UBC Graduate Research

A Generalizable Gridshell Ziraknejad, Bahar 2020-12-23

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     A Generalizable Gridshell   by      Bahar ZiraknejadBachelor of Computer Science, Sharif University of Technology, Tehran, Iran, 1993Submitted in partial fulfillment of the requirements for the degree of Master of Architecture in The Faculty of Graduate Studies School of Architecture and Landscape Architecture Architecture ProgramCommitteeAnnaLisa Meyboom, GP 2 chairYehia MadkourOliver David KriegMahbod BiaziIan Ross McDonald, Glen Stokes, GP 1 mentorWe accept this report as conforming to the required standard_________________AnnaLisa Meyboom_________________Ian Ross McDonald_________________Glen StokesThe University of British Columbia . December 2020. © Bahar ZiraknejadI have obtained formal copyright permission for all the images that I have used in this report, or I am illustrating them under UBC “Fair Dealing” as described at: https://copyright.ubc.ca/theses-and-dissertations/#What_is_Fair_Dealing_and_can_I_use_it_for_my_Thesis?IIn today’s world, technological advancements in design tools, digital fabrication processes, and wood - as a sustainable and flexible material - pose several questions and causes debate amongst  architects, engineers, and fabricators. These are not limited to: customization vs standardization and serial manufacturing; interdisciplinary approaches vs disconnected disciplinary domains of professions; a minimalist build form vs a free-form composed of an aggregation of components.  In the past decade, there is a renewed interest in wood construction across all these disciplines. Architects, engineers, and fabricators are exploring new ways of using wood by engaging recent advancements in digital design and fabrication. This exploration demands the integration of design and fabrication processes. In this integrated method, the designer knows the limits and potential of fabrication tools. This means the designer is in charge of fabrication, leading to unity between form and material. The form is informed by, not imposed on the material. This leads to innovation in design at early stages of the design, since the design is not only informed by the site constraints, but also by the material and fabrication constraints and their potentials. This integrated design-to-fabrication methodology changes the architect’s role allowing them to become a fabricator. Engineering becomes integrated with architecture software because within it we can control and program a robot for any architectural task. One designs differently - in terms of wood - when one knows how things go together because fabrication knowledge is brought into the design process. This changes the language of architecture as now the connections define the structure, and at the same time, it is expressive. A designer is in charge of tectonics and how the material comes together. This tectonics is the building’s expression designed only by the architect which is then confirmed by engineers and fabricators. A joint system is not only how the forces will be transferred to the ground, but also is an expression or the ornamentation of our building form in our contemporary era.The integrated design-to-fabrication process further leads to efficiency in fabrication and has economic benefits since there is no loss of information that flows from designer to fabricator.  In traditional methods, the production process goes through a series of steps to transform from a 3D to a 2D model and eventually develops construction drawings. The designer in this multi-disciplinary world directly interfaces with the machine, which creates a short-cut in the traditional construction drawings. Therefore the designer has more control over fabrication and construction. Abstract Fix it -Big picture - Why I am creating this system? (not why wood? ppl already know why wood)My question? what I am testingTherefore, this thesis has three main drivers: an integrated design-to-fabrication process, material-informed form, and a culture shift that demands an interdisciplinary environment where there is a smooth flow of knowledge between architects, engineers, and fabricators.  I am interested in wooden double-curved surfaces because sustainable, engineering wood and wooden double-curved surfaces have enabled us to create lightweight structures with long spans (in comparison to steel and concrete). Therefore, wooden double-curved surfaces have led to a new typology in architecture in comparison to steel and concrete. In the past, wood was a weak material compared to steel and concrete, but engineering wood has changed this conception. Engineering wood is strong and makes the wood much more suitable as a structural material. A double-curved surface allows for the aggregation of parts which creates a whole that connects us to nature. A double-curved surface shifts our vision from hierarchical structures, where there is a distinction between roofs and columns. The form becomes one continuous surface. Therefore, a wooden double-curved surface allows a weak but sustainable material to become stronger while producing a lightweight structure. With this introduction, the GP1 component of this thesis looked at recent explorations in wooden double-curved surfaces as a new architectural language to create a build space inspired by nature. Understanding the material usage and how the form and structure are informed or imposed by wood properties were key aspects of this study. This research showcases the potential of wood in creating complex and precise joinery which is achievable quickly using CNC or robotic fabrication. Therefore, this study explored the design, joint system, fabrication, and construction methods and processes of each precedent; determining whether there was an overlap between these processes. The GP2 component of this thesis proposes a system or a process that enables an architect to design a double-curved surface, or more broadly, a generalizable gridshell that can be applied to flat, single-curved or double-curved surfaces. This system encapsulates the above integration knowledge and makes complex structures readily available to architects. Therefore, this thesis not about an architectural proposal or an instantiation of a system. This thesis is about increasing access to light-weight structures using wood that is readily available and can be fabricated with a 7-axis industrial robot. Thus, it proposes an open-source system which integrates material and robotic fabrication knowledge into a parametric design process, all created in one single digital design-to-fabrication environment. IITable of Content Abstract         IList of figures         IIIAcknowledgment Dedication A Personal Story - Browsing through my previous projectsThesis Statement         1Three typologies  precedent study The question that this thesis raises      6Why I am interest in Wood Joinery?      17Catalogue of Precedents       20       1Typology 1 - Gridshell - Frei Otto’s Light Weight Principle    21Precedent 1  - Mannheim Multihalle     22Precedent 2  - Performative Wood GridShell Siracusa   34Gridshell Model Testing for Typology 1     41Typology 2 - Hexagonal Lattice Shell - Heavy Timber Section   39Precedent 3  - Pompidou Metz     40Precedent 4  - Haesley Nine Bridges Golf Club House   46Typology 3 - Geodesic Shells      Precedent 5  - Timber Wave     54Precedent Analysis Summary      65GP1 Lessons Learned       66How this thesis moves the discipline of architecture forward?   67GP2 - Joint System Design       68A Gridshell and a Joint System with Four Requirements:   69Beam Design - Scenario 1 and 2      70Scenario 1 - When the Mountain and Valley Segments are Applied   74to Double-Curved SurfaceThree ways a robot can be used for an architectural task   78Assembly Order        79Assembly of the Joint System Stabilizer     81A Ghosted Method - 3D Design Visualization with    82Fabrication in MindThe Joint System Stabilizer Design (or Tension Ring)    84Contouring Method + Parametric Rotation for Slicing the Reference Surface and its Limitation    89Planarity        94Lost in Thought - How to connect the dots? Robotic fabrcation    97 Virtual Robot Fabrication Simulation Video     104Areas of Further Developments      105Bibliography        107Glossary of Terms        108IIIFigure 1. Previous project 1 - Cardboard Seating Device authorFigure 2. Previous project 2 - After Iqbal authorFigure 3. Previous project 3 - Food Market authorFigure 4. Previous project 4 - Inspired by Frei Otto  authorFigure 5. Previous project 5  - Brachiosaurus Tent authorFigure 6. Wander Wood workshop  - 2018The team from Wander Wood workshop with supervision of Annalisa Meyboom, David Correa, and Oliver David KriegFigure 7. Thesis’s booklet cover pageauthorFigure 8. The generalizable gridshell applied to a flat surfaceauthorFigure 9. The generalizable gridshell applied to a single-curved surfaceauthorFigure 10. The generalizable gridshell applied to a double-curved surfaceauthorFigure 11. (a to e) Three typologies  - GP1 precedent studies a) https://commons.wikimedia.org/wiki/File:Herzogenriedpark_077.jpgb) https://www.youtube.com/watch?v=Pr3Alddaj70&t=100s - Designed by The University of Catania under the supervision of Nicola Impollonia and Luigi Alinic) From the paper ‘Centre Pompidou – Metz: Engineering the roof’ Struct Eng 89(18) by Ben Lewis  - P 20d) https://www.designtoproduction.com/en/e) Annalisa Meyboom, David Correa, and Oliver David KriegFigure 12. Design to fabrication process flow for Pompidou Metzauthor reproduction from designtoproduction websiteFigure 13.Digital reproduction of the Center of Pompidou MetzauthorFigure 14. 3D model visualization  - Digital reproduction of Haesley Nine Bridges Golf Club HouseauthorFigure 15. Design to fabrication process flow for Nine Bridges Golf Club HouseauthorFigure 16. Assembly of components on timber formers to form one of the 32 roof modulesFrom the book ‘Timber Gridshell’ - P 208 - Source: © Blumer-Lehmann AG.Figure 17. Beams of Haesley Nine Bridges Golf Club House: (a) Glue-laminated timber planks being (b) cut and (c) milled to shape (d) complex CNC-machined segmentsFrom the book ‘Timber Gridshell’ - P 207 - Source: © Blumer-Lehmann AG. and designtoproduction GmbHFigure 18. Centre Pompidou Metz - (a) Curved plank being fabricated  (b) Curved planks partway through the fabrication processFrom the paper ‘Centre Pompidou – Metz: Engineering the roof’ Struct Eng 89(18) by Ben lewis  - P 24Figure 19. Centre Pompidou Metz - Reference geometry shows how double curved beam should be fabricated from an oversize plank - Every single beam as a unique proportion designed by designtoproduction firm as part their “File-to-Factory” realization process. From the paper ‘File-to-Factory Production and Expertise’ Detail, by Fabian Scheurer  - P 486Figure 20. (a and b) Centre Pompidou Metz - A close-up view of the double-curved beam componentFrom the book ‘Advanced Wood Architecture book’ - P 188 & https://www.designtoproduction.com/en/ - Source:© Holzbau AmannFigure 21.Centre Pompidou Metz - More examples of reference geometries by designtoproductionFrom  https://www.designtoproduction.com/en/ &  the book ‘Timber Gridshell’ - P 193Figure 22. Centre Pompidou Metz  - Oversized glue-laminated sections machined from reference geometries (Fig. 71) to form curved planks by Holzbau AmannFrom  https://www.designtoproduction.com/en/ &  the book ‘Timber Gridshell’ - P 193 - Source:© Holzbau AmannFigure 23. Close up view funnel-shaped columns.https://www.area-arch.it/en/centre-pompidou-metz/Figure 24. The lower part of the funnel-shaped columns - shown steel chairs minimizes the chance of condensation by creating a gap between the roof membrane and the wooden gridshell. IVFrom the book ‘Timber Gridshell’ - P 196 - Source:© Holzbau AmannFigure 25. Interior view of Haesley Nine Bridges Golf Club Househttps://www.designtoproduction.com/en/Figure 26. Author at Perkins&Will  - Univesal Robot 5 (UR5) experiment  Source: Mahdiar GhaffarianFigure 27. The overall process flow - Integrated Design-to-Fabrication Visualization authorFigure 28. Construstion Map reproduced from the Timber Wave’s Rhino and Grasshopper design scriptauthorFigure 29. The structural details of Pompidou Metz’s beamsFrom the book ‘Sustainable Timber Design’ - P 118 - Used under UBC Fair DealingFigure 30. Structure detail of the Timber Wave. The diagrid is double-layered with thick plywood spacers at the intersection points. The spacers also act as connectors to the cedar planksFrom the paper ‘Beyond Form Definition: Material Informed Digital Fabrication in Timber Construction’ in Digital Wood Design, by David Correa, Oliver David Krieg and AnnaLisa Meyboom  - P 83Figure 31. Interior view of Mannheim gridshellhttps://commons.wikimedia.org/wiki/File:Herzogenriedpark_077.jpgFigure 32. The bird’s eye view of the gridshell for the Bundesgartenschau (German Federal Garden Festival)  - DaytimeFrom the book ‘Timber Gridshell’ - P 25 Figure 33. The bird’s eye view of the gridshell for the Bundesgartenschau (German Federal Garden Festival)  - Nighttimehttps://www.fastepp.com/portfolio/multihalle-gridshell/ Source: © Atelier Frei Otto WarmbronnFigure 34. Form-finding experiment by Frei Otto using catenary hanging chain based on Hooke’s principle of inverting a hanging netFrom the thesis ‘Form-Finding, Force and Function: A thin shell concrete trolley barn for Seattle’s waterfront’ by Michael W. Weller - P5 - Used under UBC Fair DealingFigure 35. (a) Hanging model by Gaudi (b) La Sagrada di Familia, a masonry construction with its structural geometry driven from physical scaled hanging modelFrom the paper ‘Timber gridshells: beyond the drawing board. Proceedings of the Institution of Civil Engineers. Construction Materials’, 166 (6), 390-402 by Gabriel Tang  - P 392  - Used under UBC Fair DealingFigure 36. Wire mesh model, at the scale of 1:500, used to decide initial architectural/spatial formFrom the paper ‘Timber lattice roof for the Mannheim Bundesgartenschau’ , 1975, Vol 53 by  E. Happold and  W. I. Liddell- P 103Figure 37. Close-up view of the hanging model showing wire links connected by ringsFrom the paper ‘Timber lattice roof for the Mannheim Bundesgartenschau’ , 1975, Vol 53  by  E. Happold and  W. I. Liddell- P 103Figure 38. Transferring chain net to the support systemFrom the paper ‘Timber lattice roof for the Mannheim Bundesgartenschau’, 1975, Vol 53 by E. Happold and  W. I. Liddell - P 103Figure 39. Hanging chain model  From the paper ‘Timber lattice roof for the Mannheim Bundesgartenschau’, 1975, Vol 53  by E. Happold and  W. I. Liddell- P 103Figure 40. Stereo photography of hanging chain model by IAGBFrom the paper ‘Timber lattice roof for the Mannheim Bundesgartenschau’, 1975, Vol 53  by E. Happold and  W. I. Liddell- P 107Figure 41. Computer plotted plan of Multihalle and Restaurant gridshell geometry - plot of 1.5 mFrom the paper ‘Timber lattice roof for the Mannheim Bundesgartenschau’, 1975, Vol 53  by E. Happold and  W. I. Liddell- P 107Figure 42. Computer plot of 3 m net of Multihalle From the paper ‘Bundesgartenschau, Mannheim’  The Arup Journal by Edmund Happold, Ian Liddell, 1975, Vol 10, 3  P - 15Figure 43. (Left) The interior view of the entrance archFrom the paper ‘Bundesgartenschau, Mannheim’  The Arup Journal by Edmund Happold, Ian Liddell, 1975, Vol 10, 3  P - 18Figure44. (Above) The building during the exhibitionFrom the paper ‘Bundesgartenschau, Mannheim’  The Arup Journal by Edmund Happold, Ian Liddell, 1975, Vol 10, 3  P - 17Figure 45. (a) Gridshell node joint detail; (b) Realization of a typical node in the Mannheim gridshellFrom the book ‘Timber Gridshell’ - P 32  - Sources: (a) © Gabriel Tang, redrawn from Burkhardt (1978: 112); (b) © Gabriel TangFigure 46. Mannheim gridshell structurehttps://www.fastepp.com/portfolio/multihalle-gridshell/  - Sources: Rasmus HauptFigure 47. (a) and (b) Pushing up the gridshell from below using “Fork-lift, scaffold, and spreader beams”From the book ‘Timber Gridshell’ - P 34Figure 48. Detail of the grid with a bracing system composed of a diagonal network of double layered 6mm steel wire (19-strand) at 4.5 m centresFrom the book ‘Timber Gridshell’ - P 33Figure 49. Performative Wood GridShell in Siracusa   Vhttps://www.youtube.com/watch?v=Pr3Alddaj70&t=100sFigure 50. Siracusa Gridshell  - Plan of modular grid made up three different moduleshttps://www.youtube.com/watch?v=Pr3Alddaj70&t=100sFigure 51. (a) to (c) Siracusa Gridshell  - Step 1 - Each module is laid flat    https://www.youtube.com/watch?v=Pr3Alddaj70&t=100sFigure 52. (a) to (d) Siracusa Gridshell  - Step 2 - Folding & carrying each module to its final location    https://www.youtube.com/watch?v=Pr3Alddaj70&t=100sFigure 53. (a) to (d) Siracusa Gridshell  - Step 3 - Connecting the modules    https://www.youtube.com/watch?v=Pr3Alddaj70&t=100sFigure 54. Siracusa Gridshell  - Detail of hinged joint    https://www.youtube.com/watch?v=Pr3Alddaj70&t=100sFigure 55. (a) to (c) Siracusa Gridshell  - Step 4 - Make the grid wet for better gradual bending     https://www.youtube.com/watch?v=Pr3Alddaj70&t=100sFigure 56. (a) to (d) Siracusa Gridshell  - Step 5 - Lifting with a crane     https://www.youtube.com/watch?v=Pr3Alddaj70&t=100sFigure 57. (a) to (d) Siracusa Gridshell  - Step 6 - Bending continues     https://www.youtube.com/watch?v=Pr3Alddaj70&t=100sFigure 58.  Typology 1 Physical Experiment  - A GridShell model at scale of 1:10 made of basswood  authorFigure 59. Step 1 - Composing an interwoven flat grid; An inverse square mesh with five layers of wood; Double layered laths running in two directions; support segments are positioned at the second layer from bottom; washers are positioned on top and bolts at the bottomauthor   Figure 60. Step 1 - Exploded axo view of the inverse flat grid in Fig. 41 authorFigure 61. Step 2 - flat grid in step 1 was folded and flipped over  authorFigure 62. Step 3 - Unfold the flat grid; now washers are at the bottom and bolts on top  authorFigure 63. Step 3  - (a) Axo view of the inverse flat grid in Fig. 41; (b) Axo view of the flat grid in Fig. 44 authorFigure 64. (Left) Step 4 - Gradual Bending (or Lifting) of the grid’s curves  - Axo of Fig. 47authorFigure 65. Step 4 - Gradually pushing the anchor points inwardauthorFigure 66. Step 5  - Tightening the nuts after the planned bendingauthorFigure 67. Step 6  - The shell at its final shape before adding the bracingauthorFigure 68. Step 7  - The shell with adequate stiffness adding the bracingauthorFigure 69. Final gridshellauthorFigure 70. The Centre of Pompidou Metz From the paper ‘Centre Pompidou – Metz: Engineering the roof’ Struct Eng 89(18) by Ben lewis  - P 20Figure 71: Chinese Hathttps://pngio.com/images/png-a785913.htmlFigure 72. Flat 2D hexagon pattern/gridauthorFigure 73. Roof Geometry - A doubly curved free-form surface. This whole geometry is one continuous surface.authorFigure 74. Project the flat grid on the doubly curved surfaceauthorFigure 75. Transformed blue curves to double Layered beams which gives an impression of woven straws in a Chinese hat.authorVIFigure 76. Hexagonal lattice with double beams running in three directions. These beams are double curved (or twisted) to follow the roof’s geometry. Some of these twisted segments are outlined in red. This drawing is the enlarged view of the orange circle in Fig. 75.authorFigure 77. Enlarged view of some of the twisted curved beams from Fig. 76.authorFigure 78. Exploded axo diagram of Joint connection detail of Pompidou Metz’s beams (Self, 2014: 269)From the book ‘The Architecture of Art Museum a decade of Design 2000-2010’ - P 269Figure 79. Roof under construction From the paper ‘Centre Pompidou – Metz: Engineering the roof’ Struct Eng 89(18) by Ben lewis  - P 25Figure 80. (a) A steel ring supports and receives the roof wood structure and enables the exhibition gallery to pass through the roof. (b) Connection of the roof’s grid to the steel ringFrom the book ‘Timber Gridshell’ - P 200Figure 81. Haesley Nine Bridges Golf Club Househttps://www.designtoproduction.com/en/-------Figure 82. Flat 2D hexagon grid divided into 32 equal modulesauthorFigure 83. Axo of Roof geometry made of 21 funnel shape columns. The red circles illustrate the funnel profile authorFigure 84. Figure b6. RCP Plan and elevation of Nine Bridges Golf Resort. authorFigure 85. RCP Plan and elevation of Nine Bridges Golf Resort after trimming the stretched 3d curves at the bottom of each cone. This trimming is required before creating the curves for each column (Fig. 85 and 86) authorFigure 86. Axo of roof composed of tessellation of hexagons and triangles (after the projection of the flat grid and the trimming of stretched curves at the bottom of each cone)authorFigure 87. (top) Axo of the roof after creating of 21 columns, each composed of 12 curves.  32 roof elements are supported by 21 columns. authorFigure 88. (right) The process of creating curved columns: (a) Enlarged view of a single cone (or funnel-shaped column); (b) Connection of the hexagon base of the cone to the base of the column on the ground using 12 straight lines; (c) Projection of those 12 straight lines to the funnel-shaped surface while making them a continuation of the roof’s curvaturesauthorFigure 89. Hexagonal lattice in plan and elevation with double beams running in three directions. These beams are double curved (or twisted) to follow the roof’s geometry. Two of the twisted segments are outlined in red and blueauthorFigure 90. (a) Axo of roof around the funnel shape column composed of 12 curved beams; (b) Enlarged view of the curved beamsauthorFigure 89. The roof of Nine Bridges Golf Resort with continuous beams like a rainforest canopy.authorFigure 90. Structure Detail  - A continuous single-layer gridshell composed of two lap joints at every crossing From the book ‘Timber Gridshell’ - P 204  - Source: © designtoproduction GmbHFigure 91. (a) While the roof is broken into 32 modules, there are only five distinct reference surfaces types; (b) Gridshell model based on the yellow reference surface in Fig. 93(a) and it represents the pre-fabricated module in Fig. 94(a).  