HexBox Canopy: A Rapid Assembly Segmented Timber Shell with Wedge Joints by Valentino Tagliaboschi

Università di Pisa Dipartimento di Ingegneria dell’Energia, dei Sistemi, del Territorio e delle Costruzioni Corso di Laurea Magistrale in Ingegneria Edile-Architettura

HEXBOX CANOPY A Rapid Assembly Segmented Timber Shell with Wedge Joints

Candidate Enrico Valentino Tagliaboschi Supervisors Jun. Prof. Dr. Christopher Robeller Digital Timber Construction (DTC) group, Technische Universität Kaiserslautern Arch. Eduardo De Oliveira Barata Code-to-Production Team, the University of Sydney School of Architecture, Design and Planning Prof. Ing. Maurizio Froli Scuola di Ingegneria, Università di Pisa Assistant Supervisor Dr. Ing. Francesco Laccone Visual Computing Lab, CNR-ISTI Scuola di Ingegneria, Università di Pisa

Acknowledgments

This thesis has been written for the final assessment required to obtain the Masterâ&#x20AC;&#x2122;s Degree in Ingegneria Edile-Architettura (Building Engineering and Architecture) at the University of Pisa, Italy. The presented research has been carried out under the supervision of the Digital Timber Construction (DTC) research group, Fachbereich Architektur, Technische UniversitĂ¤t Kaiserslautern, and Code-to-Production Team, the University of Sydney School of Architecture, Design and Planning. First of all, I would like to express my gratitude to my supervisors, Christopher Robeller and Eduardo De Oliveira Barata for such an amazing and fruitful opportunity they gave me. I really appreciate their confidence in letting me fill a leading role in the design and planning of the HexBox Canopy. I would like to thank Felix, Lynn, and Rod for their dedication and the passionate teamwork we did for this project. Furthermore, I would like to thank all the Fatuk and USyd students who attended the workshop and collaborated in the building of the pavilion in August 2019 in Sydney. Special thanks to my dear friend Vicente with who I spent lots of my German nights in Kaiserslautern. Last but not least, I would like to thank Paola, my family, colleagues and friends for their support and encouragement during these years studying at the University of Pisa. Valentino

Abstract (ENG) Keywords: Lightweight Structures, Wood-only constructions, Timber Shells, Freeform Structures, Computational Design, Digital Fabrication, Robots in Architecture The HexBox Canopy demonstrates a new “plug & play” system for the rapid on-site assembly and disassembly without formwork of a segmented timber shell, consisting of relatively inexpensive, prefabricated hexagon-shaped boxes made from plywood plates. The work builds upon previous research for the planar and offsetable tiling of freeform shell structures (Liu, 2008; Troche, 2008), which was first implemented as a lightweight, sustainable timber plate structures with CLT plates by Tolszczuk-Leclerc (2016) and plywood plates by Li and Knippers (2015). Further research has been carried out for the improved efficiency, connections, assembly, and materials of such structures. Some remarkable recent case studies are the Recycleshell (Robeller & Vogt, 2019) by DTC group for the University of Kaiserslautern new “timber construction research campus”, and the ICD/ITKE BuGa Wood Pavilion (Alvarez, et al., 2019) for the 2019 federal horticulture show, Heilbronn, the largest such structure built to date. With 1531 timber segments making up 201 boxes, the HexBox shell is made exclusively of plywood components without the addition of any kind of metal fasteners for the main load-bearing structure. The major novelty is the wood-only connections between the boxes, which are produced from cut-off waste material resulting from the cutting of the main plates of the structure. These connectors are inspired by traditional tusk tenon-and-mortise joints, which were a smart and common method in handcrafted carpentry and cabinetmaking. Rather than attempting ultra-precisely fabricated elements, the diagonal shape of wedges allows assembling boxes even when there are small imperfections. Additionally, these joints allow for gradually pulling and forcing the boxes together, closing gaps between segments that may occur during assembly. The closing of such gaps is, in fact, critical for the overall precision and performance of the structure. When working with a large amount of differently shaped elements, manual drawing and handmade cutting are out of the question. Instead, the HexBox project is taking advantage of automated processes like computational design and digital fabrication techniques.

When it comes to the assembly, this can be simplified through integrated joints, where the position and alignment of parts result from their geometry. In the HexBox project, plates comprising a structural module are glued together using a novel technique exploiting Lamello Tenso connectors that allow for the

simple and safe 1K PUR adhesive joining of thousands of miter joints with individual dihedral angles. The structure was realized as a collaboration between researchers from the University of Kaiserslautern and the University of Sydney. As a member of the HexBox design team, the author of this thesis has worked on the conceptual design up to the construction, made several scale models and 1:1 prototypes exploiting the 5-axis CNC machine of the FATUK CNC workshop and the multi-axis Kuka robot of the TUK Department of Mechanical Engineering. Furthermore, the author formed a link between the design team and the University of Sydney Designing Modelling and Fabrication Lab (DMaF Lab), liaising with the technicians and providing fabrication data. Lastly, he handled the executive design and assembly process taking care of the implementation phase and project schedule. He has also trained and supervise students on the assembly sequence and collaborated with PMI Engineers who provided the structural adequacy certificate. The canopy was completely assembled by students in the frame of an international one-week summer school, held in August 2019 at the University of Sydney School of Architecture, Design and Planning.

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Abstract (ITA) Parole chiave: strutture leggere, costruzioni in legno, strutture a volta lignee, strutture di forma libera, progettazione computazionale, fabbricazione digitale, robotica per l’architettura HexBox è una copertura sperimentale a guscio segmentato, costituita da moduli scatolari esagonali in legno multistrato, dal costo relativamente contenuto. Tale progetto impiega un inedito sistema costruttivo a secco che, senza l’impiego di centine, ne permette il rapido montaggio in situ nonché l’eventuale smantellamento. La progettazione di HexBox si basa su precedenti studi sulla discretizzazione di superfici di forma libera tramite mesh a facce esagonali piane (Liu, 2008; Troche 2008). Ricercatori che per primi hanno implementato algoritmi di pannellizzazione esagonale nel campo di costruzioni modulari a guscio di forma libera, rispettivamente in moduli in CLT e legno multistrato, sono Tolszczuk-Leclerc (2016) e Li & Knippers (2015). Ulteriori ricerche sono state successivamente condotte per migliorare efficienza, collegamenti e assemblaggio di tali strutture. Esempi recenti sono il Recycleshell (Robeller & Vogt, 2019), realizzato dal DTC per il nuovo campus di ricerca sulle costruzioni in legno dell’Università di Kaiserslautern, e il BuGa Wood Pavilion (Alvarez, et al., 2019), realizzato dall’ICD/ITKE dell’Università di Stoccarda per la mostra di giardinaggio di Heilbronn del 2019. Quest’ultima è la più grande struttura del genere costruita fino ad oggi. Costituita da 1531 elementi differenti che compongono 201 moduli strutturali, la volta HexBox ha la struttura portante principale realizzata esclusivamente con componenti lignei, senza l’aggiunta di alcun tipo di connessione metallica. Questo è stato possibile grazie all’impiego di speciali connettori lignei, i quali rappresentano la principale novità del progetto. Le connessioni tra i vari moduli esagonali sono infatti prodotte sfruttando materiale di scarto derivante dalla lavorazione dei pannelli principali della struttura. Questi connettori sono ispirati ai tradizionali giunti a cuneo tipo tenone-mortasa, impiegati comunemente nella carpenteria artigianale lignea e nell’ebanisteria. La particolare forma affusolata dei cunei di fissaggio, i quali vengono ribaditi all’interno di apposite tasche presenti sul corpo principale dei connettori, permettono un serraggio graduale delle connessioni e l’eliminazione di eventuali spazi tra i moduli scatolari dovuti alle tolleranze di assemblaggio. Piuttosto che ambire ad un’estrema precisione nella fabbricazione dei moduli strutturali, questo tipo di connettori consente l’assemblaggio anche in presenza di piccole imprecisioni geometriche. Raggiungere una perfetta viii

aderenza e continuità all’interfaccia tra i moduli esagonali è infatti fondamentale per le prestazioni globali della struttura a guscio. Quando si lavora con una grande quantità di elementi di forma diversa, la redazione manuale dei disegni esecutivi e i sistemi di fabbricazione propri della carpenteria lignea tradizionale sono certamente inadeguati. La progettazione del guscio HexBox si avvale quindi di processi automatizzati, quali la progettazione computazionale e tecniche di fabbricazione digitale che sfruttano le potenzialità di macchine a controllo numerico (CNC). Per quanto riguarda la fase esecutiva di assemblaggio e messa in opera, questa può essere notevolmente semplificata attraverso giunti integrali, in cui la posizione e l’allineamento delle varie parti risulta dalla loro stessa geometria. Nel progetto HexBox, i vari pannelli che compongono un modulo strutturale sono incollati usando una nuova tecnica che sfrutta le giunzioni autobloccanti Lamello Tenso. Esse consentono allineamento, fissaggio e incollaggio con adesivo poliuretanico di migliaia di giunti obliqui – miter joints – di angolo differente, senza l’impiego di morsetti o presse. Il guscio segmentato HexBox è stato realizzato nell’ambito di una proficua collaborazione tra ricercatori dell’Università di Kaiserslautern e dell’Università di Sydney. In qualità di membro del gruppo di progettazione, l’autore della presente Tesi di Laurea ha partecipato e curato il progetto sin dalla fase concettuale, fino agli aspetti esecutivi e di dettaglio. Ha inoltre costruito e progettato diversi modelli in scala e prototipi 1:1 sfruttando una macchina a controllo numerico a 5 assi e un braccio robotico, disponibili rispettivamente presso i laboratori della Facoltà di Architettura e di Ingegneria Meccanica dell’Università di Kaiserslautern. Successivamente, l’autore ha fatto da intermediario tra il gruppo di progettazione e il Laboratorio di Fabbricazione dell’Università di Sydney, interfacciandosi con i tecnici e fornendo i file esecutivi di fabbricazione. Ha inoltre progettato la fase esecutiva, definendo il cronoprogramma e il processo di costruzione del guscio HexBox, oltre che a formare e supervisionare gli studenti durante l’assemblaggio della struttura. Ha inoltre collaborato con PMI Engineers che ha rilasciato il certificato di adeguatezza strutturale. La copertura è stata completamente assemblata e messa in opera dagli studenti durante il workshop Code-to-production, della durata di una settimana, tenutosi presso la Scuola di Architettura dell’Università di Sydney nell’agosto 2019.

Table of Contents

Acknowledgments ��v Abstract (ENG) �� vi Abstract (ITA) �� viii Foreword ��3 The HexBox Canopy: theme, context, and numbers ��5 Project players, sponsors, and partners ��6 Thesis outline �� 7

Part one: state-of-the-art �� 11 1_ Wood as a construction material �� 13 Why wood? �� 14 Intrinsic features and mechanical properties of wood �� 15 Structural timber and timber-based products ��17 Wood-only structures ��20 Mechanical attachment for wood-only constructions �� 21 Timber framing: a remarkable example of wood-only vernacular architecture ��23 A digital renaissance of timber traditional carpentry joinery ��25 Probabilistic models for withdrawal behaviour of selftapping screws �� 27 Previous page: Photo by Katherine Lu

References ��29

2_ Segmented Timber Shells �� 33 A new generation of shell structures ��33 References ��38

3_ Planar and offsettable tiling of freeforms �� 41 An outline of differential geometry �� 41 Discretization of freeform surfaces through planar and offsettable meshes �� 47 Quad-Meshes with planar faces ��49 Offsettable meshes �� 51 Planar hexagonal meshes ��53 References ��56

Part two: investigations �� 59 4_ Morphogenesis �� 61 The material �� 61 Structural modules: the plate system and the hollowbox system ��62 Mesh tiling ��65 Joining system: wood-only wedge connectors ��71 References �� 76

5_ Planning and Construction of the HexBox Canopy ��79 Generation of geometries �� 79 Numerical control of machines: program format and definitions of address words �� 81

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G-Code generation through TPS fabrication components in Grasshopper ��85

TPS_Loftcut ��85 TPS_Sawcut ��88 Comparison between milling and sawing ��92 TPS_Drill ��92 TPS_NCsimulation ��94 Physical models and prototypes ��99 Nesting �� 100 Integration between TPS and KUKA|prc �� 105 Connection to the concrete balustrades and to the concrete ring beam ��110 FE models and structural analysis �� 112 Structural analysis report �� 114 Bill of materials and drawings �� 118 Safety guidelines and personal protective equipment 124 Building stages and time schedule �� 124 Task1_Drilling and installation of threaded bars with chemical anchors �� 125 Task2_Preparation and installation of anchoring plates to the concrete balustrades and to the top ring beam ��127 Task3_Boxes assembly �� 128 Task4_Wedge joints fabrication and assembly �� 133 Task5_Pavilion building �� 134 Task6_Coating of the entire pavilion with liquid waterproofing membrane �� 135 References �� 142

Conclusion and Further Work �� 145 List of Figures �� 148 xiii

Foreword

Since the antiquity, arched spatial structures such as masonry vaults and domes have played a fundamental role in architecture, enabling the covering of wide spans without the use of intermediate supports as well as dramatically reducing the amount of required material. At the beginning of the 20th century, architects and engineers tried to combine these forms with the wide-ranging possibilities of steel-reinforced concrete. The works of Pier Luigi Nervi (1891-1979), Eduardo Torroja (18991961), FĂŠlix Candela (1910-1997), and Heinz Isler (1926-2009) demonstrated how a new generation of shell structure could provide freedom for design exploration as well as structural performance. Despite the above-mentioned advantages, the necessity of centerings and formworks is an overwhelming drawback for the construction phase. As a matter of fact, supporting structures for the implementation of concrete shells are extremely complex, especially for free-form shapes. This usually has significant repercussions both on the overall costs of the structure and on the time frame. The HexBox Canopy has accomplished the goal of exhibiting new ways of thinking about shell structure, exploiting the intrinsic features of engineered timber. Segmental timber shells minimize supports for the implementation phase as well as allowing for a high degree of prefabrication. Components may be fabricated and partially assembled in a factory and then easily carried to the construction site for final installation. As a result, in recent years, we have been enjoying a renaissance of shell structures, thanks to the progress in timber manufacturing, especially due to the continued development of digital tools which have opened the door to extremely versatile solutions. Taking inspiration from handcrafted carpentry and cabinet making, the HexBox implements friction wedge connectors as fastening devices. A second novelty is the adoption of adhesive joining method proper to the furniture industry to the freeform timber construction field allowing for the simple and safe 1K PUR joining of thousands of miter joints with individual dihedral angles. Hence, the contributions of the HexBox Canopy to the state-ofthe-art are summarized as follows. 1. It is the first segmented timber shell to be exclusively made of plywood without the addition of any kind of Previous page: Photo by Katherine Lu

metal fasteners for the main load-bearing structure. 2. It implements an innovative technique for an extremely fast adhesive bonding of miter joints which ensure an appropriate clamping force as well as a correct alignment of workpieces. 3. The construction system does need neither formworks nor centerings. 4. The development of an in-house plugin made possible the implementation of an effective pipeline that connects the designing process directly to the fabrication. 5. The employment of hollow segments combined with the elimination of steel fasteners results in an exceptionally lightweight construction system. This contributes to reducing the overload whenever architects and engineers design additions to existing buildings.

TOP PLATE GLUING AIDS SIDE PLATES

WEDGE CONNECTORS

BOTTOM PLATE

The HexBox Canopy: theme, context, and numbers Right in the heart of Sydney within walking distance of Victoria Park, the HexBox stands on the level 2 terrace of the Wilkinson Building which houses the School of Architecture, Design, and Planning. The balcony is accessible through the Master Studio – room 209 – of the building. The design aims to devise not only a pavilion that demonstrates the advances of digital timber constructions, but also an actual structure giving a space which students can use for the entire day, providing shading from the sun and rain and respite from their computers, as well as resisting and behave properly under ordinary load conditions. As a matter of fact, these kinds of research projects frequently end up fall within the scope of artistic installations although their outstanding potentiality for novel and smart architecture techniques. Therefore, the project assumes the intrinsic features of a prototype, laying the groundwork for an innovative and versatile construction system that could potentially adapt to different conditions. On the other hand, the project meets the requirements of simplicity and rapid in-situ assembly to be easily built by a group of students in an extremely short time frame. A key factor that influenced the shape of the pavilion from the very first design proposal is the impossibility of removing the tiled ground and fixing the footings directly on the slab. This was due to an asbestos sheeting below the tiles that could not be touched or penetrated for safety reasons. The first and immediate consequence of that unpleasant building site condition was that any kind of freestanding solution must be discarded. Therefore, the only option was designing an arched structure spanning from the concrete balustrades of the balcony up to the concrete ring beam around the building’s boundary. Covering a surface of about 45 sqm, the canopy extends for 16 meters along the longitudinal direction and spans for 4.50 meters. It is made up of 201 different box-like segments consisting of a top plate, a bottom plate and a variable number of side plates in a range between 5 and 8. The generation of an overall number of 1531 of different geometries has been made possible through a plug-in for the CAD software Rhino 6 developed at the DTC research group. Two wooden footing devices – each consisting of 3 ribs and a multi-layer plywood panel – join up the curved shell with the straight concrete balustrade whereas the connection to the top concrete ring beam takes place via a series of curvilinear multilayer plywood beams. Both connection devices are fastened to the existing concrete structure through injected threaded steel bars. Previous page: Overview of the HexBox construction system.

The final assembly and building of the HexBox Canopy took place as part of an international one- week workshop held at The University of Sydney in August 2019 and attended by a group of 30 students. Due to the very short time frame for the assembly of hex-modules, a meticulous schedule has been planned. The simple and safe 1K PUR adhesive joining of thousands of miter joints with individual dihedral angles has been made possible by implementing a novel technique borrowed from the furniture industry. We used special self-clamping connectors produced by the Lamello company. A further challenge has been the connections between structural segments since one of the main goals of the design was using a minimal amount of steel connectors and additional fasteners.

Project players, sponsors, and partners The realization of the HexBox has been possible thanks to a fruitful collaboration between researchers of the University of Kaiserslautern and the University of Sydney, and the support of sponsors and partners. As a member of the HexBox design team (Christopher Robeller, Eduardo de Oliveira Barata, Enrico Valentino Tagliaboschi, Felix Schmidt-Kleespies), the author contributed to the conceptual design of the HexBox and assumed a leading role into the detailed design and implementation planning. Specifically, the role of the author mainly entailed the following aspects. Starting from a preliminary base geometry and using the digital tools provided by the DTC, he took care of details â&#x20AC;&#x201C; such as the anchoring to the existing building. He drafted the working drawings, defined the bill of materials, assembly steps, and all the relevant aspects to ensure the feasibility and construction of the project in a 7-day time frame. He also trained and oversaw students before and during the construction, ensuring they had understood assembly steps, construction requirements as well as health and safety requirements to be met. Secondly, he made both scale models and 1:1 prototypes exploiting the 5-axis CNC machine of the FATUK CNC workshop. In doing this, different machining techniques such as CNC milling and sawcut have been tried and tested. Furthermore, the author liaises with the TUK Department of Mechanical Engineering where a multi-axis KUKA robot was available for use. There, some additional prototypes and tests have been carried out thanks to the support of Magnus Volkman and his team. Lastly, the author formed a link between the design team and the fabrication team (Rodney Watt and Lynn Masuda) from the USyd Desingn Modelling and Fabrication Lab (DMaF Lab). He processed and nested all the 1531 different shapes making up the Canopy, and provided fabrication data to the fab-team. He also collaborated with Thomas Williams (PMI Engineers) who released the structural adequacy certificate. 6

The HexBox Canopy has been made possible thanks to the two main sponsors Lamello SA and Carter Holt Harvey Plywood. Respectively, they supplied the self-clamping connectors for the 1K PUR adhesive joining of structural modules, and the raw plywood plates for the robotic fabrication of canopy components. Other secondary partners of the project were the German Academic Exchange Service (DAAD), KUKA AG, IMES-icore GmbH, Doris Simon, Nina Huber, Yang Liu, and Johannes Braumann.

