Connection systems in reciprocal frames and mutually supported elements space structure networks pdf
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- A Form-Finding Instrument for Reciprocal Structures
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- Reciprocal Frames in Temporary Structures: An Aesthetical and Parametric Investigation
Metrics details. This paper investigates the relationship between the formal and informal spheres of urban life and explores the change in the relation between them. Starting with a study of the evolution and different interpretations of the spatial concept of informality, we moved from a perspective based on the traditional dichotomies to concentrate on the relations between formal and informal. In this intermediate space the presence of these two dimensions can sketch out spheres of action and foster the emergence of different perspectives from an urban, cultural, social and economic viewpoint.
A Form-Finding Instrument for Reciprocal Structures
Reciprocity is a structural principle that has fascinated designers and builders throughout the world since ancient times. Further, no single text provides an exhaustive definition of the principle of structural reciprocity and it must be critically reconstructed from several different sources.
This paper aims to fill in these gaps, providing a complete and annotated list of references, in which historical examples, as well as patents, research articles and terminological issues are discussed. A consistent definition of structural reciprocity is also proposed, and the promising developments of such a principle are outlined in order to guide designers and researchers in the future. The principle of reciprocity is based on the use of load-bearing elements which, supporting one another along their spans and never at the extremities, compose a spatial configuration with no clear structural hierarchy.
An illustrative example will help the reader better understand the concept. Let us consider three glasses, arranged on a table at the vertices of a hypothetical equilateral triangle, and then imagine covering that area using just three kitchen knives. Considering that the glasses are the only supports, the knife handles should first be placed over the glass openings, and the blades should be made to overlap one another, like a fan.
The resulting configuration is the simplest reciprocal structure made of three elements Fig. Such a system has been used throughout the world since ancient times. However, a comprehensive, annotated list of references regarding them has not been developed yet.
It is an explicit aim of this essay to respond to these needs by proposing a critical overview of the topic supported by: 1 an annotated list of references in both Western and Eastern cultures; 2 a complete lists of patents on reciprocity; 3 a complete list of publications grouped by topic; 4 a complete and annotated list of scientific terms coined and used by different authors; 5 a consistent definition of structural reciprocity; 6 several future research and design directions based on the current state of the art.
The first applications of structural reciprocity date back to Neolithic pit dwellings, Eskimo tents and Indian tepees, as documented by Popovic Larsen However, it was also present during the Roman Empire, when Julius Caesar used it for the construction of a bridge over the Rhine: the structure was made of interlocked timber elements, with the main purpose of simplifying the joints.
Apart from these ancient applications, independent from one another, reciprocity has been independently studied and used in both Western and Eastern cultures for centuries. The needs and purposes have been different, but the structural outcomes have been similar. During the last few decades, reciprocity has also become a research topic for academics, who have started to study the mechanical, geometrical and construction aspects of reciprocal structures.
In Europe, structural reciprocity has mainly been used, at least until the twentieth century, to span distances longer than the length of the available timber beams.
Footnote 1. Several architects, builders, mathematicians and scientists all reasoned separately about this problem, without evidence of being in contact with one another. Footnote 2 Between and , Villard de Honnecourt drew some short-beam arrangements in his sketchbook Villard de Honnecourt for the construction of reciprocal floors.
Between and , Alexander of Lincoln designed and built Lincoln Cathedral using reciprocal supports, as reported by Hewett Leonardo da Vinci explored at least six different spatial configurations based on the principle of reciprocity, as can be seen from his sketches in the Codex Atlanticus , folio v Leonardo da Vinci Fig.
To read the transcription of this page, refer to Williams The reciprocal systems represented by Leonardo are redrawn in b — h. Continuous lines are used to represent the working parts of the arrangements, which are clearly drawn and reproducible with physical models. Hatches are then used to identify parts of the structures which were meant to be clad. Image elaboration: authors.
After Leonardo, Sebastiano Serlio discussed the construction of planar floors with short-beams in his first book on architecture, but unfortunately proposed an unbuildable structure Serlio ; Yeomans It was finally described by Rondelet and Tredgold As we mentioned before, reciprocal structures were used in Europe for technological and construction reasons. Recent surveys and renovations of old British buildings seem to confirm this statement. The layout of the sub-floor structure of the Wollaton Hall Fig.
