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3m x 3m x 3m



Santralistanbul, Bilgi University, Istanbul



August 2017



NOPA - Non Orthogonal Planar Assemblies - International Summer School was organized by Istanbul Bilgi University and was supported by ETH Zurich and NCCR Digital Fabrication from Switzerland. Program coordinators from Istanbul Bilgi University were Prof. Dr. Şebnem Yalınay Çinici and Dr. Evren Aysev Deneç. The tutors from Istanbul Bilgi University were Cemal Koray Bingöl, Gamze Gündüz and Leyla İlman including the collaborators, Oğul Öztunç and Hülya Oral. The tutors and lecturers from ETH Zurich and NCCR Digital Fabrication were Selen Ercan, David Jenny, Orkun Kasap and Luka Piskorec including the guest crits and lecturers Hannes Mayer from ETH Zurich and Dr. Ralph Bärtschi from ROB Technologies AG. The students of the International Summer School  were Aylin Güler, Foad Sarsangi, Nilay Öztürk, Meryem N. Yabanigül, Mevan Bacgeroğlu, Emre Taş, Berk Ekmen, Bilge Kardelen Bekiroğlu, Derya Çiftnamlı, Parhes Deni Çakıridis, Deniz Hüray Tuğcu, Ecem Kırtaş, Saadet Yüncü, Semen Tanrıverdi, İlayda Turan, Hüsnü Yücel and İsmail Kocataş.


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Non Orthogonal Planar Assemblies describes a geometric principle that allows for the design of spatial structures composed of discrete linear elements with rectangular cross-section without the need for complex joint typologies. Specifically, a wooden beam with a square cross-section can be utilised to construct a co-planar assembly in such a way that all touching elements share a parallel plane, thus exhibiting a “flush” planar connection between them. This enables the use of basic jointing methods to connect pieces,  such as screwing rather than having to use any special steel element, like connecting plates, angled bolts etc. These structures are designed to branch out and extend spatially by connecting the elements on adjacent sides (which are perpendicular due to a rectangular cross-section) and angling them in the shared plane.  With this principle, it is possible to create branching structures that are non-orthogonal but nevertheless retain the property of planar connections.


It is easy to see that while this geometric principle can create branching structures, standard load-bearing typologies made with discrete linear elements are typically non-branching. However, due to the fact that every joint adds a degree of kinematic freedom to the structure, it is possible to connect any of the two branches with only two additional elements. This is possible for any two elements within the NOPA system, no matter how they are positioned in 3D space in relation to each other, assuming that they are not parallel - in which case the geometric solution acquires an infinite value. As an idiosyncratic inversal to traditional forms of building, this makes it unfavorable to iterate with parallel elements when using the NOPA design rules, thus encouraging and even requiring non-parallel, branching and converging configurations.


For the workshop, this principle was simplified into one geometric logic: For any two given planes in space, as long as they are not parallel, there exists a linear intersection. If these planes happen to be the two faces of two non-parallel rectangular elements in space, they would eventually intersect. On this intersection, it would possible to choose a point and find two lines which pass through this point and be perpendicular to the intersection line. These two lines would form the axes of the two new elements which connect the two starting rectangular elements using a simple side-to-side connection in a non-orthogonal spatial manner (Figure 1).

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