Lightweight Structures for Remote Areas

Jessica Bak

A thesis submitted for the degree of Doctor of Philosophy

University of Bath

Department of Architecture and Civil Engineering

December 2015

Attention is drawn to the fact that copyright of this thesis rests with the author. A copy of this thesis has been supplied on condition that anyone who consults it is understood to recognise that its copyright rests with the author and that they must not copy it or use material from it except as permitted by law or with the consent of the author.

This thesis may be made available for consultation within the University Library and may be photocopied or lent to other libraries for the purposes of consultation.

Jessica Bak

This thesis is dedicated to my husband Andreas and daughter Isabel.

Acknowledgements

I ﬁrstly want to thank to the Chilean Council for Science and Technology (CONICYT) for providing me with this opportunity by funding my MPhil and PhD studies at the University of Bath.

My sincerest gratitude goes to my supervisor, Dr. Paul Shepherd, whose knowledge, creativity and support has been essential for the fulﬁllment of this endeavour. I am truly honoured to have completed this research under Dr. Shepherd’s supervision and have been part of the Digital Architectonics Research Group.

This thesis would have not been possible without the invaluable advice and uncondi- tional support of Andreas Bak, from Søren Jensen’s Computational Design Group. I certainly cannot not express my gratitude for the help received at diﬀerent stages of my research.

I also want to thank my second supervisor, Professor Paul Richens, for providing me with enlightening advice, particularly during the early stages of my studies, as well as my examiners, Dr. Chris Williams and Professor Andrew Ballantyne, for making my Viva such an enjoyable experience.

Special thanks goes to Dr. Francisco Fernandoy for his guidance regarding antarctic subjects; as well as Gordon Dolbear and Aske Birkelund for their contributions to the formatting and post-production of this thesis.

iii

Abstract

The Antarctic built environment is characterised for its particular occu- pational regimen and includes whole-year stations, small-scale seasonal station and refuges, and temporary field camps. In recent years, Antarctic construction has begun to be considered of interest for the architectural and engineering communities, and interesting efforts have been made to provide solutions for spanning building, energy efficiency and improvements in indoor habitability. A fascinating array of lightweight constructions can be identified, whose contribution has not, until now, been fully documented and acknowledged. They represent remarkable examples of smart use of structural efficiency and minimal impact strategies enduring one of the harshest environments. This research is design-led and is motivated by the extension of the use of lightweight structures in remote fragile areas. The research validates the concept of polar lightweight design through a sound narrative describing the history and potential of this type of construction. For this, this research looks at the case of the Antarctic built environment. Furthermore, this research proposes that extension in the use lightweight construction could offer a sustainable solution for the predicted increase in the number of settlements being established in Antarctica. Knowledge and solutions achieved in this context can also be applied in other less demanding and fragile scenarios. In this regard, advanced computational design tools have been extensively validated for the realisation of structural surfaces of high geometrical complexity. Parametric design tools, are of particular interest to this research, as they allow the optimisation of a structure, either as a whole, or via its physical components. This research proposes that such tools can be employed for the development of Polar lightweight systems of larger scale and more complex configurations than currently seen. The first part is dedicated to the documentation and systematic characterisation of the vernacular Subantarctic and Antarctic lightweight constructions as structural systems. In the second part, the integration of polar constraints in the design of a generic lightweight structural system using parametric design tools is developed, in order to demonstrate the potential of this field for the creation of novel design methods and solutions. The particular case of a new medium-scale seasonal station is used as a case-study.

CONTENTS

Contents

Preface 1

1 Context and Research Aim 7 1.1 Introduction ...... 7 1.2 Occupation at the Antarctic region ...... 8 1.3 Overview of the Antarctic Built Environment ...... 12 1.4 Current Scenario and Perspectives for New Construction in Antarc- tica ...... 18 1.5 Design Brief for an Antarctic Seasonal Station ...... 20 1.5.1 Scope ...... 20 1.5.2 Site Conditions ...... 21 1.5.3 Environmental Conditions ...... 22 1.5.4 Logistics Conditions ...... 22 1.5.5 Overall Requirements ...... 23 1.6 Conclusions and Research Aim ...... 24

2 Characterisation of Antarctic and Subantarctic Lightweight Struc- tures 29 2.1 Introduction ...... 29 2.2 The Amundsen-Scott South Pole Station ...... 33 2.3 The Teniente Arturo Parodi Polar Station (EPTAP) ...... 38 2.4 The Shockwave Tent ...... 43 2.5 Subantarctic Indigenous dwellings ...... 47 2.5.1 The Kaweshkar (Alacalufe) Case ...... 49 2.5.2 The Yámana (Yaghan) Case ...... 51 2.5.3 The Selk’nam (Ona) Case...... 53 2.5.4 The Tehuelche (Aoniken) Case ...... 56 2.6 Antarctic Portable Dwellings ...... 62 2.6.1 ‘In the Footsteps of Scott’ Expedition Tent ...... 63 2.6.2 Sastruggi Tent ...... 64 2.6.3 The Apple ...... 67 2.7 Conclusions ...... 69

vii CONTENTS

3 Design Criteria 75 3.1 Introduction ...... 75 3.2 Design Criteria ...... 76 3.3 Geometric Scheme ...... 77 3.3.1 Aggregation ...... 77 3.3.2 Adaptability ...... 80 3.4 Modularity versus Adaptability ...... 84 3.5 Design Scheme ...... 94 3.6 Design Method ...... 103 3.7 Conclusions ...... 103

4 Nodal Forces Method and Structural Components Design 105 4.1 Introduction ...... 105 4.2 Sensitivity Study for a Single Trussed Arch ...... 106 4.3 General Characterisation of the Main Structural Component . . . . 108 4.4 Method ...... 109 4.5 Basic Material Properties ...... 114 4.5.1 Aluminium ...... 114 4.5.2 Composites ...... 115 4.5.3 Membranes ...... 118 4.6 Calculation of External Loads on a Single Trussed Arch...... 118 4.6.1 Load Case 3: Wind Derived Loads as Nodal Forces . . . . . 119 4.6.2 Load Case 2. Snow Derived Load as Nodal Forces ...... 120 4.6.3 Calculation Method of Nodal Forces ...... 123 4.7 Interpretation of FE Model Results ...... 125 4.8 Variation Study ...... 129 4.8.1 Variation Study on the Arch’s Geometry ...... 129 4.8.2 Variation Study for Joint Shape ...... 137 4.8.3 Variation Study on the Number of Subdivisions ...... 140 4.8.4 Variation Study on the Arch’s Depth ...... 143 4.9 Conclusions ...... 144

5 Multi-Objective Design Process 147 5.1 Introduction ...... 147 5.2 Revision of pre-conditions for Sensitivity Study ...... 149 5.2.1 Material properties ...... 149 5.2.2 Pre-stress ...... 149 5.2.3 Standardisation of Span Values ...... 150 5.3 Sensitivity study ...... 151 5.3.1 Uniform Cross Section of Aluminium Joints ...... 152

viii CONTENTS

5.3.2 Variations of Rod Cross-Sections According to Span. . . . . 152 5.3.3 Variation of Arches’ Depth According to Span ...... 155 5.3.4 Grouping of Arches’ Attributes for Reduction of Internal Stresses ...... 156 5.3.5 Geometry-based Method to reduce Pre-stress in Arches . . . 159 5.3.6 Uniform Load Condition of Arches’ Loaded Area ...... 165 5.4 Geometry-based Studies for the Reduction of Components ...... 173 5.4.1 Reduction of the Number of Nodes per Arch Group . . . . . 176 5.4.2 Reduction on the Number of Diﬀerent Joints ...... 188 5.5 Parametric Model ...... 197 5.6 Conclusions ...... 203

6 Complementary Studies 207 6.1 Introduction ...... 207 6.2 Study for Variable Conﬁgurations ...... 207 6.3 Components Deﬁnition ...... 213 6.3.1 Carbon Fibre Bars ...... 213 6.3.2 Angled Bar Connections ...... 214 6.3.3 Aluminium Crosses ...... 215 6.3.4 Membrane Patterning and voids ...... 225 6.3.5 Rigid Boundary Arches ...... 228 6.3.6 Ending of tunnels ...... 233 6.3.7 Anchorages ...... 234 6.4 Assembly sequence ...... 234 6.5 Examples of Possible Applications for the Glacier Union Case . . . . 243 6.6 Conclusions ...... 247

7 Conclusions 249 7.1 Introduction ...... 249 7.2 Contributions to Knowledge ...... 253 7.3 Theoretical implications ...... 254 7.4 Limitation of this study ...... 256 7.5 Future work ...... 258 7.6 Final comments ...... 260

Bibliography 261

Appendices

A Prospects on a Formﬁnding Method using Surface Evolver and Parametric CAD Tools 273

ix LIST OF FIGURES

A.1 The Surface Evolver ...... 273 A.2 Integrated geometry-based method using a Catenoid ...... 277 A.3 Testing Examples ...... 279 A.3.1 First Optimization of an Extruded Free-Form Curve . . . . . 282 A.3.2 Second Optimization of a Cylinder with a Free-Form Section 284 A.4 Further Work Using Surface Evolver ...... 286 A.4.1 Form-ﬁnding with oriented Boundaries ...... 286 A.4.2 Triple Periodic Minimal Surfaces ...... 286 A.4.3 Synclastic Surfaces Using other Energies ...... 287 A.5 Conclusions ...... 290 A.6 References ...... 290

B Calculations of Peak Velocity Pressure 293

C C-sharp Component for the Placement of Trussed Arches along a NURBS Curve 297

List of Figures

1.1 Magallanic Penguin at the Antarctic Peninsula...... 8 1.2 Antarctic territorial claim...... 9 1.3 Villa las Estrellas (Chile), one of two Antarctic settlements for a civilian community in Antarctica...... 10 1.4 Map of Antarctic permanent and seasonal research stations’ locations. 10 1.5 Maximum summer capacity of Antarctica’s small scale stations. . . . 12 1.6 Early Antarctic Construction...... 14 1.7 Industrial looking constructions...... 14 1.8 Views of the ’City in Antarctica’ study project, an air hall as a protection against climate over a residential town...... 15 1.9 Halley VI, the 6th British base commissioned in 2009...... 15 1.10 Germany’s Neumayer III Station, 1992...... 15 1.11 Seasonal station and refuges...... 17 1.12 Number of tourists visiting Antarctica during 1965-2007...... 19 1.13 Installation of the new ’Union Glacier Station, Ellsworth Hills. . . . 20 1.14 Location of the Union Glacier Station...... 22

2.1 Categories of surface structures in the context of structural system. . 32

x LIST OF FIGURES

2.2 Gaussian curvature of surfaces...... 33 2.3 The Amundsen Scott Dome after snow removal in preparation to deconstruction work...... 34 2.4 Artist’s concept of the design new USA South Pole’s design...... 34 2.5 Announcement of the competition of the new USA Polar Station. . . 34 2.6 Diagram of the South Pole Dome geodesic dome construction according to manufacturer Temcor©...... 36 2.7 1:10 scale model of Amundsen-Scott Station used to study snow drift pattern...... 36 2.8 Gusset plate showing installed Huck bolts for the Amundsen-Scott Dome...... 37 2.9 Diagram for geodesic dome construction according to manufacturer Temcor © ...... 37 2.10 Erection progress viewed from outside the South Pole dome as the frame is hoisted up the tower...... 37 2.11 Interior of the South Pole Dome’s dismounting party...... 38 2.12 Exterior of the South Pole Dome’s dismounting party...... 38 2.13 Group of domes installed at the Union Glacier Station...... 38 2.14 The EPTAP...... 38 2.15 Physical components at the EPTAP...... 39 2.16 Delivery for the construction of the EPTAP...... 40 2.17 Assembly of components for the EPTAP...... 40 2.18 Cutting pattern of the EPTAP’s PVC membrane. Image: Pol Taylor, undated...... 41 2.19 Membrane sections being attached to the structure for the EPTAP. . 41 2.20 Curved visors at the EPTAP...... 42 2.21 The EPTAP after two years of service...... 43 2.22 Chilean Air force personnel unearthing the EPTAP after 14 years of service...... 43 2.23 The Shockwave Tent in Villa Las Estrellas, Antarctica...... 43 2.24 Side view of the Shockwave tent in its original version...... 44 2.25 Stereometric structure of the Shockwave tent, Villa Las Estrellas. . . 44 2.26 Galvanised steel tubes used for the Shockwave Tent...... 45 2.27 Standard disc-shaped joint used in the Shockwave Tent...... 45 2.28 Tripod support used in the Shockwave Tent...... 45 2.29 Stereometric truss for the Shockwave tent being assembled and transported...... 45 2.30 Reinforcement elements for the Shockwave Tent being installed using the grid as a scaﬀolding...... 45 2.31 Original soft entrance cover designed of the Shockwave tent...... 46

xi LIST OF FIGURES

2.32 Front view of Shockwave implemented in Villa Las Estrellas. . . . . 46 2.33 Proposal of an adaptation of the Shockwave structural system for a hangar for the Chilean Air Force’s ﬁghter aircraft in the Atacama Desert...... 46 2.34 Map of the areas occupied by southern indigenous communities. . . . 48 2.35 Kaweshkar Dwelling, Puerto Eden, Chile...... 50 2.36 Reconstruction of a Kaweshkar in Puerto Eden...... 50 2.37 Alacalufe dwelling’s components...... 51 2.38 Last examples of Yaghan Dwellings in Lago Fagnano, Tierra del Fuego. 52 2.39 Structure of a cupula-shape Yagan dwelling with an elliptic base. . . 52 2.40 Diagram of a conic Yaghan dwelling and its main components. . . . 53 2.41 Dwelling of the southern Onas, made out of logs with the shape of an inclined cone...... 54 2.42 Illustration of a dwelling of the northern Selk’nams with a ’sub-conic’ shape made during the years 1918-1924...... 54 2.43 Photograph of a dwelling of the northern Selk’nams with a ’sub-conic’ shape taken during the years 1918 -1924...... 54 2.44 Sketches of a windscreen used by the northern Selk’nams made during the years 1918-1924...... 55 2.45 Tehuelche dwelling...... 56 2.46 Diagram with the main elements of an Tehuelche tent according to Baeriswyl...... 57 2.47 Diagram of a Tehuelche dwelling, made by Outes in 1905 based on the description made in middle 18th century...... 57 2.48 Diagram of a Tehuelche dwelling based on the description of Viedma made in middle 18th century...... 58 2.49 Semi-spherical model of a Teheulche tent belonging to the nothern Cacique Manikiken who posed with his family in Chubut, Argentina at the end of 20th century...... 59 2.50 Semi-spherical Tehuelche dwelling completely covered on fabric in Santa Cruz, Argentina...... 60 2.51 Asymmetrical tent model from a Southern Tehuelche family. Half structure is covered with animal skins, while the smallest section is covered with fabrics...... 60 2.52 Tent covered with horse skin belonging to the Caquique Cangapol, during middle 18th Century, reproduced by the Jesuit Falkner Buenos Aires Province Argentina...... 61 2.53 Touristic basecamp at Patriot Hills...... 62 2.54 Touristic basecamp at Vinson Massif...... 62 2.55 Frei Otto’s German Pavilion Expo ’67, Montreal...... 63

xii LIST OF FIGURES

2.56 ’2-Meter Dome’ tent produced by The North Face...... 63 2.57 BAS Antarctic Expedition Tent...... 63 2.58 Pyramid tent set up upon the King Edward VII Plateau as part of 1910-1913 British Antarctic Survey Expedition...... 64 2.59 Sketches of the 1985 BAS double curved surface and structure’s tent by designer Ian Liddel...... 65 2.60 Sketch of the crown joint for the 1985 BAS d tent by designer Ian Liddel...... 65 2.61 Sastruggi Room as part of the EPTAP Station, Antarctica...... 65 2.62 Diagram of the Sastruggi’s structure...... 65 2.63 Articulated joint designed for the Sastruggi Tent...... 65 2.64 Cutting patterns of the Sastruggi Tent...... 66 2.65 Installation of insulation layers at the Sastruggi Room, Antarctica. . 67 2.66 The ’Apple’ hub installed in McMurdo Station, Antarctic...... 67 2.67 The ’Melon’ hub set up in Antarctica...... 67 2.68 Panelling of the Apple and the Melon hubs...... 68 2.69 Design scheme of a prototypical Antarctic ﬁeld station...... 68 2.70 Structural Characterisation of Polar lightweight Structures...... 73 2.71 Geometrical Characterization of Polar Lightweight Structures. . . . . 74

3.1 Comparative diagram of a volume’s compactness...... 78 3.2 Examples of arrangements for touristic settlement’s using lightweight constructions...... 79 3.3 Evolution of the Schwarz’ P Surface using Surface Evolver...... 80 3.4 Prototype of the ‘Radiolaria Project’ (structural tessellation of double curved surfaces) developed by University of Kassel, Germany. . . . . 81 3.5 Prototype of free-form gridshell based on geodesic method developed by the Politecnico di Torino, Italy...... 81 3.6 Prototype of one the variations of the ‘Eccentric Umbrella Structure’ based on the Locust hind wing developed by the Israel Institute of Technology...... 83 3.7 Military base camp in Afghanistan implemented by Wheatherhaven ©. 84 3.8 Construction phases of the EPTAP...... 86 3.9 The Jotabeche Station...... 87 3.10 Alternatives of variations of the anchor system, from left to right: plates for snow and sand, crampons for rock, and shoes rocky soils. . 87 3.11 Assembly test for the Echaurren Glacier Monitoring Station. . . . . 88 3.12 Conﬁguration of components for Echaurren Station...... 88 3.13 Conﬁguration of components for Echaurren Station...... 89 3.14 Panul Warehouse...... 89

xiii LIST OF FIGURES

3.15 Panul Shed...... 89 3.16 Geometric scheme for Panul warehouse...... 90 3.17 Geometric scheme for Panul shed...... 90 3.18 Front view, progression of the Panul warehouse’s components. . . . . 91 3.19 Front view, progression of the Panul shed’s components...... 91 3.20 Model of the ‘Grotto Project’ developed by Aranda and Lash in collaboration with ARUP...... 92 3.21 Danzer Tillings...... 93 3.22 Design process of the Grotto’s modular boulders...... 94 3.23 Design proposal for a kayaking station on an isthmus on the North coast of Navarino Island...... 95 3.24 Three geographic milestones on north coast route were selected for the kayaking circuit at Navarino Island, a harbour, an isthmus, and an islet...... 95 3.25 Three geographic milestones selected for the kayaking circuit at Navarino Island...... 96 3.26 Architectural scheme of one of the three stations of the circuit, the isthmus-station...... 96 3.27 Definition of the three set of arches for the station in Navarino Island. 97 3.28 Two different enclosures at the Navarino Island Kayak Station. . . . 97 3.29 Two semi-open structures being supported by trussed arches. . . . . 98 3.30 Lateral supporting trusses...... 98 3.31 Cross-shaped pins joining the four flexible bars which compose a ‘primary arch’...... 99 3.32 Cross-shaped pin joints serve also as a support for the two bracing systems...... 99 3.33 Rectangular pieces of PVC fabric forming the membrane...... 100 3.34 Regular triangulated grid bracing the structure. The image also shows the radial distribution of the arches on the floor...... 100 3.35 Equally degree distribution of joints along the arches...... 100 3.36 Scheme for set of reciprocate bracing cables...... 101 3.37 Anchorages designed as ties and supports for flexible arches...... 102

4.1 Original subdivision scheme with restrained arch width...... 106 4.2 Second version for subdivision scheme with variable arch span. . . . 106 4.3 Vierendeel Bridge at Grammene, Belgium. Source: McGill Univer- sity’s School of Architecture, undated...... 108 4.4 Adjustable parameters on single trussed arch...... 110 4.5 Parametric pipeline...... 112 4.6 Geometry variations...... 112

xiv LIST OF FIGURES

4.7 Custom Robot API component...... 113 4.8 Automatically generated FE-model...... 113 4.9 Presentation of results in Excel...... 114 4.10 Geometric parameters on vaulted roof and domes for the valuation of external pressure coefficients...... 119 4.11 Snow load shape coefficient for cylindrical roof...... 122 4.12 Calculation of curve segments for snow load factors...... 122 4.13 Set of subdividing points on an arc for the calculation of nodal forces. 125 4.14 Diagram of geometric attributes for calculation of nodal forces. . . . 126 4.15 Numbering of nodes in an arch...... 126 4.16 Characteristic distribution of internal axial and bending stresses along a simply supported arch under compression for a symmetrical load case.128 4.17 Combined normal stresses (S value) as the addition of axial and bending stresses throughout section 1-1’ for a symmetrical load case. 128 4.18 Different versions of trussed arches with 4 m span to be compared. . 129 4.19 Schematic deformation of an aluminium joint under bending. . . . . 134 4.20 Distribution of maximum S values on the arches’ bars in Model 1 due to load case 6...... 135 4.21 Distribution of maximum S values on the arches’ bars Model 2 due to load case 6...... 135 4.22 Distribution of maximum S values on the arches’ bars in Model 3 due to load case 6...... 135 4.23 Distribution of maximum S values on cross’s bars from Model 1 due to load case 6...... 135 4.24 Distribution of maximum S values on cross’s bars from Model 2 due to load case 6...... 135 4.25 Distribution of maximum S values on cross’s bars from Model 3 due to load case 6...... 135 4.26 Distribution of minimum S values on arch’s bars from Model 1 due to load case 6...... 136 4.27 Distribution of minimum S values on arch’s bars from Model 2 due to load case 6...... 136 4.28 Distribution of minimum S values on arch’s bars from Model 3 due to load case 6...... 136 4.29 Distribution of minimum S values on cross’s bars from Model 1 due to load case 6...... 136 4.30 Distribution of minimum S values on cross’s bars from Model 2 due to load case 6...... 136 4.31 Distribution of minimum S values on cross’s bars from Model 3 due to load case 6...... 136

xv LIST OF FIGURES

4.32 Deformations of Model 1 caused by combined loads...... 137 4.33 Deformations of Model 2 caused by combined loads...... 137 4.34 Deformations of Model 3 caused by combined loads...... 137 4.35 Scheme for cross-shaped joints and diagonal cross-shape joints. . . . 138 4.36 Variation fashion for diagonal-crosses joints...... 139 4.37 Sensitivity comparison of diﬀerent geometric attributes for a single trussed arch...... 145

5.1 Top view of a curve standardised with different values...... 150 5.2 Diagram of the different attributes, values and constraints assessed for the definition of components...... 153 5.3 Cases of values’ segmentation...... 157 5.4 Angle between an arc’s segments according to different level of curvature...... 160 5.5 First geometry-based method for controlling the curvature of an arc’s bar segments...... 161 5.6 Second geometry-based method for controlling the curvature of an arc’s bar segments...... 163 5.7 Definition of a ‘Surface Segment’ and ‘Gap’...... 165 5.8 oordination of attributes for uniform loaded condition of arches. . . . 170 5.9 Coordination of attributes for the uniformity of distance between arches.174 5.10 Triangulation of a set of arches with cases of variation on the number of nodes of 2 units...... 177 5.11 Number of different aluminium joint when differentiated number of arches’ nodes according to span segment...... 178 5.12 Two examples of nodes lacing with different subdivision approaches: (a) equal angle-distance and (b) equal linear distance...... 179 5.13 Lacing of a set of arcs with increasing number of subdivision starting from the first arc (Case 1)...... 179 5.14 Lacing of a set of arcs with increasing number of subdivisions starting from the second arc (Case 2)...... 179 5.15 Lacing of a set of arcs with increasing number of subdivisions with

last lacing step altered to ‘n(i,j) to n(i+1,j+2)’ (Case 3)...... 180 5.16 Lacing of a set of arcs with increasing number of subdivisions with the second sequence inverted (Case 4)...... 180 5.17 Solution A. Lacing of a set of arcs with increasing number of subdi-

visions with last lacing step altered to ‘n(i,j) to n(i+1,j)’ (Case 5). . . 181 5.18 Lacing with an increasing number of nodes with the sequence inverted from second arch onwards. (Case 6)...... 182

xvi LIST OF FIGURES

5.19 Solution B for continuous lacing with an increasing number of nodes (Case 7)...... 182 5.20 Three dimensional test of solution A in an arbitrary set of arches. . . 183 5.21 Three-dimensional test of solution B in an arbitrary set of arches. . . 184 5.22 Three-dimensional test of lacing scheme starting from central node toward both sides...... 185 5.23 Three-dimensional test of a lacing method starting from a central node and where specific even-divided arcs have altered the number of node to n + 1...... 186 5.24 Three-dimensional test of a lacing method starting from a central node and where specific even-divided arcs have altered the number of node to n − 1...... 186 5.25 Flow chart for nodes’ lacing continuity assessment...... 190 5.26 Simplified flow chart for nodes’ lacing continuity assessment. . . . . 191 5.27 Scheme for an adaptable aluminium joint...... 191 5.28 Early model of a adaptable joint (Model 4)...... 194 5.29 First example of the parametric model applied on a curve...... 201 5.30 Second example of the parametric model applied on curve...... 202 5.31 Third example of the parametric model applied on a curve...... 203

6.1 Two membrane tunnels meeting perpendicularly...... 208 6.2 Three units meeting together...... 209 6.3 Three units meeting at the same point using a synclastic membrane. 210 6.4 Set of four units meeting at the same point...... 211 6.5 Four different units meeting on a non-orthogonal configuration. . . . 211 6.6 Rigid arch being used as reinforcement element for long tunnels and lateral voids...... 212 6.7 Conflict between two membranes pieces meeting perpendicularly. . . 213 6.8 List of the bars’ length on a surface output by the parametric model for two subsequent arches with the same span...... 215 6.9 Diagram of the bars’ length in a surface output by the parametric model...... 216 6.10 Sketch of an aluminium ring attached to a joint...... 217 6.11 Sketch of a set of pieces for an aluminium ring...... 217 6.12 Second proposal for an aluminium ring set...... 218 6.13 Study of variations for angled connectors...... 219 6.14 Assembling sequence of an aluminium ring, angled connection, carbon- fibre bars and scissor-shaped joint...... 220 6.15 Model of an aluminium ring and angled connection...... 220

xvii LIST OF FIGURES

6.16 Lists of an arch’s joint typified their length and angle produced by the Grasshopper model...... 221 6.17 Surface with aluminium joints identified by colours according to length- based type...... 222 6.18 First version of an aluminium joint...... 223 6.19 Second version of an aluminium joint...... 223 6.20 Sketch of a scissor-shaped joint connected to the membrane...... 224 6.21 Model of a scissor-shape joint...... 225 6.22 Sketch of connection between consecutives membrane pieces. . . . . 226 6.23 Example of a set of membrane cutting pattern obtained from the parametric model...... 227 6.24 Assessment of surface curvature...... 228 6.25 Section and profile of a rigid arch...... 229 6.26 Proposal for assembling of rigid arches...... 231 6.27 Rigid arch designed for perpendicular intersections with flexible arches.231 6.28 Cases of spanning arches supported by a lateral boundary arch. . . . 232 6.29 Spanning arches intersecting a boundary arch at irregular intervals. . 232 6.30 Front and back view of an intersection between a boundary arch and a set of 4 m span spanning arches...... 233 6.31 Proposal for a membrane cover as an ending element...... 233 6.32 Rigid curved panels as a closing element...... 234 6.33 Sequences for the preparation of crosses...... 236 6.34 Marking the location of arches on site and installing anchorages. . . 237 6.35 Boundary arch assembling...... 237 6.36 Boundary arch completed...... 237 6.37 Boundary arch with membrane piece attached...... 238 6.38 Assembling arches from bottom to top...... 238 6.39 Completed flexible arch...... 238 6.40 Installation of membrane segments...... 238 6.41 Flexible arch reinforced with lateral cables...... 239 6.42 Installation of bracing cables between two arches...... 239 6.43 Aluminium scissor joint with all components connected...... 240 6.44 Progression of arches instalment...... 241 6.45 Direction for the membrane piece’s deployment...... 241 6.46 Progression of membrane segments deployment...... 242 6.47 Handmade sketch of side view of an early design scheme...... 243 6.48 Side view of early design scheme with basic type of components recognise by colour...... 243 6.49 Handmade sketch of plan diagram for an early design scheme. . . . . 244

xviii LIST OF TABLES

6.50 Top view of early design scheme with basic type of components recognised by colour...... 244 6.51 Architectural plan for a design scheme...... 245 6.52 Isometric view of design scheme...... 245 6.53 Isometric view of design scheme...... 246 6.54 Isometric view of design scheme...... 246 6.55 Bar types identiﬁed according to length using colour code, side view. 247 6.56 Bar types identiﬁed according to length using colour code, perspective view...... 247

List of Tables

1.1 Variation of Population in Antarctica...... 11 1.2 Assessment of environmental impact derived from maintenance activities of the XL Scientiﬁc Antarctic Expedition 2005-2006...... 16 1.3 Average number of occupants in the University of Magallanes Re- search Station...... 24 1.4 Domestic facilities for University of Magallanes Research Station. . 25 1.5 Technical facilities for University of Magallanes Research Station. . . 26 1.6 Scientiﬁc facilities for University of Magallanes Research Station. . . 27

4.1 Parameters and Initial Values of a Generic Single Arch...... 110 4.2 Characteristic Mechanical Properties of Aluminium...... 115 4.3 Characteristic Mechanical Properties of GFRP at room temperature. 117 4.4 Characteristic Mechanical Properties for GFRP between 20 °C and −60 °C...... 117 4.5 Cartesian Values of Nodal Forces Derived from Snow and Wind on a 4[m] span Arch...... 127 4.6 Extreme combined internal stresses on Model 1, 2 and 3...... 131

4.7 Maximum Smax values on an arch’s bars by load cases in Models 1, 2 and 3...... 131

4.8 Minimum Smin values on an arch’s bars by load cases in Models 1, 2 and 3...... 131

4.9 Maximum Smaxvalues on joints bars by load cases in Models 1, 2 and 3.132

4.10 Minimum Smin values on joints bars by load cases in Models 1, 2 and 3.132 4.11 Maximum nodes displacement on Models 1, 2 and 3...... 137

xix LIST OF TABLES

4.12 Maximum bars deflection on Models 1, 2 and 3...... 137 4.13 Extreme internal stresses for arches with different joint geometry. . . 139 4.14 Extreme internal stresses in arches and joints bars with different components sizing...... 140 4.15 Extreme internal stresses in arches with different number of segments. 141 4.16 Bars segments lengths of arches with different spans and number of joints...... 142 4.17 Extreme internal stresses for arches with different mid-span depth. . 144

5.1 Sensitivity study for the definition of arches’ bars’ cross section. . . . 154 5.2 Group of arches according to span range and bars’ cross section. . . 155 5.3 Internal stresses according to segmentation of arches’ attributes Case A...... 158 5.4 Internal stresses according to segmentation of arches’ attributes, Case B...... 158 5.5 Internal stresses according to segmentation of arches’ attributes, Case C...... 159 5.6 Internal Stresses according to grouping of arches’ attributes, Case A, with 50% of pre-stress reduction...... 164 5.7 Internal Stresses according to grouping of arches’ attributes, Case A, with 90% of pre-stress reduction...... 164 5.8 Internal stresses and adjusted distance between two arches given a uniform load condition...... 169 5.9 Internal stresses and assigned loaded area according to arches’ spans given a uniform load condition...... 171 5.10 List of adjusted membrane’s segments widths according to span values.171 5.11 List of possible sequences of two consecutives spans with ±1meter of variation...... 172 5.12 Number of different aluminium joints...... 175 5.13 Brute-force test for the lacing of four arcs...... 189 5.14 Aluminium joint’s bar’s length according to different spans rounded to nearest 0.5 m...... 192 5.15 Angle between aluminium joints’ bars according to different spans values, with a span values rounded to nearest 0.5 m...... 193 5.16 Variations of angle between joints’ bars found in each length group. . 194 5.17 Reduced variations of angle between joints in each length group with a tolerance of ±1ř imposed...... 194 5.18 Aluminium joint’s bar’s length according to different spans values, with a span values rounded to nearest 1.00 m...... 195

xx LIST OF TABLES

5.19 Angle between aluminium joints’ bars according to diﬀerent spans values, with a span values rounded to nearest 1.00 m ...... 196 5.20 Length of Upper Carbon Fibre bars, according to span with a spans rounded to nearest 0.5 m value...... 198 5.21 Length of joint’s bars and angle between joint’s bars with number of nodes altered in +1 units for evenly-divided arcs...... 199 5.22 Set of resulting attributes and values...... 199

6.1 Variation in upper bars’ length in altered arches...... 214 6.2 Study for diﬀerent subdivision options of a 6 m rigid arch...... 229 6.3 Study for diﬀerent subdivision options of a 4 m rigid arch...... 230

xxi

Preface

I. Context

This is design-led research which proposes that Polar lightweight structures should be recognised as a valid design ﬁeld.

