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DEFINITION

A catenary is the curve assumed by a cord of uniform density and cross section that is perfectly flexible but not capable of being stretched and that hangs freely from two fixed points. The key point behind a catenary form is the uniform density of the material used, which is why we decided to work on our experimentation with chain link.

Catenary is a mathematical term that mainly describes the form of a chain or cable when is suspended freely between two points. This shape can also be known as a chainette. The name derives from the Latin catenaria (“chain”). Any freely hanging cable or string assumes this shape, also called a chainette, if the body is of uniform mass per unit of length and is acted upon solely by gravity.

The main force behind its particular shape is gravity. A catenary shape is not to be confused with a parabola as even Galigeo Galilei  mistakenly believed that this was the same shape that was derived from projectiles in absence or resistance. It was until later in the 17th century that the Dutch mathematician Christiaan Huygens showed that the chain curve cannot be given by an algebraic equation; he also coined the term catenary.

Understanding that the forces at play in a catenary arches is also crucial in the understanding of structures and application in architecture. In an arch which has the shape of a perfect inverted catenary curve, the voussoirs or forces correspond to the links of the chain. As the links of the chain are under tension, the forces of the inverted catenary arch are under compression and LT is centred in the voussoirs. Catenary arches are always the most stable so their thickness can be reduced. Segmental arches are also very stable, as LT is near the centre of the arch.

catenary arch

EXPERIMENTATION

The team first efforts to understand catenaries, was using cloths, standard strings, meshes and elastics. We allowed this pieces to hang freely and then applying different weights on them to observe behavior.

Some examples of how some of this different materials behaved:

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We observed that the applying a singular weight on along an axis on different points of the cloth made different indentations. As shown on first pictures, the indentation of at 1/4 of the axis was greater.

We also used different widths of strings, and later applied weights on to the string . The weights applied actually got to transform the desired curve. This proved that the weights where to heavy for the arch to support.  This informed us that the weights that will be used on our future experimentation will have to be more carefully considered.

We decided to work simply with chain as material given its flexibility and ease of use. we wanted to be able to attach as many curves as possible and chain allows this very well. After getting our hand on some chain and boards we went on and produce studies where different arrays where tested.

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DIAGRAM

We started a process of identification of catenary types which can be explained through diagraming. Along this types we can be discovering subcategories that would be extended through our experimentation with chain.

This are some types that we could start to define:

singular (one free hanging catenary between two points)

segmental (sequential of more than one along a single line)

super imposed (crossed over catenaries along an axis)

extended (catenary hanging from another catenary)

linked (a catenary attached to another)

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PRESEDENTS

Dwelling

A very early example of vernacular is with the musgum, an ethnic group in far north province in cameroon, created their homes from compressed sun-dried mud. The tall conical dwellings, in the shape of a shell. This structure allowed the structures to go very tall as it is shown

Musgum mud huts or Musgum dwelling units are traditional domestic structures built of mud by the ethnic Musgum people. The dwellings were built in a variety of shapes, such as tall domed or conical dwellings or huts, some with a reverse-V shape, and others with geometric designs.

Musgum mud

Architecture

The 20th century architect Antonio Gaudi was an architect from Reus, who was the figurehead of Catalan Modernism. Gaudí’s works reflect his highly individual and distinctive style and are largely concentrated in Barcelona, notably his magnum opus, the Sagrada Família. He designed and built with catenary systems using the same masonry blocks used by the neoclassical architects.

gaudi arches 2 gaudi arches1

Monument

Built as a monument to the westward expansion of the United States during the 1960’s, the arch typifies “the pioneer spirit of the men and women who won the West, and those of a latter day to strive on other frontiers.” The arch has become the iconic image of St. Louis.

Stitched Panorama

Calatrava Stands out as a primary expample in contemporary architecture. He works with this Catenary shapes to produced highly engineered buildings that are evidenced through out his architecture. Especially in his work at the City of Arts and Science In Barcelona.

calatrava science city1

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