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A Review of Woven Structures with Focus on Reciprocal Systems - Nexorades
Abstract and Figures
The main aim of this paper is to present the different types of load-bearing woven systems that stand by friction or with the use of a locking device. Areview of the different types of systems has been done and an attempt of classification has been proposed. The paper focuses on the different types of elements that can be used to create reciprocal systems or nexorades. Configurations with elongated, ring, tile and block elements are shown. The different parameters that define such structures are also presented. Although the description of the parameters is quite easy for simple construction, a broader approach is still needed to be done for more complex configurations.
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... Bu strüktürlerin çoğunluğu herhangi bir sabitleme olmadan sadece sürtünme ile ayakta durabilmektedirler. (Baverel ve Larsen, 2011). Tekstil tekniklerinin bina ölçeğine uyarlanmasında çivi, vida, cıvata gibi ek bağlantı elemanları olmadan uygulanabilir olmaları pek olası olmayacağı düşünülmektedir (Weinand ve Hudert, 2010 • Zorunlu etkileşimin oluşması için en az iki eleman olmalıdır. ...
... Bunların dışında en önemli noktalardan biri de karşılıklı çerçeve strüktürleri oluşturan elemanlar strüktürün tamamına oranla daha kısa ve süreksiz elemanlardır (Baverel ve Bu belge güvenli elektronik imza ile imzalanmıştır. Larsen, 2011). Karakoç'un (2017) ifadesiyle bu sistem ''kısa kiriş örgüleriyle geniş açıklıklar geçme'' prensibine sahiptir. ...
... Belirtilen parametrelerin değişimi ve ünitelerin bir araya geliş şekliyle farklı ızgara düzenleri ve strüktürel kurgular elde etmek mümkündür. ''Eğer ünite dönüşü saat yönünde ise ''sağ fan'', eğer dönüş saat yönünün tersinde ise ''sol fan'' denilmektedir'' (Baverel ve Larsen, 2011). Ünite düzenleri elemanların üst ya da aşağı gelme durumlarına göre de farklılaşır ve aşağı yönlü ya da yukarı yönlü olarak ifade edilebilir. ...
Reciprocal frame structures can be defined as systems consisting of discontinuous short beams, where there is no primary/secondary load-carrying distinction between elements such as columns and beams. In this study, where timber reciprocal frame structures are examined, the subject is handled through connection details. The aim is to determine the distinguishing features of reciprocal frame structures from other construction systems, to examine the connection details of the elements in timber reciprocal frame structures and to discuss the parameters affecting these details, to analyze and compare the nodal point solutions in pavilion structures built with these structures, and to put forward a study that can be a guide in the Turkish literature. In the literature section where a comprehensive review research was conducted, information about timber reciprocal frame structures was provided. In the analysis study, 7 examples of pavilions built between 2012-2019, which were obtained by scanning from written and visual sources such as magazines, books, articles, papers, theses, internet, etc., were analyzed. The examples were analyzed and evaluated through the general information of the building, grid layout and connection point, and the table created from various subheadings within the scope of these titles. As a result of the study; it is thought that one of the main factors in detail solutions is the type and form of module element in the grid layout, while other data such as engagement length, number of layers, cover element are secondary data affected by the form of element type. It has been seen that the advantages and disadvantages provided by various features such as production, rigidity, assembly and disassembly, reuse, aesthetic appearance of the connection detail have an important place in the formation of the structure.
... El concepto de apoyo mutuo o tangencia entre barras, definitorio de este tipo de estructuras, las incluye dentro del grupo de sistemas estructurales fuera del plano o sistemas espaciales. Se enmarcan en el ámbito de las estructuras entretejidas (como el punto, los textiles o la cestería) (1). Este tipo de sistemas se caracteriza por la carencia de elementos de unión entre sus componentes, reduciendo al rozamiento interno de sus uniones su capacidad de estabilización. ...