Based on the background of the author, this research looks at the Antarctic and Subantarctic context to demonstrate such a statement.

In recent years, Antarctic constructions have been considered of interest for designers and engineers. However, the remarkable history of lightweight construction in extreme southern environments has not yet been fully acknowledged by the design and engineering community. This research gathers suﬃcient evidence to validate the concept of Polar lightweight structures. The fascinating array of cases portrayed in this thesis ranges from Subpolar vernacular constructions to innovative structural surfaces implemented in more recent years.

There is a fast growing increase in the number of Antarctic parties willing to carry out scientiﬁc and touristic activities, who are therefore interested in deploying either permanent, seasonal, or temporary settlements. This represents a threat for the conservation of the pristine Antarctic continent.

This research suggests that the extension in use of lightweight construction could offer a sustainable solution, and that more applied research is needed on different aspects of the use of minimal construction in extremely harsh environments. One aspect to be studied is the search for larger and more flexible configurations that respond to the particularities of the remote southern context.

At the same time, advanced computational design tools have been extensively validated for generating structural surfaces of high geometrical complexity. Parametric design tools, such as Rhinoceros’ Grasshopper© are of particular relevance to this research, as they allow optimisation, either of a structure as a whole or of its physical components. This research proposes that such tools can be successfully employed for the further development of more complex Polar lightweight systems. In this case,

1 PREFACE the application of such tools requires the integration of the strict environmental, constructional and logistical constraints derived from the Antarctic context.

Therefore, the application of polar constraints in the design of lightweight constructions using parametric design tools can produce novel methods and solutions. This research provides an example of a design method that demonstrates such a proposal.

II. Research Aim

This research aims to contribute to the extension of the use of lightweight structures in remote fragile environments, especially in Antarctic and Subantarctic areas. In order to drive academic and applied research in this ﬁeld, a more active and formal inclusion of designers and engineers as part of polar research communities is required.

The author understands that an initial step towards this is the validation of Polar lightweight construction as a ﬁeld in its own right, which is of common interest for the architectural and engineering domains and is the core aim of this work.

III. Objectives

The validation of Polar lightweight polar design through academic research has been done by creating a narrative that portrays the existing evidence of this concept as a design ﬁeld.

The development of such narrative requires three main objectives to be achieved. The ﬁrst consists of providing evidence of the history of lightweight structures in Subantarctic and Antarctic areas. This should demonstrate the diversity of approaches attempted by using a systematic classiﬁcation of the examples found.

The second objective in this narrative consists of the formulation of a design problem that can challenge the complexity and scale of current Polar structures.

The ﬁnal objective is the development of a solution to such a problem which will be achieved by developing a novel design method in which the use of parametric CAD tools and polar constraints are integrated.

IV. Background

The research presented herein is design-led, and has been fully sponsored by the ‘Capacitación de Capital Humano Avanzado’ Programme from the Chilean National Commission for Science and Technology (CONICYT). The purpose of this scheme

2 PREFACE is to boost academic research and activities in areas that are key for the scientiﬁc and technological development of the country.

V. Scope of the Research

The scope of the research can be described as the intersection of the architectural geometry and structural design domains. Thereby the literature review, and its resultant classification of Polar and Subpolar surface structures is based on a structural approach, and a second classification is also offered regarding to the type of curvature that these constructions present. Following, the development of an architectural scheme of a certain level of geometrical complexity is also enabled by the structural design of components based on Polar conditions, where variations and relations between classes of components are studied in detail.

It is evident that one of the biggest challenges that Polar and Subpolar buildings face is thermal insulation, which is particularly critical when working with lightweight constructions. However, this aspect is not addressed in this research. Although this is a ﬁeld where much applied research is yet to be completed in order to make lightweight systems in very cold environments thermally sound, it is believed by the author that there is suﬃcient evidence that this will be achieved to consider the use of lightweight system as feasible. Some of the pioneering solutions for thermal insulation will be described. Other practical aspects that are not addressed by this research include strategies for energy supply and waste disposal.

VI. Thesis Structure

The research has been organised into two main parts. The ﬁrst part, described in chapters one and two, is dedicated to the validation of the concept of ‘polar lightweight design’. The second part, documented in Chapters 3 to 6, is dedicated to the description of a design-based study for a medium-scale lightweight structure for remote areas that exemplify this ﬁeld’s prospect.

Chapter 1 initiates the first part by describing the evolution of the Antarctic built environment, the particularities of the occupation regimen in that context, and the prospect that foresees an increment in the number of polar settlements, for which lightweight structures could offer a sustainable solution. A brief for the design of a new seasonal polar research station is also described. Chapter 2 offers the description of a collection of Subantarctic and Antarctic lightweight constructions. Their portrayal is mainly based on their behaviour as mechanical systems. This first

3 PREFACE part concludes with the classification of the cases found, in order to demonstrate the diversity of approaches intended by polar designers. The second part, a design-led study, is initiated in Chapter 3. In this chapter, a specific research problem is presented, which examines the possibility of conceiving a lightweight structure with an adaptable configuration that maintains a controlled number of different components and a simple assembly sequence. Reflections on the paradox of conceiving a modular-yet-adaptable lightweight system are also presented, including evidence of cases which have previously addressed such problem. Chapter 3 concludes with the description of an early scheme for the design of a lightweight construction previously conceived by the author. This is a generic system composed from a set trussed arches whose span varies. Chapter 4 describes a structural sensitivity study, which characterises the main structural component of the system, this is, the set of trussed arches with varying span. The objective of the study is to assess how the structural performance of the trussed arch is affected by the variation of its geometrical attributes. Chapter 5 describes a method for balancing the three conflicting objectives that the system should fulfil, involving the ‘partial-optimisation’ of the structural system. Through a series of studies, the controlled variation of each attribute of the main system’s components is achieved. The final section of this chapter presents a single parametric model where all the resultant attributes and their values are integrated. Chapter 6 offers a series of studies which assess the architectural and constructional feasibility of the generic system designed. The resulting inventory of physical components of the system is also presented. Chapter 7 offers conclusion and reflections on the research process and its results, as well as it proposes areas for further work.

VII. Methodology

The description of the context, included in Chapter 1, is carried out using existing literature and a number of different primary sources (such as interviews and data collection). The portrayal of lightweight structures in Chapter 2 is based on the literature and the structural characterisation of these systems is based on a classification of structural surfaces originally proposed by M. Bechthold. Chapter 3, which presents the specific design-led research is based on the author’s owns reflections and proposals and builds on their early design scheme for a lightweight structure. The sensitivity study presented in Chapter 4 is carried out via a recursive iteration between a single parametric CAD model, used to generate a sample of each trussed

4 PREFACE arch’s variation, and a Finite Element Modelling platform, used to evaluate the stress condition and deformations of each sample. Snow and wind-derived loads expected in the speciﬁed Polar location are recalculated for every iteration following the Danish Standards for snow and wind loads on structures. An initial method of manually exporting every CAD geometry into the FEM platform and assigning the nodal loads was quickly dismissed as fragile and impractical, so a custom CAD/FEM script- based software tool was later implemented, allowing the simultaneous production and evaluation of a large number of variations of the trussed arch.

Chapter 5, concerns a multi-objective study which consists of six parts. Two of these parts relate to the definition of the geometrical attributes of the set of trussed arches for which the CAD/FEM software tool was also employed. The next part looks at the reduction of the pre-stress in arches via a geometry-based method. The fourth part presents a method by which the load of the different arch types is equalised by adjusting the distance between arches. The last two parts are dedicated to reducing of the number of joints and the number of different joint types by the identification of patterns which are summarised in patterns (or pseudo codes) and lists of values which are then integrated into a single parametric model. All the resultant components, attributes and their values implement using standard components offered by the Rhinoceros’ application Grasshopper.

The architectural feasibility studies, presented in Chapter 6 look into different possibilities of aggregation using basic CAD applications. The definition of the set of physical component uses a combination of methods including digital rendering, parametric CAD definitions, handmade sketching and models. The proposal for an assembly sequence, is also developed using standard Rhinoceros applications.

Chapter 1

Context and Research Aim

1.1 Introduction

This Chapter begins by brieﬂy describing the occupation process in the Antarctic continent, as well as the evolution of the Antarctic infrastructure (Section 1.2).

The revision of the main constructive typologies employed during this process, which started about a century ago, is also oﬀered in Section 1.3. Additionally, Section 1.3 deals with the categorisation of the existing infrastructure. This is based on the scale of the buildings, which is commonly in correspondence with their use: large-scale permanent constructions used as year-round stations, summer-only stations and shelters using small scale buildings, and temporary ﬁeld camps using lightweight tents and structures.

The revision of the general aspects of Polar buildings, both technical and operational, intends to provide a clear framework for the design proposal presented in the second part of this research. Furthermore, basic design principles are identiﬁed, based on the previous experiences here described.

Additionally, the portrayal of the current and anticipated occupation scenario is presented in Section 1.4.

Finally, a design brief for a new medium-scale research station is presented in Section 1.5. The brief details the programmatic and quantitative requirements, as well as environmental, logistical, technical and site’s constraints. The design proposal of a lightweight structure presented in the second part of this thesis (Chapter 4, 5 and 6), will be based on these requirements.

7 CHAPTER 1. CONTEXT AND RESEARCH AIM

Figure 1.1: Magallanic Penguin at the Antarctic Peninsula. Photo: F. Fernandoy.2012.

1.2 Occupation at the Antarctic region

The Antarctic continent has a surface of 14,000,000 km². The variety of geographic features, climate regimes, biological diversity and ecological dynamics is not yet fully understood. Therefore, any generalisation regarding this vast territory might be subject to question.

However, it can still be stated that Antarctica can be considered the most pristine territory [Fig. 1.1], as well as the highest, driest, and coldest continent [1]. The total isolation from human civilisation can be justiﬁed by its extreme energy condition and the absence of signiﬁcant biotic systems [1].

Geographical features have been determinant in the process of human occupation in Antarctica. The lack of terrestrial connection has been responsible for the slow speed of the insertion of human settlements, which is practically free of anthropic impact.

Antarctica is the least populated continent. Human presence in Antarctica can be generally described by two different phases in its short history. The initial explorations, carried out in the late 1700s were often commissioned for sovereignty purposes, and they were followed by scientific schemes undertaken by national Antarctica programmes of different states [1]. Such disciplines include biology, geol- ogy, astronomy, glaciology, global climate change research and others. This activity is now being complimented by an increasing quantity of touristic programmes, based mainly in self-sufficient passenger ships around the coast with certain intrusions into the interior of the continent and hiking touristic programmes, which present a threat to terrestrial and coastal ecosystems [1].

8 CHAPTER 1. CONTEXT AND RESEARCH AIM

Argentina Australia Chile France N. Zealand Norway UK

Figure 1.2: Antarctic territorial claim. Source: CONMAP, 2011.

There are seven states which initially claimed sovereignty over theAntarctic Territory in the ﬁrst half of the Twentieth century: Chile, Argentina, UK, France, Australia, New Zealand, and Norway [Fig. 1.2]. In 1959, the ‘Antarctic Treaty’ was issued where the initial claiming parties, along with another group of states (Spain, South Africa, Brazil, Ecuador, Peru and Uruguay), which also expressed their interest on establishing presence for scientiﬁc purposes, agreed to manage Antarctica collectively. Consequently, their positions in respect to Antarctic territory remained unchanged [2]. Since 1961, another group of states succeeded in proving legitimate interest in Antarctic Research and therefore, could found settlements. Currently, a group of 29 ‘consultative’ members are responsible for the decision-making at Antarctica, administratively grouped by the Antarctic Treaty Secretariat (ATS). Actions are collectively coordinated by the Council of Managers of National Antarc- tic Programs (COMNAP), dependent of the ATS.

Due this agreement, Antarctic territory is under a system of special protection, by which it has been declared as a territory exclusively dedicated to ‘purposes of peace and science’ [3].

In 1991, all the consultant parts of the ATS approved the ‘Protocol to the Antarctic Treaty for Environmental Protection’, by which the whole continent was designated as a Natural Reserve. The Protocol of Madrid, valid from 1998, established all the principles, procedures and obligations for the protection of the Antarctic Environ- ment [3]. With this Protocol, all the activities are regulated and controlled, including governmental, non-governmental and private schemes. The instrument is aimed to guarantee that none of these activities will produce any adverse environmental impact, including construction tasks and their management.

The ATS members consequently have a deployed presence by the establishment of permanent, temporary or seasonal settlements in Antarctica [Fig. 1.3].

To date, there are 113 registered settlements in Antarctica. They can be classiﬁed as: whole-year stations (37), seasonal station and refuges (33), and ﬁeld camps (31). The rest corresponds to either temporarily closed stations or seasonal fuel depots [4]. The location of principal permanent infrastructure is shown in Figure 1.4.

9 CHAPTER 1. CONTEXT AND RESEARCH AIM

Figure 1.3: Villa las Estrellas (Chile), one of two Antarctic settlements for a civilian community in Antarctica. Photo: F. Luchsinger, undated.

Figure 1.4: Map of Antarctic permanent and seasonal research stations’ locations. Source: Rupert Summerson, undated.

10 CHAPTER 1. CONTEXT AND RESEARCH AIM

Year-round station Average Summer 3598 Peak Winter 1059 Seasonal Facilities (Station and refuges) Average Summer 786 Peak Winter 0 Field Camps Average Summer N/A Peak Winter 0

Table 1.1: Variation of Population in Antarctica. Source: CONMAP, 2010.

One of the most relevant characteristics of the human activity in Antarctica is the significant fluctuation on the population during the different seasons of the year, as most of the research activities are only possible to be carried out during summer season, namely from October until March. Such a variation is summarised in Table 1.1.

The average capacity of each type of building (permanent station, seasonal station, refuges, or ﬁeld camps) largely diﬀers from one another. Most of the stations have been designed to accommodate up to 50 people, while the largest, about 12 stations, can accommodated 100-200 people. The largest station in Antarctica is McMurdo (USA), which provides accommodation for up to 1000 people in summer and average of 250 people in winter [5].

Regarding small scale permanent infrastructure, most of the seasonal stations have capacity for 10-30 people; few of them (only ﬁve) have capacity for more than 40 researchers. For the eight registered refuges, capacity is estimated at between range 2 to 10 people [4].

For field camps, and apart from their regular locations, no reliable information is available on the average number of users, although it is expected to be highly fluctuant. Every summer season, each Antarctic National Program proposes new temporary settlements, according to their own scientific interests and schemes. Sim- ilar criteria apply for touristic base camps. Given that both activities are rapidly growing, the use of lightweight structures is estimated to be much higher in the coming years.

Figure 1.5 summarises the information gathered during this research in respect to the capacity of small scale Antarctic infrastructure.

11 CHAPTER 1. CONTEXT AND RESEARCH AIM

Figure 1.5: Maximum summer capacity of Antarctica’s small scale stations. Source: CONMAP, 2010.

1.3 Overview of the Antarctic Built Environment

Construction endeavours in Antarctica present multiple restrictions other than the obvious challenges introduced by the harsh environment. The employment of natural materials has been dismissed due to the environmental degradation that they might cause (i.e. the usage of gravel boxes as foundations or natural stones walls) and also due to technical reasons. Additionally, constructions must be planned within a very tight schedule, as weather conditions are dominant not only for the execution of the construction tasks themselves, but also because airborne, terrestrial and maritime transport operations are also highly dependent on favourable weather conditions for their departures and arrivals. As for the material conveyance, coastal sites can rely on the transportation capacity of maritime vessels, whilst inner terrestrial sites depend on small scale land transportation vehicles and short take-oﬀ and landing (STOL) aircraft.

Despite of the brief history of construction on Antarctica, many lessons have been learned the hard way [6]. This is why, even though this research is not focused on large scale permanent constructions, it is of interest to brieﬂy review in their rapid evolution occurred over the past century.

In-situ construction techniques were dismissed soon after the ﬁrst stable construction in the year 1899 executed by the Southern Cross Expedition [7] [Fig. 1.6(a)]. This type of building, which can be described as a wooden hut, proved cold and draughty. As insulation was improved, damp inside the facilities became a problem, with condensation forming due to a lack of ventilation. Carbon monoxide poisoning was

12 CHAPTER 1. CONTEXT AND RESEARCH AIM also present in some cases, caused by the frequent burning of fuel within the hut for heating. The shape and orientation of the building also became of importance for Antarctic construction. After a few years of use it was observed that buildings were aﬀected by strong winds blowing across a structure carrying snow, which was deposited, usually on the downwind side as the wind loses velocity while transiting the building [Fig. 1.6(b)]. As result, buildings were buried under snow, especially those with seasonal usage, which remain empty most of the time. Problems derived from placing the buildings directly on the ground were also often found, especially in coastal areas, due to the volumetric instability of rocks, associated with gelifraction processes [6]. A second stage in the history of Antarctic can be recognized by the wide use of adapted containers as the basic unit of modular structure [1]. Their adaptation was successful due the feasibility of improving their thermal insulation, practical transportability, and easy assembly. Previous problems related to the stability of buildings could be simply overcome by providing independent supports, such as isolated concrete blocks. Nevertheless, this kind of building has led to a rather industrial-looking landscape. Davis (Australia) and Rothera (UK) Stations are examples of this [Fig. 1.7]. The one of two civilian inhabited communities ‘Villa las Estrellas’ (Chile) also used this solution for its housing park [Fig. 1.3]. The recently open India’s National Center for Antarctic and Ocean Research’s Station, Bharati Station (2012), also used 134 adapted shipping containers as the inner structure for the station with a revisited design strategy from Bof Architekten. Since the adoption of the Protocol on Environmental Protection to the Antarctic Treaty by the ATS in the early nineties, it was stated that everything brought to the continent, including large buildings should be able to be removed after use, without leaving traces on the site. This has become a key constraint for the design strategy and implementation of the so-called permanent infrastructure. This means that, in term of polar infrastructure design, the categorisation of temporary and permanent can be considered as a relative matter. Radical visions of temporary and permanent design concepts are also part of the Polar design chronicle. In 1970, Frei Otto’s Warmbronn studio, Kenso Tange and Over Arup and Partners proposed the ‘City in Antarctica’ project, which consisted of an pneumatic membrane, spanning 2 km, aimed at providing shelter for an entire residential town [8] [Fig. 1.8]. On the other hand, the proposal of MAP Architect’s ‘Iceberg Living Station’, a speculative design, in 2014, consisted of a year-round facility capable of hosting 100 occupants. The station is meant to be completely holed out of an iceberg using readily available excavators (commonly used for snow clearance). The station is expected to melt away, which according to the designers would avoid the problem of material removal at the end of its life span [9].

13 CHAPTER 1. CONTEXT AND RESEARCH AIM

(a) (b)

Figure 1.6: Early Antarctic Construction. (a) Douglas Mawson’s Hut erected 1912, source: Australian Antarctic Division: (b) Douglas Mawson’s Hut buried in hard snow, 2006, source: Australian Antarctic Division.

(a) (b)

Figure 1.7: Industrial looking constructions. (a) Davis station(Australia) in 2005 (established in 1957). Image: Graham Denyer (b) Rothera Station, established in 1957. Source: British Antarctic Survey.

During recent years, Antarctic infrastructure has notoriously become of interest to architectural and engineering disciplines [10]. Consequently, recent stations are being resolved with more environmentally friendly and bespoke methods. Designers are being challenged by multiple aspects: ensuring an optimized shape for minimum snowdrift by using snow-blowing simulations and physical scale models, designing coherent modular construction strategies and using highly thermally eﬃcient materials. The stations Halley VI (UK) [Fig. 1.9] and Neumeyer (Germany) [Fig.1.10] are examples of this. Both use jack-leg supports to avoid snow accumulation, wind forces, and minimization of footprints on the site.

Additionally, remarkable eﬀorts for the improvement of energy eﬃciency in the already built environment are being made, along with the development of renewable energy supply systems [5].

One particular aspect of the variability of population for large scale building is the energy consumption during southern winter season. As an example, a medium scale permanent station, South Africa’s SANAE IV is considered relatively new and it has

14 CHAPTER 1. CONTEXT AND RESEARCH AIM

(a) (b)

Figure 1.8: Views of the ’City in Antarctica’ study project, an air hall as a protection against climate over a residential town. (a) View of a physical model. Image, F. Otto, 1971. (b) Plant view of the residential town. Image: Frei Otto, 1971.

Figure 1.9: Halley VI, the 6th British base commissioned in 2009. Source: British Antarctic Survey, 2011.

(a) (b)

Figure 1.10: Germany’s Neumayer III Station, 1992. Source: Alfred Wegener Institute for Polar Research.

15 CHAPTER 1. CONTEXT AND RESEARCH AIM

Action Emissions Waste Noise Leaks Usage of Vehicles (Including Mechanical dust) Machinery Vehicles X X X X X Energy Generation X X X X Painting X X X Fuel Storage X Construction X X Module Dismantling X X X Waste Disposal X Minor Vessels X

Table 1.2: Assessment of environmental impact derived from maintenance activities of the XL Scientiﬁc Antarctic Expedition 2005-2006. Source: Chilean Antarctic Institute, 2005. a capacity for 80 people, but during winter the number of occupants decreases to 10. During winter about 72 kW of power is needed to keep the station at 18°C. For cold period the consumption of energy can be more than double. As fuel is transported from Cape Town, logistical and transportation costs should be considered, for which the ﬁnal price at SANAE IV is more than the triple the purchase price [5].

Small scale seasonal buildings, stations and refuges used during summer months, are currently very diﬀerent. Most of them correspond to relatively old constructions (30- 40 years old) [Fig. 1.11] and were therefore built using traditional techniques and materials. This entails the execution of periodic maintenance schemes, or simply to be abandoned like the case of the Sub-base Yelcho (Chile). The implications of periodic maintenance for this kind of infrastructure imply high economics costs, complex logistical coordination and environmental risks. Table 1.2 lists the assessment of environmental threats derived from such maintenance activities carried out on a group of small scale stations and refuges belonging to the Chilean Antarctic Institute (Escudero Base, Ripamonti, Risopatrón, Shirreﬀ Camp), every 3 years, and which need to be evaluated and resolved before their execution [11].

It is usually seen that despite international collaboration between diﬀerent Antarctic National Programs being common, the capacity of these small scaled facilities is often a limitation for in-land activities, due their reduced capacity. On the other hand, during seasons of relatively reduced demand, stations must be kept operative, for instance maintaining stations at a minimum temperature (18 °C) [5], which implies a signiﬁcant consumption of energy. It should be considered that the more remote the site, the more expensive and risky the re-fuel tasks turn out to be. This suggests the pertinence of considering the capacity of variation or partial deployment in the design of small scale buildings, which can respond to a variable range of occupants.

16 CHAPTER 1. CONTEXT AND RESEARCH AIM

(a) (b)

(c)

Figure 1.11: Seasonal station and refuges. (a) Uruguayan Shelter at Antarctic Peninsula, photo: F. Fernandoy, 2011; (b) Hut refuge Fossil Bluﬀ (UK), source: British Antarctic Survey, 2011; (c) Almirante Brown station (Argentina), source: Argentinean Antarctic Institute, undated.

17 CHAPTER 1. CONTEXT AND RESEARCH AIM

On the other end of the Antarctic structure’s spectrum, ﬁeld camps play an important role in the fulﬁlment the aims of human presence in Antarctica, a ‘natural reserve dedicated to peace and science’[3], as they make possible the temporary surveys in deep inhabited areas of the continent without leaving footprints. There is a fascinating variety of small scale isolated structures which have to face a number of challenges such as logistical restrictions for transportation, limitations on energy resources, and at the same time, dealing with the most adverse climatic conditions with a minimum of material. Chapter 2 is dedicated to the collection and study of Antarctic lightweight structures.

1.4 Current Scenario and Perspectives for New Con- struction in Antarctica

The construction of new infrastructure is governed by the particular administrative situation of Antarctica, by which it is collectively managed by the members of ATS, and ruled by the three pillars of the Antarctic Treaty: the protection of the Antarctic environment, safeguarding the peace and ensuring the freedom of scientiﬁc research.

For scientiﬁc facilities, each state is free to propose and execute the implementation of infrastructure, which is evaluated and approved by their local government. State parties to the Protocol must ensure that all pertinent provisions have been implemented in their domestic legal and administrative systems and are applied in practice to all Antarctic activities under their jurisdiction.

As for scientific field camps, there is no restriction for the ATS member to install temporary structures to carry our research activities as long as they fulfil the no-trace commitment and local regulation, as explained above. It is clear that several states have been recently boosting the Antarctic agendas, by reinforcing their scientific institutions and summer expeditions, for which the usage of lightweight a structure is expected to remain of great importance for field activities.

As for touristic facilities, the scenario remains rather unclear and the need for regulations has started to arise [2]. From the early 1990s, Antarctic touristic activities have been growing continuously, particularly in the Antarctic Peninsula. They are carried out in different formats which can be classified in two main categories: non land-based (cruises, overflights) and land-based (expedition in cruisers with landing or any land based activities like trekking) [Fig. 1.12].

In view of environmental and other concerns, the regulation of Antarctic tourism has become one of the major issues of debate within ATS. A particular aspect is whether additional measures are needed to regulate, or even prohibit, future development of permanent land-facilities (like hotels, visitor centres, logistical facilities). Some

18 CHAPTER 1. CONTEXT AND RESEARCH AIM

Figure 1.12: Number of tourists visiting Antarctica during 1965-2007. Source: Bastmeijer et al, 2008. member states of ATS strongly support the idea of prohibiting them. Nevertheless, the question has not received a clear oﬃcial answer. The most important reasons for opposition are related to the environmental risks that are expected, the political tensions that it could create derived from the territorial occupation, and the threat for the development of scientiﬁc activities.

Antarctic touristic operators are ruled by the same ATS protocol, thus they need must meet local environmental regulations. In parallel, there is a self-regulation system set up by the Association of Antarctica Tour Operators (IAATO) which has established procedures and environmental standards for its member. However, during the last few years IAATO has reported the operations of some unregistered companies, which has highlighted the necessity of a clear regulation for Antarctic tourism operators [2].

Currently, touristic companies mostly make use of either governmental or scientific facilities, which allow different modalities for visitors. Some official stations have allocated some visitor centres, particularly at historic facilities. Only a few have succeed in developing their own infrastructure: at Patriot Hills and Vinson Massif, operated by Antarctic Logistics & Expeditions and at Dronning Maud Land, operated by Antarctic Logistics Centre International. It is interesting to notice that both are tented camps whose materials are stored during austral winter, being the unique modality which has been able to cope with both environmental regulations and economic goals. This also suggests that lightweight constructions could also contribute to the sustainable development of Antarctic tourism.

19 CHAPTER 1. CONTEXT AND RESEARCH AIM

(a) (b)

Figure 1.13: Installation of the new ’Union Glacier Station, Ellsworth Hills. Image: Chilean Antarctic Institute, 2014.

1.5 Design Brief for an Antarctic Seasonal Station

This section explains the requirements for a summer-only research station in Antarc- tica.

