Geometry of Structural Form

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This paper describes a precise geometric method for the inscription of structural constraints into architectural form. Based on techniques from graphic statics, the force distribution in building structures is visualized using geometric diagrams. This diagrammatic representation allows a formal description that shows the relationship between the force flow and the structural form. The formal character of this description enables the direct implementation of a parametric truss geometry that maintains major structural behavioral characteristics under deformation. An interactive model of a structural freeform roof is developed through this link between a parametric truss definition and a design-driving NURBS surface. This allows for an intuitive exploration of the constrained design space in real time. Formal explorations and the comparison with built examples demonstrate the effectiveness of this approach.

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... Tulisan ini berupaya untuk: (1) memberikan gambaran tentang logika pemodelan yang mudah dengan menggunakan alat bantu digital dalam merasionalkan bentuk kedalam kerangka struktur; dan (2) memberikan contoh dari ekstensifikasi penelitian Geometry of Structural Frame (Lachauer & Kotnik, 2010). ...
... Bentuk-bentuk surface ini dapat diterapkan sebagai pelat lantai, penutup atap, panel dinding atau kombinasi ketiganya sinambung. Setuju dengan pendapat Lachauer & Kotnik (2010), Software CAAD 3D saat ini sudah mampu membentuk hubungan geometri seperti ini, sehingga hal ini tidak terbatas oleh teknik komputasi atau paket software. ...
... Dalam perekaan struktur tahap awal ini memang ada baiknya apabila keterbatasan kemampuan struktur sudah diperhitungkan (Lachauer & Kotnik, 2010) agar tidak terjadi penurunan stabilitas dan kegunaan dari model di proses kedepan. Akan tetapi, meneruskan penelitian yang dilakukannya, optimasi bentuk struktur dapat dilakukan dalam fase perancangan lanjutanya, sehingga tidak mematikan kreatifitas awal dari visualisasi sketsa digital ini. ...
Free form surface has a multiple complexity curve intrinsically, so that special approach is needed to form the structure. Geodesic shell is well-known as the shortest path between two points on a curved surface. This method is used to generate the structure of form, which can be easily determined by its basic shape or the complex form. This paper explains how Geodesic theory can assist to generate structures in the early stage of digital sketching. A workshop that has initially started becomes a topic to this discussion. The digital sketching process to apply the theory is the aim of this paper.
... The integration of structural constraints with fabrication data in a tailored, real-time design environment has been described for the case of a digital hanging chain modeler [6]. Recently, a method for the setup of an associative model of an efficient structure for a freeform roof, using techniques from graphic statics, has been reported [7]. In this case study, a new computational strategy is introduced, that allows for real-time design of spatial bridges in early design stages, between the conflicting priorities of exciting spatial expression and efficient material use. ...
This paper presents a novel approach for the interactive design of linear structures in space. A method is introduced, that provides a maximum of formal freedom in the design of funicular, hence efficient, structures. For a given deck geometry, defined by a design driving NURBS curve via parametric modeling techniques, a tailored relaxation routine allows for controlled, real-time form-finding of the spatial funicular. Subsequently, the equilibrium of the deck is constructed using techniques from graphic statics, combined with a least-square optimization technique. Finally, the method is applied to a design example.
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