Thesis outline This thesis presents and analyzes the main thematic cores inherent in the design, fabrication, and construction of the HexBox Canopy. All those cores are intimately interconnected and therefore the order in which they follow only roughly reflect both the logical and chronological order of the actual designing process. This thesis consists of two parts. The first part frames the stateof-the-art and previous research while the second part moves on the actual design process of the HexBox Canopy. Chapter One introduces the employment of wood and woodbased materials in the building industry. The main advantages of timber constructions are presented, enlightening the potentiality of this construction material for a more sustainable and ecological way of building. The most relevant intrinsic features such as anisotropy and moisture-dependence are discussed, and an overview of engineered timber products is given. Finally, the dissertation moves on the state of the art of wood-only structures, that have rediscovered and adapted traditional woodworking joinery to contemporary fabrication processes. Computer-aided manufacturing and file-to-factory processes make wood-only structures cheap and easy to produce. Wooden connections avoid material discontinuities as well as enhancing the architectural character of such structures. Chapter Two enlightens the main benefits of segmented timber shells which make this cutting-edge construction system a more fruitful and competitive alternative than traditional concrete shells. Based on the analysis of some relevant case studies â&#x20AC;&#x201C; the Elephant House, the Landesgartenschau Exhibition Hall, and the BUGA Wood Pavilion â&#x20AC;&#x201C; two main archetypes are traceable. These are the plate system (P-system) and the hollow-box system (B-system). Chapter Three debates the planar and offsettable tiling of freeform surfaces, which topic is inherent to the designing and fabrication of timber segmented shells. After a brief outline of some basic knowledge of differential geometry, previous research and investigations are critically presented and analyzed. Freeform tiling through conical quad meshes with

planar faces and planar hexagonal meshes are the two main approaches developed in a decade-long line of research. Chapter Four focuses on how the state-of-the-art influenced the morphogenesis of the HexBox. In particular, the fundamental parameters that influenced the final global configuration of the Canopy are four: material, the shape of the structural modules, tiling strategy, and joining system. The choice of material is strictly related to the fabrication technique being adopted. The designing choices leading to the adoption of hollow-shaped segments are discussed. Two pipelines to discretize surfaces using planar conical quad meshes and planar hexagonal meshes are presented. Finally, inspired by vernacular timber framing, the advantages of wedge connectors for re-assemblable temporary structures are discussed. Chapter Five explores the implementation phase starting from the practical application of algorithmic modeling and digital fabrication tools to physical construction. Basic concepts of CNC machine and robot programming, as well as machining strategies, are presented. Then, a step-by-step description of the building stages is given.

Part one

State-of-the-art

1_ Wood as a construction material

Wood has had a fundamental role for humankind since ancient times. Not only has it been the main resource of heat, energy, and light but also timber has been an essential material for the first human shelters and settlements. In this sense, we can acknowledge that architecture as the act of modifying the wild surrounding environment to provide safer as well as comfortable lives to humans, was born with the employment of wood. Vitruvius described a mythological origin of building in the second chapter of Book the Second of his famous treatise De Architettura. He imagined a wild primordial world populated by men behaving like the beasts. Slowly, they discovered the benefits of the fire, then their sound emissions became meaningful words, and words articulated conversations. The society was born, and with it, the necessity of sheltering from seasons by means of dwellings. It was thus that men started manipulating the easiest material to work with which nature afforded: wood. â&#x20AC;&#x153;The first attempt was the mere erection of a few spars united together with twigs and covered with mud. Others built their walls of dried lumps of turf, connected these walls together by means of timbers laid across horizontally, and covered the erections with reeds and boughs, for the purpose of sheltering themselves from the inclemency of the seasonsâ&#x20AC;? (Pollio, 1874).

Previous page: Photo by Katherine Lu

Why wood? The modernity seemed to have almost forgotten timber as a structural material, even though its outstanding properties such as the high strength-to-weight ratio and the ease to work with. The increasing sensitivity to climate change and the more general environmental issue is one of the reasons behind the renewed popularity of wooden architecture. Timber allows to strongly reduce the carbon footprint of a building as wood is natural carbon storage. It is widely available and also a renewable resource if exploited in a sustainable material cycle. On the other hand, forests play a crucial role in combatting climate change by sequestering carbon dioxide through photosynthesis, maintaining biodiversity and providing other ecosystem services. As the energy industry is now moving toward the exploitation of renewable resources, also the building industry should aim to do so. In fact, the construction of buildings is currently dominated by concrete and steel, producing billions of tons of concrete every year. But just manufacturing the cement that binds concrete is one of our most polluting processes. The chemical and thermal combustion processes involved in the production of cement are a large source of carbon dioxide (CO2) emissions. Each year, more than 4 billion tonnes of cement are produced, accounting for around 8 percent of global CO2 emissions (Lehne & Preston, 2018). The United Nations projects the world population to reach 9.7 billion in the year 2050 (United Nations, 2019). Hence it is extremely evident the present construction methods have to be re-thought and reinvented to fulfill the demand of millions of houses that must be built for future generations with the minimum effect on our environment. Timber constructions can be fast, dry and particularly fit the needs of prefabrication speeding up the in-situ assembly. Some people may argue that encouraging the employment of wood and wood-based material in the building industry might be in conflict with the preservation of forests and their ecosystems. Many studies have pointed out that provided timber is harvested within sustainable limits, the combined mitigation effects of carbon sequestration in the forest as well as in long-lived wood products, together with the material and fossil fuel substitution effects, yield the best overall climate change mitigation potential. In addition, little of the harvested tree goes to waste in the forest products industry so that the co-products of the timber manufacture are generally used very effectively for other products or other processes (Hughes, 2019).

Intrinsic features and mechanical properties of wood Wood is originally a natural raw material and the properties of wooden structural elements not only vary from species to species but also within a particular species as well as in relation to the position of the trunk where the single element has been cut from. The trunk is made of longitudinal tubiform cells, therefore the structure of raw wood results porous, irregular and anisotropic in relation to the grain direction. Softwood and hardwood. A first distinction based on botanical features and physical structure is between softwood and hardwood. Softwood comes from gymnosperm trees such as conifer while hardwood comes from the angiosperm tree such as oak. The main difference between the reproduction of angiosperm trees and gymnosperm trees that the former presents flowers and fruits while the reproductive system of the latter is cones. Some examples of softwood are spruce, larch, pine, and fir whereas some examples of hardwood are beech, oak, maple, robinia, and teak. Softwood is usually lighter in color, softer, less dense and cheaper than hardwood and grows fast. Timber moisture. The intrinsic spongy structure of wood involves its hygroscopic behavior. The moisture content of timber is defined as the weight of the water in damp material divided by the weight of the material in a dry state. It affects the properties of the material such as its weight, its loadbearing capacity, its fire resistance, and its dimensional stability. Unlike steel or concrete, where dimensional changes are mostly due to temperature variations, wood swells and shrinks with changing moisture conditions. This physical phenomenon is known as shrinkage – if the volume reduces – and swelling – if the volume increases –. According to the type of wood, the degree of shrinkage is usually more than double for tangentially cut than for radially cut wood. Longitudinal shrinkage is negligible. Construction timber should always be installed in a dry state, if possible, at the moisture level expected at the location. Mechanical properties. Because of the peculiar directionality of wood, we cannot prescind from considering the direction in which external forces are applied to evaluate the loadbearing capacity of a wooden structural element. Considering a cut tree trunk, three principal axes of wood fibers can be identified: longitudinal, tangential and radial alignment of the fibers (Figure 1.1). In practice, radial and tangential alignments are hardly distinguishable from one another, and an average value is generally taken (Weinand, 2016). Along its longitudinal axis – parallel to the grain –, wood can absorb approximately four times as much compressive force than across the grain. The response to a tensile force is even more extreme (Figure 1.2) (Steiger, 2015). For structural purposes, a good practice recommendation is to install the timber so that the load is placed on its efficient

longitudinal axis, where it can absorb compressive and tensile forces. As a building material that grows and shows all the irregularities of nature, the expected loadbearing capacity of construction timber is not guaranteed from the outset. It is therefore sorted visually and mechanically according to certain characteristics such as the number and size of the branches, any deviations in the fibers, cracks, gross density and elasticity, and then graded for sale. Timber is also generally considered to be a good structural material for construction in seismic areas due to its lightweight and reasonable strength in tension and compression although timber elements do not present large deformational ductility and the response of timber elements up to failure is approximately linear elastic. Figure 1.1 The three strands of wood fibers are inserted into a Cartesian axial system. Elastic and tangential modules vary greatly. (Weinand, 2017, p.9)

Figure 1.2 Appropiate strenghs for coniferous wood (S10) as admissible tensions according to German standards. (Steiger, 2015, p. 17)

Structural timber and timber-based products Unlike in the past when timber elements were rough-hewn before the installation â&#x20AC;&#x201C; this particular evident, for example, in wooden trusses or beamed ceilings of churches â&#x20AC;&#x201C;, the industrialization of timber processing lead to new solid wood products and woodbased materials. Solid wood. The term solid wood includes round timber with the bark removed or cut softwood or hardwood. Products are available in different lengths and cross-sections that are classified as laths, planks, boards and squared timber according to the ratio of thickness to width. Depending on further refining and finishing of solid timber, several structural components are sorted by strength values, moisture content, limitations on crack width and external appearance. Further references about strength classes of solid wood can be found in EN 338. Glued Laminated Timber (glulam). It is an engineered wood product that marked a huge leap forward and expanded the potential use of wood in architecture. It is an improved form of solid timber in which the growth-related defects in wood that tent to reduce the strength have been partially eliminated. It consists of softwood boards glued together under pressure, on the board side with parallel grain. Artificial resin adhesives based on phenol, resorcin, malemine or polyurethane are used to achieve waterproof adhesion. The boards are dried before gluing and planed, and any flaws in the wood are removed mechanically. The laminated gluing means that there is next to no deformation of the timber cross-section. Glued Laminated Timber is often used for wide loadbearing structure spans because it can be supplied in cross-sections of up to 200cm, and up to 50m long (Steiger, 2015). Straight components, forms with variable cross-section and in single or double curvature or twist about the longitudinal axis are also possible. Information about strength classes and standards of glulam can be found in EN 14080. During the last decades, timber construction has undergone intensive developments and the increasing availability of an

Figure 1.3 SCT, duo and trio beams, cross beams, laminated boards. (Steiger, 2015, p. 20)

enormous diversity of new, high-performance wood-based and composite materials has been playing a fundamental role. The research into standardization of timber products is relatively recent, for example, Cross Laminated Timber (CLT) was developed just in the early 1990s and deeply investigated by Gerhard Schickhofer who presented his Ph.D. thesis on CLT in 1994. Broadly speaking, the key advantages of laminated products are their availability in large sizes and customizable dimensions; they are dimensionally stable and allow for a more homogeneous, quasi-isotropic mechanical behavior. Cross Laminated Timber (CLT). Cross-laminated timber (Figure 1.4) is a two-dimensional, solid timber product. It consists of a usually odd number of layers â&#x20AC;&#x201C; at least three â&#x20AC;&#x201C; which are glued together over their entire surface area at right angles to one another. Thus, the advantage of this product is that it has the ability to transfer the load in two directions. The softwood boards of the individual layers are sorted by strength, planned, and kiln-dried. Predominantly, spruce wood of strength class C24 is used. The product C24 is a solid softwood product, which has a bending strength of 24 N/mm2, a mean elastic modulus of 11000 N/mm2 and a characteristic density of 350 kg/m3. The boards are 40 to 300 mm wide and 6 to 45 mm thick, and they are normally connected into an infinite laminate in the longitudinal direction by means of finger joints, and, in a first production step, may be glued together at their narrow sides to form a two-dimensional board layer. Without gluing of adjacent boards, these may be arranged with joints of no more than 6 mm. CLT is manufactured in lengths of up to 16 m and widths of up to 2.95 or 3.00 m. The overall thickness for standard applications

Figure 1.4 3-layers and 5-layers CLT panels. (Stora Enso, 2013)

Figure 1.5 LVL beams type S, different thicknesses. (MetsĂ¤ Wood, 2019)

is up to 30 mm, and a special request up to 500 mm (WallnerNovak, et al., 2014). Further references about CLT standards can be found in EN 16351. Laminated Veneer Lumber (LVL). It is produced from rotarypeeled 3 mm graded softwood veneers. The multiple layers of veneers are glued together to form a continuous wide product. The fabrication of LVL has the benefit of the redistribution of large defects into small ones. The grain of all plies may (Type S and Type T) or may not (Type Q) run in the same direction depending on the structural purpose of the element (Figure 1.51.6). Type T is the same as type S in terms of grain direction but is made from lighter veneers (lower densities) with correspondingly lower load-carrying capacities (Volz, 2004). In type Q, every fifth veneer is glued in the perpendicular direction. This way of buildup increases the lateral bending strength and stiffness of the panel as well as reducing the moisture-dependent dimensional stability across. Further references about LVL standards can be found in EN14374. Plywood. Plywood (Figure 1.7) is made by gluing together dried veneers at right angles to each other. The veneers must be arranged symmetrically about the middle of the board. The majority of plywoods have an odd number of plies (at least three), but with an even number, the two inner plies are bonded together with their grain parallel (Volz, 2004). Similar to LVL type Q, the cross-graining of plywood reduces the swelling and shrinkage, providing improved dimensional stability as well as making the strength of the panel consistent across all directions. Usually, commercial formats are 2500/3000 x 1250/1500 mm and 2400/3050 x 1200/1525 mm, with a thickness between the range of 8–40 mm. Information about strength classes and standards of structural plywood can be found in EN 12369.

Figure 1.6 LVL panels type Q, different thicknesses. (Metsä Wood, 2019)

Figure 1.7 18mm-thick spruce plywood. (Metsä Wood, 2019)

Wood-only structures Parametric and algorithmic design methods combined with digital fabrication techniques are changing the development of building details, allowing for flexibility of joining methods. Not only are architectural details of extreme importance for the technical character of a project, but also, they affect its theoretical expression, impact on costs, production processes, assembly methods, and even its ecological footprint. After a long season where detailing seemed to have a minor role â&#x20AC;&#x201C; or even be trivial â&#x20AC;&#x201C; into the architectural designing process, contemporary architecture brought it back into the architectural discourse. File-to-factory processes close the gap between the conceptual design of a building and the actual realization, and Computer-Aided Design (CAD) tools combined with ComputerAided Manufacturing (CAM) tools allow us to define and manage the morphology of construction since the very first phases. Before being something technical, the connection between buildingsâ&#x20AC;&#x2122; parts is a geometrical issue and thus, the rules of geometry are the most appropriate device to handle detailing. This is even more evident with wood. Thanks to its physical properties, it is perfect for subtractive machining that opens the door to virtually endless possibilities of shaping. Timber components are usually prefabricated in factories and assembled on the building site. Therefore, connections are responsible for a significant share of costs. It is clear the more connection systems allow for a fast and easy assembly and construction phase, the less amount of work on site is needed, involving a significant reduction of costs. The tools and techniques for joining separate pieces of wood to larger compounds are deeply embedded in specific cultural contexts, adapted to local conditions, and available materials. The way in which we design intersections between wooden components greatly contribute to the architectural language of a timber building. According to (Hudert & Pfeiffer, 2019), the most common phenotypes of wooden joints widespread in many different regions of the world can be traced back to some main genotypes. Three of these archetypes are the dovetail joint (Figure 1.8a), used for joining two flat members together, the dowelled joint (Figure 1.8c), in which dowelling is employed to impart mechanical strength; and the mortise-and-tenon (Figure 1.8b), used to join a horizontal member and a vertical member of a frame. Climate, availability of raw materials, as well as conditions and constraints of individual societies, such as those of East Asia, North America, Central, and North Europe, have shaped different versions of these basic concepts, leading to sophisticated constructive and architectural languages.

Recently, research underwent some interesting developments in the adaptation of traditional joinery knowledge to modern fabrication processes, revaluing wood-only joining. The following paragraphs enlighten the main reasons why such connectors are preferable to standard steel fasteners in timber joining. Some of

the key advantages are listed below. • Wood-only connectors can be cheaper and easier to produce. They can be realized from the cut-off waste material resulting from the machining of the main parts of timber structures. • Tolerances of metalworks are about ten times less than the accuracy in wood machining. For this reason, wood-only connectors offer a better solution in timber constructions. • Wood-only connectors avoid material discontinuities in structures ensuring a global behavior, for example, in terms of deformation due to loads, moisture changings and temperature variations. • The real efficacy of self-tapping screws (STS), which dismiss predrilled holes in screwed timber connections, is affected by uncertainty due to imperfections and gaps in wood-based materials.

Mechanical attachment for wood-only constructions By wood-only constructions, we refer to timber structures whose all constituents are made up of wood, including connectors and fasteners. Therefore, the nature of the connections between parts is mechanical, namely, only forces of mechanical origins allow and enable joining. The materials comprising the pieces being joined do not form any chemical bonds at the atomic or molecular level, as occur in adhesive bonding or welding. The structural integrity is only provided by the physical interference between parts, preventing motions in some directions, thereby allowing loads to be resisted in those directions. Messler points out two aspects of mechanical joining which are worth it to dwell on (Messler, 2006). First, parts that are intentionally assembled mechanically can be intentionally disassembled. This is crucial whenever we aim to design temporary and demountable architecture. Secondly, only mechanical joining permits parts to be assembled while allowing relative motion, if wanted and where needed. We can distinguish between two subcategories of mechanical joints for wood-only structures, depending on whether 21

Integral Mechanical Attachment

a) Dovetail joint

b) Mortise-and-tenon joint

c) Dowelled joint

d) Biscuit joint

e) Butterfly key joint

f) Tusk tenon-and-mortise joint

Mechanical Fastening

Hybrid Integral/ Mechanical Fastening

Figure 1.8 In integral mechanical attachment, the intrinsic shape of parts allows establishing the connection whereas, in mechanical fastening, the connection is established by utilizing some extra parts. However, hybrid solutions are possible. In the latter case both the geometry of parts to be joined and fasteners are crucial.

connections between parts are established either because of their own interlocking shape, or because of some extra wooden parts are added with the explicit purpose of causing interference between itself and each of at least two parts (e.g. pins, wedges, pegs, keys). The first type of connection is called integral mechanical attachment (Figure 1.8a-b), while the second one is called mechanical fastening (Figure 1.8c-d).

Integral mechanical attachment accomplishes joining between parts by using some geometric features in mating parts that cause strictly mechanical interference and, perhaps, interlocking between or among those parts. The integral mechanical attachment uses specially designed or created attachment features that are part of the part (Messler, 2006). Examples

of integral joints in woodworking are the dovetail joint and the mortise-and-tenon joint. In mechanical fastening, an extra part is employed with the explicit purpose of causing interference between itself and each of at least two parts. As opposed to using some geometric feature that is integral to each of individual parts to be joined to cause interference, a supplemental device is used such as dowels and biscuits (Messler, 2006). It goes without saying these two categories are not strictly separated. There are many cases of hybridization (Figure 1.8ef) in which elements to be joined uses both the geometry of the parts and additional connectors to establish the connection. Two examples of hybrid integral/mechanical fastening are the butterfly key joint and the tusk mortise-and-tenon.

Timber framing: a remarkable example of wood-only vernacular architecture Vernacular timber framing consists of large, widely spaced timbers connected with all-wood connections, such as mortises, tenons, and pegs. According to (Benson & Gruber, 1980) the invention of the mortise-and-tenon joint dates back to sometime between 500 B.C. and 200 B.C., although more recent studies (Tegel, et al., 2012) reveal two linings of wells, excavated in Eastern Germany and dates back to the Neolithic, constructed with mortise-and-tenon joints. In addition, the tenons of one of those wells extended beyond the outer face of the joined timber and were perforated and keyed by wooden wedges. In parallel with the technical development of tools, timber framing expanded to its peak during the seventeenth century in Europe. As the United States was settled and timber was plentiful, groups of immigrants brought their own style of timber framing from the old country. This influx of styles, combined with the availability of tall, large-diameter trees, allowed for the United States to create its own strong and rich timber framing tradition (Miller & Schmidt, 2004). With the industrial progress, handcrafting techniques became progressively obsolete during the nineteenth century and replaced by machine-tool technology. Commercial sawmills developed the capacity to mass-produce small pieces of lumber and balloon framing methods developed. Historic American timber joinery. A wide repertoire of mechanical timber joints can be found in American traditional timber-framed buildings. The work of Jack A. Sobon for the National Center for Preservation Technology and Training (Sobon, 2004) illustrates common as well as unusual timber joinery found in old structures. 23

Figure 1.9 Examples of tying joints in historic American timber joinery: pegged mortise-and-tenon, wedged dovetail through mortise-and-tenon, through mortise and extended tenon secured with two pegs and a single wedge. (Sobon, 2004, pp. 2-7)

Especially interesting for our research are traditional tying joints which are joints designed to resist tension (Figure 1.9). Tying joints occurred every time horizontal members, that span from wall to wall or eave to eave, are supposed to resist the outward thrust of the roof planes. The through mortise-and-tenon was the standard in the carpenterâ&#x20AC;&#x2122;s repertory where a joint was subject to tension loads. The mortise is cut completely through the post to maximize the tenon length. Because the connection relies entirely on pins to resist withdrawal, the size and location of those elements are critical. When the joint needs an additional reinforcement, the tenon can be extended. By adding wedges through this tenon, the possibility of the withdrawal of the tie is effectively reduced. Furthermore, the wedges can be driven additionally after the building is finished and the wood seasoned. Joinery for re-assemblable timber constructions. Structures that can be easily disassembled and re-assembled on a different site without undergoing damages require smart joints. These joints shall meet two main requirements. First, they must be strong enough when put together and, secondly, they must be easy to be taken apart and reassembled. A common mortise-and-tenon joint is made up of the male element (tenon) and the fitting hole (mortise). Usually the joint is then locked with a peg using a technique called drawboring. In drawboring, the holes for the peg are slightly offset so that the peg will pull the joint tighter when it is driven in. As the wood expands and contracts over time, pegs can be driven further to keep the joint tight. Pegs can also be driven out, allowing the joint to be disassembled if necessary (Miller & Schmidt, 2004). Another variation of the mortise-and-tenon joint â&#x20AC;&#x201C; easier to be assembled and disassembled â&#x20AC;&#x201C; is the keyed through-tenon joint, also called tusk tenon, keyed tenon or wedged tenon (Meeson, 2016). This joint has a tenon protruding through the backside of a mortise member which is reinforced with keys on the backside of the mortise member through the tenon. Keys are tapered wooden wedges that are inserted into holes cut through the protruding tenon as a means of fastening. With a keyed through-tenon joint, a key is used instead of a peg to hold the joint together. In 24

both cases, pegs and keys in mortise and tenon joints are loaded in double-shear when the joint is in tension (Shields, 2011). The advantages of the keyed through-tenon joint are that keys are easier to remove and replace as well as providing added strength and stability to the joint. Because the key is outside the joint, tusk tenons can only be used with through-tenons, which are joints where the tenon goes all the way through and out the other side of the mortise.