They were clearly conceived not to be seen as the photograph of the finished ceiling does not refer anyhow to its reciprocal nature Fig. The same happens at the home of William Morris, Kelmscott Manor, where the presence of reciprocal beams in the sub-floor structure was only revealed during the most recent works of restoration Insall , Fig.
A unique example that contradicts such logic can be found at Palazzo Piccolomini in Pienza. Wollaton Hall, sub-floor structure survey. This layout shows an irregular pattern of timber short-beams which was clearly conceived not to be seen. Wollaton Hall, ceiling. The reciprocal arrangement of sub-floor timber beams is not visible as it was clearly conceived to solve a construction matter.
Photo: Peter Langley, reproduced by permission. Sub-floor structure of the William Morris house Kelmscott Manor during the most recent renovation works. This reciprocal arrangement of timber beams was clearly due to structural and construction reasons, as the carpentry was not designed to be exposed. Photo: Donald Insall, reproduced by permission.
The reciprocal arrangement of timber beams appears to be purely decorative and designed to be seen. Such a room is one of the smallest of the Palazzo.
However, it is the only one using short-beams to span a relatively short distance. Photo: Il Cenacolo srl, Rome, reproduced by permission. In Eastern culture, interest in reciprocal structures derives from two separate concepts.
Unfortunately, written documents concerning this practice are only found after the year , i. A few contemporary Asian architects, such as Kazuhiro Ishii Fig. Photo: Kentaro Tsukuba, reproduced by permission. Even though structural reciprocity has not had a linear history, and the evidence of its use seems to be fragmented, a main point in common in both Western and Eastern cultures is the use of timber as a construction material. In Europe, this occurred for functional reasons, with the aim of developing flat configurations.
In Asia, designers were mainly guided by spiritual considerations in the construction of 3D structures, which recalled symbolic shapes. In this historical framework, Leonardo da Vinci was the only one in the West to study the potential of elaborating reciprocal structures as complex 3D geometries Leonardo da Vinci It was John Wallis who first approached structural reciprocity scientifically, like a modern research topic Wallis ; Houlsby Over the last century, the principle of reciprocity has continued to stimulate the interest of designers and, for the first time, has become a topic of interest in the field of scientific research.
The first was the lamella construction system by Zollinger with reciprocal joints, which has been described in detail by Popovic Larsen Superimposition of bars allows and controls the kinematic movement of the assembly Images: United States Patent and Trademark Office, reproduced by permission.
The German engineers Erwin Walle and Sigurd Prinz patented a reinforced concrete ceiling made of prefabricated units hinged together, which curiously recalls the reciprocal slabs designed by Kahn for the Mill Creek public housing project in Philadelphia, dated — The patent was filed in and then published in three different parts.
The building element for the construction of interlocking grids patented by Gat is also worth mentioning. This was actually the first work to be also published as an article in a scientific journal Gat Footnote 3 However, it was the 3D closed circuit of sticks patented by Graham Brown that definitively inspired and kick-started academic research on structural reciprocity.
Chilton a , b , including the Ph. Structural reciprocity is a very extensive research topic, and has been approached from very different points of view. Considering the works of architecture realized over the last century, we find several unrelated examples that have implemented structural reciprocity. Long spaces were spanned with short beams in the Mill Creek Public Housing project, designed by Louis Kahn in —, but also in the Berlin Philarmonie by Hans Scharoun, which was built in —, and in a salt storage building in Lausanne, built by Atelier Gamme Architecture in Natterer et al.
In order to introduce spiritual philosophies into shapes, reciprocity was used in the Casa Negre by Josep Maria Jujol in —, Fig. Casa Negre, by Josep Maria Jujol. One of the few European examples of a reciprocal structure conceived for aesthetical purposes. Photo: Jaime Segura, reproduced by permission.
In the field of industrial design, Pino Pizzigoni realized reciprocal chairs and tables made of timber and marble elements. Two examples can be seen in Figs. Shifting to art, the sculptor George Hart used reciprocity to create simple geodesic domes. Some of his projects are actually impracticable and are therefore just rendered as drawings or prototyped though 3D printing techniques.
Chair for a Pedrini collection, designed by Pino Pizzigoni, Scanned by Carlo Deregibus and Alberto Pugnale, reproduced by permission.
