Background the

reciprocal frame historically

So who made the first reciprocal frame? Where did the idea come from? It would be difficult to find out when and where the first reciprocal frame (RF) was constructed; to do so would be like trying to establish when and where the first high-heeled shoe was produced, or when the first green wooden toy car was made. Perhaps these two would be easier to establish than the whereabouts of the first RF structures. There are two main reasons for this: the first is that very few people describe these structures as reciprocal frames;the second is that the idea is very old and the historic structures that adopted RF principles were mainly built of timber (well before steel and concrete were known to humankind), which deteriorated over the centuries or were lost in fires. Finding written documentation is not easy either, because of the absence of a common name for them.

Still, despite these difficulties which prevent us establishing where the first ideas about using structures like the RF originated, we can easily demonstrate that the RF principle has been around for many centuries.

Structures such as the neolithic pit dwelling (Figure 2.1), the Eskimo tent, Indian tepee (Figure 2.2) or the Hogan dwellings (Figure 2.3) have some similarities to the RF concept. Perhaps the latter two examples have greater similarities to the RF than the neolithic pit dwelling and the Eskimo tent. Similarly to the RF, the Indian tepee and the Hogan dwellings use the principle of mutually supporting beams. The differences between them and the RF are that the rafters forming the structure of the Indian tepee come together into a point where they are tied together and the integrity of the structure is secured in that way. Stretched animal skins provide additional stiffness to the conical form of the tepee. The animal skins have the role of the cladding roof panels used in RF structures, which in a similar way provide a 'stretched skin effect' and give additional stiffness to the structure.

▲ 2.1 Neolithic pit dwelling. (Sketch by A. E. Piroozfar.)

▲ 2.1 Neolithic pit dwelling. (Sketch by A. E. Piroozfar.)

▲ 2.2 Indian tepee. (Sketch by A. E. Piroozfar.) ▲ 2.3 Hogan dwelling. (Sketch by A. E. Piroozfar.)

The Hogan dwelling looks, in plan, very much like a complex RF structure consisting of a large number of single RFs being supported by a larger diameter RF structure, which in turn is inserted into and supported by an even larger RF. This configuration of a semi-regular form of the Hogan timber structure forms a domed roof. In most cases the Hogans are covered with mud, which not only provides a better internal climate, but also 'glues' the timber rafters together and creates a stable structural form.

Greater similarity to RFs can be seen in the later development of structural forms such as medieval floor grillages, Honnecourt's planar floor grillages, Leonardo da Vinci's structural sketches, as well as Sebastiano Serlio's and Wallis's RF-like structures.

As stated earlier, it is very difficult (if not impossible) to establish where the first RF structure was built. It is very likely that more than one civilization used structures similar to RFs. However, the only written data about structures similar to the present form of RFs can be found in Japan. There is evidence (Ishii, 1992/3) that in the late twelfth century the Buddhist monk Chogen (1 121-1206) established a technique of spiral layering of wood beams which was used in construction of temples and shrines. Unfortunately, no buildings remain that have been constructed in this way. The timber structures have been destroyed by fires, wars or lost due to decay. It is important,though, to stress that the technique which Chogen used is identical to the structural principle of the RF, and it has been used as a roof structure on other, more recent buildings in Japan. These will be presented in detail through the case studies of Japanese contemporary RF buildings later in this book.

The geometric forms of these temples in plan are reminiscent of the mandalas used in Buddhist meditation as symbols of divinities, thus the name 'mandala dach' (mandala roof) has been used for the RF in Germany. 'Mandala' is a Sanskrit word meaning 'magic circle' (Gombrich, 1979) and it is a geometric pattern which includes circles and squares arranged to have symbolic significance. They are one of the oldest religious symbols, and can be found as painted decoration on ceilings in religious buildings such as Tun-huang in China.