authorFigure 92. (a) and (b) Prefabricated roof modules being craned into the site; (c) Bird’s eye view of the  lattice shell during constructionFrom the book ‘Timber Gridshell’ - P 209 - Source: © Blumer-Lehmann AG.Figure 100. Timber Wave at UBC  - The diagrid structure made of straight  plywood components and the cedar planks under construction From the paper ‘Beyond Form Definition: Material Informed Digital Fabrication in Timber Construction’ in Digital Wood Design, by David Correa, Oliver David Krieg and AnnaLisa Meyboom  - P 85Figure 101. Structure detail. The diagrid is double-layered with thick plywood spacers at the intersection points. The spacers also act as connectors to the cedar planks. From the paper ‘Beyond Form Definition: Material Informed Digital Fabrication in Timber Construction’ in Digital Wood Design, by David Correa, Oliver David Krieg and AnnaLisa Meyboom  - P 83VIIFigure 102. The diagrid substructure detail under construction showing self-aligning hygroscopic joinery From the paper ‘Beyond Form Definition: Material Informed Digital Fabrication in Timber Construction’ in Digital Wood Design, by David Correa, Oliver David Krieg and AnnaLisa Meyboom  - P 83Figure 103.(a) Double curved reference geometry (b) The project uses geodesic methods to create a diagrid structure on a manually created double curved surface.authorFigure 104. “When unrolled from the design model, it becomes evident that the cedar planks are indeed straight“.authorFigure 105. “Visualization of the diagrid elements and multi-layered assembly system” authorFigure 106. Structural details  - The joint systemauthorFigure 107. Wood strips of the diagrid structure should be broken to multiple components considering the wood sheet dimension and the size of the robot bed.  authorFigure 108. Strip A as shown in Fig. 105. Each strip of the diagrid structure is flat considering the fact that the robot’s bed is flat. authorFigure 109. Simulation of fabrication of plywood components using the Virtual 7-axis RobotauthorFigure 110. Enlarged view of Fig. 109 showing the milling of edges of the notch on an angle  - The double layered boundary curves of these components provides the coordinates of top and bottom edges of the plywood components - Comparing these boundary edges with the Fig. 107, it confirms that only the two edges of the notches are required to be milled on an angle. author** Figure 110  to 143 - All the GP2 drawings are developed by the authorVIIIThis was only made possible with the continued guidance of my committee, my friends, and my family.To my thesis chair, Annalisa Meyboom, thank you for your wisdom and discernment without which I could not get to this point. Furthermore, thank you for your trust in my work, for helping me to find my architectural voice.To Yehia Madkour, thank you for your patience, support, and unprecedented kindness throughout this process. You generously enabled me to access the robotic workshop at Perkins&Will studio during the pandemic. I am extremely grateful. To Oliver David Krieg, thank you for sharing your immense technical knowledge and robotic scripts with me, enabling me to learn and implement an integrated design-to-fabrication process and to learn advanced Grasshopper techniques. To Mahbod Biazi, thank you for your patience, availability, and positive outlook during my thesis. You always kept my spirits high. To Mahdiar Ghaffarian, thank you for your guidance and commitment to attend the studio a countless number of times during this pandemic. To Lief Eriksen, thank you dearly for introducing me to many aspects of robotic fabrication and the challenges involved. Your technical fabrication knowledge defined many aspects of my robotic experiments.    To my dear husband, Nariman, and my two lovely boys Parsa and Yara, I would like to express my deepest gratitude. Without your continuous support and patience, I could not pursue my dreams. To my dear friend Lynn Prestash, I am grateful for your unconditional support and encouragement for the past several years. Furthermore, to my dear brother Nima Ziraknejad, and my dear friends Natalia Kharitonova, Mahsa Akbarnejad, thank you for your direct support during this thesis.To Chris Macdonald, Fionn Byrne, Daniel Gasser, Greg Johnson, Joe Dahmen, Ian Ross McDonald, Glen Stokes, and William Loasby, I am incredibly thankful for your consultation during the GP1 phase.  AcknowledgmentsIXIn memory of my father who was the first architect to inspire me in my life, and my mother who signed me up for drawing classes in my youth.  This thesis is dedicated to my two lovely and independent sons, Parsa and Yara, so that they always follow their passion at any stage in life. DedicationXA Personal Story - Browsing through my previous projects: After being in the tech industry for 16 years, I left my IT career to follow my long-lasting passion for architecture. I took some evening classes at the Emily Carr University of art and design. This seating device was the outcome of those classes. The design was my first exposure a Gridshell concept.   6 Cardboard Seating DeviceI designed and constructed “Cardboard Seating Device” to meet four requirements.  It must weigh a maxi-mum of 1.5 pounds, support a sitting person who weighs up to 140 pounds, have an average width of 12 inches and be 15 inches in height.  The actual weight of the constructed device is 1 pound and 3.4 ounces. Through the design process, I came up with seven different design concepts.  For the last two concepts, I studied and tested the strength of the work using a 1/4 scale maquette and chose above concept because of its strength, simplicity and aesthetic aspects.  I enjoy the repetition of the profile and the joint technique of this artwork which enabled me to use a minimum amount of glue. Front View Back View3/4 ViewFigure 1. Previous project 1 - Cardboard Seating Device XIThen I took a design thinking class at UBC, and I designed a Joint System made of 800 balloons. I realized that I have an interest in numbers, repetition, pattern making, and connections.  4 “After Iqbal” rug is woven using 800 “Twist and Shape” balloons.  This contemporary artwork is about transforming one ready-made object into another unlikely object which has a function, while creating a conceptual relationship between the two unlikely objects.  The rug is patterned after the general design of a Persian rug.  It is created using one material only: balloons.  The colours I chose for this balloon Persian rug reflect those favoured by the Dutch artist Piet Mondrian.  “After Iqbal” brings together concepts from modern western and ancient eastern cultures.  The rug is inspired by the book “Iqbal” by Francesco D’Adamo.  This book is based on the true story of a Pakistani boy named Iqbal Masih who was a bonded child labourer in carpet factories. Iqbal educated himself and other bonded children about their rights.  He managed to free himself and other children, but was murdered at the age of 13 soon after gaining his freedom.  His death likely resulted from his determination to free more children.    This artwork honours the children, past and present, who have been exploited in carpet factories.  Working on this rug gave me a tiny glimpse into the suffering of these children.  Just as this rug imprisons the balloons (a child’s toy), carpet factories imprison children.  Next time you see a Persian rug, remember the tragedy of child labour.“After Iqbal” RugFigure 2. Previous project 2 - After Iqbal XIIThen I joined SALA and became interested in Gridshells, and light-weight structures. The following slide was one of my studio projects at SALA. This was a conceptual design without proposing any joint system.  7Integration of Food, Music and Agriculture as an Adaptive EnvironmentView from Richards StreetView from the bridge over Richards Street Interior View 3 – Second Floor – The Strawberry Farm – An Aeroponic Growing System Interior View 1 – First Floor Interior View 2 – First Floor View from Richards Street The presented work is a design proposal for a food market in Yaletown, Vancouver.  It is an adaptive environment which will integrate an architectural space with British Columbia’s agriculture, the local food networks, and the joy of music.  The site is three separate lots.  The main site located at the corner Robson and Richards streets. The second site is on Seymour Street facing the Vancouver Symphony Orchestra (VSO) building.  The third site is located at the corner of Richards and Smithe streets.  The program of food market spreads across the three lots as an urban plan with the intention of connecting these three lots as three interconnected parks. The driving force for this design is to increase the park space in the down-town, and thereby decrease the total impervious space.  The south façade of the VSO building displays a sheet of music by Beethoven, and that inspired the organic form of the food market which expresses the movement and fluidity of music.  The food market has an undulating, floating shell with a diagrid structure.  It complements the music emanating from the VSO building next door.  The curvature of my design represents the flow between the high and low notes of a melody.  The melody of the food market is a heterogeneous space with a diverse range of programs such as produce stalls, a park, a barrier free pedestrian bridge, restaurants and cafes, and an indoor strawberry farm composed of Tower Gardens which are a vertical aeroponic growing system.This floating triangular shell is supported by double columns at the perimeter of the building.  The shell is embraced by a pe-destrian bridge and a staircase which faces the VSO building.  This structure physically joins the three lots by way of three interconnected parks.  The undulated shape of the roof shell creates a contrast with the surrounding tall cubical buildings. The main dome of the shell creates an air circulation system for the indoor farm using a stack effect mechanism.  The wood-en gridshell is a biopholic design which encourages eye contact through the extensive use of glass, thereby, providing a space that promotes interactive behaviour.  There is also an outdoor space on the Seymour site for events or happenings, especially those which may arise from the adjacent VSO building.  My design suggests an interior growing space which could be applied to many old houses which are small but are built on big lots.  This would increase BC self reliance for certain fruits such as strawberries, the production of which has declined in BC.  This interior growing space is an example of performative architecture because it provides a model for farming in cold-er seasons, especially for a city like Vancouver which has a short growing season when using traditional farming methods. In summary, I have created an adaptive environment that celebrates the integration of air, light, wood, glass, music, local food and vertical aeroponic farms.  Figure 3. Previous project 3 - Food Market  XIIIAnother gridshell project inspired by Frei Otto - Developed and designed using Grasshopper Kangaroo Physic Engine. This was my first exposure to a wooden joint system, and I became interested in Tectonics. Figure 1 - The Physical Model Figure 4. Previous project 4 - Inspired by Frei Otto  XIVAnd another Gridshell studio project called “Brachiosaurus Tent” as a proposal for children shelter to protect the 9th largest tree in BC, which is approximately 400 years old.Figure 5. Previous project 5 - Brachiosaurus TentXVIn 2018, I attended the robotic workshop seen on the right. This was my aha moment to connect my past and present lives, sparking an inspiration for this thesis and the area that I wish to concentrate after that. 1 2Preface:This thesis is inspired by a one-week workshop that I attended in which we robotically fabricated a double-curved timber surface at a one-to-one scale using a 7-axis robotic milling setup. The workshop was at the Center for Advanced Wood Processing (CAWP) and was held in collaboration with University of British Columbia, the Institute of Computational Design and Construction (ICD) at the University of Stuttgart, and the School of Architecture at the University of Waterloo (Fig. 1) . Therefore, learning by prototyping is one of the main focuses of this thesis. Figure 1. Wander Wood workshop  - 2018 Field of InquiryI attended a one-week workshop where we robotically fabricated a double-curved timber surface at a one-to-one scale using a 7-axis robotic milling setup. The workshop was at the Center for Advanced Wood Processing (CAWP). It was held in collaboration with the University of British Columbia, the Institute of Computational Design and Construction (ICD) at the University of Stuttgart, and the School of Architecture at the University of Waterloo. Figure 6. Wander Wood workshop  - 2018 1Thesis StatementIn the recent decade, there is a renewed interest in wood construction across disciplines. Architects, engineers, and fabricators are exploring new ways of using wood by engaging the recent advancement in digital design and fabrication.  This thesis is a reflection of my interest in tectonics and connections. It explores and proposes a generalizable system for creating a double-curved gridshell structure, robust enough at the size of a full-scale building. Through the study of different joint systems, a new joint system is designed, and an open-source system (a script) is developed to automate the design and fabrication of a generalizable gridshell that can be applied to a flat, single-curved, or double-curved surfaces. This gridshell only utilizes planar ready-made wood, a 7-axis industrial robot, and should not use any formwork for bending the material. This system enables architects to easily design and build double curved surfaces. Therefore, it increases access to complex and lightweight structures, and enables faster fabrication processes through an integrated design-to-fabrication process and material-informed forms.Figure 7. Thesis’ booklet cover pageFigure 8. The generalizable gridshell applied to a flat surface2Shows the variable orientation of the beams in order to be generalizable and more expressive. The Generalizable Gridshell applied to a Flat Surface3The Generalizable Gridshell applied to a Single-Curved SurfaceFigure 9. The generalizable gridshell applied to a single-curved surface4The Generalizable Gridshell applied to a Double-Curved SurfaceFinal System Reference GeometryDiagrid Structure Contour Slicing Method + Rotation at Variable AngleTwo-layered BeamsRobotically Fabricated Joint System Stabilizer (or Tension Rings) Robotically FabricatedFigure 10. The generalizable gridshell applied to a double-curved surface5Typology 1Frei Otto Mannheim Multihalle - 1975Typology 2Shigeru Ban Pompidou Metz - 2010Haesley Nine Bridges Golf Club House - 2009Typology 3UBC, ICD, and University of Waterloo  Timber Wave - 2017For my precedent study, I identified 3 typologies. They are all similar because they are double-curved surfaces made of two layers of beams running in different directions. However, they are entirely different from each other in terms of their digital modeling and their fabrication/construction processes. My thesis lands between typology 2 and 3. My ThesisPerformative Wood Gridshell SiracusaSiracusa, Sicily, Italy, 2013  Figure 11. (a to e) Three typologies  - GP1 precedent studies a) b) c) d) e) 6The question that this thesis raises:Modeling:  designtoproduction Timber Construc�on/Fabrica�on: Holzbau Amann Structural Engineering:  SJB Kempter Fitze  Structural design: Ove Arup, Hermann Blumer, Terrel Architecture: Shigeru Ban, Jean de Gas�nes Parametric workowAutomate Fabrication & Production Separation of design and Fabrication in Typology 2Figure 12. Design to fabrication process flow for Pompidou Metz Figure 13.Digital reproduction of the Center of Pompidou Metz7A concern about typology 2 is that the “parametric sophistication” of designtoproduction is an essential component of the fabrication process, coming together toward the end of the design process, instead of earlier in the conceptual design phase. Fabien Scheurer, founder of designtoproduction describes the process as follows:“In most of the cases where this fabrication [is] actually done, we’re hired by either the fabricator or by the general contractor and not by the architect. This is mainly a problem [with] the process itself. There’s a straight cut between the design phase and the building phase, which means that there’s no information coming from the backend of the process up the chain and informing the design process, which is a shame I have to say. The quality of the outcome can be much higher if the form, the shape, the design and the materiality match in a way.”Source: Mark Cabrinha’s paper in the “Digital Wood Design” bookModeling:  designtoproduction Timber Construc�on/Fabrica�on: Blumer Lehmann Structural Engineering:  SJB Kempter Fitze  Structural design:  Hermann Blumer Architecture: Shigeru Ban, Jean de Gas�nes Parametric workowAutomate Fabrication & Production Figure 15. Design to fabrication process flow for Haesley Nine Bridges Golf Club HouseFigure 14. 3D model visualization  - Digital reproduction of Haesley Nine Bridges Golf Club House8Therefore, this thesis investigates the cases where the separation between design and fabrication leads to structures or forms that are not informed by the material. When the architect focuses on form-finding alone, especially in complex structures such as double-curved surfaces, we have experienced situations where the form is imposed on the material. This method requires special equipment such as molds, clamping, lamination, and specialized digital knowledge in design and fabrication to bring the form to realization (Fig. 16 to 25). 208 MADE TO MEASURE: DIGITAL FABRICATIONFigure 7.30 Assembly of components on timber formers to shape one of the 32 roof elementsSource: © Blumer-Lehmann AG.Figure 16. Assembly of components on timber formers to form one of the 32 roof modules of Haesley Nine Bridges Golf Club House9207 MADE TO MEASURE: DIGITAL FABRICATIONFigure 7.29 (a) Glue-laminated timber blanks being (b) cut and (c) milled to form (d) complex CNC-machined componentsSource: © designtoproduction GmbH.(a)(c)(b)(d)Figure 17. Beams of Haesley Nine Bridges Golf Club House: (a) Glue-laminated timber planks being (b) cut and (c) milled to shape (d) complex CNC-machined segmentsSimilar to the Centre of Pompidou Metz, oversized glue-laminated blanks were used. Single curved and double curved components were CNC machined using a subtractive milling process. Therefore, the size of each component geometry was defined to decrease the material wasted. Designtoproduction devised those reference geometries and their corresponding digital model with a tolerance of one tenth of a millimeter. This precision was required for a fast and efficient assembly.  Also, unlike the Centre of Pompidou Metz where individual planks were assembled on-site, here sections (or modules) of 9m x 9m were pre-assembled (Fig. 16) in the factory and were craned to the site to be connected to the rest of the gridshell (Fig. xx). 10486 File-to-Factory oder: Der Wert der Experten 2010 ¥ 5   ∂9 1011 129, 11  Centre Pompidou Metz, 2003 – 2010  Architekten: Shigeru Ban, Jean de Gastines  Je nach Krümmung des zu produzierenden    Bauteils werden gerade, einsinnig oder zwei-sinnig gekrümmte BSH-Rohlinge verwendet.10, 12 Clubhaus Hasley Nine Bridges Golf Resort,   Yeoju, Südkorea, 2008 – 2010  Architekt: Shigeru Ban, KACI International   Die Fertigung der 467 individuellen Bauteile   basiert jeweils auf detaillierten 3D-Modellen. 