In architecture, the funicular curve (also funicular polygon, funicular shape, from the , "of rope") is an approach used to design the compression-only structural forms (like

masonry Masonry is the craft of building a structure with brick, stone, or similar material, including mortar plastering which are often laid in, bound, and pasted together by mortar (masonry), mortar. The term ''masonry'' can also refer to the buildin ...

arch An arch is a curved vertical structure spanning an open space underneath it. Arches may support the load above them, or they may perform a purely decorative role. As a decorative element, the arch dates back to the 4th millennium BC, but stru ...

es) using an equivalence between the rope with hanging weights and standing arch with its load. This duality was noticed by

Robert Hooke Robert Hooke (; 18 July 16353 March 1703) was an English polymath who was active as a physicist ("natural philosopher"), astronomer, geologist, meteorologist, and architect. He is credited as one of the first scientists to investigate living ...

in 1675 ("as hangs the flexible line, so, but inverted, will stand the rigid 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 In physics and geometry, a catenary ( , ) is the curve that an idealized hanging chain or wire rope, cable assumes under its own weight when supported only at its ends in a uniform gravitational field. The catenary curve has a U-like shape, ...

. In graphic statics, a ''funicular polygon'' is a graphic method of finding out the

line of action In physics, the line of action (also called line of application) of a force () is a geometric representation of how the force is applied. It is the straight line through the point at which the force is applied, and is in the same direction a ...

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 In physics and engineering, a resultant force is the single force and associated torque obtained by combining a system of forces and torques acting on a rigid body via vector addition. The defining feature of a resultant force, or resultant forc ...

. Both polygons were introduced by

Pierre Varignon Pierre Varignon (; 1654 – 23 December 1722) was a French mathematician. He was educated at the Society of Jesus, Jesuit College and the University of Caen, where he received his Magister Artium, M.A. in 1682. He took Holy Orders the following ...

(''Nouvelle Mecanique ou Statique'', 1725) and became the basis of the graphic statics in the second half of the 19th century.

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 Rotational symmetry, also known as radial symmetry in geometry, is the property a shape (geometry), shape has when it looks the same after some rotation (mathematics), rotation by a partial turn (angle), turn. An object's degree of rotational s ...

, like

dome A dome () is an architectural element similar to the hollow upper half of a sphere. There is significant overlap with the term cupola, which may also refer to a dome or a structure on top of a dome. The precise definition of a dome has been a m ...

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 The Basílica i Temple Expiatori de la Sagrada Família, otherwise known as Sagrada Família, is a church under construction in the Eixample district of Barcelona, Catalonia, Spain. It is the largest unfinished Catholic church in the world. Desi ...

basilica. This small model, on exhibit at the museum of the basilica, is often misinterpreted as a model of the basilica itself. 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

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* * * * * Structural engineering {{architecture-stub

Hanging chain model

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