The role of the mandala in meditation is described by Auboyer (1967, p. 26) in the following manner: 'The one who meditates on a mandala must "realize" through meditative effort and prayer the divinities belonging to each zone. Progress is toward the centre, at which point the person meditating attains mystical union with divinity.' On studying the form of the RF, it can be noted that the beams of the structure focus towards the central polygon which frames the sky or heaven to echo the role of the mandala. Some examples of mandalas are presented in Figure 2.4.

If we look at the history of Western architecture, it is evident that in medieval times most buildings were constructed with timber floors. The smaller buildings (such as houses and farm buildings) were built mainly in timber, whereas the more important buildings (such as churches or palaces) were built in stone (walls), with timber floors used to span between the walls and create the different levels in the building. As the

▲ 2.4 Mandala geometry. (Sketch by A. E. Piroozfar.)
▲ 2.5 Typical medieval floor grillage configuration. (Sketch by A. E. Piroozfar.)
Planar Grillage
▲ 2.6 Honnecourt's planar grillage assembly. (Sketch by A. E. Piroozfar.)

buildings became bigger and had larger rooms, there was a need for timber that could span greater distances. Often, these great timbers had to be brought from far away but when this was not possible alternative floor designs were investigated. It is likely that in such circumstances a solution for spanning distances longer than the available beams was devised in the form of a beam grillage. Medieval floors were sometimes supported on four beams, all shorter than the span.This was also a common configuration for the framing of stairwells, as shown in Figure 2.5 (Chilton, Choo and Yu, l994).These structures were usually planar grillages, but examples of three-dimensional structures can also be found. It is interesting that this 'medieval grillage structure' works in a similar way to the RF. It is actually a flat version of an RF with inner connections that transfer moments, as explained in more detail in the section of this book dedicated to structural behaviour (see Chapter 5).

One such medieval architect, Villard de Honnecourt, who studied the construction of great churches such as Cambrai, Rheims and Laon, and may even have been in charge of their building, provides us with information on how to deal with the problem of beams shorter than the span, or as he puts it: 'How to work on a house or tower even if the timbers are too short' (Bowie, 1959, p. 130).

Honnecourt gives no information on the spans he had in mind or where this solution has been applied, but some other authors do. Honnecourt's solution to this problem (presented in Figure 2.6) is a planar grillage and it adopts similar principles to the RF. If four beams in an RF were arranged so that they have no slope, and, instead of being placed on top of each other, if they were arranged and connected in the same plane, we would get Honnecourt's configuration.The difference is that an RF (with inclined members) transfers loads through compression in each member, whereas the flat configurations do not.

Honnecourt's sketches were made in the period 1225-1250. This indicates that these types of structure have been known for a very long time.

Although a great deal of research has been done on cathedral architecture, there is very little data on functional carpentry. This is perhaps because,as Hewett (1974, p. 9) stated,'.. .the roofs were normally hidden above stone vaults and only accessible with difficulty in darkness and dirt.'

There is evidence that flat configurations of structures similar to the RF have been used for polygonal chapter house roofing. An example of this is the chapter house at Lincoln, designed by Alexander and built in the period 1220-1235. The roof, which is of a puzzling complexity, encloses the ten-sided regular polygonal plan of the chapter house.'It is a real master work, which comprises of two parts - the lower a "gambrel"-type decagonal structure, and the higher part, which restored the roof to a fully pyramidal form ...' (Hewett, 1974, p. 74), as presented in Figures 2.7 and 2.8.

They are actually two superimposed queen-post assemblies set inside a pitched roof with a king post. The RF-like structure is at the base of the

▲ 2.7 Roof of the chapter house at Lincoln cathedral - 3D view. ▲ 2.8 Roof of the chapter house at Lincoln

(Sketch by A. E. Piroozfar.) cathedral - plan view. (Sketch by A. E. Piroozfar.)