9, 11  Centre Pompidou Metz, Metz, 2003 – 2010  architects: Shigeru Ban, Jean de Gastines   Depending upon the curvature of the building component to be produced, straight, single- or double-curved glu-lam blanks are used.10, 12 Hasley Clubhouse, Nine Bridges Golf Resort,  Yeoju, South Korea, 2008 – 2010  architect: Shigeru Ban, KACI International   A detailed 3-D model is generated for the fabri-cation of each of the 467 building components.This article will present two roof-structure case studies to delineate the challenges pre-sented by digital workflow as well as the prob-lems yet to be solved. At least with respect to free-form wood structures, file-to-factory pro-duction is still more of a Utopian concept than a reality. Although they vary in functional and formal terms, Shigeru Ban’s Centre Pompidou in Metz and the Clubhouse in Yeoju have a number of similarities. They are both based on the same triangular grid projected onto a curved roof shell. And aside from the wood-construction firm, the same team of special-ists took part in their realization. The figures for both projects are impressive. The roof at Metz encloses 8000 m2 and consists of al-most 1800 glu-lam beam segments – with a length of 18000 m end-to-end. A CNC milling machine fashioned the beams. The shell’s stiffness was achieved using 2000 hardwood dowels and 3500 pins to connect the six lay-ers of beams. The roof in Yeoju is one-third the size of the one in Metz and consists of 32 elements (each 9 ≈ 9 m) that are supported by 21 columns. There are just five different types. In contrast to Metz, here the beams penetrate one another. Thus, no additional connection components were necessary; in-stead, almost 15 000 complexly formed half-lap joints were executed. It is clear that these projects were not feasible – neither in the al-lotted time nor with the required level of preci-sion – without automated planning and pro-duction. Yet despite the technological progress, fashioning a free form with high pre-cision is still an art unto itself – though the mathematical groundwork was laid in the 1950s in the French automotive industry. The input for the fabrication plans for Metz consisted of a 3D DXF model in which the roof structure’s nodes were connected by straight lines. In order to arrive at the continu-ous curved glu-lam beams – from the bent lines – an elaborate NURBS model was re-constructed as reference for the curved roof surface. In Yeoju a different path was taken. The roof form was not determined by a digital model, but by gathering clearly defined boundary conditions: the position of the roof’s edge, position and angle of the column con-nections, the locations of the flat zones, etc. The program iCapp then extrapolated the re-spective reference surfaces for the five ele-ments from this relatively small amount of in-formation. In both projects, all subsequent planning phases were founded on these refer-ence surfaces. Step by step the detailed ge-ometry of every building component was de-rived from them. A so-called parametric CAD model is the key to efficiently planning such complex structures: they facilitate – based on “rules” and parameters – the automated fabri-cation. The first challenge was to find a uni-versally applicable description of the half-lap joints – i.e., one that functions for every con-ceivable angle – for the roof in Yeoju. The sec-ond challenge was to derive an algorithm from this description and to write a program that automatically constructs the half-lap joint in a 3D model. Wood-construction programs have long been available that have the attributes to create such parametric connection details. However, none of them have mastered work-ing with free forms. And so the complete planning for both roofs had to be executed on software from another discipline. There are always a number of possible paths toward realizing complex structures. Several different criteria point to the path that will be taken. Because some of these may be contra-dictory, they must be prioritized in advance. Accordingly, the result will never to optimal in the literal sense – it will be acceptable given the manner in which these conditions were specified. This is demonstrated in both projects by the segmentation of the beams. A beam’s dimensions are limited by the availa-ble raw material, the CNC machine’s size and workspace surrounding it, transportation lo-gistics, etc. A larger number of smaller com-ponents, for example, is easier to transport but requires additional connections. And the more curved or twisted a beam is, the more expensive it is to fabricate. Currently, such complex decisions cannot be made in an au-tomated process. Thus, one draws on the ex-perience and intuition of the participating spe-cialists, backed up by the quick feedback at-tained by trying out the different options. Tobias Schwinn 188 ground on which advances in wood architecture can occur. Asked about this particular motivation, Müll speculates that it might have to do with the fact that ‘the carpenter has always had the experience of being exposed on top of a structure and naturally wants to stand out’. While, from his point of view, the overall amount of non-standard work is certainly increasing, the number of timber construction companies that operate in this segment of the market is also growing. A new generation of consulting firms that specialise in information modelling, complex geometry, the interface between computer aided design (CAD) and computer aided manufacturing (CAM), and even machine control, naturally offer their services to many possible clients. Such collabora-tions have made projects like the Centre Pompidou-Metz viable and are now becoming more common-place.Centre Pompidou-Metz, France, 2010Architecture: Shigeru Ban and Jean de Gastines, Tokyo, ParisTimber construction: Holzbau Amann GmbH, Weilheim-BannholzStructural design: Ove Arup, London; Hermann Blumer, WaldstattThe curved timber grid shell of the Centre Pompidou-Metz (Figure 13.1) with its characteristic tri-hexagonal pattern and translucent fibreglass-reinforced membrane unites under one roof exhibition and event spaces, restaurant areas, and a spacious entrance hall. A hexagon in plan, the timber structure is suspended from a 77m tall central mast and transforms into four funnel-shaped columns in four of the six corners. The result is a geometrically complex free-form surface with a surface area of 8,500m² and spans of up to 40m that is materialised using prefabricated double-curved timber beams (Figures 13.2 and 13.3). These beams have been custom glue-laminated and CNC-milled to meet their individual target geometry. A main constraint of the subtractive milling process was to maintain the fibre continuity of the wood lamellas in the beam by limiting all cuts to less than five degrees relative to the fibre direction.Figure 13.2A close-up view of the double-curved timber beams during prefabrication.© Holzbau AmannFigure 13.1Night-time view of the Centre Pompidou-Metz showing the characteristic translucent roof structure.© Roland H lbeFigure 19. Centre Pompidou Metz - Reference geometry shows how double curved beam should be fabricated from an oversize plank - Every single beam as a unique proportion designed by designto-production firm as part their “File-to-Factory” realization process.  Figure 20 (a and b). Centre Pompidou Metz - A close-up view of the double-curved beam component “A main constraint of the subtractive milling process was to m intain the fibre continuity of the wood lamellas in the beam by limiting all cuts to less than five degrees relative to the fibre direction.” (Schwinn, 2017: 188)24 The Structural Engineer 89 (18) 20 September 2011Initially the roof had been considered to be supported from theconcrete Tubes, with eight raking steel struts at each Ring. As thedesign developed it became apparent that the Tubes may not beas rigid a support as assumed, and this could significantly alter thebehaviour of the roof. After extensive sensitivity analysis, initiallytrying to mimic the stiffness of the building in the single stick modeland then with the combined roof and building model, it wasdecided to effectively release the Rings. This was achieved byhaving an internal picture-frame within each Ring with only twovertical pin ended stubs supported on the Tubes. This allowed theRings to rotate, so effectively releasing the roof making theoutcome more predictable.Global buckling of the structure was investigated by combiningthe factored results of an eigenvalue buckling analysis, with theresults of a P-Delta analysis for corresponding load combinations.This procedure assumes that the structure will be built with aninitial imperfection that mimics the buckling mode shape, and isbased on the principles defined in the Eurocode. An initialimperfection of L/250 was used, although a minimum of L/400was proposed in the code (L being the length between points ofcontraflexure of the buckled mode shape). A more conservativevalue was thought prudent due to the nature of the structure. A fullnonlinear analysis was also undertaken on selected loadcombinations, to compare with the results from the above.DesignThe element design was carried out in accordance with Euro ode58 (EC5), using the recommended values in the code as no FrenchNational Annex existed at the time. The timber was typicallysoftwood glulam grade GL24h in accordance with EN 1194.Although some higher grades and some steel flitch plates wereproposed at tender stage in highly stressed areas, as it was anarchitectural desire to have all members of a uniform size. Each individual members strength utilisation was checked usingExcel spreadsheets automated with Visual Basic macros. Initiallythe analysis results were post-processed to break them down intoforces and moments on individual planks. This process alsoincorporated additional local effects not captured by the analysis.Following this the results were fed through a code design checkspreadsheet. Finally the utilisation results were fed back into theanalysis model, so that the values could be visualised as colourcontour plots.The additional effects incorporated in the post-processingincluded the following:– Bending moment due to the members being curved whilst theelements in the analysis model were straight– Bending moments in the individual planks from the vierendeelsystem– Bending moment due to the eccentricity of the planks at theirconnection– Flexure and shear buckling effectsIt was considered for tender that the doubly-curved and twistedglulam planks would be fabricated by initially curving the lathswhich make up the member, then gluing all of the precurvedelements together to form a doubly-curved plank. This fabricationprocess would have involved complicated clamping assemblies,although from discussions with a number of fabricators at the timethis was a preferred method and had been used successfully onprevious projects. To avoid reducing the allowable strength of the timber due to theinitially precurving the laths, it was assumed that the thickness ofthe lath would be reduced to achieve a radius over thickness valueof greater than 240 (as given in EC5). This was necessary as theareas of small curvature, some as small at 6m radius, weretypically at the supports where stresses were higher.Durability is always a key issue where timber structures arepotentially exposed to high moisture levels. The timber for the roofwas specified as a standard softwood species, therefore non-durable. It was decided that since the timber is typically internal,albeit in an unheated space, if condensation was to develop as thefabric is lifted off the timber the provision of natural ventilationshould preclude moisture levels from reaching a degree wheredecay may occur. Even t ose areas of the roof which are external,are typically protected from direct wetting by the fabric claddingand large overhangs. Therefore t e mo sture content would beunlikely to be greater than 20% for more than a short period,meaning decay would be unlikely. At the base of the Funnelswhere it is possible for driving rain to reach the timber, it was feltprudent to specify a moderately durable timber species. Thespecification called for a Class 3 timber in accordance with EN350-2, with the contractor proposing Larch. Larch was not usedelsewhere due to it higher cost. A clear coating was specified tohelp protect the timber duri g construction before the fabriccladding was in place. All glues were specified as Type 1 inaccordance with EN 301.DeliveryFor tender 2D drawings were prepared which represented theroof’s 3D geometry, with a 3D model (.dxf format) being issued thatdefined the overall centreline geometry of each timber member.Specifications were drafted in accordance with Eurocodes andincluded a clause requiring testing of the timber connections forstrength and stiffness.ConstructionThe construction contract was awarded to Demathieu & Bard(France) as main contractor, with their specialist timb r11  Curved plank being fabricated (image: © Holzbau Amann) 12  Curved planks part way through the fabrication process (image: ©Holzbau Amann)SE18 paper-Centre Pompidou Metz_Layout 3  15/09/2011  16:06  Page 24Figure 18. Centre Pompidou Metz - (a) Curved plank being fabricated  (b) Curved planks partway through the fabrication process24 The Structural Engineer 89 (18) 20 September 2011Initially the roof had been considered to be supported from theconcrete Tubes, with eight raking steel struts at each Ring. As thedesign developed it became apparent that the Tubes may not bea  rigid a support as assumed, and this could significantly alter thebehaviour of the roof. After extensive sensitivity analysis, initiallytrying to mimic the stiffness of the building in the single stick modeland then with the combined roof and building model, it wasdecided to effectively release the Rings. This was achieved byhaving an internal picture-frame within each Ring with only twovertical pin ended stubs supported on the Tubes. This allowed theRings to rotate, so effectively releasing the roof making theoutcome more predictable.Global buckling of the structure was investigated by combiningth  factored results of an eige value buckling analysis, with theresults of a P-Delta analysis for corresponding load combinations.This procedure assumes that the structure will be built with aninitial imperfection that mimics the buckling mode shape, and isbased on the principles defined in the Eurocode. An initialimperfection of L/250 was used, although a minimum of L/400was proposed in the code (L being the length between points ofcontraflexur  of the buckled mode shape). A m re co servativevalue was thought prudent due to the nature of the structure. A fullnonlinear analysis was also undertaken on selected loadcombinations, to compare with the results from the above.DesignThe element design was carried out in accordance with Eurocode58 (EC5), using the r commend d values in the code as no FrenchNational Annex existed at the time. The timber was typicallysoftwood glulam grade GL24h in accordance with EN 1194.Although some higher grades and some steel flitch plates wereproposed at tender stage in ighly stressed area , as it was anarchitectural desire to have all members of a uniform size. Each individual members strength utilisation was checked usingExc l spreadsheets automated with Vis al Basic macros. Initiallythe analysis results were post-processed to break them down intoforces and moments on individual planks. This process alsoincorporated additional local effects not captured by the analysis.Following this the results were fed through a code design checkspreadsheet. Finally the utilisation results were fed back into theanalysis model, so that the values could be visualised as colourcontour plots.The additional effects incorporated in the post-processingincluded the following:– Bending moment due to the members being curved whilst theelements in the analysis model were straight– Bending moments in the individual planks from the vierendeelsystem– Bending moment due to the eccentricity of the planks at theirconnection– Flexure and shear buckling effectsIt was considered for tender that the doubly-curved and twistedglulam planks would be fabricated by initially curving the lathswhich make up the member, then gluing all of the precurvedelements together to form a oubly-curved plank. This fabricationprocess would have involved complicated clamping assemblies,although from discussions with a number of fabricators at the timethis was a preferred method and had been used successfully onprevious projects. To avoid reducing the allowable strength of the timber due to theinitially precurving the laths, it was assumed that the thickness ofthe lath would be r duced to achie e  radius over thickness valueof greater than 240 (as given in EC5). This was necessary as theareas of small curvature, some as small at 6m radius, weretypically at the supports where stresses were higher.Durability is always a key issue where timber structures arepotentially exposed to high moisture levels. The timber for the roofwas specified as a standard softwood species, therefore non-durable. It was decided that since the timber is typically internal,albeit in an unheated space, if condensation was to develop as thefabric is lifted off the timber the provision of natural ventilationshould preclude moisture levels from reaching a degree wheredecay may occur. E en those are s of the roof which are external,are typically protected from direct wetting by the fabric claddingand large overhangs. Therefore the moisture content would beunlikely to be reater than 20% for more than a short period,meaning decay would be unlikely. At the base of the Funnelswhere it is possible for driving rain to reach the timber, it was feltprudent to specify a mod rately durable timber species. Thespecification called for a Class 3 timber in accordance with EN350-2, with the contractor proposing Larch. Larch was not usedelsewhere due to it higher cost. A clear coating was specified tohelp protect the timber during construction before the fabriccladding was in place. All glues were specified as Type 1 inaccordance with EN 301.DeliveryFor tender 2D drawings were prepared which represented theroof’s 3D geometry, with a 3D model (.dxf format) being issued thatdefined the overall centreline geometry of each timber member.Specifications were drafted in accordance with Eurocodes andincluded a clause equiring t sting of th  timber connections forstrength and stiffness.ConstructionThe construction contract was awarded to Demathieu & Bard(France) as main contractor, with their specialist timber11  Curved plank being fabricated (image: © Holzbau Amann) 12  Curved planks part way through the fabrication process (image: ©Holzbau Amann)SE18 paper-Centre Pompidou Metz_Layout 3  15/09/2011  16:06  Page 24a) b) a) b) 11Figure 21. Centre Pompidou Metz  - More examples of reference geometries by designtoproduction 193 M A D E  T O  M E A S U R E :  D I G I T A L  F A B R I C A T I O NFigure 7.14 (a) Digitally derived component geometries; (b) oversized glue-laminated sections machined to form curved planksSource: (a) © designtoproduction GmbH; (b) © Holzbau Amann GmbH.(a)(b)Figure 22. Centre Pompidou Metz  - Oversized glue-laminated sections machined from reference geometries (Fig. 71) to form curved planks by Holzbau Amann12Figure 24. The lower part of the funnel-shaped columns - shown steel chairs minimizes the chance of condensation by creating a gap between the roof membrane and the wooden gridshell.Figure 23. Close up view funnel-shaped columns.“The wood structure spans from a steel ring at the top of the hexagonal central tower to woven columns below that have been described as ‘tulips’ or ‘mushrooms’”. (Self, 2014: P266) 95% of the roof structure is made from Austrian or Swiss spruce, with the rest being beech and larch (dezeen). Larch is used for the lower part of the funnel where it reaches the ground because of its higher weather resistance capacity (Fig. 23 & 24).  13Figure 25. Interior view of Haesley Nine Bridges Golf Club House14In the past decade, there have been some attempts to create a multidisciplinary environment where there is no separation between the design and fabrication processes. The advancement in creating engineering wood and digital fabrication, such as using a 7-axis Kuka robot or a 6-axis Universal Robot for wood milling, has enabled architects to bring material, parametric design, and robotic fabrication knowledge into one architectural software (Fig. 27). Within this “integrated design-to-fabrication” environment, the architect’s role has changed because it enables the architect to interact with the machine directly. This integration leads to a material-informed form, understanding fabrication constraints at the conceptual design phase, and efficiency and streamlining fabrication processes by eliminating traditional plan drawings (Fig. 28). Therefore, this methodology has created a new architectural language in wood and demands a cultural shift to an interdisciplinary environment.Figure 26. Author at Perkins&Will  - Univesal Robot 5 (UR5) experiment  15Tool Path GenerationPW Interface (Scorpion)TCP Configuration Virtual Robot Simulation URScript Code Generator Generate Core Kinematics The overall process flow - Integrated Design-to-Fabrication Visualization• TCP Planes in Pose Structure • Tool's Speed• Thread Definition • Additional coding to capture fabrication information into the UR log file  • Decide for the Forward Kinematics or the Inverse Kinematics • See Fig 140• This is a graphic display only based on the Forward KinematicsParametric Design of the GeometryGH, Python, C#GH, PythonURScript prog. lang.Designed by Oliver D. KriegRhino, GHTCP Planes (positions & orientations) generated remotely by the PW InterfaceFigure 27. The overall process flow - Integrated Design-to-Fabrication Visualization 16In the case of the Timber Wave structure, there is only one sheet for construction instructions rather than a package of construction drawings. Figure 28. Construstion Map reproduced from the Timber Wave’s Rhino and Grasshopper design script17Why I am interest in Wood Joinery? Wood is sustainable and can be regenerated. It stores carbon. Interesting forms can be designed through an aggregation of a wooden joint system. Unlike steel, wood joinery is flexible, and can always be taken apart after assembly, unlike welded steel. Steel helped to develop the architecture profession as a movement from load bearing massive walls. In the past, steel changed how we designed in term of loads and it involved engineers. Therefore, it transformed the way the profession works. In the recent era, the study of wood joinery allows us to learn how the material go together. This is where things get interesting. The joint is where design can be expressed; both structurally and expression wise. With computational design, we create joint parametrically, then replicate them at different angle to create a form. Therefore, the technological advancements in wood like engineering wood, parametric design, and robotic fabrication have created into a new architectural language in wood. When we think parametrically, design is not one joint, it is a series of joints responding to different conditions that it is encountering. Figure 29. The structural details of Pompidou Metz’s beams18“Engineered timber is far more than just sustainable. The natural properties of the wooden fiber in combination with clever engineering bring forth a multitude of perfectly adapted building materials. Structural timber members are light but strong and durable, making them highly efficient. The elasticity of the material allows for «cold bending» of even doubly curved surfaces up to a certain degree. Thin layers of wood can be combined to form curved glue-laminated beams made to measure with high precision. Computer-controlled fabrication (CNC) adds another dimension to timber construction. Even complex curved shapes can be produced at high speed with flawless precision – including all connection details – and ready for assembly.”     - Designtoproduction et al., www.freeform-timber.comFigure 30. Structure detail of the Timber Wave. The diagrid is double-layered with thick plywood spacers at the intersection points. The spacers also act as connectors to the cedar planks19Technological advancements are not sufficient alone. A cultural change across multiple disciplines needs to happen in order to widely accept wood as a new building material. Antoine Picon describes “the problem posed by the introduction of a new construction material” as follows:“In architecture and construction, the introduction of the new material almost always means debate and controversy. Some of the difficulties arising from its introduction are technical, others economics, while others have more to do with the mental framework within which architects and engineers develop. New material disturbs the habits of established thought: it challenges the division of labour between practitioners. In the pivotal period of the 18th and 19th centuries, iron was no exception to the rule. More precisely, the advent of iron precipitated the abandonment of the Vitruvian tradition and the definitive split between the professions of architecture and engineer. The coincidence between technical advances and theoretical, doctrinal and professional transformations allows a better understanding of certain dynamics in the field of architecture and construction. The domain does not evolve under the pressure of technical innovation alone. In order to spread, the innovation must in any case be recognised as such by a professional community. In the case of architecture and construction, as in many other areas of material culture, innovation comes about at the intersection of technical and social issues that need to be decoded.” (Picon, 2010: 51) This innovation relates  into two concepts: material-informed design and an interdisciplinary approach in design and teaching which will be discussed further in typology-3 of this thesis (Correa et al., 2019).20More about my GP1 Precedent Study - Learning by Prototyping through reproduction of those precedents Like learning by prototyping, I gained a deeper understanding of the precedents through a 3D digital reproduction using the Rhino and Grasshopper software. This reproduction enabled me to highlight their specific design and construction features based on the criteria presented in this report. For example, it was sometimes impossible to read the curvature of the beams by looking  at available photos or drawings; whether this was an illusion of perspective or it was a real double-curved beam. Therefore, the reproduction was like a cross-reference tool to validate my findings against the reference materials. This reproduction was the most time-consuming part of the GP1 report, but the result was rewarding. 