Frame and Form

The reciprocal structures are defined as a set of self-supported elements in a closed circuit, a fairly complete definition but difficult to digest without a good graphic example. The following image shows the simplest arrangement of a reciprocal frame: three bars that overlap to bear on each other and achieve a simple and elegant structural equilibrium.

The reciprocal frames are proposed as an ingenious solution to the problem of covering a distance, or rather a surface, through elements of limited size. As can be seen in the following diagrams taken from the book reciprocal frame architecture, grids consist of elements of size smaller than the span to cover being its geometric disposition which enables a stable structure .

Basic patterns of reciprocal structures - reciprocal frame architecture

Geometric grids with reciprocal structures - reciprocal frame architecture

This is a structural idea as simple as old. Se han encontrado documentos que atestiguan que en el Japón del siglo XII se usaban técnicas constructivas basadas en este diseño estructural y no son pocos los diferentes ejemplos de edificación que a lo largo de la historia han utilizado disposiciones estructurales basadas en este principio. It may be Sebastiano Serlio and Leonardo Da Vinci who established the first geometric and structural studies of reciprocity around the year 1500. A clear example of use of a reciprocal structure can be found in the madrid codex which describes the construction of a wooden beams bridge. Under these lines homepage Leonardo codex to the scheme of the bridge (blurred in the central part of the image), shown below, an example of an arc for a temporary exposition in Germany, and a sketch for the construction stages of the reciprocal bridge .

Reciprocal Bridge - madrid codex

arc reciprocal structure - Germany expo

sketch for the construction stages of the reciprocal bridge

Due to the almost exclusive historic use of timber for carrying out these structures, few or no structures have survived to this days. We must look for more recent examples such as those in Catalan architecture of the early twentieth century byJosep Maria Jujol, close associate of Antoni Gaudí , who used reciprocal structures in Casa Bofarull and Can Negre Bofarull around 1915.

Dome Tower House Bofarull

More recently, Cecil Balmond and his team from Arup's advance geometry unit designed the Weave Bridge for the University of Pennsylvania inspired, theoretically , in the structural principle of reciprocity.

Details of the spatial lattice Weave Bridge

In conclusion, it must be mentioned that reciprocal structures are quite unknown to the vast majority of educational institutions which do not include there study in its curriculum. However, reciprocal schemes are highly educational and inspirational for the structural designer. While it is true that the marginal use in the conventional structure can respond to advances in methods of attachment and the almost unlimited freedom of form, reciprocal frames still have its place of interest in the design of prefabricated, temporary or limited-resource structures, where the use of small size elements and simplified connections represents simplicity, savings and geometric harmony.

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Interesting video of a lecture by Dr. Houlsby on the faculty of Oxford:

Professor Guy Houlsby on “An Early Structural Engineering Problem: the Oxford Connection”