A digital renaissance of timber traditional carpentry joinery Traditional joining techniques have undergone a renewed popularity thanks to digital-geometry-processing and information-tool-technology of the twenty-first century. While the parametric and detailed geometry of such connections presented a disadvantage in their laborious manual production, these techniques have proven to be ideal for algorithmic processing and digital fabrication. While the production of joints has become very efficient, the simplicity, rapidity, and precision of assembly have now gained enormous importance in many industry sectors (Robeller, 2015). Computer numerical control (CNC) machines can automatically fabricate integral joints for timber beams, similar to the traditional carpentry joints, such as mortise-and-tenons, lapjoints or birdsmouth joints. Such precisely prefabricated beams improved the efficiency and reduced the amount of manual labor both in the production and the assembly of timber-frame constructions. With the introduction of visual programming tools during the last decade, algorithmic design tools combined with the informationtool-technology became accessible to the architectural community leading to new designing methods. In larger timber construction prefabrication companies, computer-controlled 5-axis machines for the formatting of timber panels were already available from the mid-1990s. An open interface between these machines and the algorithmic design tools was also provided by standardized programming languages such as G-Code (Robeller, 2015). The CAAD Swissbau Pavilion. Realized for the Swissbau 2005 fair in Basel (Scheurer & Schindler, 2006), it is a remarkable example of the integration between a traditional-inspired wood only connection system and the novel possibilities offered by CNC-fabrication. The structure has the form of a sphere with two meters radius and reaches a height of three meters (Figure 1.10). It is made up of 320 quadrilateral wooden frames, each consisting of four wooden boards standing perpendicular on the surface of the sphere that means, overall, 1280 parts cut from 25

Figure 1.10 Swissbau Pavilion. Left: assembly of the prototype structure. Right: miter joints and dovetail connectors. (Scheurer & Schindler, 2006)

oriented strand boards (OSB). This prototype first demonstrates the potentialities of 5-axis cutting, which allowed for the fabrication of miter joints with integral dovetail-shaped longitudinal grooves which gives room to a dovetail-shaped connector produced by the company German company Hoffmann-Schwalbe (Robeller, 2015). Due to the shape of connectors that present ribs on the internal sloping surfaces, the Hofmann system holds the workpieces durably even without the use of additional chemical bonding (Hoffmann GmbH Maschinenbau, s.d.). As a matter of fact, butterfly keys and dovetail splines were commonly employed in handcrafted woodworking, however, this project demonstrated how a new fabrication technique could take advantage of an already existing technology adding value to the project, in term of the rapidity, simplicity, and precision of assembly. While previous works had already shown the use of algorithmic tools for the generation of geometrical variations, this project first demonstrates the simultaneous use of an algorithm for the generation of 5-axis CNC fabrication instructions. A manual fabrication with machine-tool-technology, or manual programming of a CNC machine, would have been infeasible for such a design. The X-fix system. The Timberdome (Robeller & Viezens, 2018) and the Recycleshell in Dimerstein (Robeller, 2019) are further examples of translating vernacular joining techniques into cutting edge timber spatial structures through the â&#x20AC;&#x153;dictionaryâ&#x20AC;? of timber digital fabrication. Both projects are based on the X-Fix system (Schilcher Trading & Engineering GmbH, 2016) which is a timber-to-timber coupling system for easy and fast joining of cross-laminated timber elements without any additional metal fasteners (Figure 1.11). Due to machining tolerances, a connector that fits perfectly is usually unfeasible, therefore a play between plates and connectors is needed. However, this involves reducing the 26

Figure 1.11 X-Fix system used in the Timberdome and in the Recycleshell. (Robeller & Viezens, 2018)

stiffness of connections. Thanks to their wedge shape, X-Fix connectors provide a valuable alternative solution, enabling to compensate for the intrinsic tolerances of the elements. This project is the first to integrate such a system, already used for prefabricated CLT walls, into timber palate shells. This system results indeed particularly performing to join elements that are nearly complanar – the average angle between Timberdome’s plates is 173°.

Probabilistic models for withdrawal behaviour of self-tapping screws A relevant point that makes the application of wood-only connections in timber structures a worthwhile branch to investigate is the uncertainty on the performance of traditional fastening methods. Some research has demonstrated that the actual positioning of fasteners, as well as potential gaps and imperfections of the material to be joined, affect the withdrawal capacity of screws. By positioning, we refer to the differentiation in the side face and narrow face of the panels (Figure 1.12) while gaps and imperfections are due to the natural growth of wood as well as the processes involved in the manufacturing of woodbased laminated products. For example, cross-laminated timber consists of crosswise glued layers of solid-sawn lumber, whereby a board layer is formed of several, side by side, lamellas. Depending on the product, the single lamellas of a layer can be pushed or even glued on their narrow sides with or without joints. Therefore, gaps may occur between lamellas. Recent research has investigated the relationship between withdrawal capacity and the existence of gaps between glued boards of CLT panels, both for self-tapping screws (STS) inserted perpendicularly to timber grain direction – in the plane side of the panel – (Silva, et al., 2014) and in the narrow face of the panel (Brandner, et al., 2018). According to (Blaß, 2009), an examination of the joints on crosslaminated timber panels of three manufacturers showed a 95%

Figure 1.12 Possible positions of screws in the side face (top) and narrow face (bottom) of CLT panels. (BlaĂ&#x;, 2009)

quantile value of the joint width of 1 to 1.6 mm for the outer board layers and of 1.8 to 4.5 mm for the inner board layers. Furthermore, some cross-laminated timber products have relief grooves that are sawn in the direction of the longitudinal fibers of the boards with a width of about 2.5 mm. Even with an unfavorable positioning of a screw between two grooves, a reliable transmission of the forces must be ensured. Therefore, (BlaĂ&#x;, 2009) suggests using a redundant number of fasteners, and for connections in the side surfaces, the penetration depth should be selected such that the connecting medium tip penetrates at least the third layer of a panel.

References Benson, T. & Gruber, J., 1980. Building the Timber Frame House. New York: Schribner’s Sons. Blaß, H. J., 2009. Bemessungsvorschläge für Verbindungsmittel in Brettsperrholz. Brandner, R., Ringhofer, A. & Grabner, M., 2018. Probabilistic models for the withdrawal behavior of single self-tapping screws in the narrow face of cross laminated timber (CLT). European Journal of Wood and Wood Products, 76(1), pp. 13-30. Hoffmann GmbH Maschinenbau, n.d. hoffmann-schwalbe. [Online] Available at: https://www.hoffmann-schwalbe.de/index.php/en/ [Accessed October 2019]. Hudert, M. & Pfeiffer, S. eds., 2019. Joinery Culture. In: Rethinking Wood: Future Dimensions of Timber Assembly. Basel: Birkhäuser Verlag GmbH, pp. 56-116. Hughes, M., 2019. Cascading Wood, Material Cycles, and Sustainability. In: M. Hudert & S. Pfeiffer, eds. Rethinking Wood: Future Dimensions of Timber Assembly. Basel: Birkhäuser, pp. 31-45. Lehne, J. & Preston, F., 2018. Making Concrete Change. Innovation in Low-carbon Cement and Concrete, London: The Royal Institute of International Affairs, pp. iv-xiv. Meeson, B., 2016. What’s in a Name? the use of Tusk Tenons and Face-Pegged Through Tenons in England. Vernacular Architecture, 47(1), pp. 61-68. Messler, R. W., 2006. Integral Mechanical Attachment: A Resurgence of the Oldest Method of Joining. I ed. s.l.:Butterworth Heinemann, pp. 1-25. Metsä Wood, 2019. Kerto® LVL. [Online] Available at: https://www.metsawood.com/global/Products/ kerto/Pages/Kerto.aspx# [Accessed September 2019]. Metsä Wood, 2019. Metsä Wood spruce plywood. [Online] Available at: https://www.metsawood.com/global/Products/ plywood/spruceplywood/Pages/Spruce-plywood.aspx [Accessed September 2019]. Miller, J. F. & Schmidt, R. J., 2004. Capacity of Pegged Mortise and Tennon Joinery, Laramie: University of Wyoming. Pollio, M. V., 1874. The Architecture. In: Book the Second. London: George Phipps, p. 32. Robeller, C. & Viezens, V., 2018. Timberdome: Construction System for CLT-Segmental Plate Shells without Screws. Proceedings of the 24th International Timber Construction Forum Garmisch-Partenkirchen.

Robeller, C., 2015. Integral Mechanical Attachment for Timber Folded Plate, Lausanne, pp. 7-21. Robeller, C., 2019. Recycleshell. [Online] Available at: https://www.architektur.uni-kl.de/dtc/2019/09/05/ recycleshell/ [Accessed October 2019]. Scheurer, F. & Schindler, C., 2006. CAAD Swissbau Pavilion. [Online] Available at: http://wiki.arch.ethz.ch/twiki/bin/view/D2p/ SwissBau.html [Accessed October 2019]. Schilcher Trading & Engineering GmbH, 2016. X-fix Greenethic. [Online] Available at: http://www.x-fix.at/ [Accessed October 2019]. Shields, L. D., 2011. Investigation of Through-Tenon Keys on the Tensile Strength of Mortise and Tenon Joints, Blacksburg, Virginia: Virginia Polytechnic Institute and State University. Silva, C. et al., 2014. Influence of moisture content and gaps on the withdrawal resistance of self tapping screws in CLT. 9º Congresso Nacional de Mecânica Experimental. Sobon, J. A., 2004. Historic American TImber Joinery. II ed. Becket: Timber Framers Guild. Steiger, L., 2015. Building Material. In: Basics Timber Construction. Basel: Birkhäuser, pp. 9-26. Stora Enso, 2013. CLT - Massive Wood System. [Online] Available at: http://www.clt.info/en/product/clt-massive-woodsystem/ [Accessed September 2019]. Tegel, W. et al., 2012. Early Neolithic Water Wells Reveal the World’s Oldest Wood Architecture. PLoS ONE, 7(12). United Nations, 2019. UN World Population Prospects. [Online] Available at: https://population.un.org/wpp/DataQuery/ [Accessed September 2019]. Volz, M., 2004. The Material. In: Timber Construction Manual. Munich: Edition Detail, pp. 31-46. Wallner-Novak, M., Koppelhuber, J. & Pock, K., 2014. CrossLaminated Timber Structural Design. Basic design and engineering principles according to Eurocode. Vienna: proHolz Austria, pp. 8-17. Weinand, Y., 2016. How can a schedule and a technologically innovative process shift the perspective of the construction industry toward sustainability?. In: Y. Weinand, ed. Advanced Timber Structures: Architectural Designs and Digital Dimensioning. Basel: Birkhäuser, pp. 6-11. 30

2_ Segmented Timber Shells

â&#x20AC;&#x153;Shell structures are constructed systems described by three-dimensional curved surfaces, in which one dimension is significantly smaller compared to the other two. They are form-passive and resist external loads predominantly through membrane stressesâ&#x20AC;? (Adriaenssens, et al., 2014, p. 1). Shell behavior allows transferring external loads to the supports predominately through forces acting in the plane of the shell surfaces, which are called membrane stresses and might be compression, or a combination of compression and tension. The maximum bending moment in the structure could then be largely reduced. Because the internal forces in shells are mainly in the form of membrane forces, the most critical issues of member design would be about how to resist in-plane forces and buckling.

A new generation of shell structures Segmented timber shells minimize supports for the implementation phase as well as allowing for a high prefabrication grade. Unlike single-layer grid shells, which usually need bending-stiff joints to stabilize the structure, segmental plate shells could generate local bending stiffness without the help of bending-stiff joints. This property helps segmental plate shells to generate relatively simple connectivity, which makes these types of structures more competitive (Li, 2017, p. 136). Segmented plates can be fabricated through the processes of milling and sawing, and partially assembled in factories and then easily carried to the construction site for the final installation. CNC processes can also allow the manufacturing of linear elements with variable sections or plate elements with a changing thickness and various boundary geometries. Adhesive and joints have also been a great influence on the evolution and the development of timber shells. Unlike shells made of stones, timber is light-weight and its self-weight is not much helpful to stabilize the structure. Therefore, it is more challenging to design a connection in timber shells because the internal forces of a member in timber shells could not be always compressions. Tensions and bending moments occur once the uneven load such as those from wind or snow dominates (Li, 2017, p. 19). Previous page: Photo by Katherine Lu

We have been enjoying a renaissance of shells structures in recent years thanks to the progress in timber manufacturing, especially due to the employments of digital tools, 5-axis machines, and robotic arms. Pioneer projects, such as ICD/ITKE Research Pavilions in Stuttgart (2010, 2011, 2016), Country Club in Yeoju (2010), Centre Pompidou in Metz (2010), Element House in Zurich (2014), Dieter-Paul Pavillon/Forstpavillion (2014), have shown that how rich the variety timber shell structures could bring. Here some paradigmatic case studies are presented. Elephant House, Zurich, Switzerland (2014). The Elephant House of the Zoo of Zurich is a multilayer composite shell structure so that the material properties, anisotropy, strength, and stiffness-solubility behavior are leveled independently from the strength-fiber. Although the 271 geometrically completely different and acute-angled skylights with up to 40 sqm size suggest any regularity, the construction can be reduced to two control sections (Kübler, 2014). The overall conception of landscape and architecture is essentially based on the interplay of light and shadow. The sequence of vegetation themes based on Thai vegetation pictures continues inside the elephant house and should let the visitor forget the boundaries between outside and inside. The main architectural requirements were to guarantee a naturalistic appearance and integration of the canopy in the landscape park, integration of all the needed plants and facilities

Figure 2.1 Ringbeam with 9 up to 120 m long tension cabels. (Kübler, 2014)

Figure 2.2 Placing of layer elements of shell-structure on site. (Kübler, 2014)

(ventilation, irrigations, sensor, etc), sufficient daylight for plants and animals (about 30-35% openings), thermal insulations and reliable water resistance. From a static point of view, some challenges were the highly variable geological conditions and the geometric singularities in the force flow as a result of the wide opening (Kübler, 2014). The design of the actual shell is based on simplicity principles implementing flat and straight standard products, ductile and robust connections between the parts are used over the whole shell surface. Multi-layered and flexible bonded material has almost identical properties on compression and tension and also have ductile behavior against the membrane thrust, and thus not tear at singularities. The wind loads required for the static analysis were determined on a physical model in the wind tunnel. Decisive asymmetric snow loads, which effects are relevant for stability studies and bending of the shell, were also determined on the model in the wind tunnel (Kübler, 2014). As an anisotropic and inhomogeneous building material, wood is in principle not obvious for a real shell structure with 271 oblique openings of any geometry. Typically, wooden dome structures are therefore constructed as trusses. Multi-layer panels were selected as a material that is easy to work on and can be shaped to the desired shape on the construction site. The free-form timber roof shell has a diameter of 80 m and it covers an area of 6400 sqm. The geometry is based on a shell loaded in compression of a reversed suspended membrane model. The shell is supported by the prestressing force of the steel cables. The forces are transferred to the supports via a reinforced concrete ring beam (Figure 2.1). Parametric software was used for an iterative form-finding process. Different programmers were needed to create a parametric 3D model. At every stage, specific requirements could be integrated into the model. The free-form surface had to be converted into flat strips for the production and erection. Each panel required a separate machine file code and fabrication drawing. The automated panel production produced unique panels for each layer and the double curvature roof shell was erected easily (Figure 2.2) due to panel construction, which made it able to bend about two axes (Kübler, 2014). Landesgartenschau Exhibition Hall, Schwäbisch Gmünd, Germany (2014). The Exhibition Hall is a pioneering prototype building for segmented timber plate shells (Figure 2.3). It was conceived at the University of Stuttgart as a collaboration project between the Institute of Building Structures and Structural Design (ITKE) and the Institute of Computational Design (ICD). As a part of the Robotic in Timber Construction research project, it was realized in collaboration with both companies of the field and public administration in Schwäbisch Gmünd, Germany in 2014. The building is the first to have its primary structure entirely made of robotically prefabricated beech plywood plates with 35

Figure 2.3 Perspective of the interior highlighting the convex and cocave shape of the plates depending on the local gaussian curvature. (Institute for Computational Design and Construction (ICD), 2014)

Figure 2.4 Constructive layers of the shell including insulation and water proofing. (Institute for Computational Design and Construction (ICD), 2014)

a thickness of just 50mm (Figure 2.4) (Achim Menges, 2015). A fascinating designing concept applied in the LaGa pavilion is the so-called â&#x20AC;&#x153;Biometric lightweight designâ&#x20AC;?, that is the transfer of principles of biological morphology to the design of technical applications. Researchers inspired their work to the modularity of the skeleton of sea urchins which is made up of microscopic interlocking polygonal plates linked by at the edge by finger-like calcite protrusions and organic fibers. Their plate layouts have trivalent patterns that are featured to give kinematic stability when adapted into plate structures. The overall peanut-like doubly-curved geometry presents a larger span of ca. 11m, a longitudinal dimension of ca. 17m, a height of ca. 6m and has been assembled from 243 planar, polygonal components. The whole structure is closed except for the entrance on one side where the glass facade was installed. A key feature of the LaGa is the application of integral finger joints which are used in connections to resist decisive in-plane shear forces, whereas the smaller axial forces and out-of-plane shear forces are taken up by crossing screws which lie in parallel planes, normal to the edge (Li & Knippers, 2015). Using additional adhesive bonding would not have been possible here due to the on-site assembly. In fact, the manufacture of glued joints requires controlled environmental conditions for application and curing. Each plate was prefabricated by a timber construction company. First, the polygonal plates were cut out from rectangular plywood panels by a CNC machine; then, with the help of a robot-arm, the finger joints and the brackets for screws were milled out. The guiding holes for screws were subsequently drilled by the robot-arm. The installation of the plates started from the plate at the corner of the building and then proceeded, row by row, until the last plate was installed. A temporary 36

Figure 2.5 On the left, perspective from one of the three arches of the Buga Wood Pavilion. (Photo by the Author) Figure 2.6 On the right, construction details of the timber segments of the Buga Wood Pavilion. (Schwinn, et al., 2019)

supporting framework with the section geometry of the inner surface of the plate shell was used to facilitate the correct positioning of each plate during assembly (Li, 2017, pp. 177-180). BUGA Wood Pavilion, Heilbronn, Germany (2019). Basing their research on the same biomimetic concepts, the project team of the LaGa built a new innovative pavilion for the Bundesgartenschau 2019 in Heilbronn (Figure 2.5). The goals of the BUGA Wood Pavilion were mainly two: reaching the triple of the span of the LaGa using the same small amount of wood per square meter and focus the design on a reusable structure which could be easily dismantled and re-assembled on a different site after that summer event without any loss of performance. Instead of using plates, the BuGa Pavilion is made up of 376 bespoke hollow wooden polygonal segments built up from a top and a bottom plate joined together by a ring of edge beams (Figure 2.6). These elements are glued together to form one structural entity, using a newly developed, prototypical robotic fabrication process. The bottom plate includes a large opening which constitutes a distinctive architectural feature and provides access to the hidden connections during assembly (Institute for Computational Design and Construction (ICD), 2019). The tangential connection system takes advantage of the combination of simple finger joints and fitted bolts. While the finger joints transfer in-plane shear forces, the bolts transfer tension and out-of-plane shear forces. Bending moments are transferred into tension in the bolts and compression in the material itself (Bechert, et al., 2018). The resulting stunning structure spans 30 meters providing an architectural attraction at the BUGAâ&#x20AC;&#x2122;s main event and

Figure 2.7 The flexibility of industrial robots allows the integration of all pre-fabrication steps of the pavilionâ&#x20AC;&#x2122;s segments within one compact manufacturing unit. (Institute for Computational Design and Construction (ICD), 2019)

concert venues. Compared to a solid wood plate, the box-like system increases the number of building parts eightfold and lead to more complex manufacturing. A novel, transportable, 14-axes robotic timber-manufacturing platform including two high-payload industrial robots mounted was used for the manufacturing of each bespoke shell segment (Figure 2.7). The process involved two main steps: the assembly which took on average 8 minutes per segment, and the high precisionmilling of the sides, taking another 20-40 minutes (Institute for Computational Design and Construction (ICD), 2019).

References Achim Menges, T. S. O. D. K., 2015. Landesgartenschau Exhibition Hall. In: S. Pfeiffer, ed. Interlocking Digital and Material Cultures. Baunach: Spurbuchverlag, pp. 42-55. Adriaenssens, S., Block, P., Veenendaal, D. & Williams, C. eds., 2014. Shell Structures for Architecture: Form Finding and Optimization. Oxon: Routledge, pp. 1-4. Bechert, S. et al., 2018. Structural Performance of Construction Systems for Segmented Timber Shell Structures. Massachusetts Institute of Technology. Detail, 2012. Kobra am Campus: Neue Anwendungen von Holz fĂźr die Architektur. [Online] Available at: https://www.detail.de/artikel/kobra-am-campusneue-anwendungen-von-holz-fuer-die-architektur-9461/ [Accessed September 2019]. InnovaConcrete, 2018. What is concrete shell architecture?. [Online] Available at: http://www.innovaconcrete.eu/what-is-concreteshell-architecture/ [Accessed September 2019]. 38

Institute for Computational Design and Construction (ICD), 2014.