21Typology 1 - Gridshell - Frei Otto’s Light Weight Principle 22Precedent 1Mannheim MultihalleMannheim, Germany, 1975Architects:  Frei Otto and Ewald Bubner of Atelier Warmbronn,         Carlfried Mutschler and Partner, Mannheim         (Joachim Langner, Dieter Wessa, and Winfried Langner) Engineers:  The Structures 3 group of Ove Arup & Partners, London         Edmund ‘Ted’ Happold and Ian LiddellFigure 31. Interior view of Mannheim gridshell “Exhibitions traditionally, because their buildings require to have dramatic impact and because they only need to have a limited life, have often been the place where new ideas are tried out-new ideas which later, in more modest form, become important in general building” (Happold et al., 1976: 247). 2325 E A R L Y  G R I D S H E L L SMULTIHALLE AND RESTAURANT, BUNDESGARTENSCHAU, MANNHEIM, GERMANY, 1975THE MULTIHALLE (MULTI-PURPOSE hall) and restaurant, for the Bundesgartenschau (German Federal Garden Festival), held in Mannheim, in 1975, marked the acceptance of the timber gridshell as a new typology for long-span architecture. At the time it was the boldest and most extensive example of timber gridshell construction. Here Frei Otto and Ewald Bubner of Atelier Warmbronn, working with the architects Carlfried Mutschler and Partner, Mannheim (Joachim Langner, Dieter Wessa and Winfried Langner) and the Structures 3 group at engineers Ove Arup & Partners, London (Edmund ‘Ted’ Happold and Ian Liddell) contrived one of the most innovative spatial grid structures of the twentieth century. Designed between 1972 and 1974, the project also involved as consultants the Institut für leichte Flächentragwerke (IL) and the Institut für Anwendungen der Geodäsie im Bauwesen (IAGB), at the University of Stuttgart. Engineers for the substructure of the gridshell were Bräuer and Späh, Mannheim.Completed in 1975, the gridshell (Figure 2.18) covers an area of around 7400 m2 with a roof surface area of approximately 9500 m2. The larger Multihalle spans up to 60 m and the Restaurant 50 m, with the gridshell rising to 20 m and 18 m respectively (Hennicke and Schaur, 1974; Burkhardt, 1978: 58).Initially using catenary hanging chain models to derive the building’s form, the measurement techniques of the day were used to derive its geometry. Subsequently, newly developed computer-aided form-finding techniques, as used on the S.T.I. experimental structure, were implemented to determine the precise geometry required to enable accurate structural calculations to be made, and for the gridshell, which contains about 34,000 nodes and around 72,000 m of timber, bars up to 100 m long, to be constructed.Figure 2.18 Aerial view of the gridshell for the Bundesgartenschau (German Federal Garden Festival), Mannheim, 1975Source: © Institute for Lightweight Structures and Conceptual Design (ILEK), University of Stuttgart.Figure 32. The bird’s eye view of the gridshell for the Bundesgartenschau (German Federal Garden Festival)  - DaytimeFigure 33. The bird’s eye view of the gridshell for the Bundesgartenschau (German Federal Garden Festival)  - NighttimeProfessor Frei Otto: “I have been thinking about grid shells for a very long time. When I was a prisoner of war in Chartres, France, I worked as an architect. We had a lot to do and worked pretty hard but we had very few materials. So l developed a lightweight theory, and one thing led to another. I made my first models of hanging shells in 1946. Everybody knows that a catenary hanging down can be inverted to an arch. In principle it is quite simple but in practice much more complicated because of buckling. Until the middle 1950s, I had never heard of Antonio Gaudi. I was very interested and happy and gradually we discovered the whole history of vaults and grid shells. The lattice shell in Mannheim is one of the latest examples; I hope only that it is not the last, as for me the use of grid shells is just beginning. Many think that Gaudi as just a sculptor. He was, indeed, a sculptor, but he could shape structures so that they were successful. He had the courage to build columns non-vertically because he was convinced his models showed him the better way...We built the so-called Essen Shell for an exhibition. A lot of things happened-some lattices broke and some finger joints opened-but in six hours we erected this roof, and it was such a rush. In the same year we built a small 10 m x 10 m shell with students at Berkeley, California. Subsequently, we carried out many studies in this field. I became interested in the question: Must a shell be completely symmetrical or ‘geometric’, and what is really the goal? It is often very difficult and inconvenient to plan a building symmetrically. So I studied ways of making asymmetrical forms using simple methods of erection. We did the grid shells for the Montreal pavilion at Expo ‘67... We studied all kinds of wood. It so happens that we reimported Canadian hemlock to Canada as a grillage, pulled the grillage out and in about eight hours had both shells in place-l8 to 20 m span. We used out tent structure as the crane to pull them up … Our Mannheim model was built on a marble plate for high precision; also our friends Linkwitz and Preuss needed a big model for their photogrammetric computer runs. We are very happy that the architects Mutschaler and Langner have given us the opportunity to realise the concept of this large shell. Sometimes I was very anxious-particularly at the beginning-when we worked on this model, because I refused to go over 40 m span. I said we would only build a shell of 20 m, and then we wanted to double the span! That means eight times more space-now we have a free form span of 60 m in one direction and 80m in the other. The construction firms did a good job-especially Mr. Toll, the Wehmeyer chief engineer...Now we hope that all visitors to the garden exhibition will derive some benefit from it. The trees and flowers are blossoming, and the building seen from the outside seems to get smaller and smaller. If the surface is wet you do not see the building, just the clouds mirrored in the rain-polished surface. But at night it is very large and if it is illuminated from within you feel you have a huge artificial sky landscaped on the roof; that is what the architects wanted, and the effect I have been trying to create over the past few years” (Happold et al., 1976: 250). 24Form-Finding Process: Otto’s works are famous for its physical form finding model that were inspired by nature - such as spider webs, leaf structures, and soap bubbles. His works demonstrate building with a minimum amount of material (light-weight shells). He used catenary hanging chain models (Fig.34) for his form-findings which was the same technique that Antonio Gaudi used in his organic structure to achieve an optimal shape (Fig. 35). Liddell says: “[this] form finding method also suggests a construction method using an equal [flat] mesh square grid of timber laths or steel rods thin enough to be readily bent into shape. A square grid can be moulded to a doubly curved surface by the deformation of the grid squares into rhombi. Such a structure Otto described as a gridshell (gitterschale)” (Liddell, 2015: 39).After some initial shapes were defined with wire mesh, a 1:500 wire mesh model was made with two large domes that are connected with covered walkways, resembling low hills blending with the landscape (Fig. 36).  After that 1:500 sketch model, the architects made the final hanging chain model to define the boundary lines and the geometry of the building. This model was at the scale of 1:100 with a straight chain line of 15 mm representing every third lath on the real structure with 500 mm spacing between the laths. The model had small rings connecting the straight chain line (Fig. 37). This grid model was assembled flat by hand and then transferred to the support system that was positioned on a marble slab marked with 2D grid lines(Fig 38). Then the boundaries were adjusted to achieve the desired geometry (Fig. 39) (Happold et al., 1975: 106).  The next step was a measurement of the model in order to have a precise geometry for construction. This was done using a stereo photography method by professor Klaus Linkwitz and his team of engineers in the Institut Fur Anwendungen der Goedesie im Bauwesen (IAGB or Institute of Applied Geodesy in Construction) at the university of Stuttgart (Fig. 40). These photos were processed by the computers at the time  - CDC 6600 computer which was as big as a room  - to  get the coordinates of the nodes using a program developed by IAGB. These processing proved that the hanging chain model was not precise; “for example, the links were not always the proper length of 15 mm, and in places they went into compression”. Therefore, the initial coordinates were adjusted to present an “ideal hanging chain with the distances between the nodes exact and all nodes in equilibrium under self-weight”. The results of this processing were the coordinates of all nodes, plotted drawings of the net, and the member forces from the equilibrium calculation (Fig. 41 and 42) (ibid.:108).Figure 34. Form-finding experiment by Frei Otto using catenary hanging chain based on Hooke’s principle of inverting a hanging net.Figure 35. (a) Hanging model by Gaudi (b) La Sagrada Familia, a masonry construction with its structural geometry driven from physical scaled hanging modelForm in Tension Structure in Compression Self-Weight Structure (b) (a) 25Figure 37. Close-up view of the hanging model showing wire links connected by ringsFigure 36. (Top left) Wire mesh model, at the scale of 1:500, used to decide initial architectural/spatial form Figure 38. Transferring chain net to the support system Figure 39. Hanging chain model This image is removed for copyright reasonsThis image is removed for copyright reasonsThis image is removed for copyright reasonsThis image is removed for copyright reasons26Figure 40. Stereo photography of hanging chain model by IAGBFigure 42. Computer plot of 3 m net of Multihalle85 m   60 m Figure 41. Computer plotted plan of Multihalle and Restaurant gridshell geometry - plot of 1.5 mThe Mannheim Multihalle spans about 80 meters (Fig. 15) and its roof area is 7400 m2, but its doubly layered shell thickness is less than half a meter. The ratio of the shell’s thickness to its span is about .00625. We can see that this is even less than the ratio of the thickness of an average eggshell to its mean diameter (about .007). It proves that this gridshell has an efficient use of materials and proportionally it is thinner than an eggshell (Mihalik, 2013). This image is removed for copyright reasons This image is removed for copyright reasonsThis image is removed for copyright reasons27Figure 43. (Left) The interior view of the entrance arch  Figure 44. (Above) The building during the exhibition The digital model enabled engineers to determine the exact geometry required for accurate structural calculations of a gridshell composed of about 34,000 nodes and around 72,000 m of timber bars up to 100 m long each, to be constructed (Fig. 43 and 44). Today, this unique structure is still the largest self-supporting timber gridshell in the world with a span of 60 m and a maximum height of 19 m. The shell is completely in compression to efficiently carry vertical loads. “The structure was designated a historical cultural monument in 1998, however, in recent years it has become critical to repair the aging gridshell to ensure its long-term survival” (Fast+Epp).  This image is removed for copyright reasonsThis image is removed for copyright reasons28Figure 45. (a) Gridshell node joint detail; (b) Realization of a typical node in the Mannheim gridshell(b) Figure 46. Mannheim gridshell structure32 E A R L Y  G R I D S H E L L Sincrease in elastic modulus (Happold and Liddell, 1975: 114–115).To achieve the required DIN 4102, Class B1 fire resistance for the translucent, grey-tinted, open weave, PVC-coated, polyester mesh fabric, developed by Degussa, the base fabric fibre coating was heavily dosed with antimony trioxide flame retardant, and non-flammable softeners were incorporated in the self-extinguishing PVC coating (Burkhardt, 1978: 131–133).Construction detailsIn a double-layer gridshell each node has to allow slip to occur between layers during erection but must transmit shear forces between layers in service. Working with the Timber Research and Development Association (TRADA) in the United Kingdom, Arup conceived and tested a joint, shown in Figures 2.26 (a) and (b), which would maintain a constant clamping load of 400 kg while allowing for 5 mm of shrinkage of the full depth of timber in the node. Connection was by an 8 mm diameter threaded steel rod, through clearance holes – slotted in the outer layers – with a 55 mm x 1 mm thick steel spreader washer at each end and a total of four proprietary 35 mm diameter Schnorr disc springs (three at the outer surface and one at the inner).To stiffen the shell, a diagonal network of twin 6 mm diameter, 19-strand steel wire ties was installed at 4.5 m centres each way (Figure 2.27). It was initially hoped that these could be installed at the mid-depth of the grid but to ensure a simple fixing they were finally installed across the outer layer, connected to the main joint bar by an aluminium cable clamp substituting for the outer nut, and with the top plain washer replaced by a 50 mm diameter bulldog connector, as shear connector. It was also found to be necessary to increase the stiffness of some of the members carrying high axial load. This was achieved by inserting double (folding) wedge blocking Figure 2.26 (a) Detail of the Mannheim gridshell node joint; (b) typical node as realised in the gridshellSources: (a) © Gabriel Tang, redrawn from Burkhardt (1978: 112); (b) © Gabriel Tang.(a)(b)(a) Structural Detail - Design Process: The decision is to use 50 × 50 mm laths of Western Hemlock timber which can be found in long lengths. The initial plan was to build the gridshell using single layers of laths running in two directions perpendicular to each other at 500 mm spacing. However in some places double layer laths were considered.Additional calculation on shell buckling and load testing on a working model of the Essen shell (Frei Otto’s previous gridshell) proved that the initial dimension of the Mannheim shell was too thin and “the collapse load of the Multihalle shell as proposedwas only slightly more than the dead load”. These tests indicated that “the collapse load of the shells had to be improved”. It was agreed rather than increasing the lath size to 100 X 100 mm, doubling the 50 x 50 mm laths would be the proper solution to achieve the required bending stiffness. Therefore, the gridshell concept consisting of doubly layer laths running in two different directions, connected with bolts at the crossing points, came to realization (Fig. 45 and 46) (Happold et al., 1975: 106).      The Principle of Otto’s Gridshell Construction:“The principle of construction was that the laths would be laid out at ground level and all the node bolts inserted but not tightened. They would then be lifted up to their intended shape as a doubly curved shell. In this process the squares of the meshes are distorted into parallelograms and the ends of the laths have to move into their edge boundaries. The grid would have to be supported in this shape until the node bolts are tightened and it becomes stiff enough to bear its own weight. So flexibility is required for the installation and rigidity thereafter” (Liddell, 2015: 41). This explains why the hinged joints (Fig. 45(a)) are larger than the diameter of the bolt in one direction, allowing the double layered laths to slide over each other during the bending process until the planned geometry is achieved. This bending and lifting process has been demonstrated in detail in the precedent 2, 3, and “Gridshell Model Testing for  typology 1”. 2934 E A R L Y  G R I D S H E L L Sthe node joints are tightened and stiffening ties are added. Also the lack of stiffness means that deviations from the designed surface profile tend not to be self-correcting, requiring more lifting points to be used. In fact, at Mannheim, it was estimated that the gridshell self-weight and collapse load of the structure, unless temporarily propped during installation, would be practically identical (ibid.: 130).Earlier gridshells, such as that built in Essen, had been shaped and lifted into place using cranes and this method had initially been proposed at Mannheim. However, the engineers at Ove Arup became aware that very large cranes would be needed and would have to be in position for several weeks until the grid could be fully stabilised. A physical wire mesh model was used to simulate the flexible double-layer grid during installation, to determine appropriate lifting points and anticipated loads. This indicated that cranes capable of lifting 16 tonnes at a radius of 40 m were necessary, requiring expensive 200 tonne capacity cranes. Excessive cost, therefore, led to the adoption of the alternative erection method – lifting with fork-lift trucks of scaffolding towers installed at 9 m spacing and supporting 2.5 x 3.5 m spreaders to carry the grid (Happold and Liddell, 1975: 131; Liddell, 2015: 46) (Figure 2.28).As the flexible grid sagged by up to 200 mm between the temporary supports, its form subsequently had to be adjusted in order to conform, within an acceptable tolerance of ±50 mm between towers, to the shell geometry defined by Klaus Linkwitz. Adjustment proceeded in strips across the shell, first, in one direction, then at right angles to it, working from the centre towards the perimeter, with the node bolts being tightened as work progressed (Figure 2.29). Smoothness of the gridshell curvature was checked by eye (Happold and Liddell, 1975: 132).Figure 2.28 (a) and (b) Fork-lift, scaffold towers and spreader beams used to push up the gridshell from belowSource: © Institute for Lightweight Structures and Conceptual Design (ILEK), University of Stuttgart.(a) (b)Figure 47. (a) and (b) Pushing up the gridshell from below using “Fork-lift, scaffold, and spreader beams”Installation and Lifting Process: “The 50 × 50 mm laths came in various lengths up to 6m. They were joined in the factory into lengths 30–40 m long by finger-jointing. Site joints were made by nailing 50 × 25 mm laths on to each side. This technique was also used to repair any joints that broke during installation. Bending tests were made on the laths to find the minimum radius of curvature before they broke. It was 10–12 m. Where the radius was less than this the laths were split into two layers of 25 mm depth” (Liddell, 2015: 44).