... Denotamos por la distancia entre los puntos de apoyo y de soporte de cada barra componente del Nodo, medida sobre su directriz (longitud de entramado). Para determinar la localización de los diferentes puntos de tangencia, consideramos vectores unitarios ortogonales a las barras dos a dos (vectores binormales) de modo que el vector es el ortogonal a las barras el vector es el ortogonal a las barras y el vector es el ortogonal a las barras lo que puede exprese matemáticamente por: [1] para toda permutación positiva (i, j, k) de (1, 2, 3). La condición de reciprocidad implica que la suma (vectorial) de las distancias de entramado entre barras en la dirección de sus ejes más las excentricidades entre barras (2R) en la dirección de los vectores binormales entre ellas, se anula (circuito cerrado de barras tangentes). ...
... Las ecuaciones [1][2][3][4][5] son generalizables a Nodos de más de tres barras, sin embargo, en estos casos, no se puede determinar la relación existente entre las distancias de entramado y los ángulos entre direcciones de apoyo mutuo como se ha hecho en [6]. No obstante, en el caso particular de los Nodos regulares, podemos proceder analíticamente a la deducción de toda su geometría a partir de la inclinación de dichas direcciones de apoyo en relación con el plano de tangencia. ...
En este artículo, se aborda la determinación de las condiciones de equilibrio de Superficies de Geometría Variable definidas por Estructuras Recíprocas mediante el estudio de un campo de fuerzas actuantes y del lugar geométrico que describen los elementos de tales estructuras a través de los diferentes estados de transformación. Se establecen las propiedades geométricas y estructurales de un Nodo Recíproco de estas estructuras con tres barras cilíndricas iguales, mediante el desarrollo de una formulación matemático-paramétrica, con el objetivo de deducir el proceso de equilibrio para la obtención analítica de sistemas de estabilización de Superficies de Geometría Variable conformadas por Estructuras Recíprocas Transformables. La finalidad de la investigación presentada aquí es la aplicación de dicho sistema de estabilización mediante un software geométrico-estructural de nueva creación, al diseño y cálculo de distintas tipologías de superficies en la configuración de arquitecturas de geometría transformable.
... Presently, with the availability of new digital technologies, many researches are exploring RF, bringing a deeper knowledge and a more scientific approach to it. One of the main interests is the possibility to achieve a higher level of formal complexity by using simple linear or planar elements with short dimensions (BAVEREL; LARSEN, 2011;PUGNALE;SAS-SONE, 2014;MESNIL et al., 2018). Hereby lies the sustainable approach of RF structures, since its components take better advantage of timber, reducing material waste, on top of wood being a renewable material (WINTER; RUG, 1998;GUTIERREZ;FLORES;PRE-CIADO, 2016). ...
... More recently, Araullo (2018) has suggested the term "DNA" as a biological analogy. The spatial configuration generated by the fans implies in overlapping of nexors eccentricity, which refers to the smallest distance between the axis of two connected elements (BAVEREL et al., 2000, DOUTHE;BAVEREL 2009, SÉNÉCHAL;DOUTHE;BAVEREL, 2011, THONNISSEN, 2014, MESNIL et al., 2018. ...
... Presently, with the availability of new digital technologies, many researches are exploring RF, bringing a deeper knowledge and a more scientific approach to it. One of the main interests is the possibility to achieve a higher level of formal complexity by using simple linear or planar elements with short dimensions (BAVEREL; LARSEN, 2011;PUGNALE;SAS-SONE, 2014;MESNIL et al., 2018). Hereby lies the sustainable approach of RF structures, since its components take better advantage of timber, reducing material waste, on top of wood being a renewable material (WINTER; RUG, 1998;GUTIERREZ;FLORES;PRE-CIADO, 2016). ...