▲ 2.7 Roof of the chapter house at Lincoln cathedral - 3D view. ▲ 2.8 Roof of the chapter house at Lincoln

(Sketch by A. E. Piroozfar.) cathedral - plan view. (Sketch by A. E. Piroozfar.)

roof, which was built of softwood (pine) and mainly held together by ironwork and forelock-bolts. It would have been better for the radial extension and shearing stresses to which the structure is subjected if it had been constructed from timber of higher quality, but it seems that cost was the reason behind the choice. This part of the roof structure is actually identical to a flat RF, and was probably used for the first time in roofs for polygonal spaces. Hewett describes it as 'ingenious' and says that '.. .the construction of the essential "ring-beam" secures the inner ends of the ten radiating ties and it is possibly the architect's invention' (Hewett, 1974, p. 81). Figure 2.8 shows the plan of this structure.

Two hundred years later, Leonardo da Vinci (1452-1519), known as one of the greatest of Renaissance thinkers, who conducted studies in physics, anatomy, medicine, astronomy, fortification, canal-making, architecture and engineering, was also interested in structures very similar to the RF (Richter, 1977). His sketch in Volume I of the Codex Madrid (Figure 2.9) shows a planar grillage of four beams, identical to the main grillage structure proposed by Honnecourt (Figure 2.6). Leonardo also explored assemblies of beam grillages, which are presented in his sketches of the Codex Atlantico, as shown in Figures 2.10a and b.

Vinci Grid Method Construction
▲ 2.10 (a) and (b) Sketches of grillage assemblies by Leonardo da Vinci. (Sketches by A. E. Piroozfar.)

Leonardo da Vinci also made drawings of arched forms created by using short timbers for his bridge designs. Examples of these are the 'temporary bridges' (Anon, 1956), originally presented in Codex Atlantico (Figure 2.1 1a, b). They are constructed from relatively short timber

▲ 2.9 Flat beam grillage by Leonardo da Vinci. (Sketch by A. E. Piroozfar.)

beams which support and are being supported by each other. The three-dimensional structure is actually formed of two mutually connected two-dimensional arches built from the short timber beams.These types of bridges are known to be used in Chinese traditional architecture. A similar contemporary example is the bamboo pedestrian bridge in Rio de Janeiro, presented in Figure 2.12.

Leonardo's arched beams are very similar to the ring beam at the chapter house of Lincoln cathedral. The only difference is that the latter is a whole circle ring beam, whereas Leonardo's bridges are created by beams that form a segmented arch. Both structures, to some degree, are similar to an RF.

Kazuhiro Ishii 1992
▲ 2.11 (a) and (b) Leonardo da Vinci's proposals for temporary bridges. (Sketches by A. E. Piroozfar.)

Another planar grillage was proposed in the Renaissance period by the Bolognese painter and architect Sebastiano Serlio. In 1537, Serlio published a prospectus for a treatise on architecture in seven books, and in the fifth book he proposed a planar grillage for a '... ceiling which is fifteen foot long and as many foot broad with rafters which would be fourteen feet long ...' (Murray, 1986, p. 31). He notes that 'the structure would be strong enough' (Serlio, 1611, p. 57). In the fourth book, tenth chapter, Serlio makes two sketches for door frames which are also planar grillage

Structure Serlio

▲ 2.13 Serlio's solution for a 15-foot ceiling. (Sketch by A. E. Piroozfar.)

▲ 2.13 Serlio's solution for a 15-foot ceiling. (Sketch by A. E. Piroozfar.)

structures. Serlio's planar grillages are very similar to Honnecourt's solution for spanning long distances with shorter beams. Figure 2.13 shows Serlio's idea.