Landesgartenschau Exhibition Hall. [Online] Available at: https://icd.uni-stuttgart.de/?p=11173 [Accessed September 2019]. Institute for Computational Design and Construction (ICD), 2019. BUGA Wood Pavilion. [Online] Available at: https://icd.uni-stuttgart.de/?p=22287 [Accessed September 2019]. Krieg, O. D. et al., 2018. Affordance of Complexity: Evaluation of a Robotic Production Process for Segmented Timber Shell Structures. Seoul, Republic of Korea. Kübler, W., 2014. Das neue Elefantenhaus im Zoo Zürich. Bautechnik, January, 91(1), pp. 55-59. Li, J.-M., 2017. Timber Shell Structures. Form-finding and Structural Analysis of Actively Bent Grid Shells and Segmental Plate Shells. Stuttgart: Institut für Tragkonstruktionen und Konstruktives Entwerfen Universität Stuttgart, pp. 136-180. Li, J.-M. & Knippers, J., 2015. Segmental Timber Plate Shell for the Landesgartenschau Exhibition Hall in Schwäbisch Gmünd— the Application of Finger Joints in Plate Structures. International Journal of Space Structures, June, Issue 30, pp. 123-140. Schwinn, T. et al., 2019. Potential applications of segmented shells in architecture. In: J. Knippers, U. Schmid & T. Speck, Hrsg. Biomimetics for Architecture. Learning from Nature. Basel: Birkhäuser, pp. 116-125.

3_ Planar and offsettable tiling of freeforms This chapter investigates the relationship between freeform shapes and their fabrication, focusing on the requirement of discrete freeform must satisfy in order to be built as segmental structures. The tiling process that allows the discretization of freeform surfaces is not univocal. Therefore, many discrete approximations are possible. One way to roughly describe the shape of a smooth surface is by using meshes. “A mesh is a collection of vertices arranged into basic elements called faces. The faces are bounded by polygons. Typically, one type of polygon dominates (e.g. triangle, quadrilateral, or even hexagon). They fit together along common edges and roughly describe the shape of a smooth surface” (Pottmann, et al., 2007, p. 381). The necessary conditions for the application of meshes in the field of segmental timber shell – and, broadly speaking, in most of the field of architectural freeform design – are mainly two. 1. Faces must be planar 2. The mesh must be offsettable The meaning and the repercussions of the first statement on the overall geometry are obvious. A face is planar if its vertices – and hence also its edges – lay on a common plane. This condition is automatically verified for triangle meshes while it is not for polygonal faces. Another remarkable fact is that any affine transformation such as an anisotropic scaling maps the starting planar mesh onto another planar mesh. Instead, the second statement is ambiguous and hides implications that might seem unexpected.

An outline of differential geometry Some remarks of differential geometry will follow. For the purposes of this thesis and for the sake of simplicity, those will be approached from a descriptive geometry point of view rather than adopting a formal mathematical approach. For a more rigorous dissertation, please refer to the scientific literature on differential geometry. Previous page: 3D visualization of the planar hexagonal mesh adopted for the HexBox.

Normal curvatures. An effective way to describe and mathematically measure the “shape” of a double-curved surface is using the notion of curvature. The notion of curvature is quite simple and intuitive for curves: it gives us information on how fast the curve tend to divert from the tangent. In the case of surfaces, the “detachment” of a surface from the tangential plane at a point P generally depends on the direction we consider. Inspired by the elementary notion of curvature for curves, a preliminary idea of curvature of a surface could be thus a measure of how fast this “detachment” is, as a function of the infinite tangential directions to the surface at a point P . Normal curvatures of a surface S at a point P are obtained as follows. Referring to Figure 3.1, let n be the normal unit vector at P and let u be a direction identified by a unit vector laying on the tangent plane to S at P . We now consider the curve σ u given by the intersection between the plane π u : P + Span(n, u) (through the normal n and the direction u ). The normal curvature of S at P along the direction u is the curvature

kσ u ( P ) of σ u at P . Moreover, we want to distinguish intersection curves that present either a concavity downwards or a concavity upwards referring to the normal n . Therefore, a more precise definition of normal curvature of S at P along the direction u is as follows:

k S (u) = sign(nσ u ⋅ n)kσ u ( P )

Figure 3.1 Geometrical visualization of the normal curvature of a surface S at a point P along the direction u.

We can argue that reversing the orientation of S – that means reversing the sign of the normal n – all normal curvatures change sign. Thus, the sign of normal curvatures depends on the orientation of S we have chosen (Sambusetti, 2012). Principal curvatures and principal directions. We can now move to the definition of principal curvatures of a surface. Because of the definition of normal curvature, varying u between all possible directions on the tangent plane to S at P , we obtain several values of the normal curvatures. The principal curvatures k ( P ) and k ( P ) are respectively the maximum and the minimum value. The principal directions – which are mutually orthogonal – of S at P are the respective directions (Sambusetti, 2012). +

−

Mean curvature and Gaussian curvature. Another important measure of surface curvature is mean curvature H S ( P ) which is the arithmetic mean of the principal curvatures. Surfaces whose mean curvature equals zero are minimal surfaces.

H S ( P) =

k + S ( P) + k − S ( P) 2

The product of the principal curvatures is called gaussian curvature K S ( P ) . This concept plays a fundamental role in the discretization of surfaces through hexagonal meshes with planar faces, which will be presented afterward.

K S ( P) = k + S ( P)k − S ( P) Figure 3.2 shows a color-based visualization of Gaussian curvature. Areas in red correspond to positive Gaussian curvature that is where principal curvatures k + S ( P ) and k − S ( P ) are of the same sign and different from zero. Points which lay in these areas are said to be elliptic points. Areas in blue correspond to negative Gaussian curvature, in other words where principal curvatures k + S ( P ) and k − S ( P ) have opposite signs, and their points are said to be hyperbolic points. Where Gaussian curvature tends to zero, in green, a cylinder locally approximates the surface if only one of the two principal curvatures equals zero, whereas the surface locally degenerates to the tangent plane if both of the two principal curvatures equal to zero. Those points are respectively said parabolic points and flat points. 43

Figure 3.2 A freeform surface with a colour-based visualization of Gaussia curvature obtained with the curvature analysis command in Rhino 6.

We observe that the sign of the Gaussian curvature does not depend on the orientation of the surface S. Considering a neighborhood of the point P, the gaussian curvature is positive when the concavity of the principal lines are pointing in the same direction and, vice versa, the gaussian curvature is negative when those concavities are pointing in opposite directions. Principal curvature lines. To obtain an overview of the principal directions, one can use principal curvature lines (Figure 3.3). A principal curvature line is a curve on a surface whose tangents are in principal direction and indicates a directional flow for the maximum or the minimum curvature across the surface. Thus, through each general point of a surface, there are two principal curvature lines that intersect at a right angle and touch the principal directions.

Gaussian spherical mapping. Let S be a regular surface. A Gauss map on S is a continuous function f that assigns to each point P ∈ S a unit normal vector n( P ) . If we regard unit vectors as points on the unit sphere S * (sphere of radius 1 whose center is the origin of the underlying Cartesian coordinate system), then we can think of f as a map f : S → S * . Most surfaces have two possible Gauss maps, corresponding to the two possible choices for the direction of the normal vectors. Let’s consider some examples. • If S is a plane, all normal are parallel and therefore any point of the plane is mapped to the same point of the Gaussian sphere. The entire Gaussian image of the plane S is this single point.

• With reference to Figure 3.4, let S be a sphere of radius R . On S , we consider a disk D with spherical center P . The Gaussian mapping maps the disk D to another disk D * on the Gaussian sphere S * . Connecting the

Figure 3.3 Network of the principal curvature lines on a hyperbolic paraboloid obtained with a VB script in Grasshopper developed by David Rutten (Rutten, 2011).

boundary circle k of D with the center of the sphere S , we obtain a cone of revolution N – which is also formed by the normal of S along k . The corresponding cone N * , which connects the boundary circle k * of D * with the center of S * , is congruent to N . Therefore, D results from D * by applying a uniform scaling with factor R and a translation. Hence, the surface A * of D * and the area A of D possess the ratio

A * / A = 1/ R 2 . Because the normal curvatures of the + − sphere S at any of its points equal k= k= 1/ R , the S S

Gaussian curvature K S = k + S k − S of the sphere equals

K S = 1/ R 2 and thus K S agrees with the ratio A * / A . Let S now be an arbitrary surface, and let P be a point on it. We consider a local neighborhood D of P on S . With the Gaussian mapping, it is mapped onto a neighborhood D * of P * on the sphere S * . If the variation of the surface normals over D is strong, the domain D * will be larger than for a weak normal variation. In other words, the ratio A * / A of the area A * of D * and the area A of D will measure the variation of normals. Now one considers the limit of the area ratio A * / A when S shrinks to a point P . Of course, also D * shrinks to a point P * and thus both areas are zero. This is no problem because the limit of the ratio A * / A exists (if the representation of S is twice differentiable). The limit of the ratio A * / A is the Gaussian curvature K at P (Pottmann, et al., 2007, p. 496). Offset surfaces. With reference to Figure 3.5, a parametric offset surface S d (u , v) is a continuum of all points at a constant

distance d along normal to another parametric surface S (u , v) and defined as:

Figure 3.4 The Gaussian spherical mapping applied to a spherical disk.

S d (u= , v) S (u, v) + d â&#x2039;&#x2026;n(u, v) Where d may be a positive or negative real number and n(u , v) is the unit normal vector of S (u , v) (Patrikalakis, Maekawa, & Cho, 2009). A notable property is that the unit normal vectors n(u , v) of S are normal to S d as well, and hence if S d is an offset of S , vice versa, S is also an offset of S d . Therefore, tangent planes at corresponding points of S and S d are parallel and at a constant distance d (Pottmann, et al., 2007, p. 691).

Figure 3.5 Offset surface Sd of a surface S at constant distance d.

Discretization of freeform surfaces through planar and offsettable meshes An essential step of the designing process of freeform structures is the subdivision into discrete elements, so-called mesh tiling. This is so crucial as it marks the passage from the conception phase of a shape to its actual realization. Meshes are piecewise linear approximations of smooth surfaces. These approximations are not univocal, as a virtually infinite number of solutions are possible. Broadly speaking, good and effective tiling should aim to pursue three are the main requirements (Tonelli, 2012). • Economic requirements in terms of machining and waste of material • Feasibility requirements (node complexity, structural reliability,… etc) • An acceptable degree of approximation, namely minimizing the deviation from the base continuous freeform geometry Planar meshes. As already mentioned, meshes provide an effective mathematical abstraction of timber segmental shells where each face represents an element of the structure – either a plate or a box -, vertices represent the “vertical” edges of each element and mesh edges represent the faces of the lateral surface of the structural segments. Since each segment of the shell is constituted by a timber panel of constant thickness, this involves that mesh faces must be planar. Hence, it might seem convenient to use triangle mesh because their faces are planar. However, there are the following issues that make other solutions attractive (Pottmann, et al., 2007, p. 676). • The number of incident edges in each vertex (vertex valence) is higher compared to other types of meshes. This means more complex nodes where a higher number 47

Figure 3.6 Geometric principle for translational surfaces. (Glymph, et al., 2004, p.190)

of plates meet each other and, consequently, a more complex assembly procedure. • Apart from very simple cases, tringle meshes do not possess offsets at constant face-face distance. Neither is it possible to use triangle mesh as the basis of a multilayer freeform construction in which only the basic requirement of parallelism of layers is imposed. Quadrilateral meshes are a good alternative to approximate any double-curved surface, as they enable to reduce the complexity of nodes as well as simplifying the fabrication of panels. However, quad faces are not supposed to be planar a priori. Much research has been devoted to methodologies to obtain planar quad meshes. One of the easiest ones is to translate any spatial curve – generatrix – against another random spatial curve – directrix – (Figure 3.6). This will create a spatial surface consisting solely of planar quadrangular mesh. Subdividing the directrix and the generatrix equally results in a grid with constant bar length and planar mesh (Glymph, et al., 2004). In other words, the philosophy behind this method is to try approximating a freeform with a translational surface. Research progressively moved on the development of algorithms, that take as input a quad mesh whose quads are not planar and delivers as output a mesh that approximates the same smooth surface but exhibits only planar quads (Liu, et al., 2006). Another interesting solution for panelling freeform surfaces in the field of architectural design is using hexagonal patterns. This is an innovative and high-quality subdivision scheme with the evident value of reducing the node valence to 3. In addition, many natural phenomena show peculiar hexagonal patterns, one of the most obvious examples and easiest to detect in nature are beehives. A hexagonal face of a mesh is identified by six vertices, then those cannot be expected to be automatically planar. Offset meshes. The offsetting of a planar mesh can be seen as the discrete analogue of offsetting a smooth surface – illustrated in the previous paragraph –. Once understood the concept of 48

offset surfaces, we can try to extend it to the discrete case of meshes. According to research on multilayer freeform structures carried out in recent years (Pottmann, et al., 2007, p. 692), there are three meaningful ways to define the offset M d of a planar mesh M at least, depending on how the constant distance d shall be measured. • Vertex offsets: The distance of corresponding vertices of M and M d has a constant value d , which does not depend on the vertex. • Edge offsets: The distance of the corresponding parallel edge of M and M d does not depend on the edge and equals d . • Face offsets: The distance of corresponding faces of M and M d is independent of the face and equals d. The third type of mesh offset, also called constant-face-distance offset in the literature (Wang & Liu, 2009), is the one in which we are interested in as we are dealing with timber segmental structures – made up of planar pates with constant thickness.

Quad-Meshes with planar faces Conjugate curve networks. Recent developments use the notion of conjugate curve network to generate quad-meshes with planar faces from a base surface. Given two families of curves A and B on a smooth surface S, these are said to form a conjugate curve network if the following property holds: Pick a curve c in the network and compute in each of its points the tangent to the curve from the other family. Then, these tangents must form a developable ruled surface. It is obvious that this developable surface touches S along c. Thus it is the envelope of the tangent planes of S at the points of c. We simply speak of the tangent developable surface along c. (Figure 3.7) A surface S carries infinitely many conjugate curve networks. To realize this, we prescribe one arbitrary family A of curves. We can then compute the conjugate family B as follows. Along each curve c of family A, we determine the tangent developable surface and consider its rulings. Thus, in each point of c we obtain such a ruling (called the conjugate direction to the tangent of c) (Pottmann, et al., 2007, p. 680). A particular example of conjugate lines network is the network of principal curvature lines that have the additional property 49

Figure 3.7 Tangent developable surface along c. (Pottmann, et al., 2007, p.680)

to intersect at right angle. Another example is the isoparameter lines of a translational surface (Liu, et al., 2006). Planar quad-meshes (PQ meshes). Quad meshes with planar faces may be seen as a discrete version of conjugate curve networks on a surface. For this reason, the conjugate curve network can be used as a starting point to generate PQ meshes through algorithms. If the input mesh has been extracted from a conjugate curve network, chances are high that the algorithm provides a solution retaining aesthetic requirements (Liu, et al., 2006). Generally, those meshes do not possess a constant-facedistance offset. This is quite obvious if think about the geometrical construction of the offset mesh. Let V be a vertex of a PQ mesh with a valence of four and let f1 , f 2 , f 3 , f 4 be the surrounding faces at V . We now compute the plane parallel to each face, one by one, at a constant distance d . The intersection between the plane of f1 and f 2 results in a straight line, and then offsetting the plane of f 3 and intersecting it with that straight line we identify a point P , which is the resulting intersection of the aforementioned planes and is a candidate to be the corresponding vertex Vd of the offset. If P lies on the plane parallel to f 4 at distance d , then the starting mesh possesses an exact offset.

Offsettable meshes Discrete Gaussian image. An offset pair of smooth surfaces with parametric representation S (u , v) and S d (u , v) defines the Gaussian image via the difference surface, scaled with factor 1/ d .

n(u , v) =

S d (u , v) − S (u, v) d

Given a pair of offset meshes M and M d , we, therefore, define the discrete Gaussian image as the scaled difference mesh S of the two (parallel) meshes M and M d

Md − M d

S is computed as follows. If m1 , m 2 ,... and m1d , m 2 d ,... are the coordinate vectors of corresponding vertices in M and M d , one forms the scaled difference vectors s1 , s 2 ,... and uses them as coordinate vectors of the vertices s1 , s2 ,... of the mesh S .

= s1

m1d − m1 m2d − m2 , s2 ,... = d d

The Gaussian image mesh S is parallel to M and M d , and that distance properties between M and M d are also reflected in distances between S and the origin.

M and M d shall exhibit constant distance d in an appropriate

sense. Hence, the Gaussian image S must have distance 1 to the origin in the same sense (i.e. S approximates the unit sphere S * ). Consider a planar mesh M , its offset mesh M d at distance

d , and the Gaussian image mesh= S ( M d − M ) / d . Then the specific offset properties are encoded in the Gaussian image 51

Figure 3.8 Left: a planar hexagonal mesh M and its constant face-distance offset mesh Md. Right: the disctrete Gaussian image S of the mesh, whose faces are tangent to the unit sphere S*. (Wang & Liu, 2009, p.11)

mesh S as follows (Wang & Liu, 2009).

•

M d is a vertex offset of M if and only if the vertices of

the Gaussian image mesh S are contained in the unit

sphere S * . In this case, M and M d are circular meshes.

•

M d is an edge offset of M exactly if the edges of the

Gaussian image mesh S are tangent to the unit sphere S*.

M d is a face offset of M if and only if the faces of the

Gaussian image mesh S are tangent to the unit sphere

S * . In this case, M and M d are conical meshes. Conical meshes. We refer to a piece of research (Liu, et al., 2006) where is presented a particular type of meshes that satisfy the requirement to possess an exact constant-face-distance offset called conical meshes. Those meshes are obtained through a particular discretization of the network of principal curvature lines. We call a mesh a conical mesh if its every vertex satisfies the following property: all the four (oriented) face planes meeting at V are tangent to a common (oriented) sphere (Figure 3.9). The authors also point out that this is equivalent to saying that these oriented face planes are tangent to a common oriented cone of revolution and show that this geometrical fact leads to 52

Figure 3.9 Left: configuration of the faces of a conical mesh at a vertex. The faces touch a common cone of revolution; Right: faces of a conical mesh at two adjacent vertices. (Liu, et al., 2006, p. 685)

a condition on the interior angles. Indeed, the sum of opposite edge angles at vertices of quad conical meshes is equal. In short:

ω1 + ω3 = ω2 + ω4

Planar hexagonal meshes Planar hexagonal meshes (PHex meshes) always satisfy the condition to be conical. Vertices of PHex meshes have a valence of 3 – if we discard cases where the hexagonal pattern degenerates –, hence there are exactly three faces meeting at nodes so that any mesh possesses constant-face-distance offset. A close relation subsists between the shape of hexagonal faces of the resulting mesh and the gaussian curvature of the input surface (Figure 3.10). Hence, we can distinguish three types of shapes depending on whether the Gaussian curvature is positive, negative or equals zero. •

K > 0 : hexagons will be convex. If the curvature is also isotropic – e.g. a sphere – regular hexagons will form.

•

K < 0 : hexagons will be non-convex, so that two of their interior angles exceed 180°, resulting in a peculiar bowtielike shape.

•

K = 0 : hexagons will degenerate into rectangles so that the lateral edges will align – e.g. on a cylinder.

Many different methods for computing planar hex-meshes have been presented in the literature so far (Wang & Liu, 2009), (Li, Liu, & Wang, 2015), (Vaxman & Ben-Chen, 2015), and the 53

Figure 3.10 Tangent plane intersection for doubly curved surfaces. Oscillating circles indicate curvature (1/R), principle curvature directions and orientation. A. Synclastic, positive Gaussian curvature K > 0. B. Anticlastic, negative Gaussian curvature K < 0. (Krieg, et al., 2014)

development and optimization for more versatile algorithms is still a subject of research. Tangent Plane Intersection (TPI). This method was presented by Christian Troche in 2008 (Troche, 2008). That is the most intuitive way to create a trivalent mesh of a free-form surface, however it presents some disadvantages pointed out in (Li, 2017, p. 148) where are shown approaches proved to be able to produce a better mesh, which is smoother and more regular than that of the tangent plane method. The starting point of the method is a dual surface triangulation that connects the generating points of the tangent planes with edges that indicate the adjacency of elements, that is which planes need to be intersected with each other to form the boundary of a TPI polygon. A generating triangle defines three tangent planes and their intersection gives a vertex of the TPI tessellation. It is obvious that the success of this method lays in the starting triangulation, nevertheless, it seems hard understanding exante whether a triangulation leads to nice hexagonal panels. In (Troche, 2008), the author proposes an algorithm that uses an adapted advancing front method. Basically, starting at an arbitrary point inside the domain, the algorithm spreads new triangles whose vertices serve as generator points for tangent plane intersections and subsequently TPI vertices. Other methods. The TPI method has two main disadvantages (Li & Knippers, 2015). First, the size and geometry of each polygon are nearly random. Second, without using penalty functions a solution might not be found in anticlastic areas. In (Wenping, et al., 2008) is presented a method using Dupin duality that divides the derivation of a trivalent polyhedron into two stages. First, a specific triangulation would be found by using the properties of Dupin duality. This triangulation would generate a corresponding 54

hexagonal mesh that each hexagon is nearly flat. Second, this hexagonal mesh would be further planarized to derive a planar hexagon mesh. Recently, a varied version of this method has been proposed. It is also a two-stage approach, but the initial triangulation is replaced with a planar quadrilateral mesh (Li & Knippers, 2015).