As explained, there are several ATS members currently boosting scientific activities. One of the most active is Chile, who since 2004 has expressly made efforts to boost and diversify its scientific activity in Antarctica[12]. In that context, it was agreed in 2013, to establish the first collectively-managed research station in Union Glacier [Fig. 1.13]. This is one of the three stations located within the South Pole Circle, together with Amundsen-Scott (USA) and Kunlun (China). The station is being managed by the Chilean Air Force and jointly operated by the Army, the Navy and the Chilean Antarctic Institute. Opened on January 2014, it is a summer-only station and operates from November to January.

The University of Magallanes (UMAG) despite being the only academic institution carrying out Polar research for over 30 years, is the only governmental organization that has not deployed permanent ﬁeld work infrastructure in Antarctica.

In this context, the following text describes a notional design brief for the implementation of a research station for the UMAG in Union Glacier. The text has been redacted in collaboration with the Polar Research Team.

1.5.1 Scope

Magallanes is the natural entrance to Antarctica. The University of Magallanes’s Antarctic and Sub-Antarctic Department (DPA) is the southernmost academic institution carrying out Antarctic research permanently. The DPA has been carrying out research since 1994 in multiple scientiﬁc areas such as radio-glaciology, tele-detection engineering, chemistry, Paleo-climate, among others.

20 CHAPTER 1. CONTEXT AND RESEARCH AIM

This brief explains the requirements for the speculative design of the first DPA Field Station, the main objective of which is to consolidate the presence of DPA in Antarctica as well as to promote the formation of Antarctic and Sub-Antarctic researchers. The challenge involves not only to create an efficient and functional design to provide scientist with a safe, effective and comfortable research space, but also to reflect the strong commitment of the DPA to comply with the Antarctic Treaty Environmental Protocol, as well the innovative spirit of this research group.

The UMAG’s Antarctic Department aims to build a new scientiﬁc research station in Union Glacier within the boundaries of the Chilean Antarctic Territory. This station should house 5 staﬀ (advanced party) at the very early and late Antarctic summer, rising to 12 during middle summer season.

Operating and living in this extreme environment requires the development of a unique approach to building due to multiple environmental and logistical factors: heavy snow fall, extremely low temperatures and all supplies (including materials, equipment and staﬀ) having to be towed inland from the ice border or ﬂown-in by small-capacity aircraft. These factors can be translated as a series of limitations for the station’s design that should be considered from the initial stage: a quick-erection method of due to a brief time window for construction using limited machinery; maintenance and repair strategies under tough weather conditions and limited weight and size of components. Main environmental issues are water production and waste disposal.

Apart from these practicalities, this call is also an invitation to explore a no-trace design culture, which is one the strongest values to be promoted by the participant of the Antarctic Treaty, as well as a novel architectural expression. The design should allow the introduction of small-medium scale human settlement with a sense of reversibility, where the whole structure could operate and be removed without causing any permanent impact to one of the most fragile and pristine existing environments.

1.5.2 Site Conditions

The site is located 1080 km from the South Pole. The structure will be adjacent to the rest of the buildings in the Union Glacier Station [Fig. 1.14], the precise position of wish (79° S / 82° W) was speciﬁed in 2013. The elevation is 700 meters above sea level.

Although the topography at the location is expected to be stable, the annual rate of build-up of snow fall can reach up to 1.5 m [12]. This implies that annual maintenance and snow-clearance will need to be carried out at the beginning of

21 CHAPTER 1. CONTEXT AND RESEARCH AIM

Figure 1.14: Location of the Union Glacier Station. Source: razonyfuerza.mforos.com. each season. Nevertheless, given that every 3 years the structure is expected to be placed 4.5 m below the current ground level, the relocation of the whole station will be required.

Foundation conditions are considered as stable [13]. This is an ice shelf, the ﬂoating extension of the grounded ice sheet. It is composed of freshwater ice which originally fell as snow, either in situ or inland and brought to the ice shelf by glaciers.

1.5.3 Environmental Conditions

General weather has been described as a benign and stable regime, making the site comparable to an ‘ice-desert’ [12], with no presence of rain and moderate winds.

In mid-summer temperatures vary between -5 °C and -15 °C, but could easily drop to -40 °C [12]. Rain has never been reported, but freezing drizzle may occur.

The annual snow accumulation is 1.2 to 1.5 m. Water equivalent weight would be 509 kg/m2 to 642 kg/m2 [14].

The average annual total sunshine is 1445 hours (34% of the maximum possible), occurring during summer with 24hr of daylight. In the winter the sun does not rise above the horizon for 100 days of the year, and during that period there is total darkness for 55 days [14]. The sun shines in the North sky.

1.5.4 Logistics Conditions

The Union Glacier is in a remote location, 3010 km or 6 hours ﬂight from Punta Arenas in Chile. It remains in darkness and isolated for 8 to 9 months of the year.

22 CHAPTER 1. CONTEXT AND RESEARCH AIM

The construction and implementation of the station should take place within an 8 week frame time, during the months of December and January, when access and weather conditions are most benign. All items (freight, plant and people) are transported by wheeled jet cargo aircraft to the site and are likely to be landed on blue ice, then transported by sledge and tracked vehicles to site. The maximum limit of cargo weight for is 13 tonnes, in good conditions. The distance of the re-supply route is estimated to be 8-10 km between the blue ice runway and site. Terrestrial transportation from the runway to the site is likely to be realized with skidoos and sledges, with structural components piled on standard cargo pallets of 3 m by 3 m.

The core aircraft ﬂeet currently used on Union Glacier’s blue-ice runway, consist of: Hercules c130, Ilyushin Il-76, Twin Otter and Basler BT-67. Additionally, snow tractors are also available for the installation and/or site preparation.

The staff to support the construction procedure would consist of 20 people. After the first year, there would be a fixed annual schedule of operation and maintenance. An advance party of 5 crew, along with 2 months of supplies would be flown to the station at the beginning of each summer season (November) to carry out snow management and making the station operative. This procedure should take no more than 7 days, weather permitting. The same operation would be carried out at the end of the Antarctic summer season, when a crew of 5 personnel would be in charge of leaving the station in a winter mode. The crew would be flown back in middle of March each year. There would be one relief operation during the summer season (late January) to renew personnel, re-supply the station and remove the waste produced.

On-site assembly of small parts and pieces of the structure should be minimized. Instead, structural components should be transported ready for installation when possible. Personnel working outdoors would be wearing large bulky items of clothing including gloves, which would reduce their manual deftness. Construction and maintenance methods proposed must consider this reduced ability. In case of urgent repair, procedures should be simple and possible to be executed by non-specialist staﬀ.

1.5.5 Overall Requirements

The primary function of the station is to provide accommodation and the necessary support facilities to enable a variable number of people to live and work in a remote polar region for up to two months. The programme, site conditions and supporting logistical activities of the medium scale station should be considered as a whole during the design process. Another key feature is that the station will remain closed during most of the year, during which period it will not be possible to carry out repair work.

23 CHAPTER 1. CONTEXT AND RESEARCH AIM

Function Summer Staﬀ Science, Engineers & Visiting Scientists 6 Communications / IT / Science Support 1 Cook / Indoor Maintenance 1 Electrician / Mechanic 1 Field Operations Director 1 Technical staﬀ/ Visiting Students 2

Table 1.3: Average number of occupants in the University of Magallanes Research Station.

The design of the facilities will strike a ﬁne balance between a zero-impact design approach and engineering practicalities. However, a low-tech approach to the construction is essential due the limited machinery available on site, for which construction, maintenance and relocation processes will be mostly rely on manual labour. This means that the ﬁnal design and its logistic maintenance requirements must be within the capacity of the targeted crew.

The typical management and staﬃng envisaged are listed in Table 1.3

The above indicates staff are likely to change which depending on the research schemes being carried out by DPA. The cycle of a typical research programme is 3 years, although the number of staff will be ratified annually.

The required domestic facilities are described in Table 1.4, technical facilities are shown in Table 1.5 and scientiﬁc facilities are listed in Table 1.6.

1.6 Conclusions and Research Aim

This chapter has portrayed the particularities of the human presence Antarctic continent. A general description of the political and environmental conditions that govern Polar constructions has been described in the second section. Other aspects to consider in the design are the geographical location, soil attributes and climate regimes. It has also been shown how logistical networks play a key role in deﬁning what is possible to be constructed. Section 1.2 also oﬀered a general inventory of existing constructions, as well as their crew capacity, while Section 1.3 explored the dynamic evolution of Antarctic constructions over their brief history.

The review of the evolution of the built environment presented in this chapter has evidenced why conventional construction techniques were rapidly discarded and how Antarctic design has risen as an exciting and interdisciplinary new ﬁeld for engineers and designers, particularly for large scale buildings.

A particular characteristic of the Antarctic population regime, which has been addressed in Section 1.2, is the highly ﬂuctuant occupation during an annual period,

24 CHAPTER 1. CONTEXT AND RESEARCH AIM

Capacity Quantity Description (Number of (Number of People Units) Mess room 5 1 Dressing & undressing bulky, wet outdoor clothing & boots before entering dry areas. Sleeping unit 2 3 Light and sound proof. High thermal insulation. First will allocate IT expert and Field Director, second will serve for Electrician and Maintenance crew and third for senior science staﬀ Sleeping unit 4 1 Light and sound proof. High thermal insulation. Containing two bunk beds. Wash rooms 1 4 Containing hot shower cabin Sanitary unit 1 4 Containing wash hand basins, Toilets and Sanitary disposal units. Consider ventilation. Kitchen 1 Area to prepare and serve up to 3 meals per day. Storage place for dried and tinned food. Bulk baggage 5 3 Storage of bulky personal items store room such as trunks, suitcases, rucksacks, etc. Common Room 12 1 Communal area for eating, relaxing and socialising.

Table 1.4: Domestic facilities for University of Magallanes Research Station.

25 CHAPTER 1. CONTEXT AND RESEARCH AIM

Capacity Quantity Description Common Work 10 people 1 Including a group of 10 work Space seated. spaces with Dual Cat 5e LAN Free access connection points, free access around. around. Space for Communications equipment (Long, Medium & Short Range Comms.) Field Operation Minimum External access. Area to pack and Room 3.5 m high prepare equipment for field Opp. Storing and repairing field Opp. Equipment, consider warm storage for equipment and materials that can be damaged by freezing. Equipment drying (i.e. tents). Reception of supplies and large samples (i.e. ice samples). Storing of Search and Rescue equipment in a state of readiness to go. Waste Storage 4 month 1 Management Plan to be defined storage according to Environmental Protocol. Sewage & domestic waste, liquid & chemicals waste to be storage in drums on pallets. Used oil to be store in a tank. Fuel Storage 4 month 1 6 months of cold/warm gas supply cylinder store, fuel, diesel generators. Storage according to Environmental Protocol Cleaning Room 4 month 1 Storage for cleaning materials and supply equipment’s. Emergency 3 people 1 Cupboards to be kitchen grade for Booth standing basic medical and surgeon up, 1 equipment. stretcher free access around

Table 1.5: Technical facilities for University of Magallanes Research Station.

26 CHAPTER 1. CONTEXT AND RESEARCH AIM

Capacity Quantity Description Clean Air 4 people 1 Rack of Instrumentation. Lab Laboratory (Lab seated and benches with cupboards. Hand A) free access wash basin. Dual Cat 5e LAN around Connection point. Engineering 4 people 1 Racks of electronic equipment. Science seated and Dual Cat 5e LAN Connection Laboratory (Lab free access point. Lab with cupboards. B) around Aquaponic Tank Camera 1 x 2 In door double decked water 3 m and camera for the simultaneous free access growth of soil-less plants and ﬁsh around. cultivation. Sunlight required.

Table 1.6: Scientiﬁc facilities for University of Magallanes Research Station. due to scientiﬁc and touristic activities being mostly be carried out during summer season. This implies that large-scale stations need to be constantly and indistinc- tively supplied to keep the whole station operational. As for medium and small scale buildings (refuges and summer stations) this implies periodic maintenance and repair operation, particularly because they are constructed using traditional materials and construction techniques. Their operations is economically costly, logistically complex and environmentally risky. The suggestion to discarding traditional techniques for small scale buildings is not based solely on their technical limitations. It is also correspondent with the current environmental policies governing Antarctica. The inherent temporary and no-trace character that all new Antarctic designs must incorporate represents a bespoke paradigm that could be potentially be rolled out many other scenarios. Some contemporary Antarctic designers refers to this concept as a ‘deployability’ operation, which entails the integration of prefabrication, collapsibility and assembly process tactics into the design [1].

On the other hand, the role of lightweight structures used for temporary field camps has been highlighted, as they allow field activities to be carried out in the harshest environment, with a minimum of material, and without causing adverse impacts on the environment once removed. This logic fits with the transitory character demanded from new infrastructure. Furthermore, the variety of models currently used evidences the intrinsic pertinence of this kind of structures in Polar areas. The necessity of creating an inventory and description of this kind of structure is addressed in the following chapter.

Section 1.4, has suggested the rise in both scientiﬁc and touristic ﬁeld activities, and shown why it is highly likely to see an increasing demand for access and the establishment of summer-only settlements in the future. Given that there is no restriction on the setting up of campsites, although environmental rules must be

27 CHAPTER 1. CONTEXT AND RESEARCH AIM fulﬁlled, this can clearly represent a threat to the pristine Antarctic environment.

The evidence of successful lightweight structures and their inherited collapsible nature, suggests that their use could and should be explore as a more efficient and less invasive design solution for new small-scale facilities, on a larger scale than currently seen. Furthermore, the deployable and/or collapsible attribute of tents could be explored to enable a responsive configuration of the structures. This represents a novel design approach, which could offer a response to the variable use characteristic of Antarctic summer-only facilities, and the problem of having an isolated minimal weight structure during winter seasons.

A method of exploring a new and more complex lightweight design of such characteristics is enabled by an early-stage request from the UMAG’s Antarctic Division to produce a speculative design for a new small scale station as part as the collectively managed Union Glacier Station. As described in Section 1.5, the request consists in the design of a summer station, with maximum capacity for 12 people, 5 for an early and closing party, and none during winter. Minimal requirements, as well as logistical conditions has also been speciﬁed in Section 1.5 and they will use for the development of design proposal at the ﬁnal stage of this thesis.

Therefore, this research proposes that lightweight structures can be used to overcome the limitations and deficiencies that traditional construction presents in remote areas. In order to achieve this, the Glacier Union case will be employed to conceive a lightweight structure for polar areas, of a larger scale, and with a more complex configuration than currently seen. By exploring this, this research aims to demonstrate that Polar lightweight design should be recognized as a design field of its own, for which evidence and an example of a novel design method based on polar conditions wil be demonstrated.

28 Chapter 2

Characterisation of Antarctic and Sub- antarctic Lightweight Structures

2.1 Introduction

This chapter presents a set of structures built in Antarctica and Subantarctic regions.

The objective of this study is to establish the recognition of Polar lightweight structures as an architectural subject in its own right, as well as to contributing to the historical documentation of the most emblematic cases and to the registration of the evolution of Polar design.

The cases are described with emphasis on their technical characteristics and classiﬁed under common criteria, relation to their behaviour as lightweight structures.

Given that there is scarce amount of published academic literature on this area, the author was required to collect scattered and material of diﬀerent forms including: personal interviews, national Antarctic Programs’ magazines, brochures, websites and handwritten technical sketches. Some corresponds to documents produced by the early explorers of Patagonia in the 16th century and some others to computer assisted models produced by contemporary designers. This material is presented and interpreted from a common perspective, namely to demonstrate not only the diversity of structures found, but also the pertinence of recognising the Polar lightweight design as an architectural paradigm.

One of the challenge of this ﬁeld is the lack of a source where to derive knowledge from. It is generally the case that specialised architectural disciplines are developed from a study-subject which is explored and reinterpreted. Such is the case of vernacular architecture with the study of local materials’ properties, or biomimetic architectures and the study of naturals system. In the case of Polar design, such source of study is not provided. Solutions and knowledge are achieved by the

29 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES repetition of the construction exercise throughout time with different techniques and materials, in a trial and error fashion. Although some unique solutions have been produced, these have not been systematically documented and shared. This chapter offers a first exercise to portray and organise the cases of lightweight structures in Southern areas.

Throughout the very diverse case studies displayed in this chapter, it is expected to contribute to the general understanding that the extension of the continent conveys a great variety of geographical features and climate regimes that aﬀect the design schemes; as well as factors as location and available logistic networks can dictate how, how much and when things can be transported. In other words, the diversity of cases and solutions included in this chapter, expects to tackle the common misconception of considering the subpolar and polar context as a white empty canvas, this time from an architectural/engineering perspective.

Lightweight systems have been vastly studied. Best recognised eﬀorts correspond to the pioneering work of German architect and structural engineer Frei Otto in regard to tensile and membranes structures [8], and Swiss structural engineer Heinz Isler for the study of thin concrete shells [15], among others.

Consequently, there are many way of understanding and classifying the vast arrangement of lightweight structural systems. This thesis adopts the one proposed by Martin Bechthold [16]. The method proposed by Bechthold proposes a straight- forward perspective, where structural surfaces are understood as systems, and attributes regarding to the system level (such as span, proportions, orientations, and aggregations), generally within the architectural domain, are discarded for the purposes of this classiﬁcation [16]. This vision makes this approach compatible with the objective of this study, where very diverse structures needed to be studied under a common perspective and classiﬁed accordingly.

According to the classiﬁcation method used, two major groups of surfaces can be identiﬁed based on their structural behaviour. As Figure 2.1 shows, these two groups are classical rigid systems and non-rigid systems.

The ﬁrst group is characterised by showing only small deformations when subject to loads. It includes one-way spanning systems such as beam-like or vault-like surfaces (in the shape of shells or folded plates) and two-way systems where loads are carried through membrane stresses, such as shells structures and gridshells. Of course, combinations of these typologies can form hybrid structures and arrangements of these basic systems are used to resolved free-form designs.

In the context of this group of rigid surface structures, monocoque structures (‘single shell’) describe the purest approach to surface structures. Another common term is ‘semi-monocoque’, representing combinations of surface and ribs, such as stressed-

30 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES skin or stressed skin-on-frame construction. In this sense, there is a similarity between some modular objects like car bodies, aircrafts or boats and semi-monocoque structures [16]. Within beam-like systems, cylindrical shells, folded plates, and other elongated shapes are included. Beam-like systems carry loads primarily through distributions of shear and bending stresses, as traditional beams. Beam-like shells have only single curvature. Grid approaches (truss-like triangular-grid or quadrilateral grid with bracing cables) are also possible, where bending stresses are resolved into axial forces. Folded plates also classify within this group. In this typology, multiple thin plates are connected along the edges to compose a more complex beam-like system [16].

Vault like systems are mainly compression structures. Most classic examples are continuous rigid shells, but also vaulted grid shells are possible (either triangular or quadrilateral grids).

Cases of gridshells, membrane stressed shells, and vault-like systems in polar and subpolar region are presented in this chapter. While few examples of hybrid structures were found, there was no evidence of free-form surfaces could possibly due the highly complex construction requirements involved either by intricate structural methods or by the large number of diﬀerent structural components required

The second group is deﬁned as a system that is expected to deform whilst in service. This group includes cable-nets and tensile membranes. Both are tension- only systems, generally pre-stressed and doubly curved. Membranes obtain their strength from either mechanical or pneumatic pre-stress [16]. Cable nets or membrane edges are mechanically pulled toward the outside, and pneumatic pre-stress involves shaping the membrane through pressure diﬀerence.

Generally speaking, mechanically-stressed membranes and cable nets are shaped by a tensile element pulling along their edges, and usually form saddle shapes. As they are generally held by cables, boundary stresses and forces are transferred to rigid masts or other elements. Edges can also be rigid beams, trusses, or arches. Stay-cables are broadly used to stabilise the supporting structure [16].

Pneumatic systems are pre-stressed by the pressure difference between a sealed air chamber and atmospheric pressure. The air cavity can be the complete interior space (air-supported system) or smaller, isolated air volumes (air-inflated system). All pneumatic membranes are curved, as only a curved membrane can effectively resist pneumatic pressure that is acting perpendicularly onto it surface [16]. Both single as well as doubly curved (generally dome-like shaped) systems exist. The tailoring of the membrane permits the relatively free definition of shape. The stiffness of cable nets and membranes is directly related to degree of curvature and the amount of pre-stress.

31 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

For non-rigid systems, only examples of mechanically stressed membranes could be found in the Southern Polar context. The necessity of pneumatic structures to assure a constant high pressure requires the use of maintenance mechanisms that are unpractical in such extreme contexts, making this option is rather unsuitable for remote areas. A similar concern could explain the lack of cable net structures. As each cable transfers load to the reciprocate layer of cables, the constant pre-stress of every cable must be assured, which in an extremely dynamic environment like polar areas could be diﬃcult. Additionally, the positioning of each individual cladding panel supported from the cable grid makes the construction highly problematic in harsh climate zones.

Figure 2.1: Categories of surface structures (white) in the context of structural system (grey). Image: M. Bechthold

The definition of these structural categories suggest that the study of the surface geometry is also fundamental for to comprehension of structural behaviour, as the curvature of a surface is directly related to its stiffness, so both approaches, geometrical and structural, are intrinsically related. Therefore, quantifying the curvature of a surface is an important aspect for the evaluation of designs. The Gaussian method allows the curvature of a surface to be measured as the instantaneous curvature in points on the surface’ [16]. Any point P contains precisely one line that is normal to the surface. An infinite number of planes can be placed such that they contain the perpendicular line and intersect with the surface in P . The value of R varies as the plane is rotated around the perpendicular line. There are generally two positions of the planes such that R takes on the largest and the smallest value. The resulting intersection lines are called curves of principal section, and the associated curvature κ is called the principal curvature in P . The curvature κ is equal to 1/R [16]. The average value of all κ values in P is called the mean curvature. The product of the two principal curvatures κ1 and κ2 is the Gaussian Curvature, and it determines three categories for curved surfaces as shown in Figure 2.2:

• Synclastic shapes: with a positive Gaussian Curvature, with both curves in the same direction.

32 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

• Anticlastic shapes: with Gaussian Curvature taking a negative value since where both curves are oriented in opposite directions.

• Developable surface: where one of the principal curvatures is zero. Here the largest radius of a principal curvature is inﬁnite as it is a straight line.

Figure 2.2: Gaussian curvature of surfaces. Image: M. Bechthold

The present chapter illustrates the presence of these three typologies of geometry in the set of Polar lightweight structures reviewed. Regarding negative Gaussian curvature shapes, and as shown in Figure 2.2, they are mostly present as modular components of sealed enclosures with a diﬀerent global geometry (usually as a membrane section of a vaulted structure), rather than single open saddle shapes as usually seen in large span tensile structures. This is linked to the structural threat represented by snow and wind induced loads.

The following is a study of the historical cases of lightweight structures in southern polar and subpolar regions, with their general descriptions and their classification in structural and geometrical terms. Sections 2.2, 2.3 and 2.4 are dedicated to the description of some of the largest and more emblematic cases of permanent lightweight constructions in Antarctica. Section 2.5 described a group of vernacular typologies from the Subantarctic regions. Section 2.6 introduces some modern bespoke portable structures designed for the Antarctic context, and section 2.7 finalises this chapter offering some reflection of the subject as well as the classification of the cases described using the method from Bechthold.

2.2 The Amundsen-Scott South Pole Station

The Amundsen-Scott South Pole Station consisted of a geodesic dome located at the geographical South Pole and existed between 1975 and 2009 [Fig. 2.3]. It was commanded by the U.S. Antarctic Program with the aim of continuing the scientific activities initiated in 1957 on celebration of the International Geophysical Year (IGY), a global effort to boost polar research. The first settlement (known as Old Pole) was designed to accommodate a team of 16 research and support personnel

33 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

Figure 2.3: The Amundsen Scott Dome after snow removal in preparation to deconstruction work. Image: Andy Martinez, USA National Science Foundation, 2009. for a whole-year round campaign, consisting of a group of ‘Jamesways’ huts and T- 5s (a type of prefabricate wooden buildings) [17]. Due of the signiﬁcant amount of results obtained from range of scientiﬁc disciplines it was decided that activities would continue beyond the IGY. In 1967, the U.S. National Science Foundation and the U.S. Naval Support Force decided to explore the feasibility of constructing a new station, since the old station’s units were becoming distorted under the heavy weight of snow and ice to such an extent that it needed to be declared uninhabitable [17].

The design was elaborated by the U.S. Naval Facilities Engineering Command in collaboration with the Naval Civil Engineering Laboratory [Fig. 2.4]. Construction was carried out by the U.S. Naval Construction Battalion 71 during two summer campaigns: 1971-72 and 1973-74 [Fig. 2.5].

Figure 2.4: Artist’s concept of the design new Figure 2.5: Announcement of the USA South Pole’s design. Source: The Antarctic competition of the new USA Polar Journal 1975. Station. Source: The Antarctic Journal, 1975.

The two main adverse factors that rule the design were the remoteness of the site (the nearest seaport at Mc Murdo Stations was located 1,300 kilometres from the Pole) and the harsh environment conditions [17]. The ﬁrst factor implied that the only practical transportation mode would be airplanes, thus components size and weight should be constrained by the capacity of an LC-130 Hercules, namely 2.5×2.5×11 m, and 9,000 kg. Construction seasons could last about 75 days (mid-November to early

34 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

February) during which average temperature would be around -32 °C. The station would remain isolated from early February to mid-October, for which reliable life- support system were required. The second factor, implied that the structure would have to cope with a series of adverse environmental conditions including: low with temperatures of -80 °C, high winds of 24 m/s (86 km/h), drifting snows with average wind speed of 6 m/s (21.6 km/h), constant displacement of the ice sheet of 9-10 m a year towards the north and, soil with a low shear strength of 500 g/cm2 to a depth of 2.5 m [17].

The dome was designed based on the geometric concepts endorsed by R. Buckminster Fuller [18]. Its great circle spanned 50 meters and 15 meters high at the centre, com- promising about 2/3 of a hemisphere. The dome enclosed three double stores high pre-fabricated buildings for quarters and operations. The structure was protective against wind and snow, but not cold as the interior needed to be kept under -18 °C to prevent deformation of the snow support used as foundations [17, 18].Its life span was required to be of 15 years.

The use of a spherical shape was justified by its geometrical efficiency, structural strength and low profile, which was essential to avoid the building to be buried by the snow [17]. Effectively, its life span could be greatly extended to over 30 years by clearing the snow off the building annually. Computer models were used to study different framing systems for Antarctic conditions including Radial Rib, Lamella, Lattice and Geodesic [19]. Although several were efficient under symmetrical design loads, the last one showed dramatically higher strength under eccentric loads with more uniform strength throughout the surface members, which make the structure’s behaviour closer to a homogenous shell [Fig. 2.6] [19]. Physical models were also used on site to study patterns of snow accumulation [Fig. 2.7] whereas other studies were run in wind tunnels, where wind loads where scaled to the size of the model, in order to determine the effect of blowing snow. A geodesic dome also presented advantages from a logistic perspective: components’ production could be repetitive which would facilitate the assembly, and no part would be too large or heavy for aircraft or handling.

Components consisted of 1,448 I-beam struts each about 3m long, connected at 490 nodes, each of them involving 84 bolts per node [Fig. 2.8]. The cladding consisted of more than 900 thin triangular aluminium panels. Aluminium alloys where chosen for all construction for several reasons: ease of fabrication, lightness for transportation and assembly and because it increase its strength and ductility at low temperature, contrary to steel or other materials available at that time, which become brittle in extremely cold environments [19]. The foundation includes 70 timber pads spread- footings buried in the snow, one for each of the 70 dome base points.

35 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

Figure 2.6: Diagram of the Figure 2.7: 1:10 scale model of Amundsen-Scott South Pole Dome geodesic dome Station used to study snow drift pattern. Source: construction according to manufac- U.S. Navy, undated. turer Temcor©. Source: National Science Foundation, 1972.

Components weight and size were also constrained by the Antarctic conditions. While the maximum weight of every component could not be heavier than 22.5 kg to allow parts to be hand-lifted and to minimize the air cargo involved, the size of fasteners must not be smaller than 3/8 inch of diameter since the dome had to be assembled by personnel wearing heavy gloves. It is interesting to notice than although the transport of personnel, material and equipment for the whole station compromised over 300 ﬂights during 3 seasons, but materials for the dome could be transported in only 3 ﬂights [18].

As Figure 2.9 shows, the panels were designed to overlap and interlock with inden- tations in the structure’s frame and were secured with extruded splines. This design option for splines and panels was load tested to 0.03 MPa of panel surface load. Although the panel showed plastic deformation, it did not collapse which provided a safety factor of 2 since the design load was 0.015 MPa [19].

The assembly sequence began from bottom to top, in anticlockwise direction around a central tower placed at snow level and was hoisted up as struts were added to the ends. [Fig. 2.10]. Multiple support cables were used to secure the structure temporarily from the tower. Exactly the reverse procedure was used to disassemble the dome [Fig. 2.11 and 2.12].

Once the NSF had built a much larger permanent station in 2008, capable of accommodating 150 people, the dome was relieved of duty and used as a cold storage warehouse after almost 35 years of service. A few signs of potential collapse, which began to be identiﬁed and repaired from 1988, determined that the structure should

36 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

Figure 2.8: Gusset plate showing installed Huck bolts Figure 2.9: Diagram for for the Amundsen-Scott Dome. Source: USA National geodesic dome construction ac- Science Foundation, undated. cording to manufacturer Tem- cor © Source: USA National Science Foundation, undated.

Figure 2.10: Erection progress viewed from outside the South Pole dome as the frame is hoisted up the tower. Photo: John Perry, U.S. Navy Seabee, USA National Science Foundation, 1972.

ﬁnally be dismantled and removed, since the Antarctic Treaty requires any obsolete structures to be removed where practicable [18].

No other example of such a large geodesic structures has been found in Southern Polar region to the date. Although in 2013 a group a three small geodesic domes covered with a tensile membrane was installed in Union Glacier Station (Chile). In this case the principal structure measured 9 m, and the two smallest ones 4.5 m in diameter and corresponded to a standard commercial product by Domoschile© [20] [Fig. 2.13].