... More recently, Araullo (2018) has suggested the term "DNA" as a biological analogy. The spatial configuration generated by the fans implies in overlapping of nexors eccentricity, which refers to the smallest distance between the axis of two connected elements (BAVEREL et al., 2000, DOUTHE;BAVEREL 2009, SÉNÉCHAL;DOUTHE;BAVEREL, 2011, THONNISSEN, 2014, MESNIL et al., 2018. ...
... While in fact, the woven structure includes other systems differentiated by the structural element used in weaving and its material characteristics. The bending resistance of the structural element is the analogical factor of four different types of woven systems starting from the loosest continuous material of 1) knitting, 2) woven fabrics, 3) basket work, to the most rigid systems of 4) reciprocal structure that uses small solid members to build a whole body with a high performance of a low-technology and a lightweight construction [114,115,116]. ...
The separation of architectural learning from bio-inspired design distances students from Nature and blocks them from the main source of inspiration. Such confusion regarding the creative problem-solving process of architectural learning has led to the disappearance of innovative ideas from the majority of architectural students` work. This study aims to improve the productivity of architectural studios by using bio-inspired design as guidance for inspiration and creative thinking throughout the integration of biomimetic structure systems with a conceptual design project for architectural freshmen. The aforementioned objective framed a methodology of two architectural studio experiments managed to outline the effects of mimicking Nature on students` cognition and architecture design productivity. The results showed the contrast between their architectural studio work before and after the integration articulates how much the simulation has enhanced their creative thinking and productivity level.
... It can be viewed as a practical method to reduce the complexity of connections in spatial structures by reciprocally connecting the elements by pairs (Senechal et al. 2011). This structure can be seen as a construction technique to cover large spaces with short elements assembled together with simple connections (Baverel and Popovic Larsen 2011). ...
Deployability of reciprocal frame (RF) structures can aid in the creation of multifunctional architectures, satisfy the needs of flexible architectures, and adapt to climatic and environmental conditions. However, changes in the perimeter of a structure during deployed and retracted states may result in low efficiency in architectural design and limit its architectural applications. The purpose of the present study was to investigate the geometric feasibility of deployable kinetic reciprocal frame (KRF) structures with constant perimeters and fixed support points. This structure can cover constant perimeter without any change while adapting, particularly providing many potential benefits in architectural applications and bridging the gap between two states. The research methodology used in this paper is a design-based examination of the geometry of fixed RF structures. The study’s findings revealed a wide range of KRF structures that can cover various geometric plans using moving elements along a specific path on adjacent elements and rotating them in fixed supports on the outer polygon without modifying
the perimeter during deployment or retraction.
The patterns of many structural systems must fulfil a property of two-colourability to partition their elements into two groups. Such examples include top versus bottom layer of continuous beams in elastic gridshells, corrugated versus non-corrugated directions in corrugated shells or warp versus weft threads in woven structures. Complying with such constraints does not depend on the geometry but the topology of the structure, and, more specifically, on its singularities. This paper presents a search strategy to obtain patterns that fulfil this topological requirement, which represent only a fraction of the general design space. Based on an algebra for the exploration of the topology of quad meshes, including a grammar and a distance, a topology-finding algorithm is proposed to find the closest two-colour quad-mesh patterns from an input quad-mesh pattern. This approach is expressed as the projection to the two-colourable subspace of the design space. The distance underlying the definition of the projection measures the similarity between designs as the minimum number of topological grammar rules to apply to modify one design into another. A structural application on elastic gridshells illustrates how two-colour topology finding can complement workflows for the exploration of structural patterns with singularities informed by the system topological requirements.