References Glymph, J., Shelden, D., Ceccato, C. & Mussel, J., 2004. A Parametric Strategy for Freeform Glass Structures Using Quadrilateral Planar Facets. Automation in Construction, March, 13(2), pp. 187-202. Klarreich, E., 2019. Math Duo Maps the Infinite Terrain of Minimal Surfaces. [Online] Available at: https://www.quantamagazine.org/math-duo-mapsthe-infinite-terrain-of-minimal-surfaces-20190312/ [Accessed October 2019]. Krieg, O. D. et al., 2014. Biomimetic Lightweight Timber Plate Shells: Computational Integration of Robotic Fabrication, Architectural Geometry and Structural Design. In: P. Block, J. Knippers, N. J. Mitra & W. Wang, eds. Advances in Architectural Geometry. London: Springer, pp. 109-125. Li, J.-M., 2017. Timber Shell Structures. Form-finding and Structural Analysis of Actively Bent Grid Shells and Segmental Plate Shells. Stuttgart: Institut für Tragkonstruktionen und Konstruktives Entwerfen Universität Stuttgart, pp. 136-180. Li, J.-M. & Knippers, J., 2015. Segmental Timber Plate Shell for the Landesgartenschau Exhibition Hall in Schwäbisch Gmünd— the Application of Finger Joints in Plate Structures. International Journal of Space Structures, June, Issue 30, pp. 123-140. Liu, Y. et al., 2006. Geometric Modeling with Conical Meshes and Developable Surfaces. ACM Transactions on Graphics. Li, Y., Liu, Y. & Wang, W., 2015. Planar Hexagonal Meshing for Architecture. IEEE Transactions on Visualization and Computer Graphics, 21(1), pp. 95-106. Patrikalakis, N., Maekawa, T. & Cho, W., 2009. Offset curves and Surfaces. [Online] Available at: http://web.mit.edu/hyperbook/PatrikalakisMaekawa-Cho/node210.html [Accessed September 2019]. Pottmann, H., Asperl, A., Hofer, M. & Kilian, A., 2007. Architectural Geometry. Exton(Pennsylvania): Bentley Institute Press, pp. 381395, 487-501, 671-707. Pottmann, H. et al., 2007. Geometry of Multi-layer Freeform Structures for Architecture. ACM Transactions on Graphics, July.26(3). Robeller, C., 2019. Recycleshell. [Online] Available at: https://www.architektur.uni-kl.de/dtc/2019/09/05/ recycleshell/ [Accessed October 2019]. Robeller, C. & Viezens, V., 2018. Timberdome: Construction System for CLT-Segmental Plate Shells without Screws. Proceedings of the 24th International Timber Construction Forum 56

Garmisch-Partenkirchen. Rutten, D., 2011. Principal curvature lines on surfaces. [Online] Available at: https://www.grasshopper3d.com/forum/topics/ principal-curvature-lines-on?id=2985220%3ATopic%3A160646&p age=1#comments [Accessed October 2019]. Sambusetti, A., 2012. Complementi ed Esercizi di Geometria Differenziale. [Online] Available at: http://www1.mat.uniroma1.it/people/sambusetti/ geometria/complementi14.pdf [Accessed September 2019]. Tonelli, D., 2012. Sinossi sullâ&#x20AC;&#x2122; ingegneria delle forme libere, Pisa. Troche, C., 2008. Planar hexagonal meshes by tangent plane intersection. Advances in Architectural Geometry, pp. 57-60. Vaxman, A. & Ben-Chen, M., 2015. Dupin Meshing: A Parameterization Approach to Planar Hex-Dominant Meshing. Wang, W. & Liu, Y., 2009. A Note on Planar Hexagonal Meshes. Nonlinear Computational Geometry. Wenping, W. et al., 2008. Hexagonal Meshes with Planar Faces, Hong Kong: HKU CS Technical Report.

Part two

Investigations

4_ Morphogenesis

Based on the state-of-the-art, the following paragraphs debate the four fundamental parameters that affected the final design of the Canopy: material, shape of the structural modules, tiling strategy, and joining system. Even though these will be analyzed separately, the reader has to keep in mind they are strictly interconnected and affect each other.

The material Timber products have to meet structural requirements and different types of constrains related to digital fabrication processes, therefore it is important to take the production technology into account since the very firsts design steps. For timber shells, a bidimensional structural behavior of the parts is required, thus any kind of directional product such as LVL panels had to be discarded. The choice range narrows to quasiisotropic engineer wood products and thus the only two options were using either CLT or plywood panels. The main advantage of the first option was that an effective construction system had already been experienced by the DTC in the Timberdome prototype (Robeller & Viezens, 2018) and presented at the Internationales Holzbau-Forum 2018. However, it would have required the support of an external company for manufacturing. Indeed, CLT panels are usually supplied in large dimensions that are very difficult to handle without industrial systems. Another fact that was considered is that the CNC milling would not have achieved the needed tolerances for thick plate elements. On the other hand, plywood is far easier to work with, it is available in thinner and smaller panels and is perfect for being cut with 5-axis milling machines. Thus, all the fabrication could be carried out within the workshop of the School of Architecture of Sydney. Therefore, the choice of the material fell on 19mm-thick structural plywood provided by the company Carter Holt Harvey Plywood (CHH PLY, 2015). Their panels are manufactured from radiata pine wood veneers. The veneers are placed at right angles to each other for maximum strength and stability then bonded Previous page: Photo by Katherine Lu

together with synthetic phenolic (PF) resin to form a strong and permanent Type A bond. Further information on mechanical properties and structural modelling of the material can be found in the paragraph “FE models and structural analysis”, Chapter 5.

Structural modules: the plate system and the hollow-box system Based on previous research, we can recognize two main different approaches in designing segmented timber shells: the plate system and the hollow-box system (Bechert, et al., 2018). This paragraph presents a comparison between these two approaches (called P-system and B-system hereafter) and discusses the design choices which led to opt for the latter for the HexBox Canopy. Both segmented timber shell construction types show advantages and disadvantages depending on the point of view we focus on. In terms of fabrication simplicity, the P-system is definitely convenient as it is made up of a single element ready to be positioned. Furthermore, much recent research has been devoted to segmented plate shells, thus many relevant examples can be found in the scientific literature. Joints between plates may be established through crossing screws (Hammerfest Hiking Cabins, SPINN Arkitekter, 2018), sawed joints (Cobra-Sculpture Pavilion, TU Graz, 2010), combining finger joints and crossing screws (LaGa Pavillion, ICD/ITKE, 2014), X-Fix (Timberdome, DTC group 2018), X-Fix and crossing dowels (Recycleshell in Dimerstein, DTC group, 2019). On the other hand, the B-system is far more complex from a geometrical point of view, as box-like segments are made up of more pieces. The minimum necessary elements to define a box-like hollow element are, indeed, a top plate and a number of side plates which depend on the shape of each segment itself – usually between five and seven for 3-valence meshes. A relevant consequence of the employment of elements with a thin cross-section is the generally low bending stiffness of the joints and the more general joint design at segments’ edges. The bending stiffness of a joint correlates with the structural height at the joint. Using the P-system, a strategy to overcome this problem is increasing the thickness of plates, for example utilizing CLT plates rather than plywood plates – which the maximum commercial thickness rarely exceeds 35-40mm. However, as the increased cross-section is mostly needed around the edges of the segments and less so in the middle, one could also argue that it would be preferable to only introduce additional material around the edges of a segment. With this in mind, the B-system seems to be a smarter solution (Krieg, et al., 2018). The box-like geometry allows lots of joining possibilities as the 62

touching sides of segments are wider and easily accessible by builders. For this reason, the B-system opens the door to a new type of connection witch lays in the average plane of the segments to be joined. While for plate shells, joints required additional fasteners to resist out of plane forces preventing the mutual rotation between plates around the edges (i.e. crossing screws or crossing dowels), the advantage of joining elements like this is that no additional connectors are required due to the greater structural height. In addition, in-plane connectors are in a safer location, under the extrados of the shell so that are protected from potential water seepage rather than being more exposed to the weather conditions. Figures 4.1-4.3 show the designing development of HexBox’s construction system. Over and above the mesh topology – which provided for quadrangular structural modules at the very beginning of the project – those figures point out the designing steps leading to the B-system adopted in the final project. The first proposal (Figure 4.1) implements 100mm-thick CLT plates where connections are established through X-Fix connectors which are basically connections inspired by traditional butterfly key joints. Then, research moved on open box-shaped elements (Figure 4.2). These new 20mm-thick plywood plate boxes are open at the bottom, and the boxes themselves are adhesive-joined. The last proposal (Figure 4.3) – which has been implemented into the final project – provides for additional bottom plates. Connecting side plates on the underside, these plates increase the stiffness of segments, ensuring an actual box-like structural behavior and preventing side plates to buckle.

Figure 4.1 On the left, the first proposal implements a P-System made up of 100mmthick CLT plates. Figure 4.2 On the right, the second proposal implements 20mm-thick plywood plate boxes, open at the bottom.

Figure 4.3 The final proposal introduces additional bottom plates.

Mesh tiling The final design of the HexBox implements planar hexagonal meshes as base geometry. However, first design proposals exploited conical quad meshes (Figure 4.5) and therefore some tests in this sense have been carried out. This paragraph shows two pipelines to discretize surfaces using these two types of meshes in order to be fabricated as segmented timber shells. A straightforward method to obtain planar conical quad mesh using Kangaroo. The Grasshopper plugin Kangaroo 2.42 (Food4Rhino, 2017) implements the goal-mesh object conicalize which adjust iteratively a quad mesh to make vertices conical. Combining it with the goal-mesh object planarize, we obtain a PQ mesh as final output that will possess constant-face-offsets. Unfortunately, we cannot provide as input any quad mesh and hope that the solver will make quads planar and vertices conical while retaining aesthetic requirements and proximity to the underlying surface. However, with a few simple adjustments, Kangaroo leads to good results within a very simple and userfriendly working environment. The example illustrated in Figure 4.4 shows the potentialities of such a workflow. Starting from a translational surface and meshing it into a quad mesh that roughly traces the principal curvature lines network, it is possible to planarize faces while keeping vertices conical within a reasonable approximation. The “conicality” of the vertices is calculated applying the criterion on angles at each vertex: | (ω1 + ω3 ) − (ω2 + ω4 ) | , while the analysis of planarity is obtained through the plugin EvoluteTools Lite (Evolute, 2015).

Figure 4.4 Next pages: a straightforward method to obtain planar hexagonal meshes in Grasshopper. Figure 4.5 First design proposal for the HexBox implementing a quadrilateral mesh with planar faces

1_Base surface A translational surface is used as base geometry.

2_Quad Meshing The quad meshing roughly traces the principal lines network.

3_Vertices Analysis (before) The “conicality” of vertices before the optimization is assessed applying the angle criterion.

4_Face planarity analysis (before) Planarity is tested using the “Analyze Planarity” command of EvoluteTools Lite.

5_Vertices Analysis (after) The angle criterion is satisfied within acceptable approximations.

6_Face planarity analysis (after) Faces after the optimization are almost perfectly planar.

7_Fabbrication The result is a PQ conical mesh. Therefore it is possible to generate plates and use a 5-axis milling machine to fabricate them.

Figure 4.6 Left: technical solutions enabling to design plate structures using 6 and 4 valence meshes which do not possess an exact constant-face-offset. Right: 3-valence meshes always possess exact constant-face-offset. (Robeller & Viezens, 2018)

A technical solution: funnel holes. Even though the combination of the conicalize and planarize components provided by Kangaroo plugin works well for simple cases such as translational surfaces, there are some more geometrical complex cases where it leads to unpleasant results or the solver does not converge. In (Robeller & Viezens, 2018) is shown how we can rely on a detailing expedient that consists of chamfering panels corners or, even better, carving a funnel hole out of each vertex (Figure 4.6). The latter option results in a continuously faced intrados of the structure, nevertheless an extra sealing on those holes is required to avoid rainwater seepage. A grasshopper definition of TPI method. The following example (Figure 4.7) illustrates the application of the TPI method to a translational surface using visual programming in Grasshopper. The Grasshopper definition produces a good triangulation and gives nice results for simple base geometries that exhibit a directional development. More complex triangulations are needed for dome-like shapes or, broadly speaking, for base geometries that have radial symmetry. In this regard, the hexagonal tiling of the Recycleshell in Dimerstein (Robeller, 2019) is an interesting example of the hex-dominant tiling of such a type of shape.

Figure 4.7 Next pages: a straightforward method to obtain planar hexagonal meshes in Grasshopper.

1_Base surface A translational surface is used as base geometry.

2_Dual Triangulation a PHex mesh with its faces tangent to the base surface S corresponds to a regular triangle mesh whose vertices are at the tangency points of the faces of the P-Hex mesh with S.

3_Gaussian Curvature Analysis The sign of the Gaussian curvature affects the shape of the resulting hexagonal faces.

5_PHex mesh

4_Fabbrication 3-valence meshes possess exact face-offset.

Figure 4.8 Preliminary design proposal for the HexBox implementing a hexagonal mesh with planar faces.

Joining system: wood-only wedge connectors For a rapid and precise on-site assembly, the HexBox project uses novel wedge connectors, inspired by traditional tying wedge joints (Figure 4.9). The archetype of this kind of connectors is the tusk mortise-and-tenon. Due to their two wedges, this joint allows for pulling and gradually forcing two parts together. One of the two wedges is straight and already integrated into the body of the connector, while the other is angled of 2.5 degrees and is after inserted to secure and fasten the two parts. The main benefit of this kind of connectors is their versatility and adaptability. The gradual tightening of the joint is crucial to compensate for certain tolerances that are intrinsic to the naturally grown material wood, to the CNC machining processes and to random imperfections due to the manual assembly of the structural hexagonal modules. Depending on the insertion depth of the angled wedge, it is possible to regulate and adjust the resulting pulling force, closing gaps between the elements which may occur during assembly, so that the wedges allow to assemble boxes even when there are small imprecisions rather than attempting ultra-precisely fabricated elements. The closing of such gaps is indeed critical for the overall precision and Figure 4.9 First version prototype of wedge connectors.

1 2

5 3

Figure 4.10 Axonometric projection showing constituent parts of wedge connectors implemented into the HexBox Canopy.

performance of the structure. Furthermore, these novel joints can be produced from waste material, such as the small offcuts resulting from the fabrication of the other components. Every connector is made up of six wooden parts produced with a standard circular saw and glued together with polyurethane adhesive. Clamping nails are inserted to secure the parts together while the adhesive is bonding the parts. The result is a smart device ready to be inserted through rectangular holes, pre-cut on each side plate of boxes so that the tightening of the joint itself is easy and fast. Constituent parts of a single wedge connector are listed below. Surfaces in red (Figure 4.10) are glued. 1. Clamping nails 2. Top plate (60x178mm) 72

3. Straight wedge

4. Stopper piece for straight wedge tightening 5. Angled stopper piece for angled wedge tightening 6. Angled wedge 7. Bottom plate (60x178mm)

Figure 4.11 Next page: overview and details of the wedge joint system.

References Bechert, S. et al., 2018. Structural Performance of Construction Systems for Segmented Timber Shell Structures. Massachusetts Institute of Technology, s.n. CHH PLY, 2015. ECOPLYÂŽ specification and installation guide. [Online] Available at: https://chhply.co.nz/assets/Uploads/2e7756d489/EcoplySpecification-Installation-Guide-September-2015.pdf [Accessed October 2019]. Evolute, 2015. Evolute. The geometry experts.. [Online] Available at: http://www.evolute.at/ [Accessed October 2019]. Food4Rhino, 2017. KANGAROO PHYSICS (by Daniel Piker). [Online] Available at: https://www.food4rhino.com/app/kangaroo-physics [Accessed October 2019]. Houck, L. D. et al., 2019. The process of rocking CLT into a HOT cabin. Lisbon, CRC Press, pp. 1187-1195. Krieg, O. D. et al., 2018. Affordance of Complexity: Evaluation of a Robotic Production Process for Segmented Timber Shell Structures. Seoul, Republic of Korea, s.n. Robeller, C., 2019. Recycleshell. [Online] Available at: https://www.architektur.uni-kl.de/dtc/2019/09/05/ recycleshell/ [Accessed October 2019]. Robeller, C. & Viezens, V., 2018. Timberdome: Construction System for CLT-Segmental Plate Shells without Screws. Proceedings of the 24th International Timber Construction Forum Garmisch-Partenkirchen.

5_ Planning and Construction of the HexBox Canopy The whole designing process of the HexBox adopted an empirical methodology based on both digital and physical models. Iterative prototyping played a fundamental role to check ideas and designing strategies through physical feedbacks. Different materials, CNC machining methods, joints, and geometrical configurations have been tested to find the right parameters that could lead to effective solutions. The constructive system had to meet the following requirements. • Employment of wood-only structural joints • Fabrication constraints intrinsic to CNC milling • Quick and easy assembly • Adaptability to geometrical constraints of the building site • Adaptability to tolerances while preserving an acceptable structural behavior

Generation of geometries Typically, drawing using standard CAD software is a mostly “manual” process, where elements are created in a very similar way to traditional hand-drawn construction sheets. Each part of the drawing is drafted one after another manually. Revisions, modifications, changes and further processing such as fabrication are often done by deleting, redrawing and manually adding further details. The generation of an overall number of 1531 of different geometries has been made possible through the plug-in TPS_ LVLboxes_WedgeJoints for the CAD software Rhino 6 coded by Jun. Prof. Dr. Christopher Robeller. The plugin takes a planar mesh as an input and a bunch of parameters defining the plate thickness, the height of boxes and the offset for bottom plate aperture. Then, it generates the actual boundary representation (B-rep) geometries as well as the deconstructed ones ready to be nested and processed for the fabrication. The plugin works independently of the input mesh valence, enabling the processing of PQ-meshes as well as PH-meshes.

Previous page: Photo by the author.

To keep track of thousands of different elements, each B-rep geometry possesses a property name automatically assigned during the generation of geometries. As already mentioned, every box is unique. For this reason, each box component has been labeled with a univocal alphanumeric code and grouped with the other components that make up the same box. For example, the elements of Box56 are: • 56_Ptop • 56_Pbottom • 56_Side_0 • 56_Side_1 • 56_Side_2 • 56_Side_3 • 56_Side_4 • 56_Side_5 Through the development of an in-house plugin, we implement an effective pipeline that connects the designing process directly to the fabrication.

Top Plate

Side Plates

Bottom Plate

Figure 5.1 Axonometric projection of an example box element.

Numerical control of machines: program format and definitions of address words The advent of computer numerical control (CNC) sped the evolution of milling machines into machining centers. It dramatically advanced machine tool control and deeply changed the culture of manufacturing. With the declining price of computers and the development of open-source CNC software, the entry price for CNC mills has dropped significantly over that time. Several tests and prototypes for the HexBox canopy have been carried out using a 5-axis CNC router provided by the fabrication workshop of the Faculty of Architecture at the TU Kaiserslautern. Therefore, different tools and fabrication strategies have been tested. With a working area of about 2x3 meters, the machine allows for flexibility in milling parts at different tool orientations. The milling tool can rotate in two separate axes, C and A, at the same time the 3 linear axes, X, Y, and Z are moving. Figure 5.2 shows the configuration of linear and rotational axes. A wide range of tool types and configurations are available for CNC routers. The tools equipment available at the workshop consists of milling tools – with different radius, length and number of flutes – and a 125mm-radius sawblade. Either one uses milling-cut or saw-cut, the user needs to input to the machine the subsequent positions of the tool central point (TCP) in terms of spatial coordinates corresponding to the 5 different axes. Location data can be entered into the controller manually, moving the axes one by one in real-time through the controller. Alternatively, a CAD/CAM system can be used to design and program the part, with the resultant program being loaded or fed into the CNC controller. The code used for machine control programs is often referred to as Geometry Code, or more commonly, G-Code. Controllers also have M-codes or miscellaneous codes, such as a code to turn on or off the spindle. Geometrical (G) and miscellaneous (M) function codes underwent a process of standardization during the years according to ISO 6983, however, they can slightly vary depending on the type of CNC machine and manufacturer. The core part of a G-code program consists of a list of blocks containing the coordinates in the five axes defining a list of vectors. Furthermore, each block of that list contains information on the kind of motion between the generic i-th block and the following (i+1)-th. The curve resulting from the interpolation of each vector is the tool path. Linear, circular or parabolic interpolation is possible between subsequent vectors. For our purpose, the linear interpolation – which is also the simplest to code – needs to be used. Vector coordinates of each G-Code block can be referred to the origin of a XYZ coordinate system which needs to be set before running a program (zero-point). This way of operating is called

ntool X

Z A

Tool Central Point (TCP) Y

Figure 5.2 Above: 5-axis CNC router by imes-icore at the Faculty of Architecture, TU Kaiserslautern. Below: axonometric scheme showing the tool central point (TCP), linear axes (X, Y, and Z) and rotational axes (A and C). (Robeller, 2015)

Figure 5.3 Comparison between G90 Absolute Position Coordinates (G90) and Relative Position Coordinates (G91). Left: The X axis is moved to the absolute position 40 and the Y axis is moved to the absolute position 20 (G90 G01 X40 Y20). Right: From the current position, the X axis is moved 40 units in te positive direction and the Y axis is moved 20 units in the positive direction.