37 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

Figure 2.11: Interior Figure 2.12: Exterior of the South Pole Dome’s dismounting of the South Pole Dome’s party. Source: the Antarctic Sun, 2009. dismounting party. Source: the Antarctic Sun, 2009.

Figure 2.13: Group of domes installed at the Union Glacier Station. Image: Domoschile, 2013.

2.3 The Teniente Arturo Parodi Polar Station (EPTAP)

Figure 2.14: The EPTAP. Image: P. Serrano, 1999.

The EPTAP (1999-2013) was located in Patriot Hills 82 °S, 1085 km from the South Pole and 855 m above sea level [Fig. 2.14]. It was the ﬁrst permanent polar structure placed on a blue ice zone. It was commissioned by the Chilean Air Force’s Antarctic Division in 1998 and designed by the University of Technology Federico Santa Maria’s Architecture for Extreme Zones Research Unit under minimal-impact principles.

38 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

The aim of the project was to provide logistical services throughout summer months for technological and scientiﬁc ﬁeld parties at the inner Antarctic plateau [21]. Personnel working at the interior of the continent must usually wait to be pulled out, as aerial operations rely on favourable weather conditions. Thus, the station played an important role in the safety of people and equipment operating in the deepest part of the continent, as well as navigational and communicational services.

The structure consisted of a membrane tunnel supported by a series of arches. The tunnel had a curved axis. Along the tunnel a series of modular structures, known as ‘Igloo Satellite Cabins©’, previously purchased by the Chilean Air Force, could be attached [Fig. 2.15]. At its original conﬁguration it engaged 320 m2, and had capacity for 24 people. The length of the tunnel was 50 m.

Figure 2.15: Physical components at the EPTAP: 1: tunnel 2: visor 3: module 4: sanitary system 5: communication 6: plug in ports. Image: Pol Taylor, 1999.

The morphology of the site represented a critical input for the design. The presence of the Patriot Hills produces the accelerates the constantly blowing katabatic winds, which ﬂow from the 4000 m Antarctic Plateau and reach a maximum speed of 42 m/s (150 km/h)[1].

This wind displaces the surface snow layer and exposes a highly dense layer of blue ice of 8 km length, 700 m depth and an annual displacement of 8 m each year [22] The potential of these areas to enable the landing of wheeled aircraft, hence to be used as ‘natural runways’ was confirmed only in 1984, and it was supposed to represent a major change in the Antarctic logistic network [22]. On the other hand, this extreme wind represented a major issue for any lightweight structure aimed to be raised. Therefore, the structure was placed on a snowfield area 800 m North of the blue ice zone, where winds decelerates and a stable layer of 2 m of hardened snow could be found. This layer of snow sited over an ice sheet would also avoid the typical sinking problem usually affecting coastal Antarctic structures.

39 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

The extreme speed of katabatic winds also meant that any static body left on the surface would interfere with the prevailing snow currents and rapidly become buried. This makes access to any enclosure particularly diﬃcult. Consequently, the tunnel was conceived as a linear element that would use the accumulation pattern as both, a structural defence against katabatic wind ﬂows and as thermal protection against extremely low temperatures (with an average summer temperature of -20 °C, a minimum recorded of -35.8 °C) [1].

The membrane tunnel was conceived to be an unheated and uninsulated enclosure that would serve both as a corridor connecting a group of isolated modules, and as storage space. The tunnel was located upwind of the units and the entrances. All the components were pre-fabricated, and designed to be transported ﬁrstly by air (using a LC-130 Hercules with a cargo capacity of 13 tons), and then land, from the runway to the station’s site, using four skidoos and sledges [Fig. 2.16]. Hence, all the station’s components were designed and adjusted to ﬁt the 3 m × 3 m standard pallet size used for transportation.

Figure 2.16: Delivery for the construction of the EPTAP. Figure 2.17: Assembly of Image: Pol Taylor, undated. components for the EPTAP. Source: University of Technol- ogy F. Santa Maria, 1999.

Assembly took place on site during two summer campaigns in 1999 and 2000, involving 85 days in total. It involved a team of 20 trained crew [23] and two aircrafts [21]. Most of the assembly was made by hand [Fig. 2.17], although a snow-cat tractor belonging to ta ourist company, Adventure Network International, was employed during the installation. Again, all these logistical constraints were considered as part of the design process.

The cross section of the tunnel was designed based on ergonometric conisderations, and later rationalised to a circular arc with 4 m of diameter [1]. Arches considered an outward inclination angle of 240 degrees [Fig. 2.17], which contributed to keep

40 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES the membrane pieces in tension. These dimensions agreed with the cargo pallets used for transportation. Pairs of inclined arches were located at a distance of 2 m along the tunnel.

In terms of materiality, the arches were formed from welded steel segments. The strength of this compression section would provide the necessary lateral resistance to oppose wind-derived loads. However, steel characteristically becomes a fragile material with temperatures below -20 °C, making it highly vulnerable to impact fractures. The decision to use this material was made in consideration of the limited budget available. As a response, the designers proposed a structural system in which the rigid elements were isolated from each other, therefor loads would be distributed within a network of ﬂexible joints, dispersing any impact force throughout the system [1].

Pair of inclined arches were tightened with strips of 50 mm nylon slings, which were compatible with the criteria of flexibility and economy. They could be easily fixed to the arcs and rails using self-perforating screws. This type of joint proved effective and easy to implement on site, for which the structure’s geometry could be erected on site in only five hours [21].

Figure 2.18: Cutting pattern of the EPTAP’s PVC membrane. Image: Pol Taylor, undated.

Figure 2.19: Membrane sections being attached to the structure for the EPTAP. Image: Pol Taylor, 1999.

41 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

The tunnel’s cladding was solved as a patterned tension membrane. Each section between arcs would comprise three discrete hyperbolic wedges. This pattern would be beneficial not only structurally, but also would facilitate the fabrication of the membrane [Fig. 2.18]. The fabric was PVC reinforced with a polyester webbing, weighting 750 g/m2. The surface incorporated an anodised finish and U.V. protection treatment, due the constant solar radiation and the thin ozone layer. Pieces of membrane were joined using a double flap of 100 mm Velcro©.

Membrane units were attached to the arcs using a large quantity of 35 mm nylon slings and buckles, which could be tightened from the inside and were favourable for manipulation with thick gloves [Fig. 2.19]. To introduce pre-stress, skidoos were used to pull each unit’s outer arcs outwards, until they achieved the necessary rotation angle [1].

The modular units, or ‘Igloo Satellite Cabins’© (see section 2.6), could be attached along the tunnel using sleeve connections. These elements are considered as essential by the designers for the expansion of the structure as a system [1]. Igloos’ panels incorporated insulation material at walls and ﬂoor of 50 mm of high density polyurethane. This provided suﬃcient thermal protection for the igloos to be used as bedrooms, toilet and communication equipment storage.

At each end of the tunnel, a concave panel of transparent 4 mm monolithic polycarbonate were placed, named as ‘visors’. These visors served both as entrances for skidoos and sledges with cargo and as a view point enabling panoramic view of the landscape [Fig. 2.20]. The double curved elements were ﬁxed to a frame formed by two arcs, enabling the panels to rotate vertically thanks to cast steel joints. The double arc frame also provided the whole structure with lateral stiﬀness.

Figure 2.20: Curved visors at the EPTAP. Image: Pol Taylor, undated.

The structure required periodic maintenance mainly due to snow drifts [Fig. 2.21]. In the Southern summer 2013-14, the structure was unburied and disassembled after

42 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

14 years of service [Fig. 2.22]. It was then translated to Union Glacier, another blue- ice zone near Vison Massif, characterised by much calmer climatic conditions [24] where a new Antarctic Base, jointly managed by the Chilean Antarctic Institute, Air Force, Navy and Army was created involving a group of diﬀerent structures. The membrane needed to be replaced but the rest of the structure was reinstalled without major inconveniences [21].

Figure 2.21: The EPTAP after two years of service. Figure 2.22: Chilean Air force Image: Pol Taylor, 2002. personnel unearthing the EPTAP after 14 years of service. Source: University of Technology F. Santa Maria, 2013.

2.4 The Shockwave Tent

Figure 2.23: The Shockwave Tent in Villa Las Estrellas, Antarctica. Image: University of Technology F. Santa Maria, 2010.

The Schockwave tent was also developed by the ARQZE Research Unit (University of Technology F. Santa Maria, Chile) in 2002. The original purpose of the structure was to serve as a hangar for aircrafts at the EPTAP Station [Fig. 2.23]. However, the cancellation of the airborne operation that summer season and a ﬁre consuming the old sport/community centre in Villa Las Estrellas, at the Eduardo Frei Chilean Antarctic Station in 2009, gave the structure a new purpose [Fig. 2.24] as a

43 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES communal sport centre. The structure lasted 3 years in service before collapsing, presumably caused by the fatigue of the poor quality bolts employed [24].

Figure 2.24: Side view of the Shockwave Figure 2.25: Stereometric structure of the tent in its original version. Image: ARQZE Shockwave tent, Villa Las Estrellas. Image: Architects, 2010. University of Technology F. Santa Maria, 2010.

The tent has been defined as a ‘polygonised fuselage’ shape by the designers [25], but it can also be described as the section of an ellipsoid. The shape of the shell was designed for its efficient aerodynamic performance, which implied resisting the characteristic Antarctic winds of up to 42 m/s (or 150 km/h). The structural system employed was designed to cope with up to one meter of snow derived loads while using minimal material [24]. The global geometry of the tent exploited the efficiency of a continuous double curved surface, and the structural system was defined as a lightweight triangulated rigid frame. The basic principles of a geodesic structural frame applied, namely, loads being distributed throughout a network of bars and nodes avoiding force concentrations, for which a minimum amount to structural elements are required [26] . The rigid surface was subdivided into 4 segments. These grid segments were reinforced with stereometric bars, which were placed independently during the assembly procedure. By adding these stereometric elements to the surface sections, the shell was then turned into a group of independent truss-behaved rigid elements [1].

The Shockwave tent provided an enclosure of 150 m2. The footprint had a length of 16 m and a width of 10 m. The highest point measured 6 m.

The principal components of the structure are standard galvanized steel tube of 38 mm diameter. The length of the tubes was limited to 1.6 m in order to avoid buckling [1] [Fig. 2.26]. The terminals of the tubes were ﬂattened to be insert on the node’s joints. The joints consisted of discs, produced from ﬂat 2 mm galvanised steel plates, where bars were jointed with bolts onto the joints [1] [Fig. 2.27]. Each truss employed two tripod feet as supports to the ground. These tripods had a steel plate, which once buried into frozen void of water, behaved as an anchorage. These supports allowed rotational and vertical adjustment [Fig. 2.28].

44 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

Figure 2.26: Galvanised Figure 2.27: Standard disc- Figure 2.28: Tripod support steel tubes used for the Shock- shaped joint used in the used in the Shockwave Tent. wave Tent. Image: ARQZE Shockwave Tent. Image: Image: ARQZE Architects, Architects, 2010. ARQZE Architects, 2010. 2010.

The membrane consisted of a polyester fabric coated with PVC. The membrane was composed from several sections, and sealed with overlapping ﬂaps with Velcro© [26]. Similar to the previous ARQZE case, membrane was joined to the metal structure using nylon slings and buckles.

The assembly procedure was planned unaided by mechanical resources, where a team of 8 people could deploy the station in a period of 24 hours. The sequence began with the assembly of the four stereometric trusses on the ground, and the ﬁxing of the tripod feet [Fig. 2.29]. A mast and rope were then required to hoist the trusses into the air [1]. Once the trusses were erected, auxiliary metal tubes were bolted on to the structure provide the shell with the necessary stability [Fig. 2.30]. The membrane was lifted to the top of the structure and then extended by hand and ﬁxed with Velcro©. When collapsed, the structure could be sectioned and packed into 1.6 m bags, each of them weighing 40 kg. The whole tent weighed about 1,300 kg.

Figure 2.29: Stereometric truss for Figure 2.30: Reinforcement elements for the Shockwave tent being assembled and the Shockwave Tent being installed using transported. Image: ARQZE Architects, the grid as a scaﬀolding. Image. ARQZE 2010. Architects, 2010.

The original scheme considered the closure of the front portal with a light membrane. This membrane was ﬁxed between the structure and an auxiliary secondary arch using ratchets, so tensioning was possible [1]. However, when the tent was employed as a sport centre a bespoke rigid wall was instead inserted.

45 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

Figure 2.31: Original soft entrance cover Figure 2.32: Front view of Shockwave designed of the Shockwave tent. Image: ARQZE implemented in Villa Las Estrellas. Architects, 2010. Image: ARQZE Architects, 2010.

Once the ARQZE group became a private company, the system began to be oﬀered commercially as a standardised product. Figure 2.33, shows a proposal from ARQZE for a military hangar in the desert implemented with as a variation of the same system described above.

Figure 2.33: Proposal of an adaptation of the Shockwave structural system for a hangar for the Chilean Air Force’s ﬁghter aircraft in the Atacama Desert. Image: ARQZE Architects, 2010.

The characterisation of a case like this, requires the revision and interpretation of the concepts proposed by Bechthold [16] for his classification of structural surfaces. The distinction made between the ‘beam-like’ structures and ‘vaulted-like’ structures, both unidirectional systems, implies the recognition of a broad spectrum of rigid surfaces, the limits of which are determined by two ideal elements: a horizontal beam and a funicular arc. A beam, as a spanning rigid element implies the presence of out-of-plane forces, namely bending and shear, for which a certain depth in the element’s geometry is required. Therefore, the combined load stresses make beam- like systems a rather inefficient solution in terms of structural optimisation. On the other hand, a funicular arch is a highly efficient element, dissolving any external load through tension and compression through an in-plane mechanism. Therefore, the closer a surface gets to a funicular shape the more efficient it is, and the less

46 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES structural depth is required. What the categorisation method presented in Figure 2.1 proposes, is a large grey area between these two limits, where the Schockwave tent appears to fit in. It could be said therefore, that the classification of such structure would depend of the assessment of its curvature-depth ratio. Nevertheless, since either classification would not be incorrect, a hybrid labelling seems a better option.

2.5 Subantarctic Indigenous dwellings

There is a fascinating variety of vernacular structures in the southern subpolar region. Nevertheless, most of the best known authors who have dedicated themselves to the study of vernacular structures, such as Torvald Faegre, Bernard Rudofsky, Paul Oliver and others have failed to include the cases from the southern subpolar region as the remarkable example of smart use of local material and structural eﬃciency that they are, probably due to the quick extinction of these groups, or the lack of English literature. These nomad and semi/nomad communities no longer exist thus, any description of their construction technologies require the revision of manuscripts and reports produced by explorers, settlers and missionaries, starting from middle 16th century until mid-20th century when the last of southern inhabitants were considered either colonised or extinguished.

It is not trivial to observe that the natural answer to the extreme weather conditions from a diverse group of indigenous communities was, in almost all cases, the utilisa- tion of structural surfaces. This can be logically explained by their nomadic/semi- nomadic style of life, but also by their deep understanding of light construction behaviour, the performance of materials available, as well as thermal eﬃciency strategies. As mentioned below, it is possible that the use of materials obtained from animals introduced by European immigrants could have been suﬃcient to dramatically modify and degenerate some of these structures’ behaviour and morphology.

Similarly to their inclusion in the general literature, no study could be found regarding the characterisation of these models, and the descriptions of technical details are rather scattered. Therefore, a ﬁrst attempt to name these constructions as structural systems is oﬀered here.

The Subantarctic cases can be classiﬁed according to the geographical location. Consequently, two main groups can be distinguished; those from insular Patagonia and those on Patagonia’s mainland, which also includes the vast Tierra del Fuego Island [27].

The regions occupied by these communities are illustrated in Figure 2.34.

The insular territory, from Chiloe Archipelago to Cape Horn Archipelago, where precipitation can reach 5000 mm annually is characterised by cold, dense and damp

47 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

Figure 2.34: Map of the areas occupied by southern indigenous communities. rainforests and narrow water passages [28]. Here, two small groups of marine hunters, fishers, divers and gatherers were hosted: the Alacalufes (or Kaweshkars), who inhabited the fragmented territory between Penal Golf and Magallanes Strait, and the Yaghans (or Yámanas) who inhabited the inhospitable islands south of Tierra del Fuego (Wollaston, Cape Horn, Picton, Nueva, Lennox and part of Navarino Islands), along the coast of the Beagle Channel and neighbours [29]. Temperature in the insular Patagonia and Cape Horn would not vary drastically throughout the year, 8 °C in summer to an average of 0 °C in winter [29], and an average annual temperature of 5.2 °C for Cape Horn [30]. Both groups supplied themselves mainly from sea-lions, birds, fish and seafood [31]. By the time the first Europeans contacted the Yaghans, in 17th century, their population was estimated around 3,000 [31], whereas the Kaweshkars had an estimated population of 5,000 [29].

Yámanas and Kaweshkars’ customs did not diﬀer greatly from each other. The same can be said regarding their physiology, which was characterised by broad, relatively short bodies and slim legs, suitable for their marine activities, when most of their time would be spent in canoes [32]. Although Kaweshwar are believed to have been more stable and suitable to walk body-structure than the Yámanas, who were expert in their rocky and fragmented territory [33]. Small family units would spent most of the time in canoes made out of trees, mainly oak cortex. In the case of Yaghans, their canoes were of up to 5 meters length, and used by group of between 12 and 40 individuals [28]. Both groups, Kaweshwars and Yámanas, would settle on land only

48 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES when suﬃcient resources had been collected or to ﬁnd shelter from extreme adverse weather.

The rapid decline of both groups started with the arrival of the whales and sea- calves hunting vessels, mainly from USA and UK at the end of 18th century, and later with Catholic missionaries. By the beginning of 20th century, the Yaghan and Kaweshkar culture were considered extinguished.

On the other hand, the Patagonia mainland and Tierra del Fuego is characterised by vast and open plains of Poaceaes, guanacos and rheas [28]. Persistent desiccating East wind of up to 28 m/s (100 km/h) and high pressure regimes are also distinctive of these semiarid zones, particularly in the summer months [34]. These zones were inhabited by two groups of terrestrial hunters and gatherers: the Tehuelches (or Aoniken) who occupied the extended area between the river Santa Cruz and the Magallanes Strait (where maximum and minimum temperatures vary from about 40 to -2 °C [35]); and the Onas (or Selk’nams) who inhabited the inner Tierra del Fuego Island’s plateaus [31] where temperatures would range from 10 to 1 °C [36].

Both group, believed by some to share a common origin [29], were characterised by a tall and robust physical phenotype, 1.80 m average height for male individuals as described by the ﬁrst encounter by P. de Sarmiento in middle 16th century and conﬁrmed by explorer Frederick A. Cook in late 19th century [29]. Due to their hunter skill, they were described as excellent runners. They were organised in bands of relatives occupying nomadic settlements. Their hunting regime would prevent them from establishing long term settlements, as well from gathering several family groups in the same place.

At the beginning of the modern colonisation of Tierra del Fuego, circa 1881, the population of the Onas was estimated to be 3,500 individuals [37]. Their extermi- nation at the end of 19th century was quiet abrupt and violent and came from the Europeans settlers funders of the still existing sheep ranches [31]. The Tehuelche population was estimated to be only 25,000 in the Argentinian region, by the mid- 19th century [38]. They adopted the use of horses introduced at the end of 17th century, which drastically altered their lifestyle. Later, they created permanent settlements around the trading colonies. The introduction of livestock at the end of 19th century represents the end of the Tehuelche culture [27].

The structures used by these two groups, are brieﬂy described as following:

2.5.1 The Kaweshkar (Alacalufe) Case

The Kaweshkar Dwelling consisted of a slighted ’ﬂattened’ cupola with an elliptic base. The structure was left on-site to be later repaired and reused by other families,

49 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

Figure 2.35: Kaweshkar Dwelling, Puerto Eden, Chile. Source: www.mediateca.cl, undated. whereas the covers, made out of seal skin and tightened to the structure using animal tendons, was transported from site to site [27]. The structure consisted of two symmetric series of bent arcs, made from ﬂexible wooden rods [Fig. 2.35]. As described by Baeriswyl et al. [39], the aspect of these structures was rather fragile, but in practice it presented an eﬃcient protection against wind loads. The average structure would require among 25 to 35 skins. The erection process has been described as straight-forward and uncomplicated, with both interlocked set of arches installed in tandem [39] [Fig. 2.36].

Figure 2.36: Reconstruction of a Kaweshkar in Puerto Eden. Photo: Maria Isabel Tonko, undated.

From a thermal aspect the dome covered with animal skin, preferably sea-lion [40] provided an excellent heat reﬂector which uniformly distributed the bonﬁre’s heat, which was always placed in the centre of the room. A regular sized dome would present a base of 3 by 2 meters and a central height of 1.80 meters [40]. Approximately 25 sea-lion skins were necessary to cover one average shelter was

50 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES app. 25 units. Each piece conforming the membrane was provided with holes, so they could be ‘sewed’ and tightened to the structure using animal tendons, providing a sound attachment system [40]. The construction was then covered with big leaves, such as ferns or tress cortex. A final set of strings in multiple directions would surround the entire dome [40]. Every Alacalufe structure presented two low and narrow entrances: one oriented towards the sea and the other towards the mountains, believed to respond to religious drivers [41]. The two accesses were also covered with animal skins. On the top of the copula, a third opening was placed for smoke escape, this was partially covered with leaves and branches. The flooring consisted of several layers of leafed branches. Inside the dome at the ground level a tight herb pad was placed around the structure to ensure the dwelling was insulated from the cold exterior. This typology can clearly be recognised as a structural surface, more specifically a grid shell. Although the grid of laths could stand on its own and works as the primary structural element, the heavy membrane also contributes to the stabilization of the grid, as well as cladding. The detail, given by descriptors, that specified that the membrane was attached or sewed to the nodes’ structure using animal’s tendons, is critical for this classification, since it proves that the membrane was actually part of the system as a bracing or shear-bearing element, preventing the deformation of the quadrilateral grid. Furthermore, the weight of the skin is also beneficial to ensure that such a light structure is not blown away. The following diagram [Fig. 2.37] shows the characteristic dimensions and main components of an exemplary Kaweshkar shelter.

Figure 2.37: Alacalufe dwelling’s components: 1) laths, 2) nodes, 3) void for passive ventilation, 4) membrane cover, 5) entrance, 6) vegetal ﬂooring, 7) insulation pads, 8) bonﬁre. Source: Journals of Chilean Architectural Association, 1991.

2.5.2 The Yámana (Yaghan) Case

There were two typologies used by the Yaghans: one was a conic structure [Figs. 2.38] and the second was an ellipsoidal copula, similar to the one used by the

51 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

Kaweshkars [Fig. 2.39] As most authors described, the ﬁrst was used as either a uni or multi-family dwelling [42], whereas the second model, similar to the Kaweshkar’s gridshell, would be used for male-only initiation ceremonies. There is a large dis- cussion about the possible origins of these two typologies. For example Camisquela suggested that Yaghans would have inherited the conic structure from the Onas, their neighbours, as well as the tradition of secret ceremonies [41]. He also proposed the ellipsoidal dome was their original dwelling, only later employed for ceremonial purposes. Although interesting, this debate remains out of scope for this study’s purpose and is not further explored.

(a) (b)

Figure 2.38: Last examples of Yaghan Dwellings in Lago Fagnano, Tierra del Fuego. a) Lola Kiapra, the last Yaghan, posed in front of the shelter, b) a variation of it. Source: R. Casamiquela personal archives, 1962.

Figure 2.39: Structure of a cupula-shape Yagan dwelling with an elliptic base. Image: M. Gusinde, 1982.

No description could be found presenting major diﬀerences between the Yaghan and Alacalufe gridshell in terms of their construction system. Given that the geography between the Patagonian archipelagos and the southern part of Tierra del Fuego Island does not change dramatically, there is no evidence to suggest a signiﬁcant change between the materials available for construction that could have caused a dissimilarity between both models.

In regards to their every-day conic model, this consisted on a group of rigid logs buried vertically in the soil in a circular arrangement, slightly bent on the top where

52 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES they were tightened together using animal leather stripes to form a cone [41]. This would have been 3 to 4 meters in diameter and between 2.5 to 3 meters height [39]. The structure was then covered with animal skins, moss and tree cortex [29]. The top of the structure would be left uncovered (except for a light layer of branches) to allow air exchange, given that a bonﬁre was located in the interior’s centre, similarly to the previous case. The structure was easily built on site, and was left abandoned once the group decided to sail again [29]

The following diagram [Fig. 2.40] oﬀers a general description of these construction types.

Figure 2.40: Diagram of a conic Yaghan dwelling and its main components: 1) poles, 2) knot, 3) bonﬁre, 4) top void, 5) animal skins, 6) tree cortex. Source: Journal of Chilean Architects Association, 1991.

As it can be seen from the drawings [Figure 2.40], the rigid elements embedded in the ground do not collaborate in the distribution of load, but work axially, supporting each other.

In terms of the structural characterisation of this typology, although it could be described as a ruled surface, it is not a structural one. The ﬁxed rigid elements form a conic shape, which although curved, it does not constitute a continuous bi- directional load bearing element. In the supposition that a large structure would be implemented with the same scheme, it would be identiﬁed as a beam/column structure.

2.5.3 The Selk’nam (Ona) Case.

It is believed the Onas utilised three diﬀerent types of construction that can be listed as follow: i) a dwelling built from sticks and branches adopting a ‘sub-conic’ shape used by northern Onas [Fig. 2.41], ii) a dwelling consisting of a truncated conic structure made from rigid logs, characterised by a undeﬁned apex used by Southern Onas [Fig. 2.42 and 2.43], and iii) a windscreen used by northern Onas consisting of a set of slightly inclined sticks set up in a semi-circle arrangement from which animal skins stitched together as a single piece was attached [Fig. 2.44] [41]. According to

53 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

Casamiquela [41] the lack of an apex on this last model, prevented the possibility of deﬁning it as either the segment of a cone, a hemisphere or a paraboloid.

Figure 2.41: Dwelling of the southern Onas, made out of logs with the shape of an inclined cone. Image: Gusinde, 1918-1924.

Figure 2.42: Illustration of a dwelling of Figure 2.43: Photograph of a dwelling of the northern Selk’nams with a ’sub-conic’ the northern Selk’nams with a ’sub-conic’ shape made during the years 1918-1924. shape taken during the years 1918 -1924. Source: Gusinde, 1982. Source: Gusinde, 1982.

There is no single hypothesis for this variety, but the most accepted explanation was stated by Gusinde [33] which proposed that their use was determined by the location within Tierra del Fuego, which determined the type of material available. Therefore, while northern Selk’nams would occupy a vast and open region deprived from trees, they would utilise the ‘sub-conics’ dwellings as well as wind-screens. Whilst the occupants of the southern part of the island, rich on forests and readily accessible branches could easily implement the conic-like structures. Father Coiazzi, oﬀered a complementary explanation suggesting that the windscreens were utilised for short-term settlements while the others structures would be implemented for

54 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES longer periods of occupancy [41]. Again, given that this section does not focus on the origin of these typologies, these hypothesises will not be further discussed.

Conclusively, although it could be said that these three cases are classified as curved structures and the last two ones more specifically as lightweight structures, it is not possible to describe them as structural surfaces. In the first case, the southern Ona case of conic structures behaved similarly to the previous case described, the Yaghan dwelling, where the rigid elements embedded on the ground do not collaborate in the distribution of load bi-directionally, but instead work axially, supporting each other. The second case (sub-conic shape dwelling), although made out of lighter material, can be described similarly to the first typology. Moreover, although the third case (the widescreen used by northern Selk’nams) used a membrane, its behaviour does not differ largely from the previous cases: a group of independent poles embedded on the ground supporting a membrane. Therefore, the rigidity and structural stiffness of the system were not provided by the membrane, but the poles, with the skin only inducing certain level of in-plane stability. In that sense, the membrane only performed as a cladding and the system does not appear to have a surface-like behaviour, with the rigid element working in bending.

From another point of view, the fact that if the membrane were removed the ‘structure’ would still remain standing, not only aﬃrms the previous statement, but also allows the objection to the inclusion of this typology as a structure instead of an object or device. Unfortunately, no description was found regarding to their minimum and maximum dimensions, which would assist in the estimation of the load involved and to its accurate classiﬁcation.

Figure 2.44: Sketches of a windscreen used by the northern Selk’nams made during the years 1918-1924. Source: Gusinde, 1982.

The mention of a fourth Selk’nam model is also found in the literature, this corresponds to a segment of an ideal cone that Casamiquela describes as a ceremonial shelter only [41], while Gusinde as a winter dwelling [33]. Its characterisation

55 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES would therefore be the same as the Yaghan conic structure, hence, it should not be considered as a lightweight structural surface.

2.5.4 The Tehuelche (Aoniken) Case

Figure 2.45: Tehuelche dwelling. Image: E. Gerreaud, 1900.

The Tehuelche case is perhaps the most complex case of the Southern vernacular structures. It represents the largest scale, probably due to the ergonometric characteristics of the Tehuelche people and the number of people hosted. There were multiple variations of the basic model, and diﬀerently from the other cases, all these variations can be considered as structural surfaces, with exception of the most recent version. This is also probably the best described and documented case, perhaps due to the extent of the territory occupied by the Tehuelches, namely all the Patagonia mainland .

Commonly, the basic model is described as a half a dome attached to a front arch, which serves as an open façade. The structure was originally covered by large pieces of animal skin, namely Guanacos [39] [Fig. 2.45]. Later, once contact with first Europeans was established in the mid-20th century this cladding could be observed as consisting of horse skin and finally, of big pieces of awning/fabric [43]. According to Baeriswyl [39], the main open façade would measure between 3 to 5 meters, the height would reach 2 m and the depth would vary between 2 and 3 meters. Similar to other cases, a bonfire would be an important and it would be located at the front of the dwelling. The description of Baeriswyl is presented in the following diagram [Fig. 2.46].

