect named Antoni Gaudi.

Source: www.studymode.com/essays/Parabolic–Arch-152166.html

Famous Parabolic Arches and Architects

• Arc de Triomphe, Paris, France– One of the most famous monuments in Paris. It stands in the  western end of the Champs-Élysées and honors those who fought and died for France in the French Revolutionary and the Napoleonic Wars, with the names of all French victories and generals inscribed on its inner and outer surfaces. It was constructed in 1806-1836 and is 50 meters (164 ft) in high.The monument was designed by Jean Chalgrin.

Arc de Triomphe, Paris, France

Jean Chalgrin

• The Gateway Arch, St. Louis, United States – A 630-foot (190 m) monument in St. Louis, Missouri. Clad in stainless steel and built in the form of an arch, it is the tallest man-made monument in the United States, and the world’s tallest arch. To go to the top of the Arch, there’s a tram in each leg of the arch. Each tram is a chain of eight egg-shaped compartments, each capable of holding five passengers. The trip to the top takes four minutesThe Gateway Arch was designed by Finnish-American architect Eero Saarinen in 1947; construction began on February 12, 1963, and was completed on October 28, 1965, for $13 million (equivalent to $180 million in 2013). The monument opened to the public on June 10, 1967.

The Gateway Arch “is really a monument to the 20th century and to the height of American power,” says historian Tracy Campbell.

Eero Saarinen, a Finnish-American

• Rua Augusta Arch, Lisbon, Portugal – This historical building and visitor attraction in Lisbon was built to commemorate the reconstruction of the city after the 1755 earthquake. The construction of the monument took many years – from 1755 till 1873.The allegorical group at the top, made by French sculptor Célestin Anatole Calmels, represents Glory rewarding Valor and Genius.

Rua Augusta Arch, Lisbon, Portugal

         

• Arch of Cinquantenaire, Brussles, Belgium – The Arch was planned for the world exhibition of 1880 to commemorate the 50th anniversary of Belgium as an independent country. However, the construction was not completed in time. It took many more years but the construction was finally completed in 1905, just in time for the 75th anniversary of the independence of Belgium. The original pavilions of the 1880 exhibition, designed by Gédéon Bordiau, were largely replaced with the triumphal arcade designed by Charles Girault in 1904 and the large halls on both sides.

Arch of Cinquantenaire, Brussles, Belgium

      

• Arc de Triomf, Barcelona, Spain – The Arc de Triomf in the capital of Catalonia was built as the main access gate for the 1888 Barcelona World Fair. It was built as the main access gate for the 1888 Barcelona World Fair by architect Josep Vilaseca i Casanovas.

Arc de Triomf, Barcelona, Spain

Josep Vilaseca i Casanovas

• Wartime brought major changes to timber construction technology in Australia, particularly in the days following the Japanese attack on Pearl Harbour.

  In 1942, the country was threatened by invasion. Civilian uses of timber were tightly controlled and domestic building without government consent was prohibited. Large numbers of Allied troops and their masses of equipment had to be housed and protected.

  Enter a whole range of lean, strong and graceful timber-based designs not previously known in Australia. Perhaps the most interesting were the parabolic-arched timber structures called ‘igloos’ – in their initial form, used to hide strike aircraft, but evolving to ‘house’ all sorts of military equipment.

  Igloos were designed by French engineer Emile Brizay (1900-1983). After serving in World War I, he trained at Angers where he received an engineering diploma in 1921. From 1923 he worked for the pioneering, concrete engineer, Eugene Freysinnet on erection of the Plougastel Bridge and aircraft hangers at Villacoublay. In 1926 Brizay accepted a position in Singapore with a French colonial firm for whom he designed and built buildings and bridges. He practiced privately from 1929, specialising in concrete and consulting with the Public Works Department.

  

Source: http://www.timberdesignmag.com/projects/parabolic-arches/