Absolute Position Coordinates (G90), namely, the entry of the coordinates is absolute, which means the given values refer to the current zero-point (Figure 5.3 left). Alternatively, it shall be possible to use incremental (relative) dimensions, this way of operating is called Relative Position Coordinates (G91). In this latter case, the entry of the coordinates is relative, which means the given values refer to the current position (Figure 5.3 right). Mixed programming of G90 and G91 is also possible. As we already mentioned, the only kind of motion we need for our purposes is linear interpolation between subsequent positions. Linear interpolation causes a movement in one or more axes directions from the start position to the target position, which is determined with an absolute or relative value. We distinguish between Rapid Interpolation and Linear Interpolation. Rapid interpolation is programmed using the path information G00 and the coordinates of the target position. The target position is approached in a straight line with the maximum possible speed and acceleration considering the limit values of the CNC axes. Whereas, Linear interpolation is programmed using the path information G01, the coordinates of the target position and the feed rate, which is the velocity at which the cutter is advanced along the workpiece. The feed rate is denoted by the word F followed by some digits – i.e. F1200 –, its units are millimeters per minute [mm/min]. Rapid interpolations are used whenever the tool is not cutting, namely for movements out of the working piece. Therefore, it is desirable for changing the position as fast as possible. In all the other cases, it is recommended setting an appropriate feed rate to avoid crashes. Another crucial piece of information we need to declare in a G-Code program is the spindle speed measured in revolutions per minute (RPM). It is denoted by the word S followed by some digits – i.e. S1200 – Feed rates and spindle speeds values are interrelated and require adjustment due to many factors: • Machining strategy (milling or sawing) • Mechanical properties of the material being cut • Rigidity of the machine and work holding • Quality and condition of the tool • Geometrical features of the tool (material, number of flutes, diameter-length ratio) • Quality and accuracy expected for the cut • Number of passes • Complexity of the cut Even though it is possible to find some formulas to determine feed rates and spindle speeds in the literature, doing several tests and check results is essential. In addition to the visual

examination of the cut quality, the user can obtain feedbacks on feed rates and spindle speeds in real-time from other evident parameters such as the noise of the cut, vibrations of the machine, smell, sawdust, and chips. Finally, an example of a CNC program used for milling plates of one of HexBox’s mock-ups is presented. %123 program name

N10 G90 block number 10, absolute position coordinates (APC)

N20 T2 block number 20, selection of tool number 2

N30 S10000 M03 block number 30, spindle speed set to 10,000 RPM, miscellaneous function command to start the spindle rotation in the clockwise (CW) direction

N40 G40 block number 40, command which cancels any cutter compensation (diameter or radius) or tool offset

N50 G00 X0 Y0 Z30 block number 50, rapid positioning, linear axes coordinates X,Y,Z (start position)

[…] N130 G01 X817.56 Y1221.89 Z12.53 C-176.77 A-7.7 F1200 block number 130, linear interpolation, linear axes coordinates X,Y,Z, rotational axes coordinates C,A, feed rate set to 1,200 mm/min

[…] N24070 G00 X0 Y0 Z30 C0 A0 block number 24070, rapid positioning, linear axes coordinates X,Y,Z, rotational axes coordinates C,A (end position)

N24080 M30 block number 24080, miscellaneous function used to end the program

Block numbering using the word N is not strictly necessary for the correct running of the program. However, it is very useful to uniquely identify a piece of code in case of errors (i.e. syntax errors, axis errors, etc).

G-Code generation through TPS fabrication components in Grasshopper CNC programs can be written manually in a code editor. However, it is clear that manual coding has become obsolete. Nowadays, CAM software allows to automatically generate machine code based on geometrical inputs. The following paragraphs illustrate the fabrication components of the grasshopper plugin Timber Plate Structures (TPS) developed by Jun. Prof. Dr. Christopher Robeller. A release that implements the main features of the fabrication components is available for free on food4rhino.com. Due to the complex geometry of the plates to be cut, normal CAM software does not currently process them efficiently. Thus, TPS represents a very important tool for a successful fabrication outcome. It has been also successfully employed for many research projects such as the Vidy Theatre, Lausanne. Many of the cutting parameters can be adjusted directly in Grasshopper, however certain machines may require some additional adaptations.

TPS_Loftcut For the 3D cutting, we define the shape of plates through pairs of polylines consisting of a lower polyline and a top polyline. The fabrication algorithm will iterate over the corresponding vertices of the two polylines. The correct alignment of the start-points of the two curves is important because the tool orientation vectors are obtained through subtraction of the upper point from the corresponding lower point. (Robeller, 2015) This means that corresponding polylines • must be closed and possess the same number of points • must have the same direction which can be adjusted using the rhino command “Analyze direction” • must have the same seam which can be adjusted using the rhino command “CrvSeam” The 3D geometry of the part is described through a loft surface between these pairs of polylines. Plates with cutouts within the outer contour are described through additional pairs of polylines for each cutout. This situation happens, for example, into the side plates of a cassette element of the HexBox where slots for wedge connectors need to be cut out. The convention used in TPS establishes that the orientation of pairs of polylines defining outer contours have to be counter-clockwise, whereas pairs of 85

clockwise polylines define cut-outs. Furthermore, lower polylines must be located on the world zero plane (Z=0). Other features that can be added automatically are notches on the interior corners of the slots for wedge connectors. Since the CNC router will cut the parts with a rotating tool, sharp interior corners are not possible. Likewise, the rounded interior corners that would result from the regular offset toolpath would not allow for the assembly of the parts. Additional notches are a solution for this problem, which are cut into the corners as far as necessary for the assembly of the parts. Basically, the toolpath is generated so that the minimum amount of material will be removed in correspondence of the interior corners to allow the insertion of the connector through the cut-outs of side plates. (Robeller, 2015) In addition to the primary input of polyline pairs – which are sorted automatically by the component –, there are several other parameters to control the cutting process (Figure 5.4), which will be written into the standardized G-Code format (ISO6983). • Zret: safe Z height to which the tool returns in between cuts • Zsec: safe Z height for transit motions between parts • Header: text values to place before the body part of the CNC program, usually containing information on absolute position coordinates (G90) tool’s number (i.e. T5), spindle speed (i.e. S12000), and tool radius offset cancel (G40) • Tool radius • Infeed: number or vertical cutting passes to cut • XYfeed: horizontal cutting speed in mm/min • Zfeed: vertical cutting speed in mm/min • Notch: Boolean value (true/false) whether to cut notches on concave corners • RotAxes: text values defining rotational axes notation There are two kinds of loftcut components embedded into the customized version of TPS used for making prototypes for the HexBox: the “standard” loftcut and the loftcut_perpendicular. Both take the fabrication inputs as described above. However, they differ for the calculation of the toolpath and therefore the G-Code being generated. The standard component is designed for true simultaneous 5-axis machines, namely machines allowing the moving of the 3 linear axes and the 2 rotational axes at the same time. Whereas, the loftcut_perpendicular component is designed for 3+2 axis machining. In this type of machining, the router will first rotate into position, and then a typical 3-axis machining operation will commence after rotation. In other words, rotations and linear movements do not happen 86

Figure 5.4 TPS Loftcut G-Code Generator

Figure 5.5 Comparison between standard loftcut (above) and perpendicular loftcut (below). The first milling strategy allows the rotation of the tool axis inside the working piece, while the latter keeps the tool axis parallel to itself during the machining.

simultaneously. Even using true simultaneous 5-axis machines, the perpendicular cutting can present some advantages for certain critical situations. Allowing rotational movements out of the working piece only reduces significantly vibrations and therefore enhances the quality of the cut. This approach is fruitful whit 5-axis machines that have low rigidity. Furthermore, it can sometimes happen, for steep cuts, that the G-code generated with the standard loftcut component exceeds the maximum admissible angle on the C axis. As the perpendicular cut minimizes the C angle, it is also useful for steep cuts.

TPS_Sawcut The Sawcut component generates the toolpath for CNC circular saw. The tool employed for cutting tests at the TUK timber lab is a “Leitz” circular saw with a thickness of 3mm, a diameter of 250mm, 80 teeth with a tooth pitch of 9.82. The main advantage of CNC saw-cutting compared to CNC milling is the high precision of the resulting cutting surfaces. Moreover, saw-cutting requires only one vertical pass even for quite thick and hard material. Last but not least, sawing produces a smaller amount of sawdust and chips. On the other hand, the nesting space between parts to be cut needs to be wider and therefore the overall matching produces more waste material. It is clear that only perpendicular cuts are allowed and movements involving rotations cannot be done inside the working piece to avoid crashes (Figure 5.6). Another important aspect to consider is that due to the higher moment of inertia of the tool, movements involving relevant variation of the angular momentum vector – typically G0 movements – need to be carried out at a slower feed rate and angular velocity (spindle speed). A piece of G-code is reported below to clarify the structure of the 88

Figure 5.6 Comparison between standard loftcut (top) and perpendicular loftcut (bottom). The first milling strategy allows the rotation of the tool axis inside the working piece, while the latter keeps the tool axis parallel to itself during the machining.

machining. […] M03 S1500 Spindle speed is decreased to 1500 RPMs

G00 X664.11 Y15.55 Z250 A0 B-85.98 The rotational axis of the tool is set perpendicularly to the cutting plane and the TCP (tool central point) is set at the primary safe high (for transit motions between parts) of 250mm

M03 S3500 Spindle speed is increased to 3500 RPMs, from now on rotational axes are kept in the same position

G01 X664.11 Y15.55 Z224.48 A0 B-85.98 F2000 The tool’s high is set to the secondary safe high (to which the tool returns in between cuts)

G01 X664.11 Y22.59 Z124.48 A0 B-85.98 F2000 The blade dives into the working piece at the start point of the cut

G01 X501.19 Y22.59 Z124.48 A0 B-85.98 F2000 The blade moves along the cutting direction until it reaches the end point of the cut

G01 X501.19 Y15.55 Z224.48 A0 B-85.98 F2000 The tool retreats to the secondary safe high

G00 X501.19 Y15.55 Z250 A0 B-85.98 The tool retreats to the primary safe high

M03 S1500 Spindle speed is decreased to 1500 RPMs. The tool is ready to rotate and reach the right position in terms of both linear and rot axes for the next cut.

[…]

Figure 5.7 TPS Sawcut G-Code Generator

The main input for the TPS_Sawcut component is a list of polylines defining the path for every single cut. In the screenshot of the grasshopper canvas (Figure 5.7), those polylines are generated by implementing a simple grasshopper definition (sawing polys) that takes as inputs the upper and lower contours of plates as it happens for the loftcut components. Other needed parameters to control the machining process are listed below. • Sicherheitsebene Z: safe Z height to which the tool returns in between cuts • Rueckzugssebene Z: safe Z height for transit motions between parts • G-Code Kopfzeilen (header): text values to place before the body part of the CNC program, usually containing information on absolute position coordinates (G90) tool’s number (i.e. T4), spindle speed (i.e. S1500), and tool radius offset cancel (G40) • Vorschub_XY (XY feed): horizontal cutting speed in mm/ min • Rtool: radius of the circular saw (125mm) • Ltool: blade thickness (3mm)

Comparison between milling and sawing cut quality and precision thickness of the working piece

machining time

sawdust and chips nesting spacing/ waste material

CNC milling Good

CNC sawcutting Better

The more the working piece is thick, the more vertical passes are needed It is dramatically affected by the number of vertical passes.

Sawcutting requires only one pass also for thick plates To a certain extent, it is independent of the thickness of the working piece.

G0 motion can be carried out at full speed. Large amount

G0 motions must be carried out at a slow speed. Small amount

It depends on the tool radius. Broadly speaking, it is fairly small.

It depends on the blade radius and the plate thickness. Broadly speaking, it is rather large unless smarter nesting strategies are adopted.

TPS_Drill The Drill component allows making holes into the working piece along the Z direction of the World reference system. The depth of holes can be adjusted to fully penetrate as well as partially penetrating the working sheet. In this context, the Drill component has been used to make pilot holes by partially penetrating the working piece. Then, screws have been positioned manually to ensure a safe fastening on the sacrificial sheet of each piece being cut. Identifying fixing points before the actual machining is crucial to avoid collisions between screws and the cutting tool. In theory, just a couple of screws on each part is enough to clamp them into place. However, a redundant number of screws is advisable for better results because it allows avoiding deflections of the raw working plate and reduce vibrations. Pilot holes points can be generated offsetting the upper polylines at an interior appropriate distance, extracting some vertices from the offset geometry, and moving them to the desired holeâ&#x20AC;&#x2122;s depth. Other important parameters for the Drill component are listed below. 92

Figure 5.8 TPS Drill G-Code Generator

Figure 5.9 TPS_NCsimulation

• Sicherheitsebene Z: safe Z height to which the tool returns in between cuts • Rueckzugssebene Z: safe Z height for transit motions between parts • G-Code Kopfzeilen (header): text values to place before the body part of the CNC program, usually containing information on absolute position coordinates (G90) tool’s number (i.e. T2), spindle speed (i.e. S10000), and tool radius offset cancel (G40) • Ltool: tool length

TPS_NCsimulation Simulation is very important to check for possible collisions. Therefore, TPS comes with a simulation component, which allows checking the machine motions. The Grasshopper component TPS_NCsimulation takes as inputs: • The G-Code, which comes right out of the fabrication components • The position to simulate: this is a number between 0 and 1, which stands for the relative position in the G-Code file. (Best connect this with a slider component, where the precision is set to multiple after comma digits) • The tool radius, which cannot be read easily from the G-code

• The tool length, which you must set equivalent to the one in your machine control system (this parameter is not written into the G-Code either, it is always relative and calculated in real-time by the machine).

Figure 5.10 Prototype Zero, realized by students of TU Kaiserslautern. Figure 5.11 Next pages: Prototype One, realized by the author.

Physical models and prototypes Prototyping has been a crucial step to ensure the feasibility of the project. Several cut tests and mock-ups have been realized both at the TU Kaiserslautern and at the University of Sydney, however, three main prototypes turned out to be the most relevant for the success of the HexBox project. Prototype Zero (TU Kaiserslautern). It is a non-freeform prototype consisting of a row of four rectangular boxes open at the bottom which are joined together by pairs of wedge connectors (Figure 5.10). With the principal purpose of analyzing the behavior of wedge connectors, elements have been made using traditional woodworking tools. In particular, the aspects this preliminary prototype was aimed to clarify concern number, size and shape of the connectors, and taper angle of wedges. Prototype One (TU Kaiserslautern). It is a freeform prototype made up of eleven hexagonal box-shaped segments (Figure 5.11). Elements have been made using CNC milling with the 5-axis router. The main purposes of this prototype were analyzing the overall buildability of the segments. In particular, the most crucial aspects to investigate were: • Performance of wedge connectors for such a freeform shape • Feasibility of bonding and clamping a relevant number of miter joints using the Lamello connectors • Assembly strategy allowing to minimize the working time while achieving the desired final quality • Tolerances required due to CNC machining and manual assembly • Influence of gaps, which may occur between adjacent Figure 5.12 Previous page and below: Prototype Two, realized at the University of Sydney by Code-to-Production Team and DMaF technicians.

segments, on the correct assembling of the structure • Risks assessment related to the building process and determination of safety measures to be adopted Prototype Two (USyd). It is a prototype consisting of ten segments of the actual structure (Figure 5.12). Unlike the previous, this prototype has been made at the DMaF Lab, employing the robot settings as well as the workflow meant to be employed for the fabrication of the real structure.

Nesting In the manufacturing industry, the term nesting refers to the process of laying out cutting patterns to minimize raw material waste. To minimize the amount of scrap raw material produced during cutting, companies usually use proprietary nesting software. The software analyses the parts (shapes) to be produced and determines how to lay these parts out in such a way as to produce the required quantities of parts, while minimizing the amount of raw material wasted. It is clear that the nesting process can be also carried out manually with a small number of pieces whereas, for a huge number of pieces as in the case of the HexBox, this becomes unfeasible. Here we employed the OpenNest plugin for Grasshopper by Petras Vestartas (Food4Rhino, 2019) which allows for semi-automatic nesting. The main issues which needed to be overcome were mainly two. • OpenNest can handle only single closed polylines or BReps while here each part is defined by a pair of polylines – two pairs for bottom plates and side plates – which have to be nested keeping their relative position • Geometries lose their properties such as the object name and the polyline direction (clockwise or counterclockwise) after being processed by the plugin

Figure 5.13 Overcut and undercut. The milling tool plunges slightly below the zero-plane on undercuts. (Robeller, 2015)

100

The first issue has been addressed processing only the bottom polylines into OpenNest, keeping track of each geometry being nested, and then reorienting the corresponding upper polylines into the new position. The second issue has been solved in a similar way, namely importing object properties into the grasshopper environment, keeping track of each geometry during the nesting process, and then those properties have been reassigned to the new geometries using the Grasshopper plugin Elefront (Food4Rhino, 2017). Elefront allows users to bake geometry to the Rhino model with the option of specifying attributes, including the object name. Another requirement to meet is minimizing the number of sacrificial sheets (wasteboards) to be replaced. The shape of plates cross-section affects indeed the wear of the sacrificial sheet. In the context of cut machining, we distinguish between overcut and undercut (Figure 5.13). Note that on undercuts the tool will plunge slightly below the zero-plane. Generally, it is better to avoid undercuts, as the tool plunges deeper than on regular cuts, but sometimes it cannot be avoided through flipping parts (when the cross-section is trapezoidal-shaped). Very steep undercuts gouge out the wasteboard quite quickly. Therefore, the fabrication strategy adopted consists of compiling all pieces with steep undercuts on separate sheets and run them every 10-15 sheets. This allows getting a bit more life out of wasteboards. The result (Figure 5.14) consists of 123 different plywood sheets, sorted in 20 groups and saved as individual Rhino files. These files come with a nesting booklet. A sample page of the booklet is shown in Figure 5.15.

Figure 5.14 Next pages: nested plywood sheets

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102

103

104

Integration between TPS and KUKA|prc The digital fabrication equipment available at the DMaF Lab, Sydney, consists of a 6-axis Kuka Robot provided with an additional Kuka linear unit which is basically an integrated external axis. With a rated payload of 120 kg and a maximum reach of 2896 mm, this robotic arm (KR 120 R2900 extra) provides an efficient solution to manufacture fairly large plywood sheets. Furthermore, the Kuka linear unit â&#x20AC;&#x201C; which is controlled by the same controller as the robot â&#x20AC;&#x201C; considerably extends the work envelope. The end effector installed is a third party spindle component provided by HSD Mechatronics Division, while the router bit is a 3/8â&#x20AC;? three flute low helix hogger from Onsrud. Even though CNC machines and robotic arms can be sometimes used for similar tasks and to achieve similar results with comparable performance, there are some big differences between these two technologies. The main feature of CNC machines is their accuracy, achieving high performance for very specific machining operations, whereas the defining feature of robots is their versatility. Not only can robots perform machining operations depending on the specific end effector installed, but also they can be employed for a huge variety of different tasks. For example, some typical tasks industrial robots are asked to do are the application of adhesives and sealants, fastening and pressing, water and laser cutting, welding processes, assembling, inserting and mounting. (KUKA AG, 2019) To sum up, CNC machines usually give higher performance in terms of accuracy for a specific machining task while a single robot can achieve many tasks with a different performance for each. Broadly speaking, industrial and mechanical manufacturing does need restrictive tolerances that robots may not achieve. Figure 5.15 Previous page: example of a nested plywood sheet excerpted from the HexBox Nesting Booklet. Below: plywood sheet after robotic machining.

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On the other hand, accuracy in timber constructions is in the order of a millimeter, that is usually obtainable employing a wellcalibrated and programmed robotic arm. As the programming, CNC machines use G-Code, while robots are programmed using a manufacturer’s programming language. Therefore, the output G-Code programs provided by TSP fabrication components cannot be straightforwardly employed to control a robotic arm. Post-processors – such as KUKA|prc – work by translating the G-Code commands into a specific program for your robot model. (Robots in Architecture, 2015) The position of a robot tool is usually calculated by an inverse kinematics algorithm. These can produce singularities, namely areas of the workspace which are basically “dead zones” caused by mathematics within the algorithm. An industrial robot can be controlled in two spaces: joint space and Cartesian space. Hence, there are two sets of positionmode motion commands that make an industrial robot move. For joint-space motion commands, you simply specify — directly or indirectly — a desired set of joint positions, and the robot Figure 5.16 KUKA|prc 5-axis NC import component and 3D simulation.