56 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

Figure 2.46: Diagram with the main elements of an Tehuelche tent according to Baeriswyl: 1) main direcction of the wind, 2) structural poles, 3) nodes made with animal tendons, 4) pole’s V-endings, 5) guanaco skin covers, 6) front entrance. Source: Journals of Chilean Architectural Association, 1991.

Canals Frau offered a more detailed description of this case. He described it as a big tent, made out of 40 to 50 guanacos skins, or horses in the last century, resting on three rows of poles [43]. Canals Frau also highlighted the ‘rectangular’ arrangement of the poles, which would have a V-top ending over which horizontal poles would laid. He also specified that the pieces of skin would be sewed using animal tendons to form a single membrane [43]. Figure 2.47 and 2.48 show some interpretations made by Outes [44] and Basaglia [45] based on descriptions made in the 18th century collected by Viedma [46]. According to the classic semi-domed shaped of the tent, Figure 2.48 could be pointed as erroneous, since the author omitted the characteristic vaulting of the structure. Other authors like Palavecino described these variations as two different models [47]. Nevertheless, Casamiquela assured that there was only one typology, whose shape could be adapted, due to the relative height of the nodes made in the front row of poles from where the membrane was attached [41], suggesting that the structure tolerates a certain degree of variation in its geometry.

(a) (b) (c)

Figure 2.47: Diagram of a Tehuelche dwelling, made by Outes in 1905 based on the description made in middle 18th century. a) rear view, b) side view andd c) top view. Image: F. Outes, 1905.

The assemby procedure is known thanks to detailed descriptions made by several ethnographers such as Palavecino [47] and Muster [48]. Muster, described the procedure would start with the rear row of v-ending top poles, which would be ca. 1 meter high. A lath was placed above them, as a ridge beam. Two meters away

57 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

Figure 2.48: Diagram of a Tehuelche dwelling based on the description of Viedma made in middle 18th century. Source: Basaglia et al., 1980. from this set of poles, a parallel row, this time 1.8 m tall, was installed which would also include a ridge beam. A third row of poles and ridge beam, also placed 2 meters away from the previous, with a height of 2.5 m would complete the structure’s frame. In the description made by Viedma, the central ﬁrst poles would always be higher than the rest [46]. Each pole would have a certain angle of inclination which would also vary. Anchorages would ﬁx the membrane all around the structure [48].

A single membrane, made out of 40 to 50 pieces of guanaco skins varnished with animal fat and red ochre was laid over the structure. This membrane was deployed from the rear of the structure towards the front. As pointed out by many authors, the skin membrane would always be mounted with the fur facing outwards, which ensured rainfall water to slide down the surface [41]. The inclined poles would be straightened by the membrane’s weight and the tension produced when deployed to the front. Once placed, the membrane would be fastened to the front row of poles with stripes made out of animal tendons. Bundles with belongings would be placed all around the tent interior’s ﬂoor serving as air insulators [48].

Although accurate, there is a critical discrepancy between this description given by Muster and the most well-known authors such as Schmid, Baeriswyl, Casamiquela, etc. This is related to the direction of the ridge beams. The longitudinal orientation given by Muster would necessarily turn the structure into a rigid frame-structure. While the idea of the frontal double arch supporting the secondary transversal ridge beams and the membrane would allow it to be classiﬁed as gridshell-like structure. Some other authors, such as Sierra [49], Borgatello [50], Canal Frau [43]], Palavecino [47], Spegazzini [51], Viedma [46] omitted this key aspect.

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Several authors [41]], identiﬁed this tent as a summer only model. In winter, the open façade would be covered with another membrane, or an auxiliary structure, as later described, and they usually would be 3-4 time larger in size [41]. While the summer tent’s structure was described by Spegazzini consisting on two rows of poles with the front row being ca. 2 meters high and the rear row about 1 meter, with either 3 or 4 poles in each row; the winter structure grid would consist on ﬁve or six rows of poles, each row counting with four poles, and two more columns of poles of minor high on each side. This variation on the number of poles was also endorsed by Schimd, who portrayed the number varying between 9 and 18, and their height ranging between 1.2 to 2.5 m. [52] Casamiquela proposed that this model, which he named as ‘incomplete cupula-shaped’ or ‘semi-cupula’, meaning half a dome, should not be considered as the basic model but a seasonal, summer, variation of it.

Instead, Casamiquela proposed the so-called ‘hemi-toldo’ (or hemi-spherical) as the prototypical model [41], which was mainly used in winter seasons. This consisted of an almost perfect semi-hemisphere or idyllic cupula [Fig. 2.49], which sometimes could have an ellipsoidal shape, as later described. This conﬁguration would be achieved by the aggregating two facing hemi-toldos (or semi-cupulas). Here, two main symmetry axe could be recognised: a front/rear axis (East-West) which would go across both semi-cupulas, and a normal axis (North-South), which he named ‘transversal axis’. All dwellings would have this normal axis with a North-South orientation, presumably due to religious beliefs. In case of a single semi-cupula, the open face would always face East. There were two accesses and they would be located at the joints of the two semi-cupolas [41]. As always the bonﬁre would be located at the centre of the space.

Figure 2.49: Semi-spherical model of a Teheulche tent belonging to the nothern Cacique Manikiken who posed with his family in Chubut, Argentina at the end of 20th century. Source: Archivo General de la Nación Argentina, 1969.

This type of structure was also used by the Northern Tehuelches, who lived nearly permanent settlements. Musters [48] reported this large type of tents could house up to 50 people inside and measure nearly 5 m high in the centre [Fig. 2.50]. Moreno also highlighted the almost circular shape of the base which diameter would measure 12 m [41].

59 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

Figure 2.50: Semi-spherical Tehuelche dwelling completely covered on fabric in Santa Cruz, Argentina. Source: Osvaldo Mondelo’s personal archives, undated.

Diﬀerent authors [53, 54, 46, 47] mentioned internal subdivisions made by hanging pieces of skins. These cubicles would serve as independent bedrooms for the diﬀerent family members.

A variation of this model is named by Casamiquela as ‘reduce symmetrical’ model (or asymmetrical model) [41]. This would present two options: a) the aggregation of a classic hemi-cupula with an front structure of smaller dimensions and diﬀerent materiality [Fig. 2.51], in which case the global shape could not be described as a hemi-spherical and b) the aggregation of two hemi-toldos, which although identical, would have a reduced depth, for which the base would describe an ellipse rather than an circle, so that the transversal axis would be clearly longer than the East/West axis. Both models were also used as winter structures [47].

Figure 2.51: Asymmetrical tent model from a Southern Tehuelche family. Half structure is covered with animal skins, while the smallest section is covered with fabrics. Santa Cruz Province, Argentina. Source: Dr. Elsa Barberia’s personal archives, undated.

A ﬁnal variation was a tall, square and slightly curved model described by Sanches- Labrador [55] and Falkner [56], at the beginning of the 20th century. In this model, the structures geometry has varied, and the roof cover is independent from the lateral skins [Fig. 2.52]. Casamiquela proposed that this model was a degenerated version of the original, triggered by the excessive weight of the horse skin, introduced by European settlers, or the natural mutation of the cupula-shaped tent to a larger sized shelter to allow more people to be housed.

60 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

Figure 2.52: Tent covered with horse skin belonging to the Caquique Cangapol, during middle 18th Century, reproduced by the Jesuit Falkner Buenos Aires Province Argentina. Source: Falker, 1911.

Despite Camisquela, proposed the hemispherical case as the prototypical model, for structural purposes half-hemispherical dwelling needs to be recognised as the basic unit that can be aggregated in diﬀerent arrangements or deformed. Despite the rich variety of construction and conﬁgurations, it is interesting that all Tehuelches’ models correspond to gridshell-like structures.

Gridshells obtain their stiffness from boundaries, which provide the necessary rigidity. A shell or gridshell that is constrained all the way around the boundary is extremely stiff and very difficult to deform. If a hole is cut in the shell, or one edge is left free, the surface becomes flexible and these free edges constitute the weakest point. In the case of the Tehuelche’s dwelling, vertical poles and double frontal arch are replicating the action of an edge, stiffening the flexible points of the structure.

As explained in the previous cases of gridshells dwellings, the weight of skin cover provides the necessary stability. The tensile strength of the membrane, provides bracing to the grid. The aggregation of two half domes, forming the hemispherical conﬁguration, does not change this description. The same is ture for the ‘reduced symmetrical’ cases, when a half-hemisphere has been deformed into a semi-ellipsoidal dome, or the cases where an anterior structure of minor dimensions is aggregated.

When the curvature is varied, like in the cases illustrated by Basaglia et al. where the relative height of the frontal nodes is levelled, the synclastic geometry of the dome is turned into a single curvature system. Therefore the system is tuned into a unidirectional load system, similar to a vaulted grid shell.

Finally, the explanation proposed by Camisquela for the degeneration of this dome- like structure into a classic frame structure due to the change in the type of skin used (from guanacos to horse) and colonial inﬂuences, appears acceptable from an structural perspective.

61 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

2.6 Antarctic Portable Dwellings

There is a rich array of modern portable dwellings being used in Antarctica. This includes tents and rigid modules. They play a key role in the exploration of the continent’s deepest areas for scientific and touristic parties while still fulfilling with the strict environmental protocols. Although these commercial structures are minimal, they have proved sufficient to provide safe shelter for explorers while still meeting criteria of collapsibility, minimal weight, un-aided deployment and no trace-left once removed. Additionally, these types of structures allow the possibility to reconfigure campsites according to every season’s requirements [Fig. 2.53 and 2.54].

Figure 2.53: Touristic basecamp at Patriot Figure 2.54: Touristic basecamp at Vinson Hills. Image: Antarctic Logistic and Massif. Image: International Mountain Expeditions, 2010. Guides, 2014.

Although there is a broad spectrum of shapes, sizes and materials of tensile tents from a structural point of view they could be classified as isolated membrane structures, where pre-tension and bending are the key criteria for the efficiency of the double curved membranes and the flexible bars composing the structure. Another well-known portable tent structure is the so-called ‘Polar Haven’ [Fig. 2.53] com- mercialized by Watherhaven ©, which could be described as a lighter version of the classic ‘Jamesway’ hub, a vaulted structure of corrugated galvanized steel designed for Artic conditions in the early 1940’s.

It could be reasonably debated as to whether these kinds of devices can be eﬀectively considered structures or objects, as they remain in the borderline as architectural cases. However, it cannot be disallowed that there always has been an interesting dialogue between portable dwellings and constructions.

Firstly, tents were the ﬁrst type of construction buildings, serving as example for the design of more permanent housing [57]. Most certainly, this transition may have happened slowly.

In recent times, the lightness of tensile tents has become a source of interest to architects for nearly half a century, particularly those ones interested on developing prefabricated extended covering constructions, such as Renzo Piano, or cable nets,

62 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES like Frei Otto [58] [Fig. 2.55]. On the other hand, several cases can be found of commercial tents which apply the principle of classic structural surfaces. A basic example of this could be the popular geodesic tent model from The North Face© which can be annually seen in use in Antarctica [Fig. 2.56].

Figure 2.55: Frei Otto’s German Pavilion Expo Figure 2.56: ’2-Meter Dome’ tent ’67, Montreal. Source: Lightness, 2006. produced by The North Face. Source: Centre G. Pompidou, 1967.

It is outside the scope of this research to make a description of the technical details of these commercial products. Instead, this section will describe three cases of portable structures that have been designed for Antarctica in particular, focusing on the inﬂuence of this context on the designer’s approach for the structure’s geometry.

2.6.1 ‘In the Footsteps of Scott’ Expedition Tent

Figure 2.57: BAS Antarctic Expedition Tent. Image: Buro Happold, 1985.

This case corresponds to a small scale project commissioned from Buro Happold and designed by founding partner Ian Liddell in 1985 [Fig. 2.57]. The objective was to design a deployable shelter for the commemorative expedition ‘In the Footsteps of Scott’ (1985-1986) led by Roger Mear with two companions. The expedition aimed to be the longest non-aided land journey (70 days), during which the team would cross Antarctica and reach the South Pole, carrying all their supplies by pulling sledges. The scheme design was governed by the purpose of revisiting the classical pyramidal

63 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES structure used by the British Antarctic Survey. Such structure used wooden poles and turned out to be too heavy to be carried (28 kg) by the expeditioners. On the other hand, no commercial tent could guarantee to withstand the extreme weather conditions of Antarctica at that time [59].

Figure 2.58: Pyramid tent set up upon the King Edward VII Plateau as part of 1910-1913 British Antarctic Survey Expedition. Image: H.G. Ponting, 1911.

The solution was to optimise the original conical volume [Fig. 2.58] towards a more dome-like body, since spherical shapes are volumetrically more efficient and they are more capable of dealing uniformly with the characteristic shifting winds of Antarctica [Fig. 2.57]. Another consideration was the logistical restrictions of transport and assembly for this expedition in particular, namely the size of the sledge (2.4 m). Thus, the structure was resolved as an umbrella-system that was partially deployable, an advantage over traditional total-collapsible tents [Fig. 2.59 and 2.60]. The main structure was comprised of six glass-fibre bars contained within a membrane. In this way the entire tent could be transported as a single package. The membrane was defined as a set of doubly curved faces made from Goretex© fabric, an outer nylon layer and an inner PTFE skin. A thermal air buffer was achieved with a second light inner membrane, helping to avoid the loss of internal heat. The assembly process thus remained simple. The membrane was pulled down from top to bottom along the bars, which were forced under compression to form a curved shape and to meet the single base ground sheet.

2.6.2 Sastruggi Tent

The Sastruggi tent is consisted of a ‘triaxial’ modular design to be attached to the EPTAP tunnel (see section 2.3) during the second season of construction in 2000, to serve as a meeting room for the occupants [Fig. 2.61]. Although only one structure was built, the Sastruggi system was designed as an ever-expansible system, where

64 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

Figure 2.59: Sketches of the 1985 BAS Figure 2.60: Sketch of the crown joint for double curved surface and structure’s tent by the 1985 BAS d tent by designer Ian Liddel. designer Ian Liddel. Source: Buro Happold, Source: Buro Happold, undated. undated.

Figure 2.61: Sastruggi Room as part of the EPTAP Station, Antarctica. Image: ARQZE Architects, 2000. other units could be repeated and aggregated along its three axis. Each module was also designed to be internally subdivided, with the peripheral units being used a sleeping cells and central units as common room. The system, created by the ARQZE Research Unit from the University of Technology F. Santa Maria (Chile), was speciﬁcally designed to support the predominant winds of the area (known as katabatic winds), which can reach up to 41.7 m/s (150 km/h) [1]. Each unit was deﬁned by a set of nine arches and anticlastic membranes forming a closed shape [Fig. 2.62].

Figure 2.62: Diagram of the Sas- Figure 2.63: Articulated joint designed for the truggi’s structure. Image: ARQZE Sastruggi Tent. Image: ARQZE, 2000. Architects, 1999.

65 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

Each unit could be collapse into few a bags weighing approximately 1, 000 kg, which allow transportation in small capacity aircrafts, such as Twin-otters.

The structure comprises a series of nine arches of extruded aluminium alloy of 92 mm in diameter. A series of three arches is ﬁxed on the ground to provide stability to the whole system, deﬁning the three axe that comprise the structure. Each axis involves 3 rings which were rotated from each other in the air. Arches were designed with two radii of curvature. Each sets of arches was joined with specially designed articulated joints [Fig. 2.63] [21].

The membrane consisted of nine sections of a 750 g/m2 PVC and polyester fused membrane. Membrane sections were designed to acquire a double, or hyperbolic curvature [Fig. 2.64(a)]. The membrane was then pre-tensioned by two processes: transversally, using a system of ratchet and longitudinally using a nylon sling, and ratchet system that where attached to the articulated joint [Fig. 2.63]. The hinging of the arcs when deployed was also used a source of tension. Similarly to the cladding, cutting patterns were produced for the ﬂooring platforms [Fig. 2.64(b)].

(a) (b)

Figure 2.64: Cutting patterns of the Sastruggi Tent. (a) membrane; (b) ﬂooring. Images: ARQZE Architects, 1999.

In the ETPAP project the ‘Sastruggi room’ was designed as a meeting room, so extra thermal insulation was required. The insulation scheme included a 20 mm layer of closed-pore polyethylene covered with a merged aluminium foil surface [Fig. 2.65]. An internal layer of ripstop nylon fabric was also included. Both extra layers were attached to the arc slots using nylon slings and Velcro. Thermal protection also involved a special ﬂooring system. Flooring consisted of laminated panels that were tensioned to the aluminium proﬁles. The insulation was provided by a triple-layer membrane of PVC, close pore polyethylene and aluminium foil. Voids of 800 mm diameter were possible in certain areas of the triangular membrane sections [Fig. 2.65][1].

66 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

Figure 2.65: Installation of insulation layers at the Sastruggi Room, Antarctica. Image: ARQZE Architects, 2000.

2.6.3 The Apple

Figure 2.66: The ’Apple’ hub installed Figure 2.67: The ’Melon’ hub set up in in McMurdo Station, Antarctic. Source: Antarctica. Image: Chris Drury, 2006. Icewall One, 1998.

The Igloo Satellite Cabin©, also known as the ‘Apple’, is a commercial product which was originated by request of the Australian Antarctic Division (AAD) in the early 1980’s [Fig. 2.66]. It can be described as a semi-monocoque rigid surface, and has been used by nearly 16 countries, including Artic and Tropical environments such as Far Northern Queesland [60].

In the early 1980’s the AAD called for the design of a lightweight, portable dwelling. Moreover, it needed to be able to be transported by helicopter and cause no impact on site [60]. The solution came in 1982 from Malcolm Wallhead, a fibreglass moulder, and consisted of a pre-fabricated and insulated fibreglass cabin. The dome was composed of eight single walled panels, interlocked so the structure could either be assembled on site or transported as a unit. The first prototype was produced by casting the eight panels from a mould made of plywood covered with fibreglass and waxed. This included three plain panels, four window panels and one door panel

67 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

[60]. The hut was 3m diameter and weighed circa 300 kg. Lateral cables needed to be installed in the panel joints and tensioned to the ground around the cabin.

The first cabin was used on Magnetic Island, near Australian Davis Station, for penguin research. Nowadays it is still in place, serving as an uninsulated storage hut. The original model has not undergone much variation over the 25 years of use. In the latest version, the original insulation has been replaced by polyurethane sheet insulation between layers of fibreglass [61]. This has increased the weight of the Igloos, but is still possible to be flown by a helicopter at up to 130 km/h speed.

(a) (b)

Figure 2.68: Panelling of: (a) the Apple and, (b) the Melon hubs. Source: Islands to Ice Exhibition, Tasmanian Museum & Art Gallery, 2006.

A variation of the ﬁrst ‘Apple’ model is the ‘Melon’, where a hemi-ellipsoid shape can be achieved by including some singly curved panels along one axis [Fig. 2.67] [60]. Figure 2.68 show the panelling of both models. Furthermore, as Figure 2.69 shows, larger schemes are possible by aggregating several units using auxiliary tunnels.

Figure 2.69: Design scheme of a prototypical Antarctic ﬁeld station. Source: Islands to Ice Exhibition, Tasmanian Museum & Art Gallery, 2006.

68 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

2.7 Conclusions

Figures 2.70 and 2.71 shows a diagram which maps the state of art of Antarctic lightweight structures according to the classiﬁcation proposed by Bechthold, in terms of their structural and geometrical characterisation. This summary demonstrates the variety of structural lightweight typologies, which was the principal objective of this literature review.

Each case described in this chapter provides valuable technical information about Polar construction, but furthermore each case tells a part of the history of Polar lightweight construction.

The richness and complexity of the extinct vernacular typologies cannot be portrayed in only a few paragraphs. However, this section makes a ﬁrst attempt at describing them and classifying them from a structural point of view. It is believed by the author that this set of lightweight dwellings deserves a better understanding and recognition as remarkable example of structural eﬃciency.

The iconic Admundsen-Scott Geodesic Dome was the ﬁrst attempt to demonstrate the possibility of structural surfaces with permanent use in Antarctica and it managed to greatly exceed its expected service lifespan. The Shockwave Tent revisited this option, deriving an interesting hybrid system and provided a glimpse of the potential for geodesic surfaces with more complex geometries in extreme environments, possible nowadays thanks to digital modelling tools.

In the case of the EPTAP station, there are several aspects that make this an outstanding project. Firstly, it proves that membrane structures with permanent use are possible to implement, and they can be used in a larger scale that traditional modules or tents. It also suggested that the combination materiality, in this case membrane structures and rigid modules, can be an optimised solution for diﬀerent programmatic or thermal protection requirements.

There has always been a dialogue between tents and lightweight structures design, most typically flowing from structural design to structure-inspired commercial products. In the case of bespoke Antarctic tents, example where this dialogue is promoted the other way around were found, where tent technology is applied on larger structures. The Sastruggi tent lays in the borderline between an isolated structure and a lightweight structural system, thanks to its ever-growing possibilities and its thermal insulation solution. As these projects show, thermal insulation is one of the main obstacles for the use of membrane constructions in Polar regions. The BAS tent promotes the benefit of evolving from a polygonal structure towards a doubly curved surface, with the aim of making it lighter and more efficient. However,

69 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES the same principle could be applied to the objective of producing a much larger spanning structure.

The diversity of cases found on structural surfaces in polar and subpolar areas demonstrates that their use is not only possible, but that it also constitutes a rich source of knowledge in different aspects of lightweight design such as structural efficiency, assembly strategy, thermal conditioning. The sources and time-frame available during this research did not allow a deeper insight into each of these themes, but it is hoped that it can provide future researchers with a valid theorical framework. Likewise, the lack of academic or formal literature on this subject remains the main challenge during this study, for which a field research would provide a valuable complement to this study.

It is believed by the author that special attention should be given to the historical/ideological aspects that have been shaping the Antarctic and Subantarctic built environment. As earlier stated its quality of being one of the most pristine environments, where human occupation can imprint irreversible changes, oﬀers a natural laboratory where minimal impact building strategies can be tested, oﬀering a unique opportunity for designers and engineers. Therefore, such evolving relationship should be observed, described and documented.

A similar effort is carried out by the Swedish Royal Institute of Technology’s Division of History of Science, Technology and Environment, where its Polar Research team is dedicated to, among others, understand the value of industrial heritage sites in the Polar Areas for historical research, as well as the relationship between Polar field stations and Culture, heritage, governance. Furthermore, they proposed that ‘Field stations are inseparable from polar research. They have also served as flag carriers, symbols of political, diplomatic and economic ambitions of the nations of their founders. They remain a surprisingly neglected element in the study of the creation of scientific knowledge, and in relation to science, diplomacy and geopolitical conflict and cooperation’ [62]. It could also be added that Polar infrastructure represents a portrait of the current engineering and technology scenario. However, in the case of Antarctic and Subantarctic areas, no reflection on this matter is to be found.

Although all the cases presented diﬀer largely in size, geometry, materiality or structural and construction scheme, a shared criteria can be acknowledged, which is the beneﬁts of using minimal structures in the most inhospitable environments. This principle is not only in line with the current environmental agreements adopted by the Antarctic community, but also, as highlighted above, has been the natural solution from the original inhabitants of the southernmost regions. It is in this statement where the major contribution of this study is found.

70 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

A second feature particular to lightweight Antarctic structures is their temporary character. Almost all the cases described above, including structures implemented as permanent facilities, provide successful experiences of no-footprint retrievals rou- tines. Therefore, it can be stated that reversibility is a fundamental attribute of modern and vernacular polar (and subpolar) structures, and this is achieved by bespoke approaches. It could certainly be argued that portable architecture has been explored for more than half a century. However, the design of Polar lightweight structures provides designers with a vast ﬁeld of new study areas that could be not replicated in any other context. For example Polar lightweight structures requires aspects of structural eﬃciency and collabsability to be integrated at the earliest stage of the design process. Furthermore, these aspects must be paired with constraints of limited transportation sources and minimally aided assembly.

Another common aspect observed in the majority of the projects presented is related to their capacity of variation. Perhaps the simplest strategy of variability is presented by the mutable configuration of field camps and indigenous camps, where the number of units varies according to the seasonal requirements. A second level of variability is presented by cases of aggregation. The Tehuelche dwelling allows different configurations: standing as only as a semi-hemisphere, aggregating two semi-cupolas (defined as the prototypical model Camisquela), or aggregating another less deep structure to the front of the hemisphere. The design of EPTAP also includes a similar strategy of variability by allowing the aggregation of semi- monocoque modules along the main tunnel, as well as the extension of the tunnel by the simple repetition of the set of arches and membrane segments. Similar operation is enabled by the Sastruggi Tent, where modules can be repeated along the three axes of the structure. The Shockwave tent also permits the variation between a vaulted and a double curved surface depending on the aggregation of the 2 type of trusses, with their proposal for Desert the Atacama corresponding to the first case, and the Antarctic case corresponding to a doubly curved surface.

Perhaps more complex examples of variability are related to those systems which allowed the adaptability in their conﬁguration. A good example of this is the Tehuelche tent, where the number of poles ranged from 9 to 18, allowing multiple sizing options of the dome, as well as the option of an ellipsoidal plan, by reducing the depth of the semi hemispheres. The curvature of the semi-cupola could also be varied, from a simply vaulted to a double curved surface, by varying the height of the nodes joining the membrane to the frontal poles. The Kaweshkar and the Yaghan dome is also believed to be able to vary in size although little study has been dedicated to that feature. The Shockwave tent also allowed the re-arrangement of the internal structure by relocating of the stereometric elements, although the impact of such operation on the global geometry could be debated.

71 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES

These diﬀerent strategies of variability aim to optimise the use of these structures, according to the diﬀerent seasons’ demands. Therefore, this feature is also related to the temporary character driving the design of Polar lightweight structure, which is not only required to be removed but also to adapt.

Nevertheless, and however positive the experiences previously presented are assessed, it should be remembered that they correspond to rather experimental models, with the obvious exception of the indigenous dwellings.

While this chapter has offered sufficient evidence for the recognition of Polar lightweight design as a paradigm, the following chapter introduces the second part of this research. This consists on a design-based study aimed at demonstrating that constraints derived from remote areas can serve for the design of innovative lightweight structures of more complex geometry and larger scale than currently seen, using the case of the Union Glacier Station as a starting point. The originality of such study is expected to prove the vast range of possibilities that this field can offer.

Chapter 3 is devoted to establishing the design criteria and the proposal of a novel design paradigm that guides this study.

72 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES Structural Characterisation of Polar lightweight Structures. e 2.70: Figur

73 CHAPTER 2. CHARACTERISATION OF ANTARCTIC AND SUBANTARCTIC LIGHTWEIGHT STRUCTURES Figur 2.71: e emtia hrceiaino oa ihwih Structures. Lightweight Polar of Characterization Geometrical

74 Chapter 3

Design Criteria

3.1 Introduction

This chapter describes the theorical agenda that guides the design-based study offered by this research. The objective of such exercise is to demonstrate that Polar lightweight design can serve to the development of novel paradigm and solutions. Chapter 1 described the context of this research, and presented a brief for a new medium scale summer-only station. This general criteria is summarised in section 3.2. Chapter 2 have provided evidence for the recognition of Polar lightweight design as a valid design field, by describing and categorising a collection of cases bespoke structural surfaces. To continue this narrative, this third chapter proposes to challenge the inefficiency of classical seasonal constructions by exploring the design of a lightweight structural surfaces to implement the Union Glacier Station. In order to that, such structural system such be resolved on a larger scale and with a more complex geometry than currently used, as it will be explained. Section 3.2 lists the criteria that this design-led study should incorporate in order to challenge currently seen Polar lightweight construction. These include commonly known problems related to the extreme polar context, as well as new geometrical aspects to be explored, this is, compactness and adjustable configuration. Based on this particular problem, a specific geometry-based paradigm is formulated in section 3.3. This problem consists on exploring the possibility of conceiving an adaptable yet semi-modular lightweight construction system for polar conditions. Evidence of cases that have resolved such paradox are briefly described in section 3.4. This chapter therefore, represents an inflection point in the narrative offered by this thesis, where a research question within the geometry-based design domain is formulated, which will guide the second part of this design-led study. As a starting point for the design-based study, an early scheme is presented in section 3.5 . This has been previously developed by the author, and although some of its

75 CHAPTER 3. DESIGN CRITERIA attributes can be considered suitable for the presented case, several others need to be further explored. Those missing aspects are described in this section and will guide the following study.

Finally, the method used to explore possible solutions is presented in section 3.6. Here, the structure for the design-based study is described, which involves optimisation at the global and at the structural level, and is developed in the following three chapters.

3.2 Design Criteria

Chapter 1 presented the context and the opportunity for designing an innovative station for Polar conditions. This design case-study will focus on a medium-scale summer-only research station in the Glaciar Union Zone Glacier in the Chilean Antarctic Territory. Apart from scientiﬁc and logistic facilities, this station should provide shelter for a variable number of crew. During winter, the station should remain closed.

The design criteria can be summarised and grouped as following:

In one hand standard constraints include:

1. Unaided assembly. The assembly procedure is to be carried out manually with minimal mechanical support and no electrical machinery available. As discussed earlier, harsh weather conditions require personnel to wear bulky items of clothing including gloves, for which manual deftness is expected to be highly reduced. In this sense, the structure’s components should be prefabricated and handleable by people unaided.

2. Straight-forward constructive sequence. The simplicity of the construction choreography relies on the avoidance of in-situ fabrication craft, in favour of standardised assembly procedures. It is essential to keep the number of diﬀerent bespoke components to a minimum. This condition, and the one above, is also critical for purposes of periodic maintenance and emergency repair.

3. Logistic constraints are placed on the weight and size of the structure’s pieces. While the cargo capacity of the available aircraft ﬂeet is rather large, the ﬁnal terrestrial conveyance will be executed by small capacity vehicles, for which components are required to be piled on standard pallets.