Estruturas recíprocas (ERs) são datadas do período neolítico, produzidas originalmente em madeira e compostas por elementos de dimensões reduzidas. Trata-se de um sistema estrutural que apresenta a capacidade de se adaptar a formas livres, complexas e com grande potencial estético, como indicado por diversas pesquisas contemporâneas. No entanto, acredita-se que essas estruturas poderiam fazer melhor uso das tecnologias digitais disponíveis de projeto, análises, fabricação e montagem. Este artigo tem o objetivo de identificar as atuais lacunas em que se pode concentrar esforços de pesquisa no sentido de tornar a tecnologia das ERs mais viável. Foi feita uma revisão sistemática da literatura (RSL) em sete bases de dados diferentes. Encontrou-se um total de 180 artigos, dos quais 49 foram selecionados para análise. Dentre eles, 27 identificaram lacunas existentes, que foram compiladas em cinco categorias: (a) dificuldades na concepção geométrica/estrutural; (b) necessidade de aprimoramento de ferramentas digitais; (c) dificuldade no projeto, análise, fabricação e montagem de conexões; (d) dificuldade de compreensão da real contribuição dos protótipos para aplicações em grande escala; e (e) necessidade de incorporar o processo de montagem no projeto de ERs. Foi possível concluir que o desenvolvimento de novos mecanismos de análise estrutural aliados à criação de novos detalhes construtivos pode contribuir para a expansão do uso das ERs.
شبکه های متقابل چندگانه یا نکسورید از خانواده سازه های فضاکار هستند. این سازه، بر خلاف سیستم های متقابل
تاریخی است، به طوریکه بیان می کند ارتباط بین اعضا نباید تنها به صورت فشرده سازی باشد. بنابراین، می توان موقعیت-
های مربوط به اعضا را تغییر داد و شبکه هایی را با انواع مختلفی از فرم ها، با هندسه مختلف از شبکه های مسطح تا اشکال
منحنی را ایجاد کرد. این سازه در کنار سازه های دیگر می تواند نقش مؤثری ایفا نماید. به طور کلی، مقاله حاضر با هدف
ترویج سازه های نوآورانه، به بررسی مورفولوژی هندسه سازه نکسورید می پردازد. دراین میان، می توان بیان کرد، اهداف
علمی و اقتصادی به وسیله کاربرد سازه های نوآورانه در معماری می تواند محقق شود. به طورکلی، ارائه ایده های بدیع از سوی معماران و طراحان سازه، همراه با نوآوری در طراحی سازه در این عرصه این امکان را فراهم می کند تا با الگوهایی قابل درک و مصالح در دسترس به تلفیق سازه و معماری افزود.
Architects and Engineers are educated and work within two separate cultures yet they are both concerned with conceptual structural design. The collaboration between the professions is especially important when designing buildings where the structure to a great degree forms the spaces, as in the cases of form generating structures such as gridshells, reciprocal frames, space trusses etc. This paper describes several specialist research based workshops developed at KA over the last two years that use physical modelling of 1:1 innovative timber load-bearing structures such as gridshells and reciprocal frames.
The objective of this paper is to discuss the characteristics of a family of space structures that are referred to as 'nexorades'. Typically, a nexorade is constructed from scaffolding tubes, connected together with swivel couplers. An important application of nexorades is for shelters of various sizes and shapes for temporary or permanent purposes. In such a shelter, the structural skeleton is provided by a nexorade and the cover is provided by a membrane material.
The objective of this paper is to propose a simple method using dynamic relaxation algorithm to find the form and perform a structural analysis of reciprocal frame systems, also called nexorades. After a brief historical note, details of the parameters that govern the design of nexorades are introduced together with details of the assembly. These parameters induce strong geometrical constrains on this kind of structures so that a form-finding step is required. It is suggested here to introduce a fictitious mechanical behaviour to solve this problem. The dynamic relaxation algorithm is used with a model that takes into account the eccentricity between the elements. Its implementation is explained and its versatility is illustrated through several examples covering various fields of applications going from form-finding problems to non-linear structural analysis of structures. In a last example the structural behaviour of nexorades is compared with more conventional triangulated structures.
p. 1866-1876 Reciprocal Frame Structures (RF) are a form of a three-dimensional grillage structure. In their simplest configuration they are formed by placing beams in a closed circuit in which each beam is supported by the preceding beam at the inner end, and by an external wall or ring beam on the outer end. In their more complex configurations gridshell-like structures with a double curvature can be formed. Although RFs have been used in many countries throughout history and are known under different names: Serlio-type ceiling; Reciprocal frames, Svastica structures, Nexorades, Lever-arch structures etc., they are not widely known and used in bildings. The most beautiful contemporary examples have been built in Japan. This paper describes and analyses the contemporary Japanese RF examples from the point of view of structural behaviour, geometry, configuration, detailing, materials used and architectural qualities of the buildings.