“Earlier gridshells, such as that built in Essen, had been shaped and lifted into place using cranes and this method had initially been proposed at Mannheim. However, the engineers at Ove Arup 44 I. Liddell / Case Studies in Structural Engineering 4 (2015) 39–49Fig. 6. Detail of grid construction.it had to be modified to take into account that one straight member represented a number of curved members and the factthat shear deflections which would reduce the out-of-plane bending stiffness could not be ignored and that same stiffnesswould be reduced by axial force.The ties were modelled as timber sections, hence the wire area was increased by the modular ratio. The ties in the modelcould take compression as well as tension, the problem of one tie going slack was ignored since the stiffness was quite low.The Multihalle model had 192 nodes, 297 members and 254 ties. The buckling collapse load for the structure was foundto be 105kg/m2, which was considered satisfactory for the heated Dome. However further testing on the shear stiffnessgenerated by the cross nodes was actually 40% of that used in the computer model. Runs with this value of shear stiffnesshad indicated that failure would occur. Hand calculations indicated that members with high axial forces would fail incompression so it was decided that the shear stiffness had to be increased in these areas.3.3. Stage 3, construction detailsThe 50×50mm laths came in various lengths up to 6m. They were joined in the factory into lengths 30–40m long byfinger-jointing. Site joints were made by nailing 50×25mm laths on to each side. This technique was also used to repairany joints that broke during installation.Bending tests weremade on the laths to find theminimum radius of curvature before they broke. It was 10–12m.Wherethe radius was less than this the laths were split into two layers of 25mm depth.3.3.1. Node jointsThe two lower laths at the cross nodes (Fig. 6) had single holes at 500mm spacing to take 8mm threaded rod. The uppertwo layers had slotted holes to allow themembers to slide over each other to take account of the bending of the pairs of lathsduring the lifting process. To maintain bolt tension during the dimensional changes from shrinkage and expansion causedby seasonal moisture variation 4 disc springs were used, 3 on the top and 1 below bearing on 55mmdiameter plain washers(Fig. 7). The springs would generate 450kg of force when compressed by 6mmWhere additional shear capacity was required folding wedges 300mm long were inserted between the laths and slidtogether so they were a tight fit. 3 - 8mm bolts were inserted through the wedges with disc springs as at the nodes.3.3.2. Cable tiesComputer runs showed that a pair of 6mm 19 wire strand through every sixth node in each direction would providesuitable stiffness. Some small aluminium cable clamps were found from the electrical industry that would take the two6mm cables and were clamped with 2–8mm bolts. The lower part of the clamp had threaded holes so it could replace thetop nut on the node bolts with the nut replaced to provide clamping action. The other hole was simply used for clamping.3.3.3. Boundary connectionsOtto had proposed a detail that would accommodate all the angles of the shell where it was attached to the boundaryconcrete wall. It used a half round timber section on which a plywood board was screwed at the correct angle. The lathswere then to be screwed to the board (Fig. 8). The engineers’ tests had demonstrated that this would not be strong enoughfor the calculated forces. They proposed that 2 layers of 25mm plywood should be bolted to steel brackets set to the correctangle.The laths could then be bolted to this plywood layer during the installation process. The setting out for this boundarycame readily from the geometrical data.Figure 48. Detail of the grid with a bracing system composed of a diagonal network of double layered 6mm steel wire (19-strand) at 4.5 m centresbecame aware that very large cranes would be needed and would have to be in position for several weeks until the grid could be fully stabilized. A physical wire mesh model was used to simulate the flexible double-layer grid during installation, to determine appropriate lifting points and anticipated loads. This indicated that cranes capable of lifting 16 tonnes at a radius of 40 m were necessary, requiring expen ive 200 tonne capaci y cranes. Excessive cost, therefore, led to the adoption of the alternative erection method – lifting with fork-lift trucks of scaffolding towers installed at 9 m spacing and supporting 2.5 x 3.5 m spreaders to carry the grid” (Fig. 47)(Chilton et al., 2017: 34). Bracing Concept: “The two lower laths at the cross nodes had single holes at 500 mm spacing to take 8 mm threaded ro . The upper two lay rs had slott d holes to allow the m mb rs to slide over each other to take account of the bending of the pairs of laths during the lifting process. Computer runs showed that a pair of 6 mm 19 wire strand through every sixth node in each direction would provide suitable stiffness” (Fig. 48)(Liddell, 2015: 44). This image is removed for copyright reasons This image is removed for copyright reasons30Dr. Gabriel Tang: “As architects work with materials to create space, the understanding of structural principles and material behaviour becomes imperative. Architects do not work against gravity to create space. Rather, architects should work with gravity by understanding how effective force transfer can help to create efficient forms and bring economy and aesthetics ... To understand structural rationale is therefore to understand a correct way of building.To take learning out of textbooks and formal lecture venues, the construction workshop reinforces theory lessons and encourages on-site thinking, spontaneous problem-solving not offered by conventional methods of teaching and learning in the design studio environment” (Tang, 2013: 390).After two decades of silence, Frei Otto’s Mannheim gridshell became an inspiration for an improved method of gridshell construction exhibited in the Japan Pavilion for the Hanover Expo designed by architect Shigeru Ban (2000), the Weald and Downland gridshell designed by Edward Cullinan Architects (2002), and Savill Garden gridshell designed by Glenn Howells Architects (2006) (ibid.:390). Yet, rather than explaining these well known precedents, I decided to demonstrate one student-driven design-and-build projects in Italy (Precedent 2) to articulate the value of learning by prototyping. This precedent is a small scale project which make them easier to understand and capture the whole construction process at a human scale. The form finding method and structural analysis in this precedent is much faster and easier using today’s digital tools without a need for historical catenary hanging chain models or stereographic photographs. However, they followed “The Principle of Otto’s Gridshell Construction” as exactly explained in the “Precedent 1” (Fig. 49 to 57) to practice the “structural principles and material behaviour” as Dr. Tang explained in his 2013 paper.  This precedent has square meshes of double-layered laths running in two different directions. The Siracusa gridshell does not requires perimeter beams because the laths are parallel with the opening edges. In addition, the bracing members are running horizontally and the lifting of the flat grid is done by a crane (Fig. 56 (a) to (d)).  31Precedent 2Performative Wood GridShell SiracusaSiracusa, Sicily, Italy, 2013   Designed by The University of Catania (Italian: Università degli Studi di Catania, Struttura Didattica Speciale di Architettura di Siracusa)Professor Luigi Alini and his teamFigure 49. Performative Wood GridShell in Siracusa32Figure 50. Siracusa Gridshell  - Plan of modular grid made up three different modulesFigure 51. (a) to (c) Siracusa Gridshell  - Step 1 - Each module is laid flatFigure 52. (a) to (d) Siracusa Gridshell  - Step 2 - Folding & carrying each module to its final locationFigure 53. (a) to (d) Siracusa Gridshell  - Step 3 - Connecting the modules (b) (c) (d) (b) (a) (c) (b) (c) (d) 33Figure 55. (a) to (c) Siracusa Gridshell  - Step 4 - Make the grid wet for better gradual bendingFigure 54. Siracusa Gridshell  - Detail of hinged jointFigure 56. (a) to (d) Siracusa Gridshell  - Step 5 - Lifting with a craneFigure 57. (a) to (d) Siracusa Gridshell  - Step 6 - Bending continues(b) (a) (b) (a) (b) (a) (c) (d) (b) (a) (c) (d) 34I designed and built a gridshell working model to experience the physicality of the wood as a structural material, and learn and feel how it bends and moves under different forces. For this purpose, a gridshell which spans 5.5 meters has been digitally simulated. Gridshell Model Testing for Typology 1Scale of 1:10 made of basswoodFigure 58. Typology 1 Physical Experiment  - A GridShell model at scale of 1:10 made of basswood35 Support segments  for bracingThe Construction method is inspired by the precedent 3 (Fig. 41 to 51). For the digital simulation of this gridshell, a flat grid of equally-size squares is created using flat curves. These curves (or laths) are directly passed into the Kangaroo physic engine in Grasshopper tool (Fig. 46) in order to apply multiple forces on them. Through this process, each flat lath or curve is bent by pulling its endpoints inward until the final shape of gridshell is achieved (or until the maximum height of the vault is achieved). During this simulation the length of each curve will not change. This means a 500 mm x 500 mm square curve is distorted to a 500 mm x 500 mm parallelogram, but there are no size changes. Therefore, the uniform look of cells in the gridshell is achieved after the planned bending. Figure 59. Step 1 - Composing an interwoven flat grid; An inverse square mesh with five layers of wood; Double layered laths running in two directions; support segments are positioned at the second layer from bottom; washers are positioned on top and bolts at the bottomFigure 60. Step 1 - Exploded axo view of the inverse flat grid in Fig. 41 36Bolts and nuts are inserted into hinged joints but not �ghtened.This loose connec�ons/ fastenings allows distor�on during bending.  Hinged joints for flexibility during bending. Figure 61. Step 2 - flat grid in step 1 was folded and flipped over  Figure 62. Step 3 - Unfold the flat grid; now washers are at the bottom and bolts on top  Figure 63. Step 3  - (a) Axo view of the inverse flat grid in Fig. 41; (b) Axo view of the flat grid in Fig. 44 (b) (a) 37Original anchor pointNew anchor pointNew anchor pointOld anchor pointGradual Bending (or Lifting) Tightening the nuts after the planned bendingFigure 64. (Left) Step 4 - Gradual Bending (or Lifting) of the grid’s curves  - Axo of Fig. 47Figure 66. Step 5  - Tightening the nuts after the planned bendingFigure 65. (Above) Step 4 - Gradually pushing the anchor points inward38Figure 67. Step 6  - The shell at its final shape before adding the bracingFigure 68. Step 7  - The shell with adequate stiffness adding the bracingFigure69. Final gridshell39Typology 2 - Hexagonal Lattice Shell - Heavy Timber Section40Figure 70. The Centre of Pompidou Metz Figure 71. Chinese hat“The building is an event in the city – and beyond. It is big, a little rough, a little pudgy, but not ostentatious. Like its sister institution in Paris, it gives the impression that it is accessible to all” (Self, 2014: 268).Precedent 3Pompidou MetzMetz, France, 2010Architects:  Shigeru Ban (Tokyo), Jean de Gastines (Paris) Engineers:  Ove Arup (London), Hermann Blumer (Waldstatt, Switzerland),     Terrell (Paris,France) Fabricators:  Holzbau Amann (Germany) 41Shigeru Ban has gone beyond the limits of timber gridshell design with the luxuriant and cheerful design for the Centre Pompidou-Metz. However, it is a completely different typology, not exhibiting Otto’s “lightweight principle”. Here the grid is constructed with a heavy timber section which does not follow the bending process of typology 1. The same characteristics are applied to another magnificent gridshell of Shigeru Ban for Haesley Nine Bridges Golf Club House in Korea (Cabrinha, 2019: 198). Roof Geometry:  The roof geometry, based on a minimum surface, was initially designed using Arup’s ‘in-house’ GSA software. The roof surface went through a gradual refinement process with collaboration between architect and engineer. (Chilton et al., 2017: 192 & Lewis, 2011: 21)  “The form-finding process was an extremely time consuming exercise, which required a great many iterations to achieve an architecturally acceptable geometry. As the architect worked predominantly in 2D or with physical models, the 3D digital geometry was conveyed via rendered elevations of the Rhino model, which the architect would print and mark-up with comments such as ‘too high’, ‘too low’, ‘more curved’.” (Lewis, 2011:21)The minimum surface theory creates a surface within a defined boundary. This theory creates an anticlastic surface geometry.  According to Lewis, for this geometry “if you take two cross-sections at right angles to each other the curvature in one direction is opposite to the curvature in the other, and the sum of the two is zero.” For this roof, the boundary is composed of the outer hexagonal edge, the three Tube Rings, the Hexagonal Tower ring, and the base of four Funnel shape columns. (Lewis, 2011:21)However, I interpret the roof geometry as a free-from, which does not fully follow this mathematical definition as Lewis describes it here:“The true minimum surface geometry initially generated from these boundary conditions was not acceptable, as the surface cut through the buildings beneath. This was overcome by increasing the ‘tension’ in a number of elements, therefore manipulating the resulting global geometry pulling the surface into the desired shape. As the structure was never intended to be a tension system the geometry could be considered a little structurally arbitrary. However, the curvature provided some structural benefits in certain areas of the roof.”Lewis ends his paper about Pompidou Metz with a discussion on the form-finding of the roof: “As the structure was never intended to be a tension system, much time was spent trying to form-find a geometry that was, in the end, a little structurally arbitrary. That said, this was the only available method at the time. Given the recent developments in free-form modeling software, such as Rhino and even ‘form-finding’ plug-ins for such software, it is believed by the author that an architecturally acceptable geometry for structures with similar constraints could now be more rapidly achieved using these methods. Possibly the best solution could come from using an initially form-found geometry from the structural software, and subsequently rebuilding it as a NURBS surface in Rhino. This would also have the downstream benefit of providing the true curved geometry instead of the faceted geometry resulting from the form-finding analysis. Also with the numerous parametric plug-ins for Rhino, such as Grasshopper, the structural centreline geometry could be more easily parametrically driven directly in the modeling software rather than by spreadsheet, thus streamlining the design and delivery process, and enabling options to be more rapidly studied from a geometrical, structural, and cost point of view” (Lewis, 2011: 26).I believe the above discussion point is still arguable.  For my thesis, I will initiate form-finding in Rhino and Grasshopper, then review it with a structural engineer and then refine the geometry through an iterative process.Doubly-curved plank fabrication and construction processes: To achieve the woven form of wooden ribs that resembles a Chinese hat (Fig. 71), the glulam planks are doubly-curved and twisted to follow the roof’s surface.  This was initially considered by curving the laths, then gluing all of the pre-curved components together, creating a doubly-curved beam. This fabrication process required complex clamping assemblies, despite it being a successful method in the previous projects (Lewis, 2011: 24). However, the German timber contractor, Holzbau Amann GmbH, suggested an easier fabrication method by manufacturing oversized straight segments of glulam and then creating the required 42twist using a CNC milling machine. This required the oversized sections sometimes ending up 50% larger than a final doubly curved geometry. Although this can be seen as a waste of wood material, the generated waste could be used for wood fuel pellets. Nonetheless, this alternate method was faster, cheaper and provided higher dimensional accuracy. (Fig. 18 to 22 and 78) The disadvantage of this method is that the axis of the machined member in certain positions is not parallel to the grain of the plank, reducing the allowable strength of the beam. A re-assessment of wind and snow loadings allowed to reduce the members’ section size to 440 mm x 140 mm which almost compensated the material wastage (Chilton et al., 2017: 192) (Fig. 23 and 76). It is important to note that during the tender phase the contractor built a full-scale mock-up of a section of the roof to test the preferred fabrication method. The fabrication was completed in about 12 months, with 1600 individual glulam segments. The planks’ maximum length was 14 m due to transportation limitations, although the final beam size was shorter than 14 m due to its curvature.The minimum beam length was approximately 1 m. These dimensions further influenced by the restriction of the milling machines. The construction was completed in about 6 months while each plank was assembled individually and supported temporarily by trestle towers (Lewis, 2011: 25) (Self, 2014: 266). To achieve this preferred fabrication method, a precise and cost-effective understanding of the complex reference geometry of the curved elements is required. This means feeding a 3-D CAD model to a fabricator and expecting “mass-customized components some days later”. This is not a easy process and it  is a “downright utopian”. “The mass-customisation system that translates the design input into production data has to be developed first” (Scheurer, 2010b: 93). For this precedent, designtoproduction GmbH, who have offices in Zürich and Stuttgart supplied Holzbau Amann the precise reference geometries using a NURBS model (Scheurer, 2010a: 90) (Chilton et al., 2017: 192) (Fig. 72 to 75). In the digital reproduction of the Center of Pompidou Metz, I created the roof surface within the defined boundary curves using Rhino’s 5 T-Spline plug-in. Then the surface is relaxed using the Kangaroo engine in the Grasshopper tool and Rhino 7 WIP’s SubD tool. The roof is supported on four funnel-shaped columns which are the extension of the continuous roof gridshell,  a circulation hexagonal core which holds the peak of the roof at a height of about 36 m, and oval steel rings where the rectangular exhibition gallery tubes punctuate the roof geometry (Fig. 70). The lowest edge of the roof is at an elevation of 8 m (Chilton et al., 2017: 186; Lewis, 2011: 22).  In the process of creating the digital model, a flat grid or a mesh of curves is laid flat on the ground to form a tessellation of equal size hexagons and triangles (Fig. 72). Then these flat curves are projected to the doubly curved undulated roof surface (Fig. 73). The projected curves (Fig. 74) become the driver to form the double layered wooden beams running in three directions while following the roof geometry.  Therefore the roof and its four funnel-shaped columns, composed of these woven beams, form one continuous surface. The gridshell does not have uniform cell sizes. This is noticeable especially around the funnel-shaped columns because the grid is stretched in these areas as a resultof this projection method (Fig. 75). The initial study to produce a less dense grid, in order to reduce the cost was rejected by the architect. The grid spacing is the architect’s aesthetic consideration to imitate the woven Chinese hat (Lewis,  2011: 22). The roof has an 8,000 m2 surface area which means 18,000 running meters of glue-laminated beams or about 1,800 doubly curved glulam segments which are individually CNC fabricated. Designtoproduction firm created a reference geometry for these doubly curved glulam segments and gave Holzbau Amann - the timber construction company - the required CAD tool to precisely mill them (Scheurer, 2010: 90) (Fig. 18 to 22).    43Figure 72. Flat 2D hexagon pattern/grid 52m overall side length,  divided by 33, gives the 1.57m plan dimension & 2.7 m perpendicularspacing of membersFigure 73. Roof Geometry - A doubly curved free-form surface. This whole geometry is one continuous surface.Figure 75. Transformed blue curves to double Layered beams which give an impression of woven straw in a Chinese  hat.  Figure 74. Project the flat grid on the dou-ble-curved surface44440 mm x 140 mmFigure 76. Hexagonal lattice with double beams running in three directions. These beams are doubly curved (or twisted) to follow the roof’s geometry. Some of these twisted segments are outlined in red. This drawing is the enlarged view of the orange circle in Fig. 75. 2.7 m1.57 m1.57 mConnection DetailsSource: The Architecture of Art Museum bookP- 269 Figure 78. Exploded axo diagram of Joint connection detail of Pompidou Metz’s beams (Self, 2014: 269)This drawing is removed for copyright reasonsFigure 77. Enlarged view of some of the twisted curved beams from Fig. 76. The above figure shows how the six layers of wood beams are woven together, with four of them (two double layers) intersecting at the crossing point. “Connections are made with prestressed threaded bars and disk springs” (Self, 2014: 263). Because of the pin joint, shear blocks (or wood spacers) are required.  As shown in the above figure the gap of 328 mm between the pair of parallel beam (or the double layered beam) is larger than the total depth of the two crossing beams ( 2 x 140 mm) that are running through the double layered beam. This may be for technical or aesthetic reasons. “The shell’s stiffness was achieved using 2000 hardwood dowels and 3500 pins” (Scheurer, 2010: 486).45The Structural Engineer 89 (18) 20 September 2011 25subcontractor being Holzbau Amman (Germany).The typical French process is similar to a UK Design & Buildcontract, where the contractor is responsible for carrying out thefinal design verification. The main difference being that the level ofdetail the design is taken to before tender is far more than is usualin a UK Design and Build, with a full submission of calculationsprovided to an independent checking engineer prior to tender.During the construction phase Arup was responsible forreviewing alternative proposals by the contractor and checkingtheir calculations and fabrication drawings. Due to contractualissues Arup was obliged to withdraw from the contract one yearafter construction began, following considerable efforts workingwith the contractor to refine its value engineering tender proposals.During the tender negotiations and subsequent final design bythe contractor, there were a number of changes to reduce cost tosuit the contractor’s methods of fabrication. The most notable costreduction change being the significant simplification of the back ofthe roof, whereby the gridshell was replaced by a system ofprimary and secondary glulam beams. Other changes included thedesign of the node connection and the method of fabrication ofthe planks. The timber contractors preferred fabrication method for thedoubly curved and twisted planks was to initially manufacture over-sized straight sections of glulam, these were then machined usinga CNC milling machine. In some cases the oversized sections were50% larger than required due to the doubly curved geometry (seeFig 11 and 12). This method provided greater dimensionalaccuracy, was faster, and according to the contractor a fraction ofthe cost of producing doubly curved glulam sections directly evenwhen considering the high wastage. The disadvantage ofmachining the curved members is that the axis of the resultingmember is at an angle to the grain of the timber, thus leading to areduction in the allowable strength of the member. Thecompressive strength of standard glulam perpendicular to thegrain is typically only about 15% of its strength parallel to the grain,with a significant reduction with only a 10° to 20° angle. It wasagreed with the contractor that a maximum angle of 5° would beallowed, with the strength of the timber reduced accordingly.During the tender phase the contractor built a full scale mock-upof a section of the roof to test their fabrication methodology.Testing was a requirement of the Arup specification to justifycalculation assumptions. An extensive program was undertaken bythe contractor at the University of Bern in Switzerland, whospecialise in timber construction. The main focus of the testingwas of individual connections, although some plank assemblieswere tested along with a complete panel almost 10m across.Observations were made on the load deflection behaviour, ultimatecapacity, and failure mode. Due to the relatively small number oftest specimens the testing was used to verify calculated values,and not as a basis of design. Due to the contractors desire to avoid site drilling for bolts at theNode connection, their alternative proposal had a timber ‘spigot’shop glued into each plank with a predrilled oversized hole throughits centre. The oversized hole was required for erection tolerance.Shear forces are transferred by friction between the timberinterfaces of the spigots, this requiring the single M24 bolt to beprestressed with the aid of a stack of 125mm diameter springwashers. This is an innovative although very complex connection,which is something we had strived to avoid at the design stage asfeedback from the industry had led us to believe a morestraightforward solution would minimise cost and risk.Taking advantage of the wind tunnel and snow drift studyresults, the contractor was able to reduce the size of the planks to440 × 140mm. The fabrication took approximately 12 months tocomplete, with the roof divided into 1600 individual glulamsections. Planks were a maximum length of 14m limited bytransportation, although much shorter lengths were required dueto the curvature. Erection took approximately 6 months with plankserected individually, temporary support was provided by individualtrestle towers. Figs 13 –16 show images of the roof underconstruction.DiscussionA point for discussion is the generation of the geometry for the roofusing structural form-finding analysis. As the structure was neverintended to be a tension system, much time was spent trying to16 Top of funnel showing some of the most highly curved members, and the transition from Larch to Spruce (image: © Shigeru Ban Architects)13 Roof under construction, May 2009 (image: © Shigeru Ban Architects) 14 Roof under construction, June 2009 (image: © Shigeru Ban Architects)15 Fabric cladding being installed, July 2009 (image: © Shigeru Ban Architects)SE18 paper-Centre Pompidou Metz_Layout 3  15/09/2011  16:06  Page 25Figure 79. Roof under construction Figure 80 (a) A steel ring supports and receives the roof wood structure and enables the exhibition gallery to pass through the roof. (b) Connection of the roof’s grid to the steel ring.200 M A D E  T O  M E A S U R E :  D I G I T A L  F A B R I C A T I O NFigure 7.21 (a) A steel ring reinforces the timber grid around the gallery penetration of the roof; (b) connection of the timber grid to the steel ringSources: (a) © Holzbau Amann GmbH;  (b) © Koffi Alate – Taiyo Europe.