4. Collapsibility. The assembly procedure needs to be reversible, in terms of allowing relocation, partial closure (in preparation for winter) or complete

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withdrawal once the station has fulﬁlled it lifespan. In any of these cases, the no-trace or ‘temporary’ condition dictated by the environmental policies is required to be fulﬁlled.

On the other hand, some further aspects that this cases should include to overcome traditional designs are:

5. Adaptive conﬁguration. The construction system should permit multiple assembly options in response to a highly variable number of occupants during summer seasons, from a minimum of 5 to a maximum of 16, whilst in winter the structure is to remain unoccupied.

6. Eﬃcient organisation. The station should be planned and resolved as a unitary building, rather than a collection of facilities, minimising external transit and access points as well as the amount of surface exposed to the elements.

3.3 Geometric Scheme

This section develops a more detailed insight into the two geometric requirements to be integrated into the design proposal, these are, aggregation and adaptability, as described in the previous section. As this section describes, the ﬁrst of these features is explored in order to output some of the shortcoming observed in the existing summer-only ﬁeld camps, generally using lightweight units; while the second of these two architectural requirements tackles one of the main aspects that makes medium-scale seasonal facilities (as pointed out in Chapter 1).

3.3.1 Aggregation

Aggregation is one of the simplest operations to be carried out with geometrical unitary objects, in this case structural surfaces, where their composition (or topology) is not required to be common [63], but which are constrained by the need for common boundary edges.

In the case of polar design, the aggregation of units serves the purpose of an efficient organization by compactness. Compactness (C) is a simple geometrical property of objects, defined by the ratio of the surface area (Stotal) required to ‘wrap’ the volume engaged, V (C = V/Stotal). The level of compactness of a building is usually an indicator of its thermal efficiency, as the more surface exposed, the higher the tendency for heat to be lost to the exterior through conduction, assuming of course the external temperature is lower than the internal [64]. The compactness of a building can be compared against three different geometrical aspects: shape,

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Figure 3.1: Comparative diagram of a volume’s compactness. Source Ministry of Public Works, Chile conﬁguration and distribution [Fig. 3.1], with the same criteria applicable to vertical organisations.

In terms of geometric eﬃciency, this leads to the problem of maximum enclosure of volume with a minimum of area, which is mostly associated with curve shapes. From a structural perspective, single and double curved structures (such as spherical shapes) are also eﬃcient in terms of load bearing, since most forces are transferred in plane with the structure. This reinforce the statement that structural surfaces can be employed in a larger scale than currently done in remote areas.

Although unitary spherical shapes are commonly employed in temporary field camps, these facilities need to be re-designed and adapted each season according to the number of occupants. This requirement is usually resolved by adding independent units, each with a minimum compactness. Permanent seasonal infrastructure, like refuges or summer research stations, have frequently been designed with the same criteria, given the practicality of independent structure’s instalment. Figure 3.2 show three examples of settlements using lightweight structures, either with temporary or permanent use, in Antarctic, Sub-Antarctic and Patagonia regions respectively, and map their configuration using independent units, reflecting a rather scattered organization fashion.

There are several basic geometrical operations of 3D transformation that can deﬁne

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(a) (b)

(c)

Figure 3.2: Examples of arrangements for touristic settlement’s using lightweight constructions. (a) Toro Lake Lodging Torres del Paine National Park, Patagonia (b) Patriot Hills Field Camp, Antarctica, (c) Whalesound Marine Research Station and Lodging, Francisco Colane National Park. Source: various, undated. a surface by clustering or collecting repeated unitary elements, the most common being: translation, rotation, helical motion, reﬂection [65]. Examples of these could be: surfaces of revolution, 3D periodic and aperiodic tiling and some cases of ruled surfaces (such as cylindrical developable surfaces ) [65].

A particularly interesting case of aggregation of repeated surfaces is that of Triple Periodic Minimal Surfaces (TPMS). Minimal surfaces with crystalline structure are of great interest in the design field due to the architectural possibilities that their enclosures enable. There is a large number of fascinating TPMSs, many of them originally discovered by Alan Schoen in his famous report for NASA in 1970 [66]. Currently, there are several digital tools that allow the exploration of minimal surface definition and replication, most associated with generic design platforms such as Rhino’s components ‘Geometry Gym’, ‘Minimal Surface’, ‘Kangaroo’ among others [67]. Perhaps, the longest established and most robust digital environment for the exploration of minimal surfaces is ‘Surface Evolver’, a mathematical software tool developed by Brakke [68]. The software works by minimising different energies on constrained surfaces using a gradient method.

In Surface Evolver, TPMS are achieved by deﬁning and then optimising the fundamental unit of the geometry, which is then suitably transformed (displaced and rotated). Figure 3.3 shows a simple exercise of aggregation of TPMS using Brakke’s Evolver[68]. Toyo Ito’s Taichung Metropolitan Opera House in Japan and the

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(a) (b) (c) (d)

Figure 3.3: Evolution of the Schwarz’ P Surface using Surface Evolver. (a) fundamental region, corresponding to a tetrahedron before its evolution, (b) fundamental region once evolved, (c) one cubical unit cell, (d) same unit cell repeated four times.

Ingenhoven Architects’ proposal for a new Stuttgart Main Station in Germany can be considered examples of this principle applied in practice. In 2011, the author explored a method to allow the interaction between the Evolver and CAD environments, which proved feasible [Appendix A].

Chapter 2 identiﬁed two basic formats of building typologies widely used as polar lightweight structures, deployable and assembled, which are logically driven by their materiality and thus, to their geometry. Assembled structures are mostly related to rigid materials and synclastic shapes with deployable structures more often based on anticlastic fabric membranes. This study will explore a generative system where both types of components, rigid and membranes, can be aggregated to diﬀerentiate the station’s varying programmatic requirements. Similarly to the generation of TPMS, basic transformation operations will be employed in this study to produce aggregations.

3.3.2 Adaptability

Chapter 2 identified three different types of small-scale temporary facilities used in Polar areas: field camps, seasonal research stations and refuges, each employed with different rules. While field camps must be designed annually according to varying seasonal demand, permanent infrastructure (refuges and summer research stations) must cope with variable numbers of occupants (see Chapter 1), which can sometimes place a limitation on the size of scientific parties, or result in an excess of energy and logistic resources required to keep the station operative.

Adaptability, related to the responsive capacity of a system to vary its conﬁguration, is the key aspect that this proposal explores. This will allow temporary stations to be more eﬃcient in terms of permitting a partial or customized use, and will therefore reduce environmental impacts and unnecessary resource consumption due to maintenance, transportation and energy consumption when not fully operative.

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Figure 3.4: Prototype of the Figure 3.5: Prototype of free-form gridshell based on ‘Radiolaria Project’ (structural geodesic method developed by the Politecnico di Torino, tessellation of double curved sur- Italy. Source: IASS Journal. faces) developed by University of Kassel, Germany. Source: ECAADe.

In the current context of structural design, there are different approaches to geometric adaptability. Perhaps the most common is provided by means of parametric design methods. Adjustable modelling design tools have been widely explored in the last decade thanks to the development of interactive parametric design tools, such as Grasshopper by McNeel & Associates, Bentley’s Generative Components and Autodesk’s Dynamo. In addition to these generic software platforms, several third-party analysis plug-ins have been developed to provide real-time performance feedback in order to assist the design process at the earliest stage in different fronts such as structural performance, thermal behaviour, components definition and others [69]. The explorative combination of generic design tools and performance analysis tools allow a variety of design options to be explored simultaneously against quantitative and qualitative criteria by adjusting numeric parameters [69]. Surfaces capable of handling global adjustments to their geometry are generally used in cases of freeform schemes.

In the speciﬁc case of structural surfaces, their implementation generally is resolved using meshes (either triangular or quadrilateral) [Fig. 3.4 and 3.5], which in principle includes structural membranes.

Structural surfaces of complex and variable geometry are generally resolved as a grids using various subdivision methods wich components, either edges or panels, that tend to vary in size. This feature can be moderate, particularly when pre- or post-rationalisation methods are involved. Evidently, when geometric variations of such surfaces are applied, the number of different components increases greatly. The complexity of the assembly process of these types of structure (surfaces with free-form or complex geometry), makes the use of these systems unsuitable for remote areas. It is widely known that working with many different pieces which are difficult to visually distinguish from each other requires a refined assembling strategy. Assembly methods relying on manufacturing and/or delivery sequences generally proves abortive, as any delay or error made in either in the labelling, stocking or

81 CHAPTER 3. DESIGN CRITERIA construction stage can have serious consequences in the field. The repercussions are even more critical when working in isolated areas or in rough climatic conditions. Additionally, surfaces of complex geometry generally require highly skilled personnel for their erection, as well as sophisticated machinery. This means that although the use of a more complex geometrical scheme is required in order to allow the aggregation of components in multiple arrangements, the variability of said geometry should be carefully controlled. In this regard, Annex II offers a case-study where two very different gridshells are compared from a construction perspective. The paper, written by the author, describes the design and construction processes of a free-form temporary structure, namely the C-Space DRL10 Pavilion Project in London, and the triple-domed gridshell Weald and Downland Open Air Museum service building in Sussex. The paper discusses the radically different paths that the implementation of a structural surfaces might follow, depending on their geometrical origin, and highlights the contrasts in the fabrication and construction processes of both projects. It could be reasonably argued that traditional computational tools have been validated as suitable platforms for the control of information along the entire implementation process for at least the last decade. BIM technology (Building Information Modelling) in platforms like ArchiCAD® and Revit® are capable of assigning extra information to each geometrical entity that compose the building model [70]. Furthermore, new parametric design tools, like Bentley’s Generative Components® or Dassault Systèmes’ CATIA®, offer even more integrative environments for the development of complex shapes, the rationalization of their constructive components, and the assessment of their structural behaviour [69]. However, this exercise points towards a much more restricted approach, where the variations of a construction system should be provided by carefully constrained geometric operations. Another aspect of adaptability in the structural design landscape is demonstrated by responsive buildings. The aim of this extension to engineering and architectural design practice is to allow the measure of actual environmental conditions to enable buildings to adapt attributes such as shape, form, colour or other characteristics via physical actuators [71]. Using intelligent mechanisms, responsive buildings can be designed to interact with their environment in order to optimise their energy consumption (such as climate adaptive facades) or to allow dynamic use of space by their occupants (such as ORAMBRA’s actuated tensegrity structures or MIT’s intelligent kinetic system) [72]. Early architectural exploration of adaptive structural systems in the mid 1960’s slowly began to struggle due to the lack of computational and structural systems sufficient to allow the exploration. By the 1980s the discipline had been transferred into the domain of engineering and nowadays engineering solutions for adaptive

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Figure 3.6: Prototype of one the variations of the ‘Eccentric Umbrella Structure’ based on the Locust hind wing developed by the Israel Institute of Technology. Source: IASS. structural system are common. They include technologies such as active dampers, piezoelectric structures, actuated tensegrity and deployable structural system [73]. Applications of actuated tensegrity systems can be found within aeronautical, space and civil fields. Nevertheless, architectural design methodologies using this type of surfaces remain so far relatively unexplored [74]. A particular interesting case is the work of Tristan d’ Estree Sterk, who proposes the revision of Buckminster Fuller’s theory of tensegrity structures to produce a new class of adaptive structures [75]. Currently, digital parametric design tools are also progressing this field, with tools such as Formsolver [76]. D’ Estree Sterk suggests that the design of an actuated structure is not sufficent to produce a responsive structure, which can only be defined as such ‘when actuators are coupled with other devices so that activities and changes within the real world can be interpreted, computed or processes and then outputted back into the real world as an action or response’ [77]. This fundamental condition is the main restriction on the use of responsive structures in remote areas. Any type of perceptive device would not be compatible with the simple construction and operational conditions imposed by a polar environment.

Another limitation of these systems is their geometrical possibilities usually con- ﬁned to regular shapes. There are few incipient examples of mechanically actuated surfaces using more complex geometries to be found in the literature. An early example of this is The ‘Eccentric Umbrella Structure’, an asymmetrical deployable surface based on the Locust hind wing [78] and developed by the Israel Institute of Technology [Fig. 3.6]. Although promising, there is no major evidence yet of the scope of such deployable system and its structural and construction feasibility [73], which are critical aspect for its potential use in remote areas.

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Figure 3.7: Military base camp in Afghanistan implemented by Wheatherhaven ©. Image: Wheatherhaven, 2014.

3.4 Modularity versus Adaptability

While the main goal of the second part of this thesis has been introduced, this is, the development of an adaptable lightweight system constructed from a low number of diﬀerent components, the application of the conventional parametric design methodology has been discarded, as has the use of actuated structures, based on the limitations that a remote context imposes. Instead, this research investigates a bespoke approach, where elements are coordinated under a much simpler, if not low-tech, strategy.

The aggregation of units is an attribute of modular structures, due their strict dimensional coordination and lack of geometric variability [Fig 3.7]. A common example of this is the case of LEGO® bricks. Eilers established that there are 915,103,765 possible arrangements of using six 2x4 LEGO® bricks, defeating the classic belief of a limit of 102,981,500 possibilities [79]. Higher conﬁgurations remain unsolved [80]. Although trivial, if the same exercise is applied to a set of components of any structural surface with bespoke panels, for instance Figure 3.4, the possibilities are reduced to one solution. If the options of aggregating more components is consulted, solutions would then be inﬁnite versus none.

The constraints stablished for this particular case (Section 3.2) entails the integration of both these apparently contradictory approaches, (a system with adaptable geometry and a modular structure) in a single solution.

The author believes that if a compromise is established between the two approaches, a variety of solutions should be possible. These hybrid solutions should balance the conﬂicting concepts of modularity and adaptability. Is in the middle of this range where the design proposal is expected to be situated, which proposes a novel design problem.

In order to this, this exercise entitles the deﬁnition of a construction system whose attributes’ variations are constrained within a pre-established range of degrees of geometric freedom (or variation).

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Consequently, this design-based study will explore the possibility of conceiving a system in between these two opposite, if not contradictory, limits. This entails, in other words, the definition of a lightweight structure that allow a certain degree of geometry adaptability and at the same time is resolved with a limited number of different physical components. It could be suggested that parametric design has taken care of such a problem. As parametric CAD tools become more broadly used by designers, the differentiation between modular and adaptable geometries is often neglected. Parametrised models, leading to geometries defined by a series of geometric attributes, are often described as modular structures, due to the possibility of preserving the topology of the structure while locally adapting the geometric or physical attributes of the generic unit. Such adjustments can be made either manually, adjusting metric sliders, or automatically using optimization algorithms in combination with multi-objective performance criteria [69]. Many examples of this approach to modularity can be found nowadays. Agkathidis states that ‘the introduction of the module, as the main instrument of geometric and structural determination, becomes crucial. The module as a pre-architectural unit is not read as a multiplying identical object, but as a variable set of rules, which due to emerging CAD/CAM technologies is able to adapt, grow and transform into surfaces and complex geometries’ [81]. While this definition can be considered valid from a topological point of view, when a component-based approach is desired, as in this case, the variation of the geometric components’ attributes is incongruent with the fundamental idea of modularity. In other words, parametric geometry can be named as ‘modular’ only from a logical point of view, and dismisses the construction perspective.

Therefore, for this case, structures of adjustable geometry, including parametrised surfaces and modular structures, stand at opposite edges of the spectrum. It is the belief of the author that problem of realising an adaptable structural system resolved with a limited number of different physical components is a paradigm that has not been identified or explored sufficiently well.

As a first step, a group of case-studies were identified and are outlined below. The brief descriptions mainly refer to the degrees of geometrical freedom and possibilities of aggregations that their structural systems allow. The architectural concepts and technical solutions have been spared. In spite of the variety of solutions found, it is of interest to note how, in each case, different geometrical operations were applied in order to provide the variation of the system’s configuration.

Case 1: Teniente Arturo Parodi Polar Station. This case has been described in detail in Chapter 2. It consisted of a 320 m2 lightweight structure located in Patriot Hills (82°S) designed and built by ARQZE at the UTFSM (Chile) in 1999 [21].

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(a) (b)

Figure 3.8: Construction phases of the EPTAP (a) ﬁrst stage in1999, (b) second stage in 2000, included an attached Sastruggi structure. Photo: P. Serrano, undated

The main structure consists of a membrane tunnel supported by steel arches, and secondary structures can be attached along its main axis [Fig. 3.8] such as standard semi-monocoque plastic cabins or the bespoke designed ‘Sastruggi tent’ (see section 2.6.2). This last one was also designed as a modular structure that can be replicated along any of it three axis.

Regarding the adaptability of the system, it is possible to extend the structure along its principal axis by the simple repetition of the set of arches and the pieces that form the doubly curved membrane. Evidently, the curved plan shape of the tunnel, due to the radial distribution of the arches, is itself the main constraint in terms of geometry. The effect of wind load applied in different directions would be a structural constraint to be considered. Additionally, multiple configurations could be obtained from the attachment of different modular units along the tunnel. In this case, the design stipulated all the ‘igloo cabins’ be attached on the downwind side of the tunnel, to keep them protected from the thermal ‘convective’ effects induced by the wind. Due to the modular nature of these cubicles and the adaptability of the ‘plug-in port’, they could also be oriented in different directions, as Figure 3.8 shows.

Another interesting feature is that it was designed to permit the aggregation of components with diﬀerent materiality (structural fabrics, plastic panels) and geometry (single- and doubly-curved elements). Evidently, the radial distribution of the tunnel, conceived in response to the dominant wind direction and to enable the accumulation of snow on the upwind side of the structure, is its main geometrical limitation for it used as a generic structure.

Case 2: Jotabeche Glacier Monitoring Station. This project is a variation of the classic semi-monocoque structure (see Chapter 1), this time for a desert climate. It was designed and built by the ARQZE Research Unit, University of Technology F. Santa Maria (Chile) and Faculty of Engineering, University of Magallanes (Chile)

86 CHAPTER 3. DESIGN CRITERIA for the Glaciology and Snows Unit of the Chilean Ministry of Public Works in 2009. It was placed in the Nevado Jotabeche (27°S 69°O, 4.700 above sea level.). In its original conﬁguration the station had a ﬂoor area of approximately 18 m2 and capacity for 8 people [82]. The structure was designed following a component-based approach [83], which enabled its transportation, assembly and eventual disassembly without any impact on the site [Fig. 3.9]. Transportation included the use of helicopters, mountain vehicles and animal traction (donkeys), which needed to be incorporated into the design.

Figure 3.9: The Jotabeche Station. Photo: P. Serrano, 2009.

The adaptability of the structure is related to multiple features. Firstly, the steel platform is not only capable of coping with the irregularity of the soil due to a manual levelling system with a variation of up to 50 cm, but also the embedded foundation system can be changed depending on the diﬀerent soil conditions: ﬂat strip footings for sand and snow, crampons for ice and shoes for rocky soil [Fig. 3.10] Internal sub-divisions are achieved with the installation of plywood panels. This allows the Jotabeche station to have a separate space allocated as a toilet and a second space dedicated to the production and storage of water.

Figure 3.10: Alternatives of variations of the anchor system, from left to right: plates for snow and sand, crampons for rock, and shoes rocky soils. Image: A. Veliz, 2009.

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A deployable membrane can be attached to the two ends (Figure 3.9 only shows a membrane attached to one end) permits the eventual extension of the refuge by adding more of the same components (panels and base platform). The inner space can also be easily modiﬁed by attaching or removing division panels without aﬀecting the fuselage due to a simple bolting system.

This simple design strategy proved successful, as a second station was commissioned by the same institution, this time for use in the Northern Ice Field of Chilean Patagonia (47◦S) [28]. In this case a larger space was achieved by using 12 panels [Figs. 3.11 and 3.12].

A component-based design approach proved adequate for an adaptable semi-monocoque structure located in a remote site, where a limited set of features allowed a certain degree of design freedom. The limitations of such geometry are obvious, due its linear arrangement. More complex conﬁgurations of this type are represented by cases such as Weatherhaven modules [84] [Fig. 3.13] and Igoo Cabins (see Chapter 2), which use connecting sleeves and panels deﬁned as part of a sphere’s for expandable arrangements.

Figure 3.11: Assembly test for the Echaurren Figure 3.12: Conﬁguration of Glacier Monitoring Station. Photo: P. Serrano, components for Echaurren Station. 2010. Image: A. Veliz, 2009.

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Figure 3.13: Polar settlement using Weatherhaven modules. Source: Weatherhaven.com, 2015.

Case 3: Panul Warehouse and Shed. This project was built in 2004 by the WAR Applied Research Oﬃce for a private company which commissioned the construction of a warehouse (410 m2) and a large shed (2140 m2) for aquaculture production [Figs. 3.14 and 3.15]. The structures were located on an inhabited area in Coquimbo Province, northern Chile (29°S).

Figure 3.14: Panul Warehouse. Image: D. Figure 3.15: Panul Shed. Image: D. Rosenberg, 2004. Rosenberg, 2004.

The design team had to cope with the fact that only two materials were available for construction: standard polycarbonate sheets and pine wood planks. This condition raised the opportunity for a variable design and build process based on modular pieces and material tolerance. The Architects described the project as an opportunity to “highlight the value of designing a construction strategy, allowing the creation of form rather than predeﬁning it” [85]. Consequently, the design took into account the way in which the structure was going to be built, and at the same time, the building process could be fed by a preceding simulation and manipulation of the shape [86]. As a result of the development of such an adaptable construction

89 CHAPTER 3. DESIGN CRITERIA process, certain aspects of the building’s shape could be manipulated and variations could be generated.

The adaptability of the design was demanded by two diﬀerent constraints. The warehouse needed to be rectangular front and back to allow a complete sliding displacement of the facade, required for the transportation of production equipment (water cisterns). It was therefore decided that three pin-joint frames could provide the geometrical variation of the volume, from a double-pitched roof at the centre, changing to a ﬂat roof at the edges [Fig. 3.16]. On the other hand, the shed needed to coincide with the irregular morphology of the terrain. Thus the structure was resolved as two displaced rectangular pavilions with double-pitched roofs presenting a break in the central faces so opposite wings gradually rotate until they meet each other [Fig.3.17].

Figure 3.16: Geometric Figure 3.17: Geometric scheme for Panul shed. scheme for Panul warehouse. Image: M. Alonso and D. Rosenberg Image: M. Alonso and D. Rosenberg

With this in mind, a modular strategy was chosen for the implementation of these two structures, using two components - conventional wooden trusses and warped plastic sheet. The design process was intrinsically based around these components, their dimensions and the relation between classes of components. Therefore, rela- tional rules that allowed the change in position between identical constructive units

90 CHAPTER 3. DESIGN CRITERIA were the starting point for the design. The position of the trusses was ﬁxed by pinned joints with only one degree of freedom, rotation. The tolerance of the materials, in this case the warping capacity of standard polycarbonate sheets, was considered as the limit for the gradual ‘distortion’ of the shape. This mechanical characteristic was used to establish a relationship between the polycarbonate and the variation of the wooden trusses. Articulated joints were placed on the trusses and steel joints were placed on each foundation and between each pair of trusses, in order to allow the rotation of these elements.

As geometric variations lead to a wide range of structural conditions (from optimal stability up to collapse), the constructive units were identical and designed for strength in their most critical position. The geometrical deﬁnition for the gradual variation in the position of the components was estimated using conventional CAD design tools [Fig. 3.18 and 3.19].

Figure 3.18: Front view, progression of the Panul warehouse’s components. Image: M. Alonso and D. Rosenberg, 2004.

Figure 3.19: Front view, progression of the Panul shed’s components. Image: M. Alonso and D. Rosenberg, 2004.

If required, both structures could be unassembled and re-configured in many other ways as a response to different conditions of use or context. Consequently, all the parts were pre-fabricated, transported to site and assembled un-aided by mechanical machinery. Again, this strategy facilitated the implementation of the project which would have been difficult using traditional construction processes.

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Case 4: The Grotto Project. This proposal was the Aranda/Lash Architects’ entry for the 2004 Contemporary Art Centre and The Museum of Modern Art in New York annual design competition, the ‘Young Architects Program’ in association with Arup AGU.

Figure 3.20: Model of the ‘Grotto Project’ developed by Aranda and Lash in collaboration with ARUP. Source: ‘Tooling’, 2007.

The competition required the design of a temporary pavilion in New York for the summer music and architectural event ‘Warm Up’ [87]. The Grotto design tried to resemble the classic artificial Victorian grotto structure, usually installed in gardens to resemble a cave [Fig. 3.20]. The structural unit of the grotto is a boulder, which like a brick can be stacked, but unlike the brick, each boulder is a different shape [87]. Due a restricted budget, the designers could employ only four different boulder types, and replicated each of them 60 times (240 builders in total). The challenge was to develop a set of modular boulders that could be combined in a way that would defy a conventional sense of order [88, 87]. The solution involved a combination of algorithms developed by Arup AGU to transfer the modularity from the Danzer tiling technique to a set of four faceted boulders [89].

It is well known that there are many plane-filling 2D tiling techniques, but only a few non-trivial three-dimensional sets of space filling bodies. Danzer’s work proved successful at defining a set of prototiles that, according to some matching conditions, preserved the quasiperiodic symmetry attributes of the Penrose tiling, and was therefore considered a 3D analogy of Penrose tiling [89]. This set of prototiles consisted of 4 tetrahedrons, named the 4 Danzer prototiles (A, B, C, K respectively) and they were selected from a group of fifteen tetrahedra which originated from the platonic icosahedron [89]. The set of tetrahedra are shown in the first column of Figure 3.21. Each of these ‘prototiles’ can be successively subdivided into a set of smaller versions of themselves under very specific rules of adjacency.

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Figure 3.21: Danzer tillings. The r tetrahedral of the Danzer Tiling are shown in the right column. The second and third column show a top and bottom view respectively of the set in their ﬁrst iteration, and the reordering of the vertices that their subdivision produces. Source: Charalumpous 2007.

The iterative nature of these prototiles was used by Shea and ARUP’s AGU, who carried out the computational implementation of the Grotto, to create the shape grammar formalism used in the Aranda/Lash tiling project [90]. Briefly, in order to define a set of space-filling boulders, the Type K Danzer Tile was carried to the seventh generation. This arrangement consisted of 11,382 tethahedrons whose

93 CHAPTER 3. DESIGN CRITERIA vertices were then translated into a cloud of points. Such a set of points was used to deﬁne the bisectors from where a cluster of 3D Voronoi cells was originated.

An inspection of this aggregation of Voronoi cells showed it could be constructed from 4 different boulders that not only preserved the space filling property of the Danzer prototiles, but also retained its modular property by sharing facets [Fig. 3.22]. Once identified, this set of boulders (named Boulder, Eraser, Plug and Monster by the team) had their individual ability to form clusters, which showed an overall non- repetitive pattern [87].

For the implementation of the architectural brief, a reverse design technique was necessary. That is, the Grotto model was designed by ‘excavating’ or extracting units out of an original cluster, as opposed to construction an arrangement from the ground up. This was due to the intrinsically modular nature of the boulders and their inherited rules of adjacency. The creation of an arrangement out of the set of 240 boulders, would simply end up in ‘dead-ends’, where a tile would be broken or gaps impossible to ﬁll with the given set of components would be produced. The boulders were fabricated out of Expanded Polystyrene Foam (EPS) cubes. Given that most of the spaces in the Grotto involved purely compressive structure, the majority of EPS boulders could simply be glued together. Only few of them, located at larger ‘vault-like’ spaces, required steel reinforcement [87].

Figure 3.22: Design process of the Grotto’s modular boulders. From left to right: Danzer tiling developed by Arup AGU, Danzer ’K ’ tile after seven generations, Conversion to a 3,066 points cloud, Boulder cluster formed by four components, Set of boulders named. Image: Aranda/Lash Architects, 2005.

3.5 Design Scheme

While the previous section has presented solutions to general architectural problems, this section provides a starting point for the design of an adaptive structure speciﬁcally for Polar conditions.

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Figure 3.23: Design proposal for a kayaking station on an isthmus on the North coast of Navarino Island.

Figure 3.24: Three geographic milestones on north coast route were selected for the kayaking circuit at Navarino Island, a harbour, an isthmus, and an islet.

This design study was carried out by the author in affiliation with the Technology F. Santa Maria University in 2006. The study defined a generic constructive system capable of adapting to different terrain morphologies, to be used as a series of kayaking stations along the so-called ‘Scenic Route’ [91], on the north coast of Navarino Island (54°S) [Fig. 3.23].

The resulting system was expected to be placed at a number of locations at natural milestones along the route [Fig. 3.24]. A constraint-based scheme was used to resolve each station, based on minimal programmatic requirements and the natural characteristic of the terrain at each station [Fig. 3.25].

As this route is inserted into a natural reservoir, the Cape Horn Biosphere Reserve, minimization of any possible environmental impact was essential. In addition, the development of a tectonic language that could mimic each site’s morphology of the terrain was considered for the architectural scheme [Fig. 3.26]. These two conditions required a structural lightness as well as geometric variability.

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(a) (b)

(c)

Figure 3.25: Three geographic milestones selected for the kayaking circuit at Navarino Island: (a) a harbour, (b) an isthmus, and (c) an islet.

Figure 3.26: Architectural scheme of one of the three stations of the circuit, the isthmus- station.

96 CHAPTER 3. DESIGN CRITERIA

(a) (b) (c)

Figure 3.27: Deﬁnition of the three set of arches for the station in Navarino Island (a) complete arches, (b) half-arches and (c) asymmetrical arches. Images: J. Bak, 2006

(a) (b)

Figure 3.28: Two diﬀerent enclosures at the Navarino Island Kayak Station, implemented from two diﬀerent set of arches, (a) changing rooms employs complete arches; (b) storage room, as a semi-opened area, utilize half arches. Images: J. Bak, 2006.

The structural scheme was resolved as a membrane structure, supported by a set of ﬂexible arches, and a double bracing system composed of a combination of a structural membrane and tensile cables.