This book investigates different models of the fourth dimension and how these are applied in art and physics. It explores the distinction between the slicing, or Flatland, model and the projection, or shadow, model. The book compares the history of these two models and their uses and misuses in popular discussions. The book argues that Picasso used the projection model to invent cubism, and that Minkowski had four-dimensional projective geometry in mind when he structured special relativity. The discussion is brought to the present with an exposition of the projection model in the most creative ideas about space in contemporary mathematics such as twisters, quasicrystals, and quantum topology. The book proposes that the powerful role of projective geometry in the development of current mathematical ideas has been long overlooked and that our attachment to the slicing model is essentially a conceptual block that hinders progress in understanding contemporary models of spacetime.
The Reciprocal Frame (RF) is a three-dimensional grillage structure consisting of mutually supporting beams, mainly used in roof construction. The paper presents the research done in developing different possible RF morphologies for a medium span building. The undertaken case study, presented in this paper, shows the potential of the structural system and the great variety of RF morphologies which can be developed. The critical analysis of the solutions as well as the survey of the students' design experiences which were investigated through questionnaires and interviews are also presented. In the end an overview of the potential for most appropriate RF application is outlined.
In this insightful book, which is a revisionist math history as well as a revisionist art history, Tony Robbin, well known for his innovative computer visualizations of hyperspace, investigates different models of the fourth dimension and how these are applied in art and physics. Robbin explores the distinction between the slicing, or Flatland, model and the projection, or shadow, model. He compares the history of these two models and their uses and misuses in popular discussions. Robbin breaks new ground with his original argument that Picasso used the projection model to invent cubism, and that Minkowski had four-dimensional projective geometry in mind when he structured special relativity. The discussion is brought to the present with an exposition of the projection model in the most creative ideas about space in contemporary mathematics such as twisters, quasicrystals, and quantum topology. Robbin clarifies these esoteric concepts with understandable drawings and diagrams. Robbin proposes that the powerful role of projective geometry in the development of current mathematical ideas has been long overlooked and that our attachment to the slicing model is essentially a conceptual block that hinders progress in understanding contemporary models of spacetime. He offers a fascinating review of how projective ideas are the source of some of today's most exciting developments in art, math, physics, and computer visualization.
Practical and material orientated academic research has become increasingly important for architectural practice, due to several factors. First, it contributes to contemporary concepts in architecture and improves their implementation. Today’s architects are looking for a deeper understanding of technical and technological questions related to architecture: technology, construction methods and structural considerations are no longer seen as merely bothersome necessities, as was often the case in the past. The importance of such aspects and the potential of including them as active stimuli in the architectural design process are largely recognised. It is the limitations in time and capacities that more often than not confound the realisation of such ambitions. Academic research can fill this gap and provide architectural practices with the necessary resources. Second, research has a duty to address one of the biggest architectural challenges of our time, namely how to achieve sustainable building. Society’s burgeoning awareness of the urgent need to use renewable materials for building construction is an undeniable reality and has become an important parameter for architectural production. As a result, timber constructions experience a new popularity and the importance of research on timber has increased. The potential of this field becomes evident with some of its latest developments and innovations. Cross- laminated timber panels open up new dimensions for massive timber construction and prefabrication in context with the digital chain. Technologies such as wood welding and the densification of wood create new possibilities not only for architecture but also for furniture and product design. Timber as a building material is therefore capable of satisfying both the demands of contemporary architecture as well as the requirements of sustainable building.