View source for Funicular curve

{{Short description|Compression-only shape mirroring a hanging chain}}
{{about|a geometric shapes|a means of transportation|Funicular}}
[[File:Analogy between an arch and a hanging chain and comparison to the dome of St Peter's Cathedral in Rome.png|thumb|Analogies between the hanging chains and standing structures: an arch and the dome of [[Saint Peter's Basilica]] in Rome ([[Giovanni Poleni]], 1748)]]
In architecture, the '''funicular curve''' (also '''funicular polygon''', '''funicular shape''', from the {{lang-la|fūniculus}}, "of rope"{{sfn | Oxford University Press | 1996 | loc=funicular}}) is an approach used to design the compression-only [[Structural form (engineering)|structural forms]] (like [[masonry]] [[arch]]es) using an equivalence between the rope with hanging weights and standing arch with its load. This duality was noticed by [[Robert Hooke]] in 1675 ("as hangs the flexible line, so, but inverted, will stand the rigid arch").{{sfn | Woodman | Heyman | 2003 | loc=The voussoir arch}} If the hanging rope carries just its own weight (in this case it is usually called a "chain" and is equivalent to a free-standing arch with no external load), the resulting curve is a [[catenary]].{{sfn | Tomlow | 2011 | p=219}} 

In [[graphic statics]], a ''funicular polygon'' is a graphic method of finding out the [[line of action]] for a combination of forces applied to a solid body at different points, a complement to the [[force polygon]] used to obtain the value and direction of the [[resultant force]].{{sfn | Escudier | Atkins | 2019 | loc=funicular polygon}} Both polygons were introduced by [[Pierre Varignon]] (''Nouvelle Mecanique ou Statique'', 1725) and became the basis of the [[graphic statics]] in the second half of the 19th century.{{sfn | Markou | Ruan | 2022 | p=1390}}

== Hanging chain model ==
Multiple ropes with weights can be connected together forming a '''hanging chain model''' of a complete structure. The uses of this "outlandish", complicated in comparison with even pre-computer techniques, like graphic statics, method were rare, yet interesting. Usually the technique was used for planar structures as well as the ones with [[rotational symmetry]], like [[dome]]s. The method can also be applied to arbitrary three-dimensional structures, as first shown by [[Gaudi]] while designing the [[church of Colònia Güell]]. Gaudi had built a 1:10 scale hanging chain model of the church that did not survive. He also used a smaller copy that was at the time stored in the [[Sagrada Família]] basilica. This small model, on exhibit at the museum of the basilica, is often misinterpreted as a model of the basilica itself.{{sfn | Tomlow | 2011 | p=219}}
<gallery>
File:Maqueta polifunicular.jpg|Original 1:10 scale hanging model of the church of Colònia Güell uses cloth cutouts to show the (inverted) appearance of the church
File:Maqueta funicular.jpg|Smaller model on the display at the museum
File:Exterior i entrada a la Cripta de la Colònia Güell 02.JPG|Complex system of supports at the entrance of the church at Colònia Güell
</gallery>

==References==
{{reflist}}

== Sources ==
* {{cite book | last=Woodman | first=Francis | last2=Heyman | first2=Jacques | title=Oxford Art Online | chapter=Masonry | publisher=Oxford University Press | date=2003 | isbn=978-1-884446-05-4 | doi=10.1093/gao/9781884446054.article.t054954}}
* {{cite book | title=The Concise Oxford Dictionary of English Etymology | publisher=Oxford University Press | date=1996-01-01 | isbn=978-0-19-283098-2 | doi=10.1093/acref/9780192830982.001.0001 | ref={{sfnref | Oxford University Press | 1996}}}}
* {{cite book | last=Escudier | first=Marcel | last2=Atkins | first2=Tony | title=A Dictionary of Mechanical Engineering | publisher=Oxford University Press | date=2019 | isbn=978-0-19-883210-2 | doi=10.1093/acref/9780198832102.001.0001}}
* {{cite journal | last=Tomlow | first=Jos | title=Gaudí's reluctant attitude towards the inverted catenary | journal=Proceedings of the Institution of Civil Engineers - Engineering History and Heritage | volume=164 | issue=4 | date=2011 | issn=1757-9430 | doi=10.1680/ehah.2011.164.4.219 | pages=219–233 }}
* {{cite journal | last=Markou | first=Athanasios A. | last2=Ruan | first2=Gengmu | title=Graphic statics: projective funicular polygon | journal=Structures | volume=41 | date=2022 | doi=10.1016/j.istruc.2022.05.049 | pages=1390–1396| doi-access=free }}

[[Category:Structural engineering]]


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