(a)(b)200 M A D E  T O  M E A S U R E :  D I G I T A L  F A B R I C A T I O NFigure 7.21 (a) A steel ring reinforces the timber grid around the gallery penetration of the roof; (b) connection of the timber grid to the steel ringSources: (a) © Holzbau Amann GmbH;  (b) © Koffi Alate – Taiyo Europe.(a)(b)Assembly of planks began from the top central ring and continued downward with scaffolding holding up the planks (Self, 2014: 266). This is not a modular system and curved planks were assembled one by one (Fig. 79 and 80(a)).  46Precedent 4Haesley Nine Bridges Golf Club HouseYeoju, South Korea, 2009Architects:  Shigeru Ban (Tokyo), Kyeongsik Yoon (KACI International) Structural Engineer:  Hermann Blumer (Waldstatt, Switzerland) Fabricators:  Blumer Lehmann (Switzerland)Figure 81. Haesley Nine Bridges Golf Club House47Haesley Nine Bridges Golf Club House has a grid structure and its repeating elements provides adequate lateral resistance that eliminates a need for bracing members for the facade of the building, resulting in a beautiful rainforest canopy floating 15 m above ground (Fig. 81) (Chilton et al., 2017: 210). The opening above the funnel-shaped columns provides sufficient air and light for space beneath this canopy. This gridshell structure is inspired by a traditional Korean weaving pattern and is another outstanding large-scale gridshell that because of its similarities to the Centre of Pompidou Metz, fits in typology 2 of this report. The gridshell again has a hexagonal-triangular pattern made of glue-laminated timber with a heavy timber section size. The oversized sections follow fire resistance regulatory requirements (Chilton et al., 2017: 198). Similar to Shigeru Ban’s Centre of Pompidou in Metz, this 2D grid is projected to a double curved roof, resulting in non-uniform cell sizes and beams segments that are either straight, single curved or double curved to follow the roof’s reference geometry. Except for having a different timber fabricator, the same teams had a close collaboration in the realization of this other Shigeru Ban’s gridshell (Fig. 15). While the size of gridshell in Korea is one-third of the one in Metz, it still portrays impressive figures in terms of beam fragmentation and involves the same challenges in terms of its digital workflow and the CNC milling of the beams. The gridshell for Nine Bridges Golf Club House is composed of 15,000 half-lap joints (Scheurer, 2010: 486).  “At least with respect to free-form wood structures, file-to-factory production is still more of a Utopian concept than a reality ...It is clear that these projects were not feasible – neither in the allotted time nor with the required level of precision – without automated planning and production. Yet despite the technological progress, fashioning a free form with high precision is still an art unto itself – though the mathematical groundwork was laid in the 1950s in the French automotive industry. The input for the fabrication plans for Metz consisted of a 3D DXF model in which the roof structure’s nodes were connected by straight lines. In order to arrive at the continuous curved glulam beams from the bent lines, an elaborate NURBS model was reconstructed as reference for the curved roof surface. In Yeoju a different path was taken. The roof form was not determined by a digital model, but by gathering clearly defined boundary conditions: the position of the roof’s edge,the position and angle of the column’s connections, and the locations of the flat zones, amongst others.The iCapp program then extrapolated the respective reference surfaces for the five elements from this relatively small amount of information. In both projects, all subsequent planning phases were founded on these reference surfaces [Fig. 58 and 93(a) are representation of these reference surfaces]. From these, the detailed geometry of every building component was derived step by step. A so-called parametric CAD model is the key to efficiently planning such complex structures: they facilitate – based on “rules” and parameters – the automated fabrication. The first challenge was to find a universally applicable description of the half-lap joints – i.e., one that functions for every conceivable angle – for the roof in Yeoju. The second challenge was to derive an algorithm from this description and thus to write a program that automatically constructs the half-lap joint in a 3D model. Wood-construction programs have long been available that have the attributes to create such parametric connection details. However, none of them have mastered working with free forms. And so the complete planning for both roofs had to be executed on software from another discipline.There are always a number of possible paths toward realizing complex structures. Several different criteria point to the path will be taken. Because some of these may be contradictory, they must be prioritized in advance. Accordingly, the result will never [be] optimal in the literal sense – it will be acceptable given the manner in which these conditions were specified. This is demonstrated in both projects by the segmentation of the beams. A beam’s dimensions are limited by the available raw material, the CNC machine’s size and workspace surrounding it, transportation logistics, etc. For example, a larger number of smaller components, is easier to transport but requires additional connections. And the more curved or twisted a beam is, the more expensive it is to fabricate. Currently, such complex decisions cannot be made in an automated process. Thus, one draws on the experience and intuition of the participating specialists, backed up by the quick feedback attained by trying out the different options.” (Scheurer, 2010: 486)I created a digital reproduction of the Nine Bridges Golf Club using Rhino 6 and the Kangaroo engine in the Grasshopper tool for this report (Fig. 82 to 91). The remainder of this section illustrates the step by step of this reproduction and delineates the joint system and modularity of this structure which differentiates this gridshell from the one in the Centre of Pompidou Metz. The assembly process of the Nine Bridges Golf Club’s gridshell can be a great inspiration for the ability to assemble and dismantle the grid structure for this thesis. Additionally, I hope this thesis could be a platform to explore the “automated fabrication and production” delineated in Shigeru Ban’s two gridshells. 4836 m 72 m 9 m 9 m 9 m 13.6 m Figure 83. Flat 2D hexagon grid divided into 32 equal modules. The grid of 36 m x 72 m in the above plan is broken into 32 modules (each 9m x 9m). The bases of the 21 columns (in three rows of seven) are marked in red in the plan. The elevation drawing is produced by the vertical projection of the hexagonal grid onto the roof’s surface (shown in Fig. 82). Figure 82.. Axo of Roof geometry made of 21 funnel shape columns. The red circles illustrate the funnel profile. Figure 84. RCP Plan and elevation of Nine Bridges Golf Resort. 49Figure 86. Axo of roof composed of tessellation of hexagons and triangles (after the projection of the flat grid and the trimming of stretched curves at the bottom of each cone).   Figure 85. RCP Plan and elevation of Nine Bridges Golf Resort after trimming the stretched 3d curves at the bottom of each cone. This trimming is required before creating the curves for each column (Fig. 87 and 88). 509 m9 mFigure 88. (right) - The process of creating curved columns: (a) Enlarged view of a single cone (or funnel-shaped column); (b) Connection of the hexagon base of the cone to the base of the column on the ground using 12 straight lines; (c) Projection of those 12 straight lines to the funnel-shaped surface while making them a continuation of the roof’s curvaturesFigure 87. (top) - Axo view of the roof after the creation of 21 columns, each composed of 12 curves.  These support 32 roof ele-ments. 9 m 9 m 13.6 m Roof Plan Sec�onAxo(a) (b) 51Figure 89. Plan and elevation drawings of hexagonal lattice with single layered beams running in three directions. These beams are straight, single-curved, or double-curved (i.e. twisted) to follow the roof’s geometry. Two of the twisted segments are outlined in red and blue.Figure 90. (a) Axo view of roof around the funnel shape column composed of 12 curved beams; (b) Enlarged view of the curved beams. (a) (b) 52204 M A D E  T O  M E A S U R E :  D I G I T A L  F A B R I C A T I O NFigure 7.24 Interior view of the gridshell, Haesley Nine Bridges Golf Resort, Yeoju, South KoreaSource: © Blumer-Lehmann AG.Figure 7.25 Reference surfaces for the five gridshell element typesSource: © designtoproduction GmbH.Figure 7.26 Multiple lap-jointed components assembled to form a continuous single-layer gridshell surfaceSource: © designtoproduction GmbH.Figure 91. The roof of Nine Bridges Golf Resort with continuous beams like a rainforest canopy. Figure 92. Structure Detail - A continuous single-layered gridshell composed of two lap joints at every crossing. There is a major difference between this joint systemand the one used in the Centre of Pompidou Metz. Unlike using a single bolt to fix the crossing members,which allowed some rotation between grid layers, and requires shear blocks, an interlocking system is used here that eliminates  rotation at the crossing points: “To allow for continuous girders in all three directions, they are split into five layers with two lap joints at every crossing. The complete roof contains some 3,500 curved timber components with almost 15,000 lap joints. Even though many parts are similar, 467 individual components with over 2,000 different joints had to be described in detail. This was only possible by formally describing the whole structure in a parametric system [algorithm] that automatically generated the detailed models from a reference surface and some numerical parameters” (Scheurer et al, 2011;77). This algorithm was invented by designtoproduction and was supplied to the fabricator Blumer Lehmann. 53209 M A D E  T O  M E A S U R E :  D I G I T A L  F A B R I C A T I O NFigure 7.31 (a) and (b) Prefabricated roof sections being craned into position; (c) bird’s eye view of the gridshell during constructionSource: © Blumer-Lehmann AG.(a)(b)(c)209 M A D E  T O  M E A S U R E :  D I G I T A L  F A B R I C A T I O NFigure 7.31 (a) and (b) Prefabricated roof s cti ns being craned into position; (c) bird’s eye view of the gridshell during constructionSource: © Blumer-Lehmann AG.(a)(b)(c)209 M A D E  T O  M E A S U R E :  D I G I T A L  F A B R I C A T I O NFigure 7.31 (a) and (b) Prefabricated roof sections being craned into position; (c) bird’s eye view of the gridshell during constructionSource: © Blumer-Lehmann AG.(a)(b)(c)Figure 93. (a) While the roof is broken into 32 modules, there are only five distinct reference surfaces types; (b) Gridshell model based on the yellow reference surface in Fig. 93(a) and it represents the pre-fabricated module in Fig. 94(a). Figure 94. (a) and (b) Prefabricated roof modules being craned into th  sit ; (c) Bird’s eye view of the  lattice shell during construction“Pre-fabrication shifts the work from the cold and wet building site to the controlled environment of the workshop, but adds logistics problems. On top of that it shifts the complexity to the front of the process. It becomes vital to have all issues resolved before shipping a puzzle with 3,500 parts and a team of 35 assembly specialists half way around the world” (DesigntoProduction).(a) (b) 54Precedent 5Timber Wave UBC, Vancouver Campus, BC, 2017Architects:    Achim Menges  and Oliver David Krieg (ICD at the University of Stuttgart),           David Correa (University of Waterloo), and           AnnaLisa Meyboom (UBC SALA)Engineer:      AnnaLisa Meyboom Fabricators:  UBC Centre for Advanced Wood Processing (CAWP ) with helps from           industry participants, and Master of Architecture students Figure 95. Timber Wave at UBC  - The diagrid structure made of straight  plywood components and the cedar planks under construction “By coupling stock cedar planks with a robotically fabricated diagrid substructure, the project uses geodesic methods to create a double-curved [surface named] timber wave” (Correa et al., 2019: 81).55“The prototype showcases distinctive wood fabrication possibilities that integrates computational design, material characteristics, and digital fabrication in a direct design to production paradigm, leading not only to innovation in timber construction, but also for a re-interpretation of wood architecture” (Correa et al., 2019: 86).  The Timber Wave is a robotically fabricated timber prototype which demonstrates the flexibility of the wood material in creating double curved surfaces. The project was fabricated and assembled in collaboration between SALA, ICD, and the School of Architecture at the University of Waterloo through a one-week interdisciplinary workshop. The workshop was conducted by the architects and structural engineer of the project in collaboration with local wood researchers, industry participants, and students. The annual workshop has been organized by the project leads since 2016, and through the prototyping of organic wood structure at full scale, it aims to present three concepts: material-informed form, Integrated design-to-fabrication process, and an interdisciplinary approach in design and teaching. What is a Material-informed Form?These workshops provide opportunities to learn the anisotropic and hygroscopic characteristics of wood and explore its impact “as a driver of design intent and form”. This only come to realization through “a robust design-to-fabrication workflow capable of integrating complex parameters and associative relations inherent to fabrication, assembly and material performance”(ibid.: 88).The prototype’s form “is not imposed on the material but rather informed by the material. The material characteristics, limitations and structural properties inform the design, providing constraints but offering possibilities. The resulting techniques and forms are presented here as initial steps towards a new language of design in wood, which will better reflect the current design ethos” (ibid.: 76). For example, the curvature of the Timber Wave double curved surface is restricted by the elastic bending of cedar planks used in this project. Also, the size of diagrid substructure components is driven by the plywood sheet size and the bed size of the 8-axis Kuka robot (Fig. 100, 101, and 102).  What is an Interdisciplinary Approach and Why?As Antoine Picon says: “The innovation must in any case be recognized as such by a professional community. In the case of architecture and construction, as in many other areas of material culture, innovation comes about at the intersection of technical and social issues that need to be decoded” (Picon, 2010: 51). David Correa relates this innovation into one overarching concept: material-informed design, which argues that innovation in material is concurrent and catalytic to other changes in the design and construction industries. This refers to an interdisciplinary approach in design and teaching as follows: “In an era of unprecedented connectivity and global economies, disciplinary research remains a highly territorialized domain. The development and execution of these projects as week-long workshops as opposed to term long academic endeavors, is indicative of the larger challenges that lie ahead. While interdisciplinary research is highly lauded as a pinnacle of modern research, institutional structures of disciplinary funding and professional teaching accreditation struggle to identify frameworks that can support these types of initiatives ... Technical developments or architectural design visions in isolation are not  enough  to support meaningful building construction innovation ... Meaningful development of new technologies into commercial applications, however, only emerge at this intersection. Interdisciplinary research at full scale, like the work presented here, is positioned to be fertile ground for this type of exchange. The learning opportunities offered by full scale prototyping projects are unique as they provide a defined scenario with real testing conditions for design investigation, quality control, structural performance testing, material research, project management and cost evaluation” (Correa et al., 2019: 88).What is an Integrated Design-to-Fabrication Process?This integration refers to the integration of advanced robotic fabrication process into design process which embeds “cross-disciplinary knowledge into architectural software...Technically, the prototypes were developed using integrated ‘design-to-fabrication’ computational and form finding tools, implemented using a 7-axis robotic milling set-up” (ibid.: 74). Therefore, “an integrative design process, or design-to-fabrication process, is by definition and inter-disciplinary design process. Computational, robotic, structural, material and pedagogical tools and methods are positioned in support of each other both within and outside of disciplinary boundaries”(ibid.: 88). To be specific, the coordinate path that the robot head follows for timber milling, is encoded (or integrated) within Grasshopper(a visual programming language for architects). Then, these fabrication instructions are fed to a 7-axis robot which makes “traditional instructions such as plan drawings [for fabricators] become redundant”. The integration of fabrication into design tools is achieved by the Grasshopper plug-in “VirtualRobot”(Fig. 106 to 108). Therefore, the Timber Wave prototype became a full scale application of this new technology which allows the direct generation of machine code from the architectural design tool (ibid.: 75). 56Figure 96. Structure detail. The diagrid is double-layered with thick plywood spacers at the intersection points. The spacers also act as connectors to the cedar planksBeyond Form Definition … 83Fig. 11 (Right): Detailed photograph of the diagrid substructure. The diagrid is double-layeredand has thick plywood spacers at the intersection points, which also act as connectors to the cedarplanksFig. 12 (Left): Detailed photograph of the diagrid substructure during assemblyFigure 97. The diagrid substructure detail under construction showing self-aligning hygroscopic joinerystructure is that unlike Shigeru Ban’s lattice works (Typology 2), the wood components are not doubly curved. The cedar planks are a straight-off-the-shelf material, usually used as standard horizontal cladding. During the assembly, these cedar planks are bent in one direction in order to follow the curvature of the diagrid substructure. The diagrid substructure is composed of double layered plywood components that are custom milled using a 7-axis Kuka robot. When these straight plywood components connect to each other, the final doubly curved geometry is created. The robot’s flat bed supports this (Fig. 103 to 104). Another interesting feature about this diagrid Timber Wave Structure:This structure is composed of two complementary systems; a diagrid system (Fig. 96) and cedar planks (Fig. 101). The planks are fastened to the diagrid’s intersection points using standard wood screws. “The diagrid substructure can be assembled on site and is flexible but self-supporting at first. The intersection points of the diagrid are designed to be structurally rigid only in combination with the horizontally arranged cedar planks’’. The interesting point about this double curved 57Figure 98. (a) A double-curved reference geometry which is manually created. (b) The project uses geodesic methods to create a diagrid structure on this reference surface.