The ‘ﬂexible arches’ were grouped into three categories: complete (or symmetrical) arches, semi-arches and asymmetric arches [Fig. 3.27]. This diﬀerentiation responded to the necessity of both closed and semi-open enclosures within a same station [Fig. 3.28].

Each group of arches was deﬁned within a range of size variation. In this sense, arches forming each individual structure could be progressively varied in high (restricted by ergonometric constraints). On the other hand, each set of arches needed to have a uniform width in order to make the cable bracing system possible (as described below). In the case of asymmetric arches, this condition also required the position of the point of inﬂection to be the same for the whole array.

As for the structures composed of semi-arches [Fig. 3.28(b)], the inclusion of a rigid trussed arch (from now on called boundary arch) was necessary, as a supporting element for ﬂexible spanning arches forming the open side. As shown in Figure 3.29, these supporting elements could be located either at the front or the back of

97 CHAPTER 3. DESIGN CRITERIA

(a) (b)

Figure 3.29: Two semi-open structures being supported by trussed arches, (a) storage room with frontal face open, (b) semi-covered public stands with the back open as it fallows the natural shape of the hill.

Figure 3.30: Lateral supporting trusses. Image: J. Bak, 2006.

98 CHAPTER 3. DESIGN CRITERIA

Figure 3.31: Cross-shaped pins joining the four ﬂexible bars which compose a ‘primary arch’. Image: J. Bak, 2006.

Figure 3.32: Cross-shaped pin joints serve also as a support for the two bracing systems: tensile cables, supported with a plaque, and PVC membrane hanging from a fasten buckle system. the structure. Additionally, each structure was provided with lateral restraint by including a boundary arch at each end [Fig. 3.30]. Once again, the shape of these lateral supporting elements was not justiﬁed from a structural point of view.

Material was removed from the flexible arches by replacing a single, solid cross- section with four flexible standard carbon-fibre bars. In this way the arches were efficient not only in the amount of material used, but also because of the four bars were tightened together at both ends , reducing the number of supports embedded on the ground. This last feature constituted a major construction benefit under harsh environmental conditions. The structural behaviour of the flexible arches’ optimised geometry was once again not analysed in detail. The four bars were fixed with aluminium cross-shaped pinned joints [Fig 3.31].

At the same time, these elements were also designed to provide a fastening point for the tensile cables and buckles holding the PVC membrane, as shown in Figure 3.32. There was no estimation of the number of diﬀerent joints necessary in order to achieve all the diﬀerent sections required by the system. Membrane segments could easily be resolved as rectangular pieces, since adjacent faces should have the same length [Fig. 3.33], although no proper patterning analysis was carried out.

The cable bracing system was deﬁned using the same principle of triangulation as geodesic tents, which supposes the formation of a regular triangular grid [Fig. 3.33].

99 CHAPTER 3. DESIGN CRITERIA

Figure 3.33: Rectangular pieces of PVC fabric forming the membrane. Images: J. Bak, 2006.

Figure 3.34: Regular triangulated grid Figure 3.35: Equally degree distribution bracing the structure. The image also shows of joints along the arches. Images: J. Bak, the radial distribution of the arches on the 2006. ﬂoor.

Initially, this grid was formed by two perpendicular sets of continuous cables attached to the arches [Fig. 3.34 and 3.35].

The desire to have a regular grid of joints was challenged by the fact that every arch had a diﬀerent length, therefore placing joints at equal distances was not a solution. Instead, the joints were positioned at equal angles around the arches, as measured from the centre of the arch [Fig. 3.34]. Hence, each arch had the same number of joints, enabling cables to be connected on a ‘consecutive-position’ fashion along the set of arches. This lacing scheme is shown in Figure 3.36, where arches are represented by black line segments, with nodes numbered according to their position, and the two reciprocate set of cables and highlighted and blue and red. The starting point of the lacing are represented by arrows.

It was established that the arches should be constrained to have the same width (or span), due to both the need to allow a radial distribution on the plane (preventing arches to overlap onto each other), as exempliﬁed in Figure 3.35. It was also believed that this condition was necessary for the uniformity of cables’ triangulation. However, the arches’ height (thus, the length) could vary progressively.

Nevertheless, the implications of having a variable width for the system’s structural

100 CHAPTER 3. DESIGN CRITERIA

Figure 3.36: Scheme for set of reciprocate bracing cables. and cables’ geometric continuity were not surveyed. For instance, this characteristic would imply that every arch is defined with a different geometry (or arches can be defined as a set of semi-circumference’s segments, each of them with variable degree of curvature) which imply that each arch would perform in a differently fashion. These assumptions are questioned and reviewed in Chapter 4.

As pointed out in Chapter 2, the absence of cable net structures in polar and subpolar region can be explained due to the diﬃculty to assure a constant tension under extreme conditions and the technical complexity of their installation process. In order to overcome these complications, this scheme proposed that cables should be instead conceived as discontinuous segments installed in a zig-zag fashion between two consecutives arches. Figure 3.32 illustrates an early proposal for the joint where two discontinuous cables are attached.

The use of discrete bracing elements contributes to both, facilitate the assembling procedure and to assure the feasible maintenance or repairing of the structure.

The behaviours of this discrete elements should be no diﬀerent than a net formed by continuous elements, as long as the regular triangulation principle is preserved. This feature was sustained in the new version of this system.

Anchorages were designed to receive the four ﬂexible bars of the primary arches, as well as coping with a rocky soil condition [Fig. 3.37]. The type of soil originally considered was subject to the phenomenon of gelifraction on its upper layer (approx-

101 CHAPTER 3. DESIGN CRITERIA

Figure 3.37: Anchorages designed as ties and supports for ﬂexible arches. Images: J. Bak, 2006. imately 300 mm) and so the anchorage was designed to penetrate to a depth of 400 to 500 mm where a permanently frozen soil (permafrost) could provide stability.

Consequently, the versatility of this system, capable of handling a wide range of different shapes, is achieved by coordinating its different set of components. Thus, two groups can be recognized: standard components including flexible bars, tensile cables, heavy-duty buckles and anchorages; and a second group of customized elements which compromises joints, membrane segments and trussed rigid arches. Given this second group, the modularity of the system can be questioned, for which its classification can be instead considered to be closer to a free-form approach.

There were several features of this system that made it suitable for the purpose of a semi-modular lightweight construction system. However, there were still a number of unexplored aspects which needed to be addressed. These can be listed as following:

1. Materiality of the components.

2. Structural feasibility of the ﬂexible arches.

3. Structural feasibility of the rigid boundary arches.

4. Geometrical variations (maximum and minimum spans).

5. Design of structural components.

6. Minimum number of nodes necessary (without increasing the number of different components or aﬀecting the continuous bracing system).

7. Other possibilities of aggregation apart from axial extensions.

8. Definition of the number of different components necessary for the multiple configurations required.

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3.6 Design Method

The design process of an adaptable construction system with a controlled number of diﬀerent components is interconnected procedure rather than a linear one as the following chapter will show.

When working with the design of structural organisations, optimisations can occur in both architectural and engineering domains [16]. As pointed of by Bechthold, modiﬁcations at the global level (usually within the architectural domain) can involve choices of main surface type, span, proportions, orientations, and aggregations. While optimising the surface itself entails the detailed design of its constituent elements, choices are related to detailed studies of the surface support and properties, choices of membrane versus shell, surface thickness, reinforcement, pre-stress and optimization of curvature and edge conditions [16]. The design process presented in this thesis involves a dialogue between aspects of both accounts. Criteria gained from the literature review related to Polar structures served in the decision making at several stages of the design process.

3.7 Conclusions

This chapter proposed a transition in the narrative of this research. Whilst the ﬁrst two chapters have identiﬁed the particularities of the Polar built environment and presented a digest of bespoke lightweight structures, this chapter proposes such a domain can also be consider an inspiring design paradigm, from which innovative design solutions can be explored.

Furthermore, this chapter has set the initial conditions, including design criteria and an early architectural scheme, to develop the Union Glacier station. This case will be use to challenge and to further development the typologies of Polar lightweight structures so far realised.

It was established that this endeavour requires the exploration of a construction system with a more complex geometry and at a larger scale than currently seen, one which is capable of performing under extremely severe Antarctic conditions.

In order to achieve this, two key aspects must be incorporated: adaptable conﬁgu- rations and compactness.

This chapter has also shown that when logistic and environmental constraints are incorporated, a novel paradox arises, which consists of the design of a lightweight system capable of allowing multiple conﬁgurations whilst using a restricted number of diﬀerent components. Such a paradigm was endorsed with the examination of

103 CHAPTER 3. DESIGN CRITERIA case studies that achieve such a condition. This chapter therefore, suggests that there can be many different design strategies to develop a constructive system which allows the variation of a structure using a controlled number of different components. Strategies for geometrical variations range from a simple repetition of a module (case 1) and the two dimensional aggregation of a set of components (case 2), to the progressive distortion of a single construction element to produce irregular shapes (case 3) and the definition of a complex algorithmic grammar to produce a set of space-filling elements (case 4). Despite the variety of shapes and strategies, the condition of realising a generic system that could be demounted and reassembled in different configurations was fulfilled. Such variations can be derived from either programmatic requirements or from environmental features.

As most of these case studies demonstrate, the design process is supported by novel CAD methods. Nevertheless, where logistic constraints are imposed (such as human performance in extreme environments, load capacity of transportation systems, etc.), a much more controlled approximation to geometry freedom is required. Although parametric design platforms provide an environment for studies of the variation of generic structural surfaces with complex geometry; it is generally the case that the results would not meet the requirements of Polar design, given the large number of components that each variation requires or the lack of repeatability and technical complexity required for their implementation. Additionally, although actuated structures are starting to be seen in adaptive design scenarios, there is not enough evidence of their load bearing capacity in extreme cold, nor of the wide range of geometric possibilities required here. Similarly, free-form surfaces are high complex to design and construct, which makes them equally unsuitable for extreme environments.

Instead, it is proposed that for remote structures, modularity and geometric adaptability deﬁne a range, where hybrid solutions can be explored based on the logistic constraints imposed by the remote context on this case.

Consequently by setting the conditions this case, a novel design paradigm could also be deﬁned.

The chapter has also presented an early-stage scheme design for a structural system for use in remote environments. A number of improvements were identiﬁed in order to allow its use in a Polar context, and the following chapters address these challenges to demonstrate the feasibility of such modular-adaptive hybrid concept. A methodology to address these challenges was also presented, highlighting two main characteristics that suggest the novelty of such an approach, namely the competition between modularity and adaptability, and the necessity of integrating both geometrical and engineering domains.

104 Chapter 4

Nodal Forces Method and Structural Com- ponents Design

4.1 Introduction

This fourth chapter initiates the second part of this research, which focuses on the design of an adaptable lightweight construction system for polar areas under a strict logistic-based approach. This study will oﬀer an example of how criteria derived from a remote context can inﬂuence the design process and furthermore guide a novel design method.

The study uses an early design scheme previously developed by the author, presented in Chapter 3, as a starting point. The further development of the scheme into a lightweight structure suitable for Polar conditions demands the deﬁnition of a design strategy that can balance the competition between a modular practical design and an adaptable conﬁguration (see Chapter 3). The solution of this paradigm, constitutes one of the core contributions of this research.

There are certainly many computer aided design platforms capable of manipulating quantitative information related to constraint-based design. However, the main focus of this design-driven research is not the development of advanced software design tools, nor the optimisation of the design process. It is however, to investigate how polar-derived criteria can inform and guide the design narrative in which, either traditional or advanced design resources can contribute. In that sense, the conceptual structure that guides the variation study for a ‘semi-modular’, yet adaptable, lightweight structure is presented in this chapter.

This study by design has been broadly organised into three parts: a sensitivity study (Chapter 4), a multi-objective study(Chapter 5), and a configuration study(Chapter 6). While the first, presented in this chapter, considerates different geometric features of the system’s components, the second, presented in the next

105 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN chapter looks at aspects of both structural and geometric optimisation in order to reduce the number of components and simplify assembling whilst still allowing geometric variability. However, some distance is kept from the classification since, as mentioned in Chapter 2, structural performance and geometric attributes are intrinsically related. Therefore, cross-referencing between both domains appears in both these chapters. The final part of this design study, Chapter 6, describes different possible arrangements for the system, the definition of its components and a proposal for its assembly sequence.

4.2 Sensitivity Study for a Single Trussed Arch

This chapter describes a set of studies conducted for the deﬁnition of the basic structural component of the proposed system, namely, a single trussed arch.

As explained in Chapter 3, the main limitation of the design scheme is the restriction on the arch’s’ width [Fig. 4.1], although the height was allowed to be varied (therefore each arch is defined by a circumference of different radius). It was initially believed that this restriction was necessary for the continuity of the triangulating bracing cables. However, a revision of such a statement showed that the variation of the arches span does not affect the continuity of the triangulation when the number of subdivisions is preserved [Fig. 4.2]. As Chapter 5 will show, this last restriction can also be subject to a controlled modification.

The variation of the arch span is a basic condition for the implementation of the Union Glacier Union Polar Station, where the required dimensions vary from 4 to 12 m.

Figure 4.1: Original subdivision scheme Figure 4.2: Second version for subdivision with restrained arch width. scheme with variable arch span.

The principle of this structural arch, like any other trussed component, is a series of slender lightweight bars forming a single robust element, whose resistance to vertical loads is provided by the global geometry of the arch, rather than the amount of

106 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN material employed. Flexible materials obtain their strength from bending, where pre-stress is applied.

However, the idea of continuous ﬂexible bars proposed in the design scheme was discarded at an early stage for multiple reasons:

i) The standard length of carbon ﬁbre bars range from 1 to 5 m [92]. Whilst the shortest version would imply an excessive number of joints, the longest version makes the transportation or manipulation unsuitable for a Polar context,

ii) Joints between bars would need and would be located at irregular intervals depending on the span of the arch. This would require an additional type of joint, while bars would still need to be ﬁxed to the cross-joints in order to stop them from sliding,

iii) The failure of one particular bar segment would require the replacement of the entire arch, therefore the whole system would be aﬀected.

To avoid such problems, segmented bars connected at the cross-shaped joints were considered.

The design of the arch was carried out by a sensitivity study, where multiple aspects related to the geometrical attributes were inspected independently by comparing the structural and construction eﬃciency of diﬀerent options. The arch’s attributes compared include: a) the global geometry of the arch, b) the shape of the joints, c) the number of nodes (or subdivision), and d) the depth of the arch’s mid-span point. Each of these steps will be described in this chapter.

Section 4.3 begins by characterising the main structural component, this is, a trussed arch of variable section.

Section 4.4 describes the analysis method used during this study. The challenge consisted in providing a sound method capable of handling a large number of CAD samples of a single trussed arch. These samples consisted on variations of a single trussed arch in which diﬀerent geometrical attributes were modiﬁed, to be later compared using FEM tools.

Section 4.5 describes the basic mechanical properties of the materials proposed for the main structural component. A brief reﬂexion on their use in extreme cold environments as well as on feasibility of the components productions, is also oﬀered in this section.

Section 4.6 described the method and standards used for the calculation of external loads, namely snow and wind. In this case, the challenge consisted on establishing

107 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN an accurate method for the application of distributed loads as nodal forces on each arch’s nodes, capable to be used in every diﬀerent sample produced.

Section 4.7 explains how results obtained from the FEM platform were interpreted, selected, and compared during this study.

Section 4.8 is ﬁnally dedicated to the comparative study of the variation of a single arch’s attributes. These include: variation study on the arch’s geometry (section 4.8.1), variation study for joint’s shape (section 4.8.2), variation study on the number of Subdivisions (section 4.8.3) and variation study on the arch’s depth (4.8.4). As a result, the main geometrical characteristics of the new version of a trussed arch are established. Finally, conclusions (Section section §4.9) focses on the sensitivity of a single arch’ structural performance to the variation of each of this attributes is identiﬁed, which will guide the following chapter.

4.3 General Characterisation of the Main Structural Component

The primary structural element of the semi-modular system presented in this study can be described as a trussed arch of non-uniform cross section, and it is presented in diﬀerent size versions. Regardless of these variations, this truss typology can be classiﬁed as a case of a Viernedeel truss form.

Figure 4.3: Vierendeel Bridge at Grammene, Belgium. Source: McGill University’s School of Architecture, undated.

The Viernedeel truss or frame is one of the most common typologies [Figure 4.3]. Its design and calculation method was established by Arthur Vierendeel in 1896 and it was ﬁrstly used in Belgium in 1902 as a bridge [93, 94]. This typology is characterised by an absence of triangular bracing elements and pin-joints. Instead, the Vierendeel girder presents rectangular voids and rigid connections.

In the Vierendeel conﬁguration, shear is transferred from the chords to the joints by bending moments and, and such moments are then transferred to the vertical

108 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN elements. Consequently, all components are subject to combined internal forces, involving axial, shear and bending forces. This is a key diﬀerence from the typical pin-connected truss, in which shear is transferred axially through diagonals members and all components are axially loaded [95].

The presence of bending in chords and vertical webs implies that all members require signiﬁcantly larger cross-section area compared to an equivalently loaded truss’s, even though diagonals are removed. As a result, a heavier frame needs to be employed when using the Vierendeel form of truss [95].

Furthermore, given that elements of the Vierendeel girder are subject of combined stresses, this is a statically indeterminate structure [96]. Thus, the required calculation method were considered laborious, and its feasibility, questionable at the time of its appearance. Such process can nowadays be aided by computational methods. Despite of the development of a more reﬁned calculation method and the development of the electric welding arc technology contributed to the local popularity of these system in the early 20th Century [95] (mainly used for short span bridges within Belgium), the use of Vierendeel system quickly declined by the mid Century.

Consequently, a general agreement about the structural efficiency of the Vierendeel actions has not been settled. The benefit of such configuration is instead given by its architectural possibilities, as it still represents a design solution for cases where expressions demands a rectangular grid of openings, such as building structures where large shear walls or diagonal elements need to be avoided due to the building’s functionality or aesthetics [95, 93].

In the case of the scheme presented in this thesis, the use of such typology is justified by the benefit of avoiding diagonal members in order to reduce the number of elements a minimum, as well as the necessity of a simplified assembly process. The characteristic effects on the Vierendeel form of truss on the arches’ mechanical behaviour are present in the case of this thesis’s scheme. These actions will be discussed in this Chapter’s Section section §4.7. Design solutions are discussed in Chapter 6 .

4.4 Method

In order to initiate the comparison study of the diﬀerent geometric attributes of an single arch, three aspects were predetermined: i) the initial geometry, for which a parametric CAD tool was employed, ii) the external load conditions, for which a nodal forces calculation method was used, and iii) the mechanical properties of

109 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

Figure 4.4: Adjustable parameters on single trussed arch.

Parameter Initial Value Unit a Radius of the semi-circumference 2 m b Separation of the 4 bars at the base (from centre) 2.5 cm c Separation of 2 vertical bars on the top (from centre) 7.5 cm d Separation of 2 horizontal bars on the top (from centre) 7.5 cm e Number of crosses (including supports) 17

Table 4.1: Parameters and Initial Values of a Generic Single Arch. the material considered. The ﬁrst two were deﬁned generically as they would be employed throughout the design study.

The study began reproducing the basic structural component, the single trussed arch, in a parametric design platform: Rhino 3D® Grasshopper®, a visual programming language application [67]. It is well known that there are many ways to construct one particular geometrical typology using a given parametric design platform. In each of them, geometrical components and their quantitative parameters can be structured differently forming a single directed acyclic graph model [69]. Even the simplest case, such as the one presented in this section, can be defined in numerous different ways. For Rhinoceros’ Grasshopper® users, these models are commonly referred to as definition. Although the detailed description of this particular trussed arch’s representation is unimportant, it is convenient for the study unfolding ahead to report the basic variables and attributes used by this simple model [Fig. 4.4 and Table 4.1].

This first definition was progressively updated according to the different stages of the study.

The interaction between the CAD model and FEM platform was initially carried out ‘manually’, by exporting the CAD elements as a single group of line segments into Autodesk® Robot Structural Analysis®. There, a number of conditions needed to be established before running the force calculation, including: the value of external loads, their assignment to corresponding nodes, materials properties, the type and

110 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN location of supports (given that this ﬁrst study was for comparison only, pre-stresses derived from bending were not included in these calculations).

The load cases considered included self-weight, snow and wind derived loads. The last two were applied as nodal forces on the lower nodes of each cross-shaped joint, in order to simplify the setting-up of models.

Relevant combinations of load case were included according to the Eurocode standards specifically the Danish national annex. [97]. The list includes linear load cases of Serviceability Limit State’ (SLS) and Ultimate Limit State (ULS), hence cases combined linearly. For structural design of systems with large deflections, a non-linear load case is most commonly used. Although for the purpose of this study, a linear set of load combinations was considered sufficient. Cases included are as follows:

Load Cases

1. Self-weight (Dead load)

2. Snow Loads

3. Wind Loads

Serviceability Limit State Load Combinations

4. Dominant Snow = 1.0 · (1) + 1.0 · (2) + 0.3 · (3)

5. Dominant Wind = 1.0 · (1) + 1.0 · (3)

Ultimate Limit State Load Combinations

6. Dominant Snow = 1.0 · (1) + 1.5 · (2) + 1.5 · 0.3 · (3)

7. Dominant Wind = 1.0 · (1) + 1.5 · (3)

Although in this case a very simple model was being studied, some diﬃculties presented by this method needed to be overcome. It is estimated than this operation was repeated over 100 times during the research (some other attributes were initially studied, but later discarded) and the method proved extremely time-consuming and susceptible to induced errors, particularly during the setting up of pre-analysis conditions.

Furthermore, the system’s design would be updated at each step of the study, according to the best option outputted by the FEM model results. Consequently, any error found at a given stage would imply the revision of the whole thread of

111 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

Figure 4.5: Parametric pipeline.

Figure 4.6: Geometry variations. options studied. Although the study was completed using this method, the presence of inconsistencies in some of the results and the diﬃculty of tracking down the cause of possible induced errors, suggested that a more ﬂuent interactive method between both platforms was required.

Therefore a second round of tests was conducted using a custom interactive software tool developed in collaboration with the Søren Jensen® Computational Design Group. This application could be defined as a scripting approach, and its objective was to produce the large number of models needed during the sensitivity study with a uniform method. Figure 4.5 shows the organisation of this software tool. The different geometry variations were created using a Grasshopper® model. The model was prepared to take multiple parameter variations and create all the possible geometry variants by cross-referencing the chosen input parameters [Fig. 4.6]. An initial assessment based on engineering judgement (value ranges identified by the previously manual method) was used to keep the number of possible parameter combinations at a reasonable level.

A custom C# component was used to reference the Autodesk Structural Analysis API (Application Programming Interface) and create the various FE-Models from the Grasshopper geometry [Fig. 4.7]. Wind and snow loading calculations were implemented in the parametric model and calculated based on the Grasshopper geometry. This loading was then added to the FE-models and relevant load combinations were created, as earlier detailed. Furthermore, cross-section geometry, support

112 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

Figure 4.7: Custom Robot API component.

Figure 4.8: Automatically generated FE-model. conditions and material properties were encoded. Each FE-model was calculated and the stress and deflection results written to a text file. All FE-models were also saved in a separate file for further investigation [Fig. 4.8].

The resulting output files were combined to a single file and formatted automatically by using Power Query for Excel©, to take advantage of Excel built-in functions such as pivot tables, filters and slicers to organize the data and easily compare hundreds of different geometry variations, as shown in Figure 4.9. The most critical models could be identified and studied in more detail within the Robot FE environment.

This pipeline resulted in a fully automated process where tedious manual tasks were eliminated, allowing the investigation to be more ﬂexible, extensive and less prone to errors. It was possible to add more geometry variations at a later stage and the results updated accordingly.

113 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

Figure 4.9: Presentation of results in Excel.

4.5 Basic Material Properties

The original scheme provided a general description of the possible materiality for the structure: a lightweight composite for the structural arches, aluminium for the joints and tensile fabric for the membrane [91].

The use of tensile fabric and aluminium as structural materials for lightweight structures has been extensively validated since appearance in 1920’s and 1970’s respectively [58]. Furthermore, some of the study cases shown in Chapter 2, have documented the successful use of the both materials in Antarctic environments.

In the case of carbon fibre/epoxy-resin systems, their mechanical behaviour under low temperatures is intrinsically related to its origin, and it is therefore also well- documented. One of the earliest studies was carried out by NASA [98], where uni- axial stress was applied to specimens with a quasi-isotropic fibre lay-up at a range of decreasing temperature using cryogenic fuels. In general, the study demonstrated no major effect with temperature on either tensile modulus or average tensile strength, and a rather modest increase in the matrix stiffness [98]. This idea seems to be generally supported [99, 100, 101].

4.5.1 Aluminium

Aluminium alloys are in general a good option for key rigid elements as in the case of the proposed joints, especially when compared to the obvious second option, steel. The advantage is mainly due to the inherent resistance to most normal atmospheric environments (it does not rust, suﬀer from corrosion, and self-heals when scratched) and also because of its lightweight nature, inherited from a low density (nearly a third of steel’s) [102].

In this case, lightness is an essential requirement for fast and easy installation. Power tools and machinery required for assembly can be considerably reduced by using a lightweight metal. This characteristic also allows non-traditional assembly methods to be employed.

114 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

Property Symbol Value Unit Modulus of Elasticity E 75 GPa Shear Modulus G 27.8 GPa Tensile Yield strength σy 120 MPa Shear Strength τ 72.28 MPa Poisson’s Ratio υ 0.35 Density ρ 2, 797 kg/m3

Table 4.2: Characteristic Mechanical Properties of Aluminium. Source: Autodesk Robot Structural Analysis, 2012.

Aluminium technology appeared in the 1940’s, coinciding with the development of the aviation industry. No other material with similar characteristics to aluminium could compete and so its manufacturing technology developed over a period of about 20 years [58], leading to production processes which are nowadays ﬂexible and reasonably aﬀordable. The use of bespoke or non-standard components is possible thanks to extrusion and casting methods. The fabrication of the joints proposed by the design scheme would require of this last manufacturing process given the bespoke geometry of this elements. Characteristic mechanical properties of aluminium are listed in Table 4.2. (Autodesk® Robot® Material Database):

The use of aluminium alloys at low-temperature has been extensively documented and successfully validated by the aeronautic and aerospace industries [103, 104, 105] and a class of structural aluminium alloys is used at temperatures as low as −270 °C. Aluminium does not undergo brittle to ductile transition, and therefore shows little change in properties under cryogenic temperatures. Whilst yield strength can show an increment, impact strength remains practically constants [104]. The main problem, however, is represented by the decrease on deformation, which is an inhibiting factor in industries that must consider public safety codes [104]. Such restrictions do not apply to this design scheme.

4.5.2 Composites

The presence of plastic composites in Polar lightweight structures remains restricted to commercial tents. Although they have proved reliable at a small scale, their employment in larger structures remains rather unexplored. Evidence of this material’s potential can be found in nautical sport products.

The knowledge and understanding of the advantages of composites as a structural material has developed only in the recent years [58, 106, 107] . In general terms, it can be said that fibre-reinforced materials balance the properties of the fibre to resist tensile and compression loads, whilst the matrix material, a polymer, transfers shear to produce a more efficient material [107].

115 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

In contrast to metals, the use of the specific properties of the material’s components permits a significant reduction of self-weight. Furthermore, the possibility of producing composites for specific purposes and with specific load-bearing capacity, enhances this advantage over traditional construction materials [58]. In general, design guides using composite materials are very conservative. They take into account a variety of possible failures, such as creep and creep rapture, fatigue, environmental degradation, etc. [108]. A general rule for design is to limit the allowable stresses, therefore:

For Glass Fibre Reinforced Polymer (GFRP), Maximum allowable Stress = 0.2ffv and, For Carbon Fibre Reinforced Polymer (CBRP), Maximum allowable Stress

= 0.55ffv With ffv as the strength parameter being considered [106]. However, the fast increase in the use of composite materials during the last decade has contributed to a better understanding of their fundamental properties and their long service life, enabling more speciﬁc uses. Consequently, security factors are therefore being reduced to less conservative levels [107]

A disadvantage of composite materials is their brittleness, particularly with carbon ﬁbres. For example, metal would undergo plastic deformation before braking, whilst composites on the contrary, either remain intact or break. Along with the high production cost, this remains as one of the main reasons for the slow introduction of such materials into the construction industry. Such diﬃculties have however been considerably reduced in the last decade [58].

While the author does not focus on contributing to the knowledge in the material’s properties, the general characteristics needed to be considered in the design, as there is a great ﬂexibility on the design in the material (plastic composite) matrix.

In general terms, the spectrum of possibilities for plastic composites would be defined between pure glass fibre, and pure carbon fibre reinforced polymer. In the case of glass-based composites, the maximum fibre volume is 70%. Most of the fibres will be in the longitudinal direction, while the rest are supplied as a random matt (CSM) on the external surface to provide robustness [106]. In the case of CFRP, fibre can be laid up in different orientation so the volume of fibre in each direction is lower, but a more isotropic material can be obtained [106]. The cost of GFRP is significantly lower that carbon-fibre reinforced plastics.

According to the Danish provider Fibreline ®, GFRP materials exceed the E23 grade. The following general properties can be achieved [107]:

116 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

Property Symbol Value Unit

Modulus of Elasticity (Longitudinal) EL > 23 GPa Modulus of Elasticity (Transversal) ET > 7 GPa Shear Modulus G 7.67 GPa Tensile Strength σt > 240 MPa Bending Strength σb > 240 MPa Shear Strength τ > 25 MPa Poisson’s Ratio υ 0.3 Density ρ 2, 0 kg/m3

Table 4.3: Characteristic Mechanical Properties of GFRP at room temperature. Source: [106]

Furthermore, according to Fibreline ® data for temperatures between −20 and 60◦C, GFRP achieves the following [107]:

Property Symbol Value Unit

Modulus of Elasticity (Longitudinal) EL 23 − 28 GPa Modulus of Elasticity (Transversal) ET 8.5 GPa Tensile Strength σy 240 MPa Bending Strength σb 240 MPa Shear Strength τ (not provided) MPa Poisson’s Ratio υ 0.37 − 0.3 Density ρ 2, 000 kg/m3

Table 4.4: Characteristic Mechanical Properties for GFRP between 20 °C and −60 °C. Source: Fibreline, 2011

For carbon ﬁbre reinforced plastics it should be possible to get at least 60% of all the ﬁbres in the longitudinal direction, therefore a value for longitudinal Young’s

Modulus (EL) of 130 GPa is considered possible. Significantly higher stiffness of the fibres can be obtained with bending strength (σb) and tensile strength (σt) developing values of up to 600 MPa. However, these properties would be associated with higher production costs [106].