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moves by translating or rotating each joint to the desired joint position, simultaneously and in a linear fashion. For Cartesianspace motion commands, you specify a desired pose for the end effector and a desired Cartesian path. To find the necessary joint positions along the desired Cartesian path, the robot controller must calculate the inverse position and velocity kinematics of the robot. Singularities arise when this calculation fails (for example, when you have division by zero) and must, therefore, be avoided. (Mecademic, n.d.) Within the Grasshopper working environment, KUKA|prc allows for the translation of G-Code into KUKA Robot Language code which runs on the robot controller. The KUKA|prc CORE component is what generates the robot code for the specific robot selected from the Virtual Robot panel and provides the graphical simulation of the robot motion inside Rhino. The plug-in comes with a series of virtual end-effectors available in the Virtual Tools panel, however it is possible to implement any custom tool and show its geometry into the simulation just importing the Mesh of the custom tool being used. After lots of cutting tests and the proper calibration of the robot, the Code-to-Production team with the technical support of DMaF Lab drew up a fabrication checklist defining a step-bystep workflow from the setting of a nested sheet to the labeling and storing of the final parts.

PART 1: SETTING UP SHEETS IN RHINO / GRASSHOPPER & OUTPUTTING SRC FILE FOR CUTTING 1. Open sheet number in Rhino that you intend to cut 2. Check that nested sheet contents are in the correct location in Rhino and that the two lines for each component side are at the correct level 3. In Grasshopper reference the nested sheet contents in the Geometry container in the TPS setup 4. Using the position control check that the TPS preview is cutting correctly 5. Copy the outputted Gcode in the Panel by right-clicking and select Data Only 6. Copy this text into a notepad file or sublime text editor 7. Make sure that the file type is renamed .NC 8. Once the NC file is generated you will need to reference this file into Grasshopper again. You can just set up a path in the panel and make sure it matches you freshly generated NC file 9. Once you have correctly added the path your Kuka Core should be nice and grey 10. Using the Kuka Core simulation slider check that the robot simulation is cutting all of the cut-outs 11. Check there are no errors in the Kuka Core. You may need to change the position of the Orientation Point. This can 107

be done by selecting the Point container in Grasshopper and then moving the axis in Rhino 12. Once satisfied, output the SRC file to a pen drive and load to robot

PART 2: CUTTING SHEETS 13. Check table has not debris, chips of timber remaining that might set the sheet out of level. If required give uneven areas where screws holes are a quick sand 14. Load 19mm plywood sheet onto table and make sure it is square up against the guides. Make sure it is level 15. Project the nested sheet layout that comes with the corresponding Rhino file you have just processed and manually screw al parts at the projected fixing points 16. Run the program 17. Once program has completed the slot cutouts for wedge connectors, pause the program, enter work area and remove slot cutouts. These pieces may interfere with the following machining 18. Once completed resume the program 19. Once program is completed, use broom and vacuum to remove all sawdust and chips 20. Using the printout guide (nesting booklet) to mark the names of all the cutouts using masking tape and a sharpie 21. Unscrew all cutouts and stack in an ordered area 22. Remove all debris from bed 23. Sand flat any uneven areas on sacrificial sheet 24. You will probably need to replace the sacrificial sheet every 10-15 times.

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Figure 5.17 Step-by-step pictures of the fabrication, from the setting of a nested sheet to the labeling and storing of the final parts.

14a

14b

18a

18b

18c

19a

19b

21a

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21b

21c

Connection to the concrete balustrades and to the concrete ring beam As the rest of the structure, also connections to the existing building needed to be built simple and cheap to make. This involves using off the shelf material so as to minimize fabrication time and costs. Unlike many experimental pavilions, which are usually freestanding structures, the design of the HexBox’s supports must carefully take into account the boundary conditions of the building site. Footings on the balustrade side of the terrace meet the following requisites. First, they do not interfere with the existing concrete slab because of an asbestos lining below the tiles that cannot be removed for safety reasons. Secondly, footings fit the tolerances of the architectural survey of the building site. The given survey was indeed carried out using standard surveying means – measuring tape and laser distance measurer – so accuracy in the range of 1 to 5 centimeters must be expected. Since the assembly of the structure has been planned to be carried out from the ground up, footings also provide support and reference in positioning the first rows of boxes as well as resisting bending moments due to the first cantilevering part under construction. Thus, rib footings provide safe and strong anchoring of the canopy while gradually reducing the complexity of the freeform shell in order to join it up with the straight balustrades. The rib elements are cut to fit exactly the curvature of the canopy and bending moments are supported across two boxes each and transferred to the balustrades. Catenary shells are indeed very efficient for dead loads and, more broadly for symmetrical load conditions whereas panels undergo out-of-plane bending for unsymmetrical loads (i.e. wind loads). Therefore, ribs contribute a lot to increase the stiffness of the lower boxes, where moments are greater. Furthermore, the left gap between the parapet and the canopy enables the rainwater drainage through the gutter at the foot of the balustrades. Finally, the ribs connect to the balustrades via a 4-layered plywood plate, whose thickness could have increased – or decreased – if necessary during the construction, so the entire footing devices could still adapt to some inaccuracies along the direction perpendicular to the balustrades. Moreover, the geometry of the footings allows having a few cemeteries of play in the direction parallel to the parapet. In fact, it is possible to deal with imprecisions that may occur just sliding the ribs along that direction.

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Concerning the top connection to the concrete ring beam of the Wilkinson Building, the major issue has been compensating the difference in thickness between the concrete ring beam and the semi-columns of the building façade. Therefore, the connection detail consists of a series of curvilinear 7-layered plywood beams that make surface flush with those semi-columns. As in the case of footings, the layered structure of the top connections allows

adding as well as removing one â&#x20AC;&#x201C; or more â&#x20AC;&#x201C; of the plywood layers so as to compensate tolerances that may occur during construction. Finally, the connection of the last row of boxes is established through self-tapping screws.

5 6

Figure 5.18 Footing. 1-concrete balustrade, 2-stainless steel anchor studs, 3-parapet plate, 4-ribs, 5-crossing self-tapping screws, 6-support plate.

2 3 1 5 4

Figure 5.19 Footing. 1-concrete ring beam, 2-stainless steel anchor studs, 3-curvilinear beams, 4-last row of boxes, 5-self-tapping screws.

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FE models and structural analysis The following section presents an exploratory structural analysis carried out on the HexBox. Many simplifications have been adopted concerning the model adopted for the materials, the interaction between segments, and load conditions. While in no way pretending to be exhaustive, the following results just aim to give some idea of the global structural behavior of the HexBox under the action of self-weight. The analysis has been carried out thanks to a fruitful collaboration between the DTC+CodeToProductio team and the engineer Thomas Williams of PMI Engineers, a structural engineering practice based in Sydney. PMI Engineers contribute to the HexBox project as a sponsor, reviewing the structure and supplying the structural adequacy certificate for sign off. Liaising was indispensable so that several Finite Element shell models have been established from the mid-surface of panels by the DTC in concert with the engineer using Rhino + Grasshopper. Then, those models have been sent to PMI to be processed using the software Robot Structural Analysis by Autodesk. This workflow has been possible thanks to a plugin for Grasshopper built by PMI which created a pipeline between Rhino and their analysis software. Material modeling. Theoretically, it would have been possible to consider the orthotropic nature of wood panels and thus assigning different mechanical properties depending on the principal directions of cross-laminated panels. This approach has been adopted, for example, for the structural analysis of the Timberdome that is made up of CLT segments (Robeller & Viezens, 2018). However, this rigorous approach would have considerably complicated and slowed down the designing process. Indeed, the actual veneers’ directions of cutout panels making up boxes depend on their orientation into nested sheets. For our purposes, it was considered appropriate to adopt some simplifications and therefore create an equivalent virtual isotropic material that approximates seven-layer 19mmthick plywood plates produced by the Australian plywood manufacturer Carter Holt Harvey which mechanical properties are listed below. Plywood given a structural grade of F7 in accordance with AS2269.0 Young’s Modulus:

7900 MPa

Bending Strength:

20 MPa

Density: 10kN/m3 (conservative overestimate by a safety factor of about 2) A 50% reduction factor on Young’s modulus value has been adopted to account for the cross-laminated nature of the plywood. 112

Interaction between segments. Another issue to be addressed was the modeling of connections between panels. Some previous research on segmented timber shells adopts a spring model for the implementation of the connection of edges. For example, (Bechert, et al., 2018) simulates the degrees of freedom of the connection using three axial stiffnesses and one bending stiffness. It is clear that such a spring model aiming to effectively describe the HexBoxâ&#x20AC;&#x2122;s wedge connectors needs further research and investigations. A plausible path for more advanced structural modeling of interface sections between adjacent segments may be as follow. Relying on connectors for the transferring of in-plane and outof-plane shear stresses as well as tension stresses, whereas, the contact between two adjacent side plates enables the transfer of compression stresses. Therefore, bending moments can be transferred considering the compression transferred by contact material, the tension in the fitted connectors, and the lever arm between the connectors and the center line of either top or bottom plate. For the porpuses of this, two FE models have been processed into the FE solver. In the first model, connections between boxes are considered rigid. This means that the entire shell structure behaves as a single object so that stress characteristics are fully transmitted between adjacent segments of the structure. Top, bottom, and anchoring plywood plates are modeled as mesh elements representing the mid-surface of plates to which the appropriate thickness is assigned within the FEM software environment. Couples of adjacent side plates are represented by single midsurface mesh elements to which a double thickness is assigned. In the second model, each plywood box is modeled separately as independent mesh objects and appropriately spaced. Wedge connectors are modeled as line elements connecting the boxes. Those lines represent rigid links that enable the assessment of the forces through connectors. This model ignores friction between segments and the aliquot of compression stresses transferred by contact. However, the engineer considered such a model as more conservative than the first one and able to describe better the real structural behavior of the canopy. For this reason, only the results of the analysis of this discrete model are here reported. Load conditions. The following analysis takes into account only self-weight loads adopting a safety factor of about 2. In the case of complex freeform structures, it is possible to assess the effects of wind loads via laboratory experiments. Furthermore, powerful numerical tools providing reliable results â&#x20AC;&#x201C; such as computational fluid dynamics (CFD) simulations â&#x20AC;&#x201C; are also available today and able to compete with the experimental approach. (Rodrigues, et al., 2017) However, advanced simulations fall outside the general scope of this piece of research and definitely deserve further investigations. 113

Structural analysis report Please find below calculations for the HexBox Canopy. Structure Modelled in Robot Autodesk, using a shell model with rigid links between boxes to approximate wedge connections. Model imported from Rhinoceros. With reference to the Figure 5.: • Bottom, Top and Side panels were modelled as 19mm thick plywood with a 50% reduction factor on their young’s modulus values to account for the cross laminated nature of plywood. • Ply76 (base connection panel) was modelled similarly but as 76mm thick. • Ply152 (top connection panel) was modelled as 152mm thick.

Figure 5.20 View from top of structure showing colour coded panel thickness.

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Figure 5.21 View from underside of structure showing support points.

Figure 5.22 View of total deflections in the structure due to self-weight. 9.1mm Max deflections.

Stress analysis. Stresses as shown in Figure 5.22 are well within the 20MPa allowable range, with a factor of safety (FOS) of 5. Maximum stresses are also shown mostly locally around the hexbox sides which is a result of how the structure was modelled. Structure was modelled using rigid links located at each wedge connector point and disregards the effect of the hex-boxes bearing directly on to each other to transmit loads back to the fixing points. This is a conservative approach, but we have shown that the structure has strength in reserve for this conservative approach. The maximum loads through these rigid links are as follows: Fx:

2.64 kN

Fy:

1.46 kN

Fz:

1.31 kN

Figure 5.23 Diagram showing principal stresses due to self-weight.

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Figure 5.24 Image showing wedge blocks used to connect hex-boxes. Figure 5.25 Close up of Hex box connections and rigid links shown as red lines connection boxes at each face.

These loads are through the global coordinate system, rather than the local coordinate system of each rigid link. The shear capacity of a 60 x 57mm plywood connector is ~8.9kN, and the tension/compression capacity is ~27kN so connectors are sufficient for the imposed loads (ignoring bearing of hex boxes and friction between components due to tensioning of wedge connectors). Supports. Number of Supports (Chemset Bolts) Modelled: 20. Maximum Reaction (support) loads as follows: Fx:

4.42 kN

Fy:

4.46 kN

Fz:

3.48 kN

Capacity of M10 Ramset 101 bolts chemset 90mm into 25MPa Concrete

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Tension Capacity (Fy):

9.3 kN (FOS ~ 2)

Shear Capacity (Fx + Fz):

14 kN (FOS ~ 2.5)

Figure 5.26 Plan view of structure showing vertical (z axis) reaction loads in kN.

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Bill of materials and drawings This paragraph presents tables listing components, subcomponents, parts, raw materials and quantities of each needed to build the HexBox Canopy. Tables show also the specifications of products employed for the construction. Polyurethane adhesive and self-clamping connectors have been used to bond plywood components, whereas injection adhesive has been used to anchor threaded studs into the concrete. Finally, some relevant drawings are reported. Boxes

201

Top plates

201

Bottom plates

201

Side plates

1129

Total pieces Connectors

1531 508

Number components each

Total pieces

3048

Nesting sheets Boxes Bottom detail Top detail Connectors Increasing factor

95 17 16 3 10.00%

Total sheets Sel-clamping connectors (Lamello Tenso P-14)

144 1129

* one each side plate

Steel anchor studs + nut + washer (M10 grade 5.8)

118

Top (250mm)

Bottom (200mm)

Polyurethane adhesive (KLEIBERIT 501) Specific gravity (20Â°) [g/cm3]

1.13

Coat weight [g/m2]

150

Grams per bottle [g/bottle]

500

Parts to be glued Boxes 2/3 bottle for 10 boxes g/box Total [g] # bottles Parapet plates (1) # components # surfaces to be glued Plate surface [mm2] Plate surface [m2] Total surface [m2] Total [g]

201 Â 33.3 6693.3 13.39

4 3 1944000 1.944 5.832 874.8

# bottles

1.75

Parapet plates (2) # components # surfaces to be glued Plate surface [mm2] Plate surface [m2] Total surface [m2] Total [g] # bottles

4 3 1856104 1.856 5.568 835.2 1.67

Support plates (1) # components # surfaces to be glued Plate surface [mm2] Plate surface [m2] Total surface [m2] Total [g] # bottles

3 2 506453.8 0.506 1.013 151.9 0.30

Support plates (2) # components # surfaces to be glued Plate surface [mm2] Plate surface [m2] Total surface [m2] Total [g] # bottles

3 2 484280.2 0.484 0.969 145.3 0.29

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Ribs # components # surfaces to be glued Plate surface [mm2] Plate surface [m2] Total surface [m2] Total [g] # bottles

24 18 344229.8 0.344 6.196 929.4 1.86

Wall plates # components # surfaces to be glued Plate surface [mm2] Plate surface [m2] Total surface [m2] Total [g] # bottles

7 7 3880200 3.880 27.161 4074.21 8.15

Connectors # surfaces to be glued Plate surface [mm2] Plate surface [m2] Total surface [m2] Total [g] # connectors # bottles

4 1800 0.002 0.007 1.08 508 1.10

Total number of bottles needed

Ramset chemset 101 Injection Kit Density [kg/l]

1.7

Compressive Strength [Mpa]

Tensile Strength [Mpa]

12.2

Flexural Strength [Mpa] Cartridge volume [ml]

28.3 380

Cartridges per kit

120

28.51

Concrete ring beam # holes Diameter [mm] Depth [mm] Volume [mm3]

14 12 123 13910

Volume [ml] Filling coefficient Net volume [ml]

14 0.8 11.13

Total volume [ml]

156

Concrete balustrades # holes Diameter [mm] Depth [mm] Volume [mm3] Volume [ml] Filling coefficient Net volume [ml] Total volume [ml]

16 12 124 14024 14 0.8 11.22 180

Total number of cartridges needed*

*one kit contains 2x 380ml cartridges and 4x static mixer nozzles

Figure 5.27 Next pages: site plan and elevation excerpted from the working drawings sheets.

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122

123

Safety guidelines and personal protective equipment Although each working stage involves some risk for the safety and health of workers, the most dangerous ones concern the actual building and installation of structural modules, the use of the circular saw and the coating operations.

Dropping down of some hex-boxes during the installation. Even though boxes are relatively lightweight, the fall of a cluster of them on workers’ heads may involve injuries as well as head trauma in the worst case, depending on the drop height. Moreover, the fall on toes may involve painful injuries or even fractures to the metatarsals and phalanges. For these reasons, possible dangerous outcomes of such accidents had to be prevented wearing appropriate personal protective equipment. Hence, all the people attending the workshop had to get and wear the following equipment: • Safety shoes • Hard hat

Hazards resulting from the use of the circular saw. Sawing operations involve ambient noise and projection of particles. Furthermore, inaccurate employment of such a tool may lead to abrasions, cuts, and amputations. Thus, the use of this tool was strictly forbidden to people without a proper license and we also suggested wearing a hearing protection device (HPD).

Falling from above during coating operations. Coating operations were expected to be carried out from the ground and from the windows of the upper floor using painting rollers. In the unlikely case, those had to be done on the pavilion roof, workers should wear a harness. This is in fact machining subject to the danger of falling from above that may lead to serious injuries as well as to death.

Building stages and time schedule The building of the HexBox Canopy was held within the framework of an elective, at the University of Sydney. This elective was an intensive started on 10th August 2019 and ended on 16th August. It included 9 working hours per day split into a morning session (8:30 am – 1:00 pm) and an afternoon session 124

(2:00 pm – 6:30 pm). Students were arranged in teams made up of students from TUK and USyd. The construction consisted of six main tasks which are listed below. Even though those may seem in chronological order, some of them overlapped and were simultaneously carried out by different student teams. T1_Drilling and installation of threaded bars with chemical anchors T2_Preparation and installation of anchoring plates to the concrete balustrades and to the top ring beam T3_Boxes assembly T4_Wedge joints fabrication and assembly T5_Pavilion building T6_Coating of the entire pavilion with liquid waterproofing membrane The following paragraphs illustrate each task step-by-step as reported in the HexBox Construction Manual. Workshop Handouts containing that manual were prepared by the author of this Thesis and provided to students before the elective.

Task1_Drilling and installation of threaded bars with chemical anchors This task involves the identification of drilling points (16 on the concrete balustrades + 14 on the top concrete ring beam), drilling operation and insertion of threaded bars. Tools • Percussion drill • Ramset chemset 101 Injection Kit • 14Xstainless steel anchor studs M10, grade 5.8, length 250mm, hexagonal head with nut and washer (concrete ring beam) • 16Xstainless steel anchor studs M10, grade 5.8, length 200mm, hexagonal head with nut and washer (concrete balaustrades) • Chalk • Hammer • Folding meter rule

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Step1_ Place and hold parapet plates and wall plates in position, use them as a jig to mark drilling points with chalk. Step2_ Drill holes to specified diameter and depth using a percussion drill. Step3_ Remove dust and debris by brushing and blowing 3 times each. Step4_ Screw mixing nozzle onto cartridge and dispense 2-3 trigger pulls of adhesive to waste until the colour is green/grey with no streaks. Step5_ Insert tip of nozzle to bottom of hole and dispense adhesive. Step6_ Fill hole to about 2/3 full. Step7_ Insert threaded stud with rotating motion to release trapped air. Step8_ Wait until adhesive has fully cured before loading.

Figure 5.28 Task1_Drilling and installation of threaded bars with chemical anchors.

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Task2_Preparation and installation of anchoring plates to the concrete balustrades and to the top ring beam The preparation involves gluing together plates that make up the top and bottom support panels and the footing ribs. The installation concerns the implementation of such devices. Tools • 1K PUR adhesive • Clamps • Chisel • Decking paint • Paintbrush • Socket wrench • Nuts and washers

Figure 5.29 Task2_Preparation and installation of anchoring plates to the concrete balustrades and to the top ring beam .

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Step1_ Gather all layers making up top details and bottom details. Make sure those are sharp and clean. Use a piece of sandpaper to remove splinters from the edges if necessary. Step2_ Glue layers together, be careful to overlap them in the right order. Step3_ Use clamps and screws to keep layers well aligned and held while the adhesive is drying. Step4_ Once adhesive has fully cured, unclamp elements and remove excess adhesive with a chisel and a piece of sandpaper. Step5_ Apply a thin layer of decking paint using painting rollers. Store parts in a clean area to get the decking paint to dry. Step6_ Install anchoring plates to the concrete balustrades and to the concrete ring beam. Make sure holes are clean and remove glue residue, otherwise threaded studs will not fit through. Step7_ Fasten anchoring plates using nuts, washers and a socket wrench Step8_ Complete footing devices adding ribs and support plates.