(b) (a) Beyond Form Definition … 85Fig. 15 (Right): When unrolled from the design model, it becomes evident that the cedar planksare indeed straight. They are only bent in one direction when connected to the diagridFig. 16 (Left): The diagrid structure and the cedar planks during assemblyprovides precise geometric definition through robotic fabrication and self-aligninghygroscopic joinery, the planks are then easily aligned with the diagrid and fastenedthrough standard wood screws.By using advanced timber fabrication techniques and taking full advantage of theextended fabrication range of the multi-axis set up, large sections of plywood werecustommilled and assembled on-site into a unique one-to-one scale architectural pro-Figure 99. When unrolled from the design model, it becomes clear that the cedar planks are actually straight.Figure 103. (a) Double curved reference geometry (b) The project uses geodesic methods to create a diagrid structure on a manually created double curved surface.structure is that the thick plywood spacers are part of the joint system, positioned right at the intersection points. The four wooden dowels connect the double layered diagrid components and the spacer together and therefore no metal fasteners are required. “In order to ensure a permanent connection between these elements, dried wooden dowels are inserted during assembly. As the installation is located on site, exposed to a higher [relative humidity] R.H. environment, the dowels equalize their moisture content and therefore expand to lock the layered connection”(Fig. 102) (Correa et al., 2019: 82).Visualization of an Integrated Design-to-Fabrication Process:The digital modeling of this double curved building system and its fabrication instruction codes are done using the Rhino and Grasshopper tools. I created all the drawings in this section using the Rhino 3D model and Grasshopper scripts that Oliver David Krieg provided. At first, a double curved surface is created manually in Rhino. This double curved surface (Fig. 103(a)) becomes the reference geometry for the overall shape of the Timber Wave. The horizontal geodesic curves (black curves in Fig. 103(b)) are the driver for the diagrid structure. This method resulted in almost uniform cell sizes for the diagrid. The spacing of these geodesic curves are controlled parametrically based on the width of the cedar planks. Therefore, cedar planks follow the geodesic curves. The straight length of cedar planks are calculated using a curve-unrolling script within the Grasshopper tool (Fig. 104).   58Strip (A) Strip (A) The joint system detail is shown in Fig. xx The wood strips fit together precisely because the edges of the notches are cut on an angle using the 7-axis Kuka robot.Figure 105. “Visualization of the diagrid elements and multi-layered assembly system”. Figure 106. Structural details  - The joint system  599;1;89;0;810;1;310;1;010;1;110;1;210;0;3 10;0;010;0;110;0;20;1;00;1;10;1;20;1;30;0;00;0;10;0;20;0;3Strip (A) 9;1;89;0;810;1;310;1;010;1;110;1;210;0;3 10;0;010;0;110;0;20;1;00;1;10;1;20;1;30;0;00;0;10;0;20;0;3Strip (A) Figure 100. Wood strips of the diagrid structure should be broken to multiple components considering the wood sheet dimension and the size of the robot bed. Figure 102. Simulation of robotic fabrication of plywood components using the Virtual 7-axis Robot Figure 101. Strip A as shown in Fig. 105 Each strip of the diagrid structure is flat considering the fact that the robot’s bed is flat.60Figure 104. Robotic fabrication of the “Timber Wave” components at UBC CAWPFigure 103. Enlarged view of Fig. 109 showing the milling of edges of the notch on an angle  - The double layered boundary curves of these components provides the coordinates of top and bottom edges of the plywood components - Comparing these boundary edges with the Fig. 107, it confirms that only the two slanted edges of the notch are required to be milled on an angle. Top boundary curveBottom boundary curve61Figure 105. The “Timber Wave” assembly62Visualization  of a Virtual Robot:Using Correa’s words, “The experimental [installation of robotically fabricated pavilions in 2016 and 2018] were full scale applications of the developed technologies. Both were created with a custom design-to-fabrication computational tool allowing for the direct generation of machine code from the design files ... A simulation of the robotic milling process and export of robot control files are fully integrated in the computational design process“ (Correa et al., 2019: 75 and 84).A literal interpretation of the above argument is illustrated in Fig 112. In the past, architects were mainly using Rhino and Grasshopper as computational design tools for 3D modeling. Now, with the newly developed interface from ICD such as the VirtualRobot plug-in within Grasshopper (Fig. 112(c)) , architects can simulate robotic movements for a custom milling within an integrated design-to-fabrication tool. In this example (Fig 112(a)), we can imagine the green curve is the boundary edge of the shape that is going to be cut by the robot. Using a grasshopper script (Fig. 112(b)), the green curve is divided by five points (the red cross marks in Fig. 112(a)).  Then the coordinates of these five points are captured in an output file (highlighted in yellow in Fig 112(b)). Once this file is imported to the Kuka Robot, it provides instructions on how to mill by moving between these five coordinates. The milling process can be more precise by adding more control coordinates. The number of control points can be parametrically controlled within the Grasshopper script (Fig. 113 and 114). Therefore, by integrating the fabrication process into the design process, as shown in this example, an integrated design-to-fabrication process comes to reality.    This process also proves how working with a multidisciplinary approach, the boundary between an architect and a computer scientist (or a computer programmer) is blurred; the architects can write python, visual basic (red boxes in Fig. 112(b)), or a C++ plug-in scripts in the Grasshopper software for this integrated design-to-fabrication workflow. Therefore, it proves that we are on the path to make this knowledge exchange part of the routine practice of an architect: “While many industries have made leaps and bounds in adopting highly flexible and fully automated fabrication workflows using robotics, the construction and design industry are only just starting to open the door to these technologies. Recent developments in robotics combined with more accessible design-to-fabrication tools can now offer architects, designers and fabricators unprecedented access to a new design paradigm”(Correa et al., 2016). Figure 106 (a) to (c). Visual presentation of generating machine code for a robotic fabrication (b) (a) (c) Visual basic scripts integrated within Grasshopper63Figure 108. Generating 10 coordinates to provide movement instructions for a robotic fabrication Figure 107. Generating five coordinates to provide movement instructions for a robotic fabrication 64“[The Timber Wave ] prototype presented here [attempted] to demonstrate the importance of a conceptual shift from representation and form definition to informed material investigation, the re-purposing of robotic fabrication as method for informed material manipulation and the role of teaching as shift from lecture to active interdisciplinary dialogue. These investigations take small steps toward the larger research agenda of looking at what might be possible in wood in the future, what are the architectural languages and building types that these new possibilities can facilitate.[The project was] presented as a medium to begin a dialogue about methods of construction: integration of material behavior in the design process, integration of computational tools and fabrication processes and most importantly, the knowledge transfer to new architects and designers. The development, execution and teaching methodologies necessary for these projects have inevitably generated larger questions about disciplinary roles, existing design paradigms and the potential of future powerful design, analysis and fabrication tools—questions that are essential for the future of the practice and the sustainable future of our cities” (Correa et al., 2019: 89). Figure 109. The finished prototype65  Area (M2)  Span (m) Thickness (mm) Single Layer (SL) Double Layer (DL) Bending Lamination Twisting Manufacturing Cost Form Finding / Geometry Definition  Structural grid pattern Erection Technique Wood Type  Joint Type Modular Typology 1 Mannheim Multihalle  7,400  60 – 80   50x50 DL Yes (on site)  No  No Lower hanging models All in compression - Less Elaborative Quadrilateral, constant edge length of 0.5m Uninform  Pushed up from below hemlock, a straight grained conifer western hemlock Pin-joint Yes Performative Wood GridShell Siracusa   Less than 10m  DL Yes (on site) No  No Lower (GH Kangaroo physic Engine) Less Elaborative Quadrilateral, Uninform Lifted up with crane   Pin-joint Yes Typology 2 Pompidou Metz 8,000   20 m cantilever 40 m span   140x440 DL Yes (off site)  Yes Yes Higher  Rhino Surface – form in tension & compression – More Elaborative Tessellation of hexagon & triangles, Non-Uninform  Individual membrane assembled at site standard softwood glulam - spruce (95%) and larch (%5) Pin-joint No  Haesley Nine Bridges Golf Clubhouse 2,592    SL Yes (off site) Yes Yes Higher Rhino Surface – form in tension & compression – Compressive arches -  More Elaborative Tessellation of hexagon & triangles, Non-Uninform  Prefabricated modules assembled at site   Lap Joint Yes Typology 3 Timber Wave    DL Yes, only for the cedar wood planks (on site) No No Lower Rhino Surface – form in tension & compression -  More Elaborative Geodesic, Uninform  Individual membrane assembled at site  Cedar Planks and Plywood for the diagrid Dowel System No      (1) This is developed surface area (source: Lewis, 2011:20)  (2) Source: Ben Lewis paper & Timber Grdishell – P 186 S but Shell structure of architecture says (20-45 m & 22 cantilever – P266 of the Architecture of Art Museum says: maximum span is 40 m and cantilever is 20 m.  (3) Bending is only for the wood plank and not the diagrid structure (4) “the fabrication processes to produce the doubly-curved and twisted planks is very complex” (Lewis, 2011:22)  (5) Metz wood type is from Self, 2014: 266 -> “Wood species were used in relation to their density and the particular loads the beams would be taking in specific structural pieces” – Lewis: softwood glulam with grade GL24h in accordance with EN 1194 Precedent Analysis Summary66GP1 Lessons Learned• The digital and physical reproduction of the precedents listed in this report allowed the author to not only have a deeper understanding of each precedent, but also enabled them to highlight their priorities in each of those designs with respect to the thesis’ goals. The 3D digital reproduction was done using the Rhino and Grasshopper software. • GP1 enabled the drawings to speak about the design process rather than relying on some lengthy description. The GP1 report aimed to produce a good extension to the existing literature for the precedents listed in this report. • On a more technical level: • Typology-1 follows Frei Otto’s Principle of construction. It is a great example of lightweight structure but has a high chance of laths’ breakage (as a result of unexpected bending forces) in comparison to the enhanced gridshells in typology-2 and 3. • The pin joint method requires shear blocks to avoid rotation. • The lap joint method does not require shear blocks because the members are interlocked into each other. • A double-curved surface can be composed of members that are curved in one direction only (typology-1).  • A double-curved surface can be composed of members that are double-curved and twisted in order to flow perfectly along the surface (typology-2 and 3). • A double-curved beam can be realized using a subtractive method out of an oversized straight beam. This method is faster than the time consuming bending of members with complex clamping assemblies (typology-2). • ICD virtual robot is a Grasshopper plug-in which brings an integrated design-to-fabrication tool or the file-to-factory concept to a reality (typology-3).• Mass-customized fabrication and production require an automation or an algorithmic process (typology-2 and 3).   67Based on the number of gridshells that already exist in our world, you may ask, what is my position as a designer or the novelty of this thesis? Based on all the pros and cons described earlier about the three typologies of the gridshell, the unique aspect of this thesis proposal is that it proposes a system (not an architectural proposal or an instantiation of a system). Therefore, the proposed system is not about a form-finding exercise for a particular site. It is an open-source system (or computer script) that is generalizable in order to be applied to many surfaces: flat, single-curved, and double-curved surfaces. Of course, certain limitations exist, such as avoiding shallow intersection angles where an industrial robot can not fabricate the material.  When these circumstances happen, the robot’s flange hits the wood panel. This is a hazard moment, and it should be identified and re-adjusted during the design process. There is also the robustness aspect that is considered in this thesis. As seen in typology-2’s precedents, this robustness exists because they are permanent structures with a heavy beams’ thickness (140 mm x 400 mm in the case of Pompidou Metz). In addition to the complicated subtractive fabrication method, special equipment such as molds (or formworks) and clamps have been used to produce the double-curved beams. As discussed in previous sections, these beams are required to achieve continuity and to smoothly follow the curvature of the reference geometry. Plus, the complex fabrication of typology-2’s structures have been achieved by the collaboration of computer scientists at the Designtoproduction firm with world leader fabricators such as Holzbau Amann and Blumer Lehmann. Unfortunately, these types of machines and expertise do not exist at wood workshop centers such as UBC Centre for Advanced Wood Processing (CAWP). On the other side, typology-3 uses an integrated design-to-fabrication process. The gridshell is designed, fabricated, and assembled within an interdisciplinary environment where the knowledge can smoothly flow between architects, engineers, and fabricators. They also have double-curved beams which have been created on the fly at the assembly time without using any special equipment. However, this geometry is achieved because the thickness of the three-layered beam in this structure is only 1 1/4”. This narrow thickness allows bending based on wood’s anisotropic and hygroscopic properties. Additionally, Timber Wave is a temporary wood structure with thin beams that will deflect in over time.  Therefore, a generalizable gridshell system for a robust structure, fabricated without using any equipment other than a 7-axis industrial robot, is a valid thesis proposal. In this generalizable system, the beams are only curved in one direction when the system is applied to single-curved and double-curved surfaces. This planarity is required due to the fabrication limitation of an industrial robot. The beams’ segments can only be laid flat on the machine’s bed. This thesis is also different from typology-1 because it is not limited to the wood’s bending properties. Therefore, the proposed joint system with over-laying Mountain and Valley segments - as described in the next section - will be a new addition to the existing world of gridshells and joint systems. How this thesis moves the discipline of architecture forward?68GP2 - Joint System Design  69A Gridshell and a Joint System with Four Requirements: Continuity Distribution of Loads Planarity Modularity 70Beam Design - Scenario 1 and 2In this GP2 design, the beams are created using only two types of segments, called Mountain and Valley segments. In a traditional waffle structure, the beams running in one direction have their notches on one side only, thus the intersecting beams have their notches on the opposite side of the beam. On the contrary, in this design (Fig. 110 and 111), I distribute each rib or segment’s load by alternating which side of the beam upon which the notch resides. The Mountain segment has its middle notch at the bottom part of the segment, and the valley piece has the middle notch at the top part of the segment. Therefore, a single beam (or a rib) in a gridshell is composed of a pattern of Mountain and Valley segments. Each Segment is composed of two layers. Therefore, four colours are used to illustrate these two segments. If you look closely, you will see other notches because each segment spans up to four cells of a gridshell. Each segment interlocks to the next segment using half-dove tail joints. The reason for the step (or the half-dove tail joint) is to resist lateral forces; therefore, the two segments can not horizontally slide over each other. The two layers of the Mountain and Valley segments are laminated using an automated gluing process. This automation is achievable using a robot to ensure high quality standards. This two-layered system is designed because of fabrication and assembly requirements. Therefore, based on the latter requirement, the back and front layers can be used interchangeably for each segment before the lamination. That’s why I have defined two scenarios. In scenario 1, the mountain segment has the blue layer in the front, and the grey layer in the back and the valley segment has the orange layer in the front and the yellow layer in the back. For scenario 2, the lamination’s order is the opposite.71Distribution of LoadsMountain Segment Valley Segment Front View  - Scenario 1: Back View  - Scenario 1: Continuity Valley Segment Mountain Segment Figure 110. First composition scenario of Mountain and Valley segments of a beam when the generalizable gridshell is applied to a flat surface and the beams are perpendicular to each other. Figure 111. AXO view of the front and back view of scenario 1 72Distribution of LoadsMountain Segment Valley Segment Front View  - Scenario 2: Back View  - Scenario 2: Continuity Valley Segment Mountain Segment Figure 112. Second composition scenario of Mountain and Valley segments of a beam when the generalizable gridshell is applied to a flat surface and the beams are perpendicular to each other. Figure 113. AXO view of the front and back view of scenario 2 73This study model illustrates a portion of a two-layered Mountain segment based on scenario 2. The lamination line is shown with this dashed white line (Fig. 114.c).  A CNC expert fabricator told me that it is impossible to create this step efficiently out of one piece of wood (Fig.114.a). I experienced a similar issue when I worked with the Universal Robot 5 (UR5), and because of its bed leveling issue, I always need to mill deeper in the wood. In addition to a clean fabrication requirement, this two-layered system became an advantage during the assembly process (Fig. 120). Figure 114. (a to c) A study model fabricated by a CNC machine based on the Scenario 2 a) Layer 1 Back layer Layer 2 Front layer  Layer 2 Front layer  Layer 1 Back layer  Lamina�on Line b) c) 74Fig. 115 and 116 show how the Mountain and Valley system can be parametrically applied to a double-curved surface. The framework (in the top of Fig. 115) is a Grasshopper overlay to show how the strips (or a ghosted version of beams) are unrolled into the cartesian plane during the design process to get ready for robotic fabrication. Then 3D model of these single-curved beams are designed on that flat plane based on the above planar framework. Therefore, the planarity requirement in this design is achieved with the beams curved in one direction only; dictated by the industrial robot’s limitation. A  pattern of Mountains and Valley segments along the ribs defines the members’ hierarchy (Fig. 117). In this diagram, the slicing plane further illustrates the planarity or the point that the segments are single-curved while the whole gridshell can be a double-curved surface. This pattern at each intersection node resembles the moments as the wood is woven. If you follow the UP, DOWN annotations in Fig. 118, you can feel this pattern: the crossing ribs sometimes go over the coloured beam in the diagram and sometimes it goes under the coloured beam.Scenario 1 - When the Mountain and Valley Segments are Applied to  Double-Curved Surface75Valley Segment Mountain Segment Front View  - Scenario 1: Back View  - Scenario 1: Distribution of LoadsMountain Segment Valley Segment Continuity Planarity Figure 115. First composition scenario of Mountain and Valley segments of a beam when the generalizable gridshell is applied to a  double-curved surface. Figure 116. AXO view of the back view of scenario 1 with an enlarged view of a notch showing the bunny ears for a precise interlock into a crossing member.  76A  Pattern of Mountains and Valley SegmentsValley Segment Mountain Segment Continuity Planarity 1/2 Mountain Segment Slicing PlaneFigure 117. The slicing plane proves how all ribs are made of single-curves segments. 77Because of the Mountain and Valley design, the intersections create a pattern along the rib, as if the wood is woven. Distribution of LoadsUPDOWNUPUPDOWNDOWNUPDOWNFigure 118. A close-up view of Fig. 117.  78Three ways a robot can be used for an architectural task: By attaching a spindle and a router bit to the robotBy attaching a gripper to the robot(Out of scope of this thesis)By attaching a glue dispenser to the robotFabricationGluingAssemblyFigure 119. Attaching different tools to the Universal Robot (UR5)Source: a) Author, b and c) https://academy.universal-robots.com/modules/CB3/English/module3/story_html5.htm-l?courseId=2257a)b)c)79Module 1 is connected to module 2 (Fig. 120 a to e) by interlocking the dovetails joints from the side. Here you can see the benefit of having two layers for each segment and using them interchange-ably. Each Mountain and Valley segment is labelled with 1, and 2 representing scenarios 1 and 2 described earlier. Therefore, this generalizable gridshell is a modular system: you make a 3x3 module and attach it to the next 3x3 Module from the side. Another aspect of this joint system is the “Joint System Stabilizer” or a “Tension Ring” (shown as a white box in Fig. 120 d and e) at each intersection node to secure the crossing segments and avoid member’s rotation. The tension rings are screwed to each side of the mountain and Valley segments (Fig. 121 a and b). For the remainder of this report, these two terms will be interchangeable. Assembly Order80Study Model ModularityThe first five segments can be assembled in any order. The sixth segment has to be slide from the side.  