Less then a century later (1699), John Wallis described the inclined and planar grillage assemblies he had studied in his Opera Matematica. In 1652-53, while lecturing at King's College Cambridge, he built physical models of grillage structures.Wallis investigated how to span longer distances with elements shorter than the span by looking at three- and four-beam RF assemblies that had sloping beams. The multiple grillages were planar assemblies (Figures 2.14 and 2.15). It is not clear from his writings whether these structures were built on a large scale at the time, going beyond the small-scale physical models that he used for teaching and exploring the geometrical and structural principles. It is very likely that Wallis was only a scientist and researcher, fascinated by these structures which he explored in great detail, and that he was never involved in scaling them up and using them in real building structures. Despite that, his contribution is of great importance because he was the first to describe the geometry of flat grillages and to study their structural behaviour. Wallis's Opera Matematica is the first known written document exploring the load transfer of the structure.

Wallis also explored the different planar morphologies of grillages and worked out their geometry in order to study load paths through the structure. The assemblies are constructed by connecting elements which are notched and fitted into one another. The structures that

▲ 2.14 Three- and four-beam RF assemblies. (Sketch by A. E. Piroozfar.)
Kazuhiro Ishii 1992
▲ 2.15 Planar morphology of grillage structures. (Sketch by A. E. Piroozfar.)

Wallis studied are very similar to Leonardo's grillage assemblies. Some examples that he studied are presented in Figure 2.15.

Other interesting historical examples of flat grillages are presented in the atlas, Traite de L'art de la Charpenterie, written by A. R. Emy, who was a Professor of Fortification of the Royal Military School, Saint-Cyr, and a member of the French Royal Academy of Fine Arts. It was published in Paris in 1841. Unfortunately, the book gives no information in the text about where these structures (presented in Figure 2.15a and b) were used, and the spans and sizes of the elements involved. Nevertheless, it represents further evidence of the long-term historical development of grillage structures.

Metal Stud Framing Basics

▲ 2.16 Example of a grillage structure (a) over a square plan and (b) over a circular plan. (Sketches by A. E. Piroozfar.)

▲ 2.17 Flat grillage by Serlio. (Sketch by A. E. Piroozfar.)

Thomas Tredgold, in his book Elementary Principles of Carpentry, devotes a whole section to 'Floors constructed with short timbers'. It is interesting to note that Tredgold (1890, p. 142) describes these ceilings as '... structures which can not be passed over without notice and yet are scarcely worthy of it . . .' and as '. . . more curious than useful . . .' because they are seldom applied. They are only useful when the timber is not long enough. He describes the 'Serlio-type ceiling' and gives another example designed by Serlio (Figure 2.17), as well as the research done by Dr Wallis. The main difference between the structures that Tredgold describes and the RF is that they are planar grillages in which the members are joined by mortises and tenons.

Several three-dimensional grillage structures that have a greater similarity to the RF were constructed in the twentieth century. These include the roofs at Casa Negre, San Juan Despi, Barcelona (1915) and Casa Bofarul, Pallararesos, Tarragona (1913-18), both designed by the Spanish architect Jose Maria Jujol (Flores, 1982). Inspired by Gaudi's architecture of spiral forms, such as the ceiling of Casa Battlo, Jujol designed roof structures of mutually supporting and spiralling beams. In both buildings the structures used are identical to the RF.

▲ 2.18 Mill Creek Public Housing Project In Philadelphia 1952-53 - plan view. (Sketch by A. E. Piroozfar.)

The floor structure used in the Mill Creek Public Housing Project in Philadelphia, designed in 1952-53 (Figure 2.18) by the architect Louis Kahn, used a four-beam planar grillage in the high-rise buildings (Scully, 1962). The main advantage of using the planar grillage in this housing project is the avoidance of columns within the plan, which consequently made it easier to plan the spatial organization of the spaces. The span is 15 metres. The configuration is identical to a planar medieval four-beam grillage. Unfortunately, this project was never realized.

▲ 2.19 Salt storage building in Lausanne in Switzerland. (Sketch by A. E. Piroozfar.)

A more recent planar grillage structure is the roof of a salt storage building at Lausanne in Switzerland (Figure 2.19). Eleven tapered,glulam

▲ 2.18 Mill Creek Public Housing Project In Philadelphia 1952-53 - plan view. (Sketch by A. E. Piroozfar.)