Task3_Boxes assembly Overall, the canopy is made up of 201 different boxes and every box consist of a top plate, a bottom plate and some side plates. Even though some boxes have a number of sides different from 6 – the number varies in a range between 5 and 8 indeed – the average box is hexagonal-shaped. Hex-boxes differ their shape depending on the Gaussian curvature of the canopy surface varying from convex, where the curvature is positive, to concave where the curvature is negative. Hence, you are going to assemble honeycomb boxes as well as bow tie boxes. The following assembling example is showing how to make a honeycomb box; however, the presented steps can be extended to every kind of box. As already mentioned, every box is unique. For this reason, each box component has been labeled with a univocal alphanumeric code and grouped with the other components that make up the same box. It is useful to keep in mind during the assembling that the enumeration of side plates increases counterclockwise looking to a box from a top point of view. Tools • 1K PUR adhesive • Screws 128

• Electric screwer

• Sandpaper • Profile biscuit joiner tool (Lamello Zeta P2) • 6 self-clamping connectors (Lamello Tenso P-14) • Cutter • Folding meter rule • Workshop’s handout files • Rubber mallet • Clamps Cutting self-clamping connectors’ grooves. Before starting, make sure the Lamello Zeta P2 has already been correctly set. The right knob must be set on “max” while the left one must be set on “14”. Check also the additional thickness has been correctly inserted into its slot. Step1_ Gather all 6 side plates of a box and make sure those are sharp and clean. Use a piece of sandpaper to remove splinters from the edges if it is necessary. Step2_ Lay down one of the side plates on your working table with its inner face pointing upward – you can recognize the inner and the outer face because of the miter joint orientation. Step3_ Adjust the Lamello Zeta P2 to the miter joint angle, lock the angle adjuster tightening the knob on the left side of the machine when the desired angle is reached. Then, slide the machine along the chamfer towards the upper edge of the side plate, which is the edge where the top plate of the box is going to be located. Step4_ Turn on the machine and wait a couple of seconds until the cutting spindle is running. Make sure to keep the position of the machine safely holding both the angle adjuster and the plate. Then, dive the machine and return it back right after. Step5_ Turn off the machine and put it back on your working table. Check the groove has been correctly cut. Step5_ Repeat these steps for all the miter joints. Inserting Lamello self-clamping connectors. Before inserting Lamello connectors, you have to decide a position for the “female” and the “male” connector. For an obvious geometrical reason, it is necessary to decide where to embed the former and the latter as a convention, otherwise, side plates next to each other will not fit. Figure 5.30 Next page: Task3_Boxes assembly. Cutting grooves and inserting Lamello self-clamping connectors.

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Gluing boxes. In the following steps, you are going to carefully put adhesive to the elements making up a box. These are probably the most crucial phase of the assembly sequence, therefore, do not rush and keep in mind glueâ&#x20AC;&#x2122;s drying time is 20 minutes, that is enough to remedy problems might occur. Although figuring out the right collocation of plates is quite intuitively for most of the boxes, it may be tricky for some of those. Therefore, you can take a look at the workshop handouts every time you need to. Here, you can find a 3D model of the boxes you are assembling and check the right position of every plate. As already mentioned, the enumeration of side plates increases counterclockwise looking to a box from a top point of view, so once you have identified the right position of just one of those, it is easy to place the others. Step1_ Gather all the 8 plates making up a box (6 sides + 1 top + 1 bottom) and arrange them to their right position. Step2_ Put a little amount of glue along the chamfered faces of the side plates and push them until the connectors are locked in place. A gentle click sound signalizes that connectors have been successfully locked. Step3_ Once side plates have been assembled to form a hexagonal shape, glue them to the bottom and top plate. Step4_ Glue the top plate as you did for the bottom in the previous step. Step5_ During the drying process, plates need to be clamped. For this, you can use clamps or add some clamping screws on the bottom and top plate. Be sure all plates are well aligned before clamping them. Step6_ After 30 - 40 minutes, unclamp parts and remove excess adhesive with a cutter and a piece of sandpaper.

Figure 5.31 Next page: Task3_Boxes assembly. Assembling, gluing and clamping.

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Task4_Wedge joints fabrication and assembly The fabrication stages involve sawing the six components of 508 wedge joints. Every wedge joint is made up of six wooden parts and some clamping nails. All components of wedge joint connectors are produced using a table saw. The saw cutting and assembling of the total amount – or a considerable part – of the connectors is scheduled to be carried out simultaneously with box assembly. As the precision of the connector’s part is crucial for the joint strength, the production must be carried out by experts on carpentry. Tools • Table saw • 1K PUR adhesive • Nail gun • Sandpaper • Pencil As the sawing operation, plywood sheets are cut in strips of appropriate width, depending on the connector’s component being cut. Then, strips need to be cut again to obtain single Figure 5.32 Task4_Wedge joints fabrication and assembly.

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components. A jig is made and employed to speed up the assembly as well as increasing the precision. Step1_ Gather all the 6 parts making up a single connector and make sure those are sharp and clean. Use a piece of sandpaper to remove splinters from the edges if necessary. Step2_ Put a little amount of glue on the center of surfaces to be glued – remember the glue is expanding during the drying process – and arrange pieces into the jig in the right position. Step3_ Once you have aligned all pieces correctly, clamp glued parts with nails. Step5_ Put a sign with a pencil on the angled-wedge insertion side, collect all the pieces and store them to let the glue dry. Do not insert tapered wedges before the glue has dried otherwise you will probably not be able to remove them.

Task5_Pavilion building Overall, the building of the HexBox is divided into eight steps (Figure 5.34). The first three steps concern the predisposition of the building site and the installation of the secondary parts of the structure. The last five steps concern the actual assembly of the segmented timber shell. For convenience, segments are sorted in five groups depending on the scheduled building order. Tools • Personal protective equipment • A rubber mallet • Clamps of different dimensions • Laser distance meter • Scaffolding • Building props • Folding meter rule Step1_ Drilling and installation of threaded bars with chemical anchors. Step2_ Installation of anchoring plates to the concrete parapet and to the top ring beam. Step3_ Installation of the footing ribs. Step4_ Installation of the first group of plywood boxes, which form the first load-bearing arch of the structure. Use props as supports for the cantilevering arch under construction. 134

Step5_ Grow lengthwise the first load-bearing arch adding

gradually the second group of plywood boxes. Step6_ Grow lengthwise the first load-bearing arch, adding gradually the third group of plywood boxes. (step5 and step6 can be executed simultaneously) Step7_ Installation of the fourth group of plywood boxes. Connection of the fourth group with the rest of the shell. Step8_ Installation of the fifth group of plywood boxes.

Task6_Coating of the entire pavilion with liquid waterproofing membrane This task was accomplished after the workshop days. It involved two coats of liquid waterproofing membrane and accurate filling in of some critical joints between boxes with silicone. Tools • Personal protective equipment • Painting rollers • Silicone • Liquid waterproofing membrane

Figure 5.33 Next pages: Task5_Pavilion building. Illustration of the building steps. Figure 5.34 Next pages: Task5_Pavilion building. Construction phase and final pictures.

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References Food4Rhino, 2017. ELEFRONT (by Front). [Online] Available at: https://www.food4rhino.com/app/elefront [Accessed May 2019]. Food4Rhino, 2017. TIMBER PLATE STRUCTURES (TPS) (by C.Robeller). [Online] Available at: https://www.food4rhino.com/app/timber-platestructures-tps [Accessed November 2019]. Food4Rhino, 2019. OPENNEST (by petras_vestartas). [Online] Available at: https://www.food4rhino.com/app/opennest [Accessed November 2019]. ISO 6983-1:2009(E), 2009. Automation systems and integration Numerical control of machines - Program format and definitions of address words. KUKA AG, 2019. KUKA. [Online] Available at: https://www.kuka.com/ [Accessed December 2019]. Mecademic, n.d. What are singularities in a six-axis robot arm?. [Online] Available at: https://www.mecademic.com/resources/ Singularities/Robot-singularities [Accessed December 2019]. Robeller, C., 2015. Integral Mechanical Attachment for Timber Folded Plate, Lausanne, pp. 104-107. Robots in Architecture, 2015. KUKA|prc parametric robot control. [Online] Available at: https://www.robotsinarchitecture.org/kuka-prc [Accessed December 2019].

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Conclusion and Further Work

The state-of-the-art of timber construction offers a large variety of technical solutions. As presented in the first part, many possibilities of engineered timber products are available (CLT, LVL, plywood, etc) and many joining techniques have been devised and tested (screws, nails, bolts, adhesives, integral joints, wood-only connections). Therefore, architects and engineers can glean ideas and valuable information from an ample repertoire of examples and implement those in a large variety of construction systems for segmented timber shells. Furthermore, the last decade of developments in the planar and offsettable tiling of freeform has been crucial for the development of segmented timber shells. However, commercial and user-friendly software that can make such tiling algorithms accessible to the wider architectural community is not yet available. Despite many concerns, the HexBox project represented a great learning experience and had positive outcomes thanks to the synergistic collaboration between all the people involved. Overall, the design faced ambitious challenges, providing some first valuable feedback about the proposed construction system for segmented timber shells. The implementation phase involved joining forces in an international big team, and we needed to be perfectly prepared to make a very tight schedule work. Finishing a project of this complexity and size in the given time, without previous experience other than some prototypes, required a high level of organization and communication. The biggest 1:1 prototyped for the HexBox realized by the author of this thesis is made up of 11 hexagonal-shaped boxes while the actual Canopy consists of 201 segments. This means 20 times change in scale that certainly required a high level of foresight. The main concern was, in fact, the managing of tolerances. In this regard, wedge connectors demonstrated to be ideal to achieve such a goal. The whole fabrication pipeline that connected the generation of over 1500 geometries to robotic fabrication can be improved and fully automatized, aiming to reduce userâ&#x20AC;&#x2122;s manual work as much as possible. But all in all, it proved to work well. Without the smart use of algorithmic design and digital fabrication technologies, the HexBox would not have been possible. Somehow this reflects the challenges in big building projects and the whole BIM discussion. Standard building processes are slow, Previous page: Photo by Katherine Lu

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with many delays and errors. Whereas, digital technologies for planning, collaboration, project management, production, and fabrication are the key to improvement. Further research. The presented project offers a fruitful starting point for future developments of such a smart construction system. As a matter of fact, the HexBox is halfway between the field of temporary structures and the actual world of timber constructions. An outlook may be improving that system in order to be employed for large-scale permanent buildings. To accomplish this goal, additional specific investigations are necessary to fully assess the structural behavior, durability, and energy performance. In terms of structural performance, the next step should be scaling up the HexBox system to long-span shells usually utilized, for example, in concert halls and sports halls. Surely, this would involve a high degree of complexity. Further work would be necessary to develop more accurate structural models enabling a better understanding of the structural response to external loads. A key question regards the numerical determination of wedge connectors performance, including the influence of shrinkage and swelling on these friction joints. Lamello Tenso connectors combined with polyurethane adhesive have proved to be satisfactory for our purposes, although connections between plates need to be re-devised and optimized to be adopted for permanent long-span structures. Finger joints and dovetail joints increase the contact surface area between parts, and then the strength of glued connections. Therefore, they may be appropriate for resisting to more severe stress conditions. As the durability and energetic performance, structural modules could integrate additional technical layers providing for thermal insulation and waterproofing as well as cladding to ensure higher residence to weathering. Furthermore, the hollow modules could host plant facilities such as lighting or speakers which could be embedded straightforwardly into the prefabrication.

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List of Figures

Figure 1.1 The three strands of wood fibers are inserted into a Cartesian axial system. Elastic and tangential modules vary greatly. (Weinand, 2017, p.9). . . . . . . 16 Figure 1.2 Appropiate strenghs for coniferous wood (S10) as admissible tensions according to German standards. (Steiger, 2015, p. 17). . . . . . . . . . . . . . . . . . . . . 16 Figure 1.3 SCT, duo and trio beams, cross beams, laminated boards. (Steiger, 2015, p. 20) . . . . . . . . . . . . . . . . . . . 17 Figure 1.4 3-layers and 5-layers CLT panels. (Stora Enso, 2013).18 Figure 1.5 LVL beams type S, different thicknesses. (Metsä Wood, 2019). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Figure 1.6 LVL panels type Q, different thicknesses. (Metsä Wood, 2019). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Figure 1.7 18mm-thick spruce plywood. (Metsä Wood, 2019) . . 19 Figure 1.8 In integral mechanical attachment, the intrinsic shape of parts allows establishing the connection whereas, in mechanical fastening, the connection is established by utilizing some extra parts. However, hybrid solutions are possible. In the latter case both the geometry of parts to be joined and fasteners are crucial.. . . . . . . . . . . . . . . . . . . . . . . . . 22 Figure 1.9 Examples of tying joints in historic American timber joinery: pegged mortise-and-tenon, wedged dovetail through mortise-and-tenon, through mortise and extended tenon secured with two pegs and a single wedge. (Sobon, 2004, pp. 2-7). . . . . . . . . . . . 24 Figure 1.10 Swissbau Pavilion. Left: assembly of the prototype structure. Right: miter joints and dovetail connectors. (Scheurer & Schindler, 2006). . . . . . . . .26 Figure 1.11 X-Fix system used in the Timberdome and in the Recycleshell. (Robeller & Viezens, 2018) . . . . . . . . . . 27 148

Figure 1.12 Possible positions of screws in the side face (top)

and narrow face (bottom) of CLT panels. (Blaß, 2009). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Figure 2.1 Ringbeam with 9 up to 120 m long tension cabels. (Kübler, 2014). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Figure 2.2 Placing of layer elements of shell-structure on site. (Kübler, 2014). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Figure 2.3 Perspective of the interior highlighting the convex and cocave shape of the plates depending on the local gaussian curvature. (Institute for Computational Design and Construction (ICD), 2014). . . . . . 36 Figure 2.4 Constructive layers of the shell including insulation and water proofing. (Institute for Computational Design and Construction (ICD), 2014). . . . . . 36 Figure 2.5 On the left, perspective from one of the three arches of the Buga Wood Pavilion. (Photo by the Author). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Figure 2.6 On the right, construction details of the timber segments of the Buga Wood Pavilion. (Schwinn, et al., 2019) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Figure 2.7 The flexibility of industrial robots allows the integration of all pre-fabrication steps of the pavilion’s segments within one compact manufacturing unit. (Institute for Computational Design and Construction (ICD), 2019). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Figure 3.1 Geometrical visualization of the normal curvature of a surface S at a point P along the direction u.. . . 42 Figure 3.2 A freeform surface with a colour-based visualization of Gaussia curvature obtained with the curvature analysis command in Rhino 6.. . . . . . . . . . . . 44 Figure 3.3 Network of the principal curvature lines on a hyperbolic paraboloid obtained with a VB script in Grasshopper developed by David Rutten (Rutten, 2011). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Figure 3.4 The Gaussian spherical mapping applied to a spherical disk. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Figure 3.5 Offset surface Sd of a surface S at constant distance d.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 149

Figure 3.6 Geometric principle for translational surfaces. (Glymph, et al., 2004, p.190) . . . . . . . . . . . . . . . . . . 48 Figure 3.7 Tangent developable surface along c. (Pottmann, et al., 2007, p.680) . . . . . . . . . . . . . . . . . . . . . . . . . . 50 Figure 3.8 Left: a planar hexagonal mesh M and its constant face-distance offset mesh Md. Right: the disctrete Gaussian image S of the mesh, whose faces are tangent to the unit sphere S*. (Wang & Liu, 2009, p.11) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Figure 3.9 Left: configuration of the faces of a conical mesh at a vertex. The faces touch a common cone of revolution; Right: faces of a conical mesh at two adjacent vertices. (Liu, et al., 2006, p. 685). . . . . . . 53 Figure 3.10 Tangent plane intersection for doubly curved surfaces. Oscillating circles indicate curvature (1/R), principle curvature directions and orientation. A. Synclastic, positive Gaussian curvature K > 0. B. Anticlastic, negative Gaussian curvature K < 0. (Krieg, et al., 2014). . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Figure 4.1 On the left, the first proposal implements a P-System made up of 100mm-thick CLT plates.. . . . . . . . 63 Figure 4.2 On the right, the second proposal implements 20mm-thick plywood plate boxes, open at the bottom. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Figure 4.3 The final proposal introduces additional bottom plates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 Figure 4.4 Next pages: a straightforward method to obtain planar hexagonal meshes in Grasshopper. . . . . . . . 65 Figure 4.5 First design proposal for the HexBox implementing a quadrilateral mesh with planar faces. . . . . . . . . . 65 Figure 4.6 Left: technical solutions enabling to design plate structures using 6 and 4 valence meshes which do not possess an exact constant-face-offset. Right: 3-valence meshes always possess exact constant-face-offset. (Robeller & Viezens, 2018) . . . . . . 68 Figure 4.7 Next pages: a straightforward method to obtain planar hexagonal meshes in Grasshopper. . . . . . . . 68 Figure 4.8 Preliminary design proposal for the HexBox imple150

menting a hexagonal mesh with planar faces. . . . . 70 Figure 4.9 First version prototype of wedge connectors.. . . . . . . 71 Figure 4.10 Axonometric projection showing constituent parts of wedge connectors implemented into the HexBox Canopy.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Figure 4.11 Next page: overview and details of the wedge joint system.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Figure 5.1 Axonometric projection of an example box element..80 Figure 5.2 Above: 5-axis CNC router by imes-icore at the Faculty of Architecture, TU Kaiserslautern. Below: axonometric scheme showing the tool central point (TCP), linear axes (X, Y, and Z) and rotational axes (A and C). (Robeller, 2015) . . . . . . . . . . . . . . . . 82 Figure 5.3 Comparison between G90 Absolute Position Coordinates (G90) and Relative Position Coordinates (G91). Left: The X axis is moved to the absolute position 40 and the Y axis is moved to the absolute position 20 (G90 G01 X40 Y20). Right: From the current position, the X axis is moved 40 units in te positive direction and the Y axis is moved 20 units in the positive direction. . . . . . . . . . . . . . . . . . . . . . . 82 Figure 5.4 TPS Loftcut G-Code Generator. . . . . . . . . . . . . . . . . 87 Figure 5.5 Comparison between standard loftcut (above) and perpendicular loftcut (below). The first milling strategy allows the rotation of the tool axis inside the working piece, while the latter keeps the tool axis parallel to itself during the machining.. . . . . . . 88 Figure 5.6 Comparison between standard loftcut (top) and perpendicular loftcut (bottom). The first milling strategy allows the rotation of the tool axis inside the working piece, while the latter keeps the tool axis parallel to itself during the machining.. . . . . . . 89 Figure 5.7 TPS Sawcut G-Code Generator . . . . . . . . . . . . . . . . 90 Figure 5.8 TPS Drill G-Code Generator. . . . . . . . . . . . . . . . . . . 93 Figure 5.9 TPS_NCsimulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 Figure 5.10 Prototype Zero, realized by students of TU Kaiserslautern.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 151

Figure 5.11 Next pages: Prototype One, realized by the author..95 Figure 5.12 Previous page and below: Prototype Two, realized at the University of Sydney by Code-to-Production Team and DMaF technicians. . . . . . . . . . . . . . . 99 Figure 5.13 Overcut and undercut. The milling tool plunges slightly below the zero-plane on undercuts. (Robeller, 2015). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 Figure 5.14 Next pages: nested plywood sheets . . . . . . . . . . . . 101 Figure 5.15 Previous page: example of a nested plywood sheet excerpted from the HexBox Nesting Booklet. Below: plywood sheet after robotic machining.. . . 105 Figure 5.16 KUKA|prc 5-axis NC import component and 3D simulation.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 Figure 5.17 Step-by-step pictures of the fabrication, from the setting of a nested sheet to the labeling and storing of the final parts.. . . . . . . . . . . . . . . . . . . . . . . . 108 Figure 5.18 Footing. 1-concrete balustrade, 2-stainless steel anchor studs, 3-parapet plate, 4-ribs, 5-crossing self-tapping screws, 6-support plate.. . . . . . . . . . . .111 Figure 5.19 Footing. 1-concrete ring beam, 2-stainless steel anchor studs, 3-curvilinear beams, 4-last row of boxes, 5-self-tapping screws.. . . . . . . . . . . . . . . . . . 111 Figure 5.20 View from top of structure showing colour coded panel thickness.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Figure 5.21 View from underside of structure showing support points. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 Figure 5.22 View of total deflections in the structure due to self-weight. 9.1mm Max deflections.. . . . . . . . . . . . . 115 Figure 5.23 Diagram showing principal stresses due to selfweight.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Figure 5.24 Image showing wedge blocks used to connect hex-boxes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 Figure 5.25 Close up of Hex box connections and rigid links shown as red lines connection boxes at each face..116

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Figure 5.26 Plan view of structure showing vertical (z axis) reaction loads in kN.. . . . . . . . . . . . . . . . . . . . . . . . . 117

Figure 5.27 Next pages: site plan and elevation excerpted from the working drawings sheets.. . . . . . . . . . . . . . 121 Figure 5.28 Task1_Drilling and installation of threaded bars with chemical anchors.. . . . . . . . . . . . . . . . . . . . . . 126 Figure 5.29 Task2_Preparation and installation of anchoring plates to the concrete balustrades and to the top ring beam .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Figure 5.30 Next page: Task3_Boxes assembly. Cutting grooves and inserting Lamello self-clamping connectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 Figure 5.31 Next page: Task3_Boxes assembly. Assembling, gluing and clamping. . . . . . . . . . . . . . . . . . . . . . . . . 131 Figure 5.32 Task4_Wedge joints fabrication and assembly.. . 133 Figure 5.33 Next pages: Task5_Pavilion building. Illustration of the building steps.. . . . . . . . . . . . . . . . . . . . . . . . 135 Figure 5.34 Next pages: Task5_Pavilion building. Construction phase and final pictures.. . . . . . . . . . . . . . . . . 135

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