Sliding Mechanism22 221222111121Assembly Order - Make a 3x3 module and attach it to the next 3x3 Module from the side. Identifies scenario 1 of the mountain or valley segments. Identifies scenario 2 of the mountain or valley segments. SlidingModule 2Module 1Module 1Module 2Figure 120. (a to e) Assembly Order d) a) e) b) c) 81Assembly of the Joint System Stabilizer Figure 121 (a and b). The assembly of the Joint System Stabilizer (or Tension Ring) with four screws.    b) a) 82One of this thesis’ learning outcomes was 3D modeling with fabrication in mind (aka “Ghosted method”). In this method (Fig. xx), I don’t need to extrude surfaces in the 3D space to produce a beautiful render because we only produce enough information sufficient for the robot to fabricate our geometry. In this case, when I know that I need two layers of wood that will be laminated together  - based on the fabrication and assembly’s requirement or limitation  - then I reflect that from the beginning of my design. As illustrated in this diagram, the center slice (or surface) of each layer of the wood is only created in the 3D model; there is no need to extrude this surface. Then, these surfaces along with some key points in relation to that surface are unrolled in the “World XY” plane, and then passed to the fabrication script. These key points identify the extrusion direction in the “World XY” plane, or what is called a “tool path” for the robot. Therefore, this ghosted method creates an integrated design-to-fabrication environment. An environment enables architects to use Rhino to create a reference geometry and then call the generalizable gridshell plug-in proposed by this thesis to design the joint system and interact with the robot for fabrication.  This plug-in is written with Grasshopper and Python scripts. A Ghosted Method - 3D Design Visualization with Fabrication in Mind 83Layer 2 Front layer Layer 1 Back layer  Layer 1 Back layer Layer 2 Front layer  Lamina�on Line Layer 2 Front layer Layer 1 Back layer  Laminaton Line  Tension Ring Top Surface Figure 122 (a to e). 3D Modeling  - A Ghosted Method  - (d) The white points in relation to the tension ring’s top surface identify the extrusion direction (shown with the black arrow) of the tension ring’s top surface.  b) a) c) e) d) 84The original square shape of the tension ring (or TR) (Fig. 123) is transformed to a parametric design (Fig. zz6 xx) when the system is applied to a surface that has beams that are not always perpendicular to each other. So when the beams are intersecting at an angle, rather than mimicking the square shape to create point A, I offset the geometry (show with the red lines) to avoid a large TR which, structurally may not be useful. Therefore, the geometry of the Joint System Stabilizer is in harmony with variable angle at each intersection (Fig. 124). Additionally, its extrusion is in harmony with the beams’ intersection line (Fig. 125). The Joint System Stabilizer Design (or Tension Ring) 85TR when the Beams are Perpendicular to each other BATR when the beams are not perpendicular to each other Smaller AngleLarger AngleB’AFigure 123.  The tension ring when the beams are perpendicular to each other.    Figure 124. The tension ring when the beams are not perpendicular to each other. Points A’ and B’ represent point A and B in Fig. 123.    A’86The geometry of the Joint System Stabilizer (TR) is in harmony with variable angle at each intersection. Figure 124.  Each TR has a slight variation from the other ones because of the beams are intersecting at different angles.  b) a) C) 87The Tension Ring’s Extrusion in Harmony with the Beams’ Intersection Lines Figure 125 (a and b). The green arrow is a Grasshopper overlay to show the extrusion direction.  b) a) 88Unrolled Joint System Stabilizer Surfaces after being Extruded Figure 126.  A array of Joint System Stabilizers 89Contouring Method + Parametric Rotation  for Slicing the Reference Surface and its Limitation As discussed earlier (Fig. 10), a contouring method is used to slice the reference geometry.  The angle or the orientation of this contour slice can be parametrically defined by the architect for a single-curved or double-curved surface.  Additionally, the architect can rotate each contour slice by a certain degree to create a variable intersection angle for each beam (Fig. 127 and 128). If a design is about expression and intent, then I am adding all these complexities to be more expressive and make the script as generalizable as possible. This slicing creates a foundation for the diagrid structure of the beams. Therefore, with the power of computational design and a 7-axis industrial robot that can cut on an angle, we can achieve variable angles at each intersection (Fig 129). Unlike a projection method for slicing the reference geometry, this rotation allows two sides of the beams to always be visible as we gaze at or walk through the structure. In the projection method that I used for my food market project (Fig. 130), the structure was less expressive because of the vertical projection of the slicing grid to the reference surface. Of course, when the angle is too shallow, the generalizable script should provide a warning to the architect to adjust the contour slice orientation or the rotation angle.  Otherwise, the robotic fabrication script fails because it gets to a situation where the robot’s flange gets tangled with the material which is not safe. Therefore, the same angle limitation that is currently applicable to the ICD robotic fabrication script should be applied to the generalizable gridshell script. 90Contouring Method + Parametric Rotation  +2s-2sFigure 128. In the center, the rotation angle is 0, and as you move to the right, the rotation angle increases by two degrees. Likewise, as you move to the left in decreases by 2 degree. This 2-degree variation can be parametrically defined.      Figure 127. The grey diagrid shows the original surfaces based on the contour slicing method. The green diagrid shows the rotating surfaces.   91Variable Angle at each Intersection αβFigure 129.The α and β angles vary at each intersection 92Figure 130 (a and b). One of my previous gridshell project - (a) Less expressive view - (b)  More expressive viewb) a) 93These elongated orange arrows further illustrate the 2-degree variation of the intersecting beams #1, 2, 3, 4, 5, and 6. Normal Vector Figure 131 (a and b). Fig. 131.a shows how the rib marked with the white arrow in Fig. 131.b intersects with the crossing ribs #1 to 7 at different angles. # 1 # 2 # 3#4# 5# 6# 7A 2D view of this beam is shown on the left.     # 1    # 2    # 3   # 4     # 5     # 6       #7Variable Angle at each Intersection Identifies beam’s intersection line94Planarity Figure 132. This diagram shows the beams are single-curved although the whole surface or geometry is double-curved.   95PlanarityFigure 133. A close-up view of the figure 132. 96PlanarityIn this design, all intersecting curves are planar  (or with a deviation of less than a millimeter) in order to achieve planarity. Figure 134. First, the angle between the diagrid curves (shown in red) are calculated. These red curves identify the lamination lines. Then, based on the half of the material thickness of each layer of the wood, points A, B, C, and D at each intersection will be identified. The blue curves are creating by interpolating these points. The blue curves identify the slice that passes through the middle of the each layer of the wood.  Figure 135. The small intersecting planes at each intersection are a replication of the plane of each curve to further illustrate the planarity of this generalizable gridshell.  The green Grasshopper arrows are aligned with the intersecting line of these small planes at each intersection node. These green arrows identify in which direction the blue curves should be extruded based on the width of the beam.  BACD97Pose StructureFeature PlaneWaypoint Move Target PositionSpeed VectorTCP TCP PlaneTool PathTool OrientationRPMRouter BitPythonPolyScopeLog FileThreadURScriptMulti-passIntegrated Design-to-Fabrication ProcessPrototypingFlange PlaneGrasshopperUR5Forward Kinematics Inverse Kinematics Lost in Thought - How to connect the dots?Figure 136. Connecting the dots98The Thinker sculpture is a reflection of me at the end of GP1, lost in thought on how to connect the dots: Learning all the robotic terms required for a milling task, and learning how to program a Universal Robot 5 (UR5) using Grasshopper, Python, and the UR5’s programming language called URScript.  To connect the dots, I did a direct study between GP1 and GP2 components of my thesis. This direct study attempts to test the idea of file-to-factory production, which can only be achieved using an interdisciplinary approach. A desire for a cultural shift in both industry and educational environments where the free movement of knowledge between disciplines leads to innovation. An environment that allows architects to not only design form and function, but also explore and test materials and prototype the build forms. Therefore, through learning by prototyping methodology, I tried to promote this new culture where the lines between the architect, engineer, fabricator, and computer scientist are blurred. This direct study aimed to test and practice the above single digital design-to-fabrication environment, composed of integrating material and robotic fabrication knowledge into a parametric design process. To be more specific, this direct study is a showcase of the integration of Rhino, Grasshopper(GH), Python, and the Universal Robot (UR) URScript programming languages into one single platform (Fig. 27).  Therefore, this direct study had two main objectives: • To understand the robot’s kinematics and program the robot for an architectural fabrication through different test scenarios. This experiment enabled me to have a fruitful conversation with my thesis chair and my thesis committee and develop an integrated design-to-fabrication process for the generalizable gridshell.  • Smoothen the path for upcoming students, architects, or designers interested in robotic fabrication; therefore, the final report of this direct study was a tool (or a user manual) for transferring the knowledge.As for my research about robotic fabrication in this multi-disciplinary world, I still consider this direct study a drop in the ocean. Therefore, the direct study was not a completed study but rather a new beginning. 99Living in today’s multi-disciplinary world, “computer skills aren’t an optional skill, they are a basic skill. We have to make sure all of our kids are equipped for the jobs of the future, which means not just being able to work with computers, but developing the analytical and coding skill to power our innovation economy ...Right along with the three ‘Rs’.”               - Barack Obama100The Universal Robot 5 (UR5) Simulating Human’s Arm ShoulderElbowWrist 1Wrist 2Wrist 3BaseCircular arrows show +/- 360 ° freedom at each jointFigure 137. The Universal Robot arm with its joint colored in darker gray. This could be a recommended  position for a milling task.  101What is a Tool, TCP, and Tool Flange?Figure 138 a) Top view - Tool’s flange orientation  b) Axo view of the tool’s coordinate system  - Tool’s flange orientation in relation to the Tool Control Point’s orientation (or TCP’s orientation).  a) b)TCPThe tool flange’s origin and its planeFigure 139 a) The right-hand rule to find the Z-axis based on the X and Y-axis. b) Robot’s base and the wrist-3 orientation. A waypoint (or a target position)“Default TCP has all coordinates on the end of the robot flange with +Y pointing away from the tool IO point.”The robot’s power cable always shows the Y-axis direction of the robot’s base coordination system.    Robots’ origin - robot’s base coordinate system (or the “Base Plane”)a)b)RxRyRzRxRyRzThe tool IO pointTool FlangeThis plane represents the point’s orientationX - AxisY - AxisZ - Axis102Visualization of TCP configuration TCPThe flange’s origin and its planeThe plane represents the point’s orientationTCPThe robot’s power cable always shows the Y-axis direction of the robot’s base coordination system   .Robots’ originExploded viewX - AxisY - AxisZ - AxisThe tool IO pointRouter BitRobot’s bed holding a wood board for fabrication.b)a) Scenario 1 ) When router bit hight is 39.5 mm: set_tcp(p[-0.0009, 0.1512, 0.0894, 1.5392, -0.3131, 0.0000]) Scenario 2 ) When router bit hight is 50 mm: set_tcp(p[-0.0009, 0.16178, 0.0894, 1.5392, -0.3131, 0.0000])a)b) When the height (“H value in shown above) of the router bit changes, it impacts the position of the robot’s flange center point in its Y-axis direction. Z value = 89.4 mmY value =  151.2 mm H  valueTCPThe flange’s origin or center point. This point is reposi-tioned based on the height of the router bit. Figure 140 (a and b) TCP configuration identifies the distance between TCP and the flange of the robot. This setting instructs the robot on how to interact with the material (or the wood board).   103Figure 141.   Source: Mahdiar GhaffarianFigure 142.   Source: Mahdiar GhaffarianFigure 143.   104Virtual Robot Fabrication Simulation VideoLocated at this link: https://drive.google.com/drive/folders/1IW3bGd52lO_Xlnq9-Mdy8f6T0qkibIUO?usp=sharing105Areas of Further Developments • The nesting of the geometry on a panelized wood is currently a manual process, similar to what happened in the Timber Wave structure. More research is needed to optimize the material efficiency and on how the grain of the material itself can enhance the final system in the case of curved beams.  • Plywood can be a good candidate for this generalizable gridshell system. However, when the length of Mountain or Valley segments exceed eight feet (which is the standard size of a plywood sheet), then plywood may not be the right material.  Some research is needed in the area of European CLT (a thinner engineering wood material in comparison to CLTs found in North America). The advantage of CLT is its long length of up to 20 feet.• At the moment this thesis only proposes a exposed structure. Additional investigation is required to design a cladding system for this generalizable gridshell. • More testings and modelings are required to further identify the limitation (the breaking points) and potential of this system. • More engineering reviews are required to ensure the stability of the system.  • More testing is required to integrate other slicing methods to this open-source system. • Develop a diagram to show the generalizable gridshell script as a Grasshopper plug-in with all the required parameters such as: reference geometry, material thickness, contouring slice angle in both direction, rotation angle for the contouring method, et cetera. 106I would like to mention that the past few years were an amazing journey for me with many challenges, lessons, and achievements – from the first design thinking course that I had at SALA when I created a joint system using 800 balloons, to the expanded and in-depth joint system discussed in this thesis. A thesis demonstrating and documenting the process of weaving a gridshell using the Mountain and Valley wood segments.  My goal in thesis was not to simply report nor to produce a finished industrial product, but rather to perform research and experimentation on design and creation of a double-curved generalizable gridshell system which is robust enough so that its design model can be adopted for full-scale buildings. In addition to this gridshell model, a computer script was also developed that can be applied to flat, single-curved, or double-curved surfaces.107Cabrinha M., Testolini D, and Korman B, ‘Lattice Shell Methodologies: Material Values, Digital Parameters’ in ‘Digital Wood Design’, Springer, 2019. ISBN: 978-3-030-03676-8: 198 Chilton J., Tang G., Timber Gridshells Architecture, structure and craft, Routledge, 2017. ISBN: 978-1-315-77387-2: 34, 186-210Correa D., Krieg O.D., Meyboom A., ‘Beyond Form Definition: Material Informed Digital Fabrication in Timber Construction’ in ‘Digital Wood Design’, Springer, 2019. ISBN: 978-3-030-03676-8: 61 - 92Correa D., Krieg O.D., Meyboom A., https://vimeo.com/191518785, 2016Designtoproduction, SJB Kempter Fitze, Lehmann Timber Construction http://www.freeform-timber.com/Dezeen, https://www.dezeen.com/2010/02/17/centre-pompidou-metz-by-shigeru-ban/   Dubbeldam W., ‘The Domino Effect’ in ‘57 Pavilions’, 2018. ISBN:978-1-940743-70-7: 9-10Fast+Epp https://www.fastepp.com/portfolio/multihalle-gridshell/Happold, E., and Liddell W. I. ‘Timber Lattice Roof for the Mannheim Bundesgartenschau’, in ‘The Structural Engineer’ 53.3, 1975: 99-135Happold, E., and Liddell W. I. ‘Timber Lattice Roof for the Mannheim Bundesgartenschau’, in ‘The Structural Engineer’ 54.7, 1976: 247-57Liddell, I. ‘Frei Otto and the development of gridshells’, Case Studies in ‘Structural Engineering’, 4, 2015: 39-49Mannheim Multihalle, https://mannheim-multihalle.de/en/blog-2/the-wonder-of-mannheim/Mihalik J., Tan M., and Zengeza S., http://shells.princeton.edu/Mann2.html, 2013Picon A., ‘The first steps of construction in iron: problems posed by the introduction of a new construction material’ in ‘Before steel’, Niggli, Zürich, 2010. ISBN:978-3-7212-0756-9Scheurer F., ‘Materialising Complexity’, 2010: 90 - 93Self R., ‘The Architecture of Art Museum - A Decade of Design 2000-2010’, Routledge, 2014. ISBN: 978-1-315-81714-9: 263 - 269Scheurer F., Stehling H., ‘Lost in Parameter Space?’, in ‘Architectural Design’, 2011: 70-79Scheurer F., ‘File-to-Factory Production and Expertise’, in ‘Detail’, 2010: 482-486Schwinn T., ‘Manufacturing perspectives’ in ‘Advanced Wood Architecture’, Routledge, 2017. ISBN: 978-1-315-67882-5: 188 Bibliography UR5 Resources: https://academy.universal-robots.com/modules/CB3/English/module1/story_html5.html?courseId=2182https://www.usna.edu/Users/weaprcon/kutzer/_files/documents/User%20Manual,%20UR5.pdfhttps://www.usna.edu/Users/weaprcon/kutzer/_files/documents/Software%20Manual,%20UR.pdfAbove two PDFs are complete user manuals for UR5/CB3 (version 3.0) and PolyScope interface (version 3.2). https://www.youtube.com/watch?v=YGVYQFRjuBM&feature=youtu.behttps://manualzz.com/doc/6351933/cb3_basic_training_3..                Above link is a very good power point presentation to understand PolyScope GUI. https://www.youtube.com/watch?v=YGVYQFRjuBM&feature=youtu.be   The above video shows how a UR  programmed for a “pick and place” task using a gripper tool.https://academy.universal-robots.com/modules/CB3/English/module3/story_html5.html?courseId=2257 An online course for TCP definition and how to configure TCP using the PolyScope interface. https://blog.hirebotics.com/engineering/universal-robots-programming-feature-point-orientationhttps://s3-eu-west-1.amazonaws.com/ur-support-site/32554/scriptManual-3.5.4.pdfhttps://s3-eu-west-1.amazonaws.com/ur-support-site/18383/scriptmanual_en_1.3.pdfhttps://s3-eu-west-1.amazonaws.com/ur-support-site/29983/Script%20command%20Examples.pdfThe above links are a complete documentation of URScript programming (version 3.5.4 and 1.3). 1081) Anticlastic structures: Tensile surfaces, that is, surfaces which carry only tension and no compression or bending, rely on double curvature for their stability. Stability is provided by the opposition of two curvatures which enable the surface to be tensioned without losing its form.Anticlastic surfaces are those in which the centres of curvature are located on opposing sides of the surface. This is commonly-described as a saddle shape. sis an anticlastic surface.Source: https://en.wikipedia.org/wiki/Catenary4) Geodesic: In differential geometry, a geodesic is a curve representing in some sense the shortest path between two points in a surface, or more generally in a Riemannian manifold. It is a generalization of the notion of a “straight line” to a more general setting.Source: https://en.wikipedia.org/wiki/GeodesicSource: https://www.designingbuildings.co.uk/wiki/Anticlastic_structures2) Minimum surface: In physics and geometry, a catenary is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends.3) Catenary: The catenary curve has a U-like shape, superficially similar in appearance to a parabolic arch, but it is not a parabola.The catenary is also called the alysoid, chainette,[1] or, particularly in the materials sciences, funicular.ex: A chain hanging from points forms a catenary; Antoni Gaudí’s catenary model at Casa MilàGlossary of Terms1095) NURB Model: NURBS, Non-Uniform Rational B-Splines, are mathematical representations of 3-D geometry that can accurately describe any shape from a simple 2-D line, circle, arc, or curve to the most complex 3-D organic free-form surface or solid. Because of their flexibility and accuracy, NURBS models can be used in any process from illustration and animation to manufacturing.NURBS curves and surfaces behave in similar ways and share terminology.A NURBS curve is defined by four things: degree, control points, knots, and an evaluation rule.Source: https://www.rhino3d.com/nurbs6) Anisotropic: is the property of being directionally dependent, which implies different properties in different directions, as opposed to isotropy. It can be defined as a difference, when measured along different axes, in a material’s physical or mechanical properties (absorbance, refractive index, conductivity, tensile strength, etc.)An example of anisotropy is light coming through a polarizer. Another is wood, which is easier to split along its grain than across it. Source: https://en.wikipedia.org/wiki/Anisotropy7) Hygroscopic: Wood can absorb water as a liquid, if in contact with it, or as vapour from the surrounding atmosphere. Although wood can absorb other liquids and gases, water is the most important. Because of its hygroscopicity, wood, either as a part of the living tree or as a material, always contains moisture.Source: https://www.britannica.com/science/wood-plant-tissue/Hygroscopicity 

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