Planar Grillage

▲ 2.19 Salt storage building in Lausanne in Switzerland. (Sketch by A. E. Piroozfar.)

beams are used to cover the regular polygonal plan of this building, which has a span of 26 metres (Natterer, Herzog and Volz, 1991).

▲ 2.20 Langstone Sailing Centre - section through the interlocking timber structure. (Sketch by A. E. Piroozfar.)

Another design using a similar structure to the RF is the roof of the Langstone Sailing Centre, constructed in April 1995 (Figure 2.20). Influenced to a great extent by traditional shipbuilding technology, the Hampshire County Architect's concept was to produce a 'locked chain' effect for the roof. By use of a series of physical models, Buro Happold, who were the engineers for the project, studied the structural and geometrical implications. The roof structure is constructed of pairs of interlocking pitched pine timber members which span 10.5 metres. The members are connected by shear plate connectors hidden neatly by oversized washers. An extremely high degree of accuracy was necessary because single bolts passed through up to eight shear plate connectors and the clearance in the holes was only 2 mm (The Structural Engineer, 1995).

Both the Langstone Sailing Centre roof structure and Leonardo's temporary bridges are assemblies of simply supported interlocking beams, which means in practice that both types of structure 'work' in the same way. It is interesting to note that the structure has been referred to as 'unique' (The Structural Engineer, 1995, p. 3), although the structural principle is identical to Leonardo's structures.

More recent RF buildings that have been innovative in their use of the RF principle and integrated it architecturally in the design will be described and analysed in detail through the work of Japanese and UK designers presented later in this book. The projects present a detailed account of the design process for each scheme, as well as describing their designers' vision. Often, through the interviews with the designers (architects and engineers) and clients, the missing links which help us to

▲ 2.20 Langstone Sailing Centre - section through the interlocking timber structure. (Sketch by A. E. Piroozfar.)

▲ 2.21 Hans Scharoun's Berlin Philharmonic reinforced concrete RF. (Photo: Peter Blundell-Jones.)

understand how and why the RF was integral to the particular design project have been established. The reciprocal frame projects include the work of Japanese designers: architect Kazuhiro Ishii with his designs for the Spinning house, Seiwa Burnaku Puppet Theatre and the Sukiya Yu house; architect Yasufumi Kijima with his design of the Stonemason Museum; and engineer Yoichi Kan with Torikabuto, the Life Sciences Laboratory. In addition, the work of UK designer, Graham Brown, who was the first to name the reciprocal frame, is presented through his designs for the Findhorn Foundation whisky barrel house and Colney Wood burial park buildings. Also, at the end of the book several recently constructed RF buildings are presented.

This account has presented only some of those structures that have been built in the past and which have some similarities to the RF. They are by no means the only examples. RFs and structures similar to them have been built by many cultures throughout history. If one tried to include all these structures the list would be beyond one book. Still, one ought to mention Hans Scharoun's Berlin Philharmonic reinforced concrete RF (Figure 2.21), the multiple grids by Gat (Figure 2.22), the Rice University bamboo canopy by architect Shegiru Ban and engineer Cecil Balmond (Figure 2.23), as well as the work of many researchers such as John Chilton, Vito Bertin, Messaoud Saidani, Olivier Baverel, Joe Rizotto and many others. The research work will be presented in more detail in the geometry and morphology chapters of this book.

Multiple Grids Gat
▲ 2.23 Rice University bamboo canopy by architect Shegiru Ban ▲ 2.22 Multiple grids by Gat. (Sketch by A. E. Piroozfar.) and engineer Cecil Balmond - detail. (Sketch by A. E. Piroozfar.)

This section shows that the inspiration to use RFs and similar structures in buildings has come from many different sources. Although scattered all over the world, they all contribute in their own way to the unique language of RF architecture, forming stepping stones in its history.

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