Table prototype designed by Pino Pizzigoni, However, reciprocity differs from mutuality because a transitive relation between at least two elements occurs only if such a relation is perfectly symmetric.
The concept of structural reciprocity therefore refers to a specific subset of structures, which are characterized by two main properties.
First, in each and every element the functions of supporting and being supported by other elements must be separated instead of being overlapped. For instance, in simply supported beams constraints are placed at the extremities and loads act at the midpoints—the functions correspond to different position on the element and no inversion is possible. In contrast, constraints and loads both occur at the ends of truss bars—so the functions overlap here and the definition of supporting and supported ends becomes merely conventional.
This first property also implies that only beams and two-dimensional elements can form a reciprocal structure. The forces are transferred through bending and shear with beams, both in-plane or out-of-plane for 2D components. Second, each and every element must be supported by the other one it supports.
As stated above, a perfectly symmetric relationship is needed to distinguish a reciprocal structure from a simply mutual one. An example will be helpful here. Let us consider the beam arrangements shown in Fig. In Fig. This system is not reciprocal because the supporters and those being supported are not the same: beams B are supported by beams C, while they sustain, instead, beam A.
Such circularity allows us to state that beam B is, at the same time, supported by and supporting beam A. In sequential systems, the positions and roles of the members are related, while in loops the concepts of beginning and end do not exist, and the positions of the elements are totally interchangeable.
Footnote 4. The relationship between elements in mutual and reciprocal structures: a left antisymmetric, which can be found in the Sindone chapel by Guarini; b right symmetric, which corresponds to the arrangement of the Puppet Theatre by Ishii see Fig. The drawings are schematic and not to scale. Images: authors.
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Collective intelligence Collective action Self-organized criticality Herd mentality Phase transition Agent-based modelling Synchronization Ant colony optimization Particle swarm optimization Swarm behaviour. Evolutionary computation Genetic algorithms Genetic programming Artificial life Machine learning Evolutionary developmental biology Artificial intelligence Evolutionary robotics. Reaction—diffusion systems Partial differential equations Dissipative structures Percolation Cellular automata Spatial ecology Self-replication. Rational choice theory Bounded rationality. Systems theory is the interdisciplinary study of systems , which are cohesive groups of interrelated, interdependent parts that can be natural or human-made. Every system is bounded by space and time, influenced by its environment, defined by its structure and purpose, and expressed through its functioning. A system may be more than the sum of its parts if it expresses synergy or emergent behavior.
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In this paper, the reciprocal frame constructions are analyzed, starting from When it comes to combining elements, RF structures have been used for RF structures need a precise spatial definition when free or irregular forms are French architect Villard de Honnecourt  gave a solution based on a mutually supportive.
Reciprocal Frames in Temporary Structures: An Aesthetical and Parametric Investigation
Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. Chilton Published Engineering. Although the structural principle of closed circuits of mutually supporting beams was known by Leonardo Da Vinci and has been used for hundreds, if not thousands of years Popovic Larsen  , its rediscovery and renaming as the Reciprocal Frame, by the designer Graham Brown in , has led to more structures of this type being built in the UK over the last 20 years. Save to Library.
Reciprocity is a structural principle that has fascinated designers and builders throughout the world since ancient times. Further, no single text provides an exhaustive definition of the principle of structural reciprocity and it must be critically reconstructed from several different sources. This paper aims to fill in these gaps, providing a complete and annotated list of references, in which historical examples, as well as patents, research articles and terminological issues are discussed. A consistent definition of structural reciprocity is also proposed, and the promising developments of such a principle are outlined in order to guide designers and researchers in the future. The principle of reciprocity is based on the use of load-bearing elements which, supporting one another along their spans and never at the extremities, compose a spatial configuration with no clear structural hierarchy.
Reciprocal frame structures: a systematic literature review and identification of critical points for design and production. Reciprocal Frame Structures RFs date from the Neolithic period, where they were originally produced in wood and comprised of small sized elements. It is also a structural system that can adapt to freeform and complex geometries, with great aesthetic potential, as indicated by several contemporary research studies. However, these structures could make better use of the digital technologies available for design, analysis, manufacturing and assembly. This paper aims to identify the current gaps where research efforts focus on in order to make RF technology more viable.
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