The values presented for the structural materials will guide the sensitivity study described in the following sections. The initial comparative study considered the use of the cheapest version of composite, GFRP. However, it was quickly understood that under the expected load conditions, a much stronger version of ﬁbre composite was required, thus this option was replaced for CFRP. Aluminium properties remained constant throughout the design study, and the modiﬁcations made consisted of variations of the components’ geometry only.

117 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

4.5.3 Membranes

The use of tensile membranes as a structural material has been explored since the middle of the 20th century. Most common options include synthetic cloths, such as polyester, whose strength can reach up to 0.9 kN/mm2 [109]. Glass fibre cloths can develop much higher tensile strength, ranging from 2.8 to 4.6 kN/mm2 [109]. Coatings are also commonly added in order to improve waterproofing, durability, reduce dirt retention, and provide UV protection. Common solutions include polyvinyl chloride coated polyester (PVC), polytetrafluoroethylene (PTFE), Teflon-coated glass fibre, and silicon-coated glass fibre [109].

This is a well-researched topic and suﬃcient evidence is available to justify the use of tensile membranes in large-scale structures. Chapter 2 provided examples of its use in Antarctic environments. Given that its use for the design scheme presented in this research does not represent any new aspects to be explored, the structural behaviour of the tensile membrane in this case has not been studied in detail.

Perhaps another relevant challenge proposed by this design is related to the thermal conditioning of the station. Although thermal insulation of tensile membranes does not form part of this study’s scope, some eﬀective solutions have been suggested in some of the case studies presented in Chapter 2, speciﬁcally sections 2.3 and 2.6, both developed by ARQZE®. No data characterising the thermal behaviour of these materials in these two cases has been collected. Nevertheless, this problem suggests that novel solutions could be further investigated.

4.6 Calculation of External Loads on a Single Trussed Arch.

This section describes the method used to calculate external forces aﬀecting a single arch. A nodal forces method was employed, in order to accommodate the variation of diﬀerent components to be studied.

A set of diﬀerent tools were used for this calculation. Whilst external nodal forces were calculated manually, calculation of internal stresses, such as bending and axial forces, were made by exporting the CAD model into a Finite Element Modelling platform (Autodesk® Robot®), where external nodal forces were then added into the model.

As discussed earlier, two types of external loads were applied as nodal forces: wind (Case 1) and snow (Case 2). Since the action of distributed loads are summarized at the nodes, the length of the arch segments (distance between nodes) and gap (distance between two consecutives arches) had to be estimated. Self-weight was

118 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN calculated automatically by the FEM software, although the eﬀect of the structural dead load are minimal due to the light nature of the structure.

As a starting point, the minimal case of 4 m span was used, with a length of 6.28 m. This restriction was presented in Chapter 1, and it was based on a minimal height of 2m. The arch was subdivided into 12 segments, in this new version, containing 13 nodes and a standard distance between arches of 1 m. At each node, a cross-shaped joint was placed. Crosses at both ends were discarded, as they are to be replaced by pinned supports.

The following sections describe the calculation of wind and snow loads. The study follows the method indicated by the European Standards, speciﬁcally the Danish wind load standard [110] for wind actions and the Danish snow load standard DS/EN 1991-1-3: 2003 [111] for snow loads.

4.6.1 Load Case 3: Wind Derived Loads as Nodal Forces

Relevant factors for the calculation of wind Loads for vaulted roofs and domes are listed in Appendix B. As indicated by the Eurocode standard [110], the peak velocity pressure can be determined as qp = 0.21 kN/m2.

For a vaulted roof and when the condition that f/d = 0.5 is observed [Fig. 4.10], as in this case, then the values of pressure coeﬃcients are: ’

A = (0.8) B = (−1.2) C = (−0.4)

Figure 4.10: Geometric parameters on vaulted roof and domes for the valuation of external pressure coeﬃcients. Source: Eurocode standards, 2007.

The pressure coeﬃcients determined above is dependent on the position on the arch. The arch is divided in the the following ranges:

1 1 3 3 Range A: 0 to 4 l Range B: 4 l to 4 l Range C: 4 l to l

119 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

Where l is the length of the arch.

For this particular case the ranges are as follows:

Range A: 0 to 1.57 m Range B: 1.57 m to 4.71 m Range C: 4.71 m to 6.28 m

A simple way of calculating the forces applied to each node could be described by:

P = ldqpcpe

Where,

P is a point load acting perpendicular to the surface [kN] qp is the value of Peak Velocity Pressure value [kN/m2] l is the lenght of the segment between nodes [m] d is the distance between arches (standard value of 1.00 [m]) cpe is the correspondent form factor according to the node’s position along the curve.

Each of these nodal forces would then be decomposed into their Cartesian components. However, it must be considered that the segment assigned to one node could be part of two diﬀerent form factor zones, for which some of the nodes would be assigned with the incorrect nodal force. A parametric method was therefore developed, which could oﬀer more precise solutions, as explained in section 4.6.3.

4.6.2 Load Case 2. Snow Derived Load as Nodal Forces

Similarly, snow loads were calculated based on the method indicated by DS/EN 1991-1-3: 2003 (E), and then converted into nodal forces.

The most critical case of ground snow loads (sk) indicated in the standards corresponds to northern Finland, where snow cover can reach up to 120−150 cm in April [112], which is slightly lower to the case of Union Glacier (See Chapter 1). This value of ground snow load was then increased linearly by 20 % in order to simulate the Glacier Union case. The characteristic value of the snow load on the ground is therefore determined as:

sk = 1.2 · 3.9 kN/m2 = 4.68 kN/m2

120 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

Accordingly, for persistent/ transient design situations, snows loads (S) are given by:

s = µicectsk

Where, s is the snow load on the roof, acting vertically [kN/m2]

µi is the snow load shape coefficient (see below) ce is the exposure coefficient = 0.8 ct is the thermal coefficient = 1.0 (N/A) sk is the characteristic value of snow load on the ground [kN/m2]

As shown in Figure 4.11, the value of shape coeﬃcients is variable along the ‘vaulted roof’ and is dependent on its geometry. Snow load on a vaulted roof should be considered in two cases:

(i) Symmetrical blanket loading

(ii) Assymetrical loading (incl. drifting)

For case (i) the shape coeﬃcient is deﬁned as follows:

For β > 60◦,

µ = 0 for β ≤ 60◦,

µ = 0.8

For case (ii) the shape coeﬃcient is deﬁned as follows:

For β > 60◦,

µ3 = 0 for β ≤ 60◦,

121 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

Figure 4.11: Snow load shape coeﬃcient for cylindrical roof. Source: Eurocode standards, 2003.

2 µ = 0.2 + 10 · h/b = 0.2 + 10 · = 5.2 3 4

However, the recommended upper value for µ3 is 2.0 [111]. Therefore for cases where ◦ β ≤ 60 , then the shape coeﬃcient µ3 takes this last value.

As for this particular arch, signiﬁcant segments are shown in the following Figure:

(a) (b)

Figure 4.12: Calculation of curve segments for snow load factors.

The diﬀerent snow load values can be determined as follows:

Forβ > 60◦, µ = 0, then

s = 0.0 kN/m2

For β ≤ 60◦, µ = 0.8, then

s = 0.8 · 0.8 · 4.68 kN/m2 = 3.0 kN/m2

122 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

◦ Forβ > 60 , µ3 = 0, then

s = 0.0 kN/m2

◦ For β ≤ 60 , µ3 = 2, then

s = 2.0 · 0.8 · 4.68 kN/m2 = 9.36 kN/m2 for the highest peak of the asymmetrical trapezoidal load.

Again, the simplest way of determining the point loads would be to apply these load values, according to the node position along the arch, over the area assigned. In this case forces would act only vertically. Similar to the wind load case, this method can be considered to be imprecise, and an alternative method was developed, which is presented in the following section.

For the sake of this study only the symmetrical snow load case was investigated.

4.6.3 Calculation Method of Nodal Forces

The calculation of nodal forces was carried out via a parametric approach using Rhino’s Grasshopper©, where the resultant loads would react to the arch’s geometry.

Inputs required are: i) a curve, ii) qp (Peak Velocity Pressure value), and iii) sk (characteristic value of snow load on the ground). As a result, the Grasshopper deﬁnition outputs two lists of vector forces applied on each node. The approach for such application can be described as:

1. The arc is subdivided into a set of point lists (showed in Figure 4.13), which include:

∆ is the node points (ni), a point where a cross-joint is placed.

X is the midpoints between Nodes Points (∆).

is the division points between shape/pressure coeﬃcient ranges.

2. n number of arch segments (sn) is diﬁned by dividing the arch at ∆, X and .

3. The length (ln) of sn is calculated

4. The centre of sn (symbolised by ◦ in Figure 4.13)

123 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

5. The corresponding form factor (µn) is asigned to sn in relation to the position of ◦ along the curve. −→ 6. For wind loads, a unit normal vector ( n n) to the surface acting inwards is −→ calculated at ◦, for snows loads, a unit vector (0, 0, −1) is assigned as k .

7. Force magnitudes are calculated by:

Pn = lnwµnp

Where:

Pn is the force magnitude at the node [kN]

ln is the segment lenght of the nth segment in the case of wind loads and projected lenght in the case of snow loads [m]

w is the width (standard value of 1.0 m)

µn is the pressure/shape coeﬃcient of the nth segment.

p is the surface load [kN/m2]

8. Forces are calculated by multiplying with the unit vectors:

−→ −→ V n = Pn n n

for wind and,

−→ −→ V n = Pn k

for snow.

−→ 9. For each segment sn the closest node ni is found and the force V n is assigned to that node.

10. The total wind and snow loads can be respectively calculated as the sum of n forces assigned to the ith node:

−→ X P i = V n

or,

124 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

Figure 4.13: Set of subdividing points on an arc for the calculation of nodal forces.

−→ X −→ P i = lnwµnP n n

for wind case and

−→ X −→ P i = lnwµnP k

for snow case.

11. Nodal forces are discomposed into X, Y and Z components, in order to be used on a FEM platform. Nodes are identiﬁed in Figure 4.15. Nodal forces values are shown on Table 4.5.

4.7 Interpretation of FE Model Results

The different attributes studied are based on a geometric optimisation approach. Therefore, a predefined set of options was defined for each attribute, as the following section shows. This implies that such a method should not be realised as a ‘structural optimisation’ process, but a variation study, where the effect on the structure’s mechanical behaviour is observed and then solution negotiated with Polar-assembling criteria.

The main results were used to compare maximum and minimum values for displacement, deﬂection and internal stresses (normal combined stresses) for each case. Whilst attention was given to the possible origin of such critical values, the study does not seek solutions to reduce maximum load states, given that variation options

125 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

wnlnp Pi

ln w2l2p Vn ni nn sn l2

s2 k w l p 1 1 Vn l1

Formfactor B s1

n1 Projected length Formfactor A Figure 4.14: Diagram of geometric attributes for calculation of nodal forces.

Figure 4.15: Numbering of nodes in an arch.

126 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

Nodal Forces [kN] Case Node FX FY FZ 0 0.0 0.0 0.0 1 0.0 0.0 0 2 0.0 0.0 -0.55 3 0.0 0.0 -1.25 4 0.0 0.0 -1.63 5 0.0 0.0 -1.82 Snow load 6 0.0 0.0 -1.77 7 0.0 0.0 -1.82 8 0.0 0.0 -1.63 9 0.0 0.0 -1.25 10 0.0 0.0 -0.55 11 0.0 0.0 0.0 12 0.0 0.0 0.0 0 -0.04 0.0 0.0 1 -0.09 0.0 -0.02 2 -0.08 0.0 -0.04 3 0.01 0.0 0.02 4 0.07 0.0 0.12 5 0.03 0.0 0.13 Wind load 6 0.0 0.0 0.13 7 -0.03 0.0 0.13 8 -0.07 0.0 0.12 9 -0.06 0.0 0.06 10 -0.04 0.0 0.02 11 -0.04 0.0 0.01 12 -0.02 0.0 0.0

Table 4.5: Cartesian Values of Nodal Forces Derived from Snow and Wind on a 4[m] span Arch.

127 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

(a) (b)

Figure 4.16: Characteristic distribution of internal axial (a) and bending (b) stresses along a simply supported arch under compression for a symmetrical load case.

Figure 4.17: Combined normal stresses (S value) as the addition of axial and bending stresses throughout section 1-1’ for a symmetrical load case. are pre-set. The following chapter will look into design solutions that permit the components to function under the allowable limits.

In order to visualise the deformation of each model, the displacements and deﬂections were calculated as a resulting vector (utotal), where:

q 2 2 2 utotal = ux + uy + uz

The main result obtained from Robot is the normal combined stresses (S value). These stresses consists of the combined results for bending and axial stresses. As pure axial stresses have a uniform distribution over the cross section, this result could be dismissed if a simple comparison is required. Figures 4.16 and 4.17 gives a general explanation of this.

Due to the diﬀerent materiality and structural function, results were also evaluated separately for the two principal components considered: carbon ﬁbre bars forming

128 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN arches and aluminium bars forming cross-shaped joints.

In the case of displacements, the results obtained are valid for both groups of elements as it assesses the reposition of nodes, rather than the behaviour of bars.

FEM outputs normal combined stresses (S value), with a minimum and maximum value for each bar. Since bending and axial stresses are not uniform along the arc, the S value does not have a uniform distribution for each cross section as explained in Figure 4.16, although bending and axial stresses have symmetrical values, (due to the fact that the cross sections have a regular geometry along the arch). Therefore, each bar has a maximum and minimum S value, and this is why the global maximum and minimum values are found in diﬀerent bars. Hence, results shown on each section refer to the ‘highest’ maximum (Smax) and the ‘lowest’ minimum (Smin) global S value for each group of components (arches and crosses).

4.8 Variation Study

In this section, a group of comparative studies is presented. In each of this studies a set of preﬁxed options are contested in order to establish the geometrical attributes of the main structural component, a trussed single arch. The studies are based in the smallest version of these element, this is 4 m span.

4.8.1 Variation Study on the Arch’s Geometry

(a) (b) (c)

Figure 4.18: Diﬀerent versions of trussed arches with 4 m span to be compared. (a) Model 1, section at the supports (from node to axis): 50 mm, section at the top (from node to axis): 150 mm; (b) Model 2, section at the supports (from node to axis): 150 mm, section at the top (from node to axis): 50 mm; (c) Model 3, section at the supports and top (from node to axis) 100 mm.

The objective of this section is to evaluate diﬀerent design options for a trussed arch. This is the key element of the proposed system.

129 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

The goal of the original arch design was to reduce the number of elements needed to be buried in the ground. This is of greatest importance from both an environmental and construction perspective when working in remote protected areas. Below ground level operations is one of the most complicated types of tasks when operating in permafrost, and when in the case of the presence of rocky soils, is exasperated by the effect of gelifraction on the upper layer [91]. Avoiding this kind of operation not only benefits the logistical and operational aspects of a field party, it also, and more importantly, contributes to minimising invasive activities that can cause permanent alterations to pristine areas. Furthermore, this strategy is also convenient when considering the implementation of an adaptable structure, where components are allowed to be re-organised periodically with the minimum of operational complications.

Although the original scheme already proposed the minimization of support points, it was necessary to understand the eﬀect of such geometry in the structural behaviour of the system by contrasting it with other options.

As discussed previously, each arch comprised four bars. The difference between the three different models tested consisted of the variation of the cross section, that is, the distance between the bars along an imaginary central axis. All the cases were symmetrical, so that the variation of the cross section were only found between the top and ends of the arch. Nevertheless, an asymmetrical design could potentially be implemented. An application for such a case could be a construction on a site with a known and constant dominant wind direction. Means of architectural expression could also require an asymmetrical profile.

Even though the external loads, material properties and the number of bars were later modiﬁed, this exercise oﬀers a fair comparison in terms of global geometry, as the three cases present the same span (4 m), same number of crosses (12) and same load cases (see section 4.4). Also, sections were varied proportionally in order to approximately utilise the ‘same amount’ of material. Figure 4.18 shows the three models. In Model 1, the section at the supports (from node to axis) was 50mm and section at the top (from node to axis): 150 mm. Model 2, presented the opposite version, so that the section at the supports (from node to axis) was 150 mm and the section at the top (from node to axis) was 50 mm. Model 3, consisted on an arch with uniform cross section, therefore the section at the supports and top (from node to axis) was 100 mm.

Arches were assumed to be carbon ﬁbre hollow tubes with a diameter of 32 mm and 3 mm thick, whereas crosses were designed as aluminium with 25 mm diameter and 2 mm thickness. Young’s Modulus in the case of Carbon Fibre is 23 GPa, whereas Aluminium is 75 GPa. Once again, these values were later revised and modiﬁed.

130 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

Max. of Smax Min. of Smin Bar Type Geometry Load Case Load Case [MPa] [MPa] Model 1 221 6 -213 6 Arches Model 2 289 6 -251 6 Model 3 258 6 -213 6 Model 1 573 6 -562 6 Joints Model 2 652 6 -624 6 Model 3 552 6 -583 6

Table 4.6: Extreme combined internal stresses on Model 1, 2 and 3.

Max. of Smax [MPa] Bar Type Load Case Model 1 Model 2 Model 3 1 0 0 0 2 147 194 172 3 15.6 21.0 21.8 Arch 4 46.0 53.8 52.7 5 15.6 21.0 21.8 6 221 289 258 7 23.4 31.5 32.7

Table 4.7: Maximum Smax values on an arch’s bars by load cases in Models 1, 2 and 3.

Results obtained from the FE models are shown in Tables 4.6 to 4.10

Comparing the results obtained for the normal combined stresses of arches’ bar segments, it can be said that no radical diﬀerence is observed between the three models, although Model 1, with highest maximum and minimum stress values of 221 and −213 MPa respectively, shows a discrete advantage over Model 2 of nearly

38 MPa and a more substantial advantage over model 3 of 70 MPa, for Smax values.

Therefore, Model 3 was shown to be a least eﬃcient geometry for both maximum and minimum combined stress values.

All models had highest stresses under Case Load 6, ULS with dominant snow (see section 4.4), for both maximum and minimum values. Tables 4.7 and 4.8 show the

Bar Type Load Case Min. of Smin [MPa] Model 1 Model 2 Model 3 1 0 0 0 2 -107 -167 -140 3 -20.1 -19.2 -22.0 Arch 4 -34.3 -50.4 -46.4 5 -20.1 -19.2 -22.0 6 -162 -251 -213 7 -30.1 -28.9 -33.1

Table 4.8: Minimum Smin values on an arch’s bars by load cases in Models 1, 2 and 3.

131 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

Bar Type Load Case Max. of Smax [MPa] Model 1 Model 2 Model 3 1 0 0 0 2 386 436 376 3 43.9 54.6 56.2 Joint 4 101 125 109 5 43.9 54.6 56.2 6 573 652 552 7 65.9 82.0 84.2

Table 4.9: Maximum Smaxvalues on joints bars by load cases in Models 1, 2 and 3.

Bar Type Load Case Min. of Smin [MPa] Model 1 Model 2 Model 3 1 0 0 0 2 -379 -417 -397 3 -44.3 -55.2 -57.4 Joint 4 -98.7 -121 -104 5 -44.3 -55.2 -57.4 6 -562 -624 -583 7 -66.5 -82.8 -86.0

Table 4.10: Minimum Smin values on joints bars by load cases in Models 1, 2 and 3. maximum Smax and minimum Smin values for each model, according to the diﬀerent load cases.

The results from the crosses bars show a less clear difference. In this case, Models 3 seems to have a slight advantage over Model 1, of 20 MPa in the case of positive combined stresses (552 versus 572 MPa). However this result is inverted when negative values are compared, with Model 3 showing stresses 20 MPa higher than Model 1 (-583 and −562 MPa, respectively). Given the symmetry of these results, it is not possible to say which option is more beneficial for the use of cross-shaped joints. On the other hand, there is a clear disadvantage in Model 2, which exceeds the most efficient Model’s values in almost 100 MPa, in both positive and negatives parameters. Again, all maximum values are caused by Load Case 6, which in this case, also largely overcomes the rest of the load cases, as shown in Tables 4.7, 4.9 and 4.10.

An explanation for the eﬃciency shown by Model 1 over Models 2 and 3 can be found by relating the geometry of each arch with the distribution of Moments Forces [Fig. 4.18].

Model 1 is the option that most closely follows the moment curve. The zone where the largest moment is located, mid-span zone, Model 1 opposes them with the largest Moment of Resistance. At the supports, where Moments are zero, the geometry

132 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN also reduces its cross section to the minimum. Model 2, on the other hand, can be described as an arch with a uniform section undertaking bending stresses with a non-uniform distribution. Therefore, some areas would be underused and some others would be over-used. Similarly, Model 3, which showed the poorest results, offers a minimum of Moment of Resistance in the mid-span zone, whereas the largest cross section is found at the supports, where the bending stresses are at a minimum. It can be argued that other zones of nearly zero bending stresses are found at some intermediate points, where the cross section of Model 1 is not reduced to zero. However, if the cross sections of the three models are compared at this same point, they should be the nearly equivalent. Therefore, it can be said that at these zones, the three models perform equally inefficiently at that point. With regards to axial stresses, they were not considered given that their value is dependent on the combined cross sectional area of the bars, which is equal for the three models. Given that the objective of this section is to evaluate the effect of the geometry on the performance of these models, the fact that the results obtained for maxima internal stresses can be found outside the elastic range for both materials, especially in the case of aluminium crosses, is not an aspect to be completely corrected at this stage. However, a general explanation for the much higher values of stresses obtained in the aluminium bars, when compared to the arches’ values, can be found in the characteristic effect of the vierendeel actions and the small distance between parallel bars forming the arch (upper and lower). As with any element under bending forces, the upper tension and lower fibres are subjected to normal stresses with opposite signs. The opposite directions of these stresses cause extremely high shear forces on the nodes of the aluminium bars, which are perpendicular to the arch’s rods [Figure 4.19]. As in the case of the high stresses found in the carbon fibre elements, this can obviously be related to the reduced cross section of the four bars involved. Solutions to these problems are explored in the following chapter. But as for this section’s purpose, the values obtained for the combined internal stresses of carbon fibre bars are considered the main result to be observed, as these are the primary structural components using a rather unknown material. Figures 4.20, 4.21 and 4.22 show the local distribution of highest Maximum Com- bined Normal Stresses for arches’ bars for Models 1, 2 and 3 respectively; whilst figures 4.23, 4.24 and 4.25 show the distribution of minimum Smin values for each model, all of them due to Load Case 6. Figures 4.26 to 4.31 replicate the same mapping, this time for the aluminium bars forming the joints. The stress maps have been scaled according to local minimum and maximum values for each structure, therefore maps are strictly not comparable between them, but they serve to show the location of critical values.

133 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

Figure 4.19: Schematic deformation of an aluminium joint under bending.

In general, it can be seen that whilst most of the elements are subject to a moderate level of maximum stresses in relation to each group’s scale, only a few components, located in the inner arches and near the support areas, present the extreme values. The same pattern is observed for the three models. Similarly, in the case of minimum stresses, it can be seen that most of the elements present stress level closer to neutral or moderate values, whilst only a few bars, again near the supports, are accountable for the extreme stress values.

Another pattern observed in the results is that maximum Smax values are constantly higher than minimum Smin values. This can be explain by the difference of length between outer bars (affected mostly by tension forces) and inner bars (mostly affected by compression forces), and an almost linear relationship between the component’s length and the amount of stress undertaken. Therefore, Smax can be considered as the main indicator for critical stresses values.

The inspection of the results related to the deformation of the structures, for both the translation of nodes (displacement) and the bending of bars between nodes (deﬂection), were considered for simple load cases only, given that deformations should be considered in serviceability limit state. Therefore, it was expected that the results would be dominated by simple snow loads (Load Case 2).

Comparative results for displacements are shown in Table 4.11, whilst global maxima for the bar deflections are shown in Table 4.12. The results did not show a significant difference between the three models, with model 2 showing a slight disadvantage of 3mm displacement. However, this difference is not critical enough to conclude which model is more convenient in terms of deformations. In general, although the results were further reduced with the modification of component attributes (described in the following chapter), the level of deformation reached at this stage can be considered to be acceptable for the serviceability limit governing this type of design, where some level of flexibility is expected. It should also be considered that the assessed loads correspond to the deformation expected to accumulate during a year-long period.

134 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN Distribution of maximum S values Distribution of maximum S values e 4.22: e 4.25: Figur on the arches’ bars in Model 3 due to load case 6. Figur on cross’s bars from Model 3 due to load case 6. Distribution of maximum S values Distribution of maximum S values e 4.21: e 4.24: Figur on the arches’ bars Model 2 due to load case 6. Figur on cross’s bars from Model 2 due to load case 6. Distribution of maximum S values Distribution of maximum S values e 4.20: e 4.23: Figur on the arches’ bars in Model 1 due to load case 6. Figur on cross’s bars from Model 1 due to load case 6.

135 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN ncossbr rmMdl1det odcs 6. case load to due 1 Model from bars cross’s on 6. case load to due 1 Model from bars arch’s on Figur Figur 4.29: e 4.26: e itiuino iiu values S minimum of Distribution values S minimum of Distribution ncossbr rmMdl2det odcs 6. case load to due 2 Model from bars cross’s on 6. case load to due 2 Model from bars arch’s on Figur Figur 4.30: e 4.27: e itiuino iiu values S minimum of Distribution values S minimum of Distribution ncossbr rmMdl3det odcs 6. case load to due 3 Model from bars cross’s on 6. case load to due 3 Model from bars arch’s on Figur Figur 4.31: e 4.28: e itiuino iiu values S minimum of Distribution values S minimum of Distribution

136 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

Maximum Displacement of Nodes [mm] Arch Geometry Load Case ux uy uz utotal Model 1 0 0 -23 23 2 Model 2 0 0 -26 26 2 Model 3 0 0 -23 23 2

Table 4.11: Maximum nodes displacement on Models 1, 2 and 3.

Maximum Displacement of Nodes [mm] Arch Geometry Load Case ux uy uz utotal Model 1 0 0 2 2 2 Model 2 0 0 3 3 2 Model 3 0 0 2 2 2

Table 4.12: Maximum bars deﬂection on Models 1, 2 and 3.

Figures 4.32, 4.33 and 4.34, show the general distribution of the arch deformations in each model due to snow loads. The results have been resized to ﬁve times the scale of the structure to make this feature visible. The resultant ﬁgures are consistent with the dominant vertical deformation caused by snow accumulations.

Finally, it is possible to conclude that in terms of internal stresses, Models 1 and 3 show a clear advantage over Model 2, for both types of components. Between the two best options Model 1 present a moderate advantage over Model 3. This conﬁrms the structural eﬃciency of the geometry used in the original scheme. In terms of deformations, no model shows a clear advantage and values are in general acceptable. Additionally, when constructability and environmental impact criteria are included, Model 1 becomes the most convenient option, as this represents the least invasive option.

4.8.2 Variation Study for Joint Shape

As described previously, the trussed arch due part of its resistance to the eﬃcient distribution of the four ﬂexible bars forming a single rectangular section, rather than to the four bars’ sections. Therefore, in order to question the convenience of the

Figure 4.32: Deformations Figure 4.33: Deformations Figure 4.34: Deformations of Model 1 caused by com- of Model 2 caused by com- of Model 3 caused by combined loads. bined loads. bined loads.

137 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

Figure 4.35: Scheme for cross-shaped joints and diagonal cross-shape joints. early scheme, two diﬀerent options for this group of bars’ distributions were tested, including the original and a new one.

As shown in Figure ﬁgure 4.17, the internal combined bending stresses are distributed gradually from tension to compression through the arch’s cross section. The cross-shape of the joints implies that two of the bars would be located in the neutral zone, therefore, not contributing to the load-bearing of bending stresses derived from vertical external loads.

The change of this attribute does not aﬀect the assembly procedure, so from a construction perspective, this is an unbiased variation. However, it could allow the arches to work more eﬀectively, requiring fewer components, or less material.

Consequently, a second option was investigated, preserving the number of tubes utilised. This time, two of the rods were placed on the upper zone, where highest tension stresses are found, and two in the lower zone, where compression stresses are at a maximum. Therefore, the joint adopted a diagonal-cross shape [Figure 4.35]. The structural analysis of this last option implied the recalculation of nodal external forces, as loads needed to be distributed between the two lower bars, rather than just one.

The results of this variation on the internal stresses applied on the selected Model 1 are shown in Table 4.13, where they are also compared to the previous version.

Both types of components seemed to beneﬁt from this variation. Arches show a reduction of around 10% on the maximum stress values and 27% in the value of negative stresses. However, the crosses themselves proved to be most aﬀected by this variation, with maximum positive and minimum negative stresses being reduced

138 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

Bar Type Joints Geometry Max. of Smax [MPa] Min. of Smin [MPa] Diagonal-cross 201 -154 Arches Cross 221 -215 Diagonal-cross 368 -361 Joints Cross 573 -562

Table 4.13: Extreme internal stresses for arches with diﬀerent joint geometry.

Figure 4.36: Variation fashion for diagonal-crosses joints. by 205 and 202 MPa respectively (approximately 35%). All maxima results were consistently due to Load Case 6.

In terms of deformations, displacement deflections due to wind showed a maximum of 2 mm, while snow-induced deflections reached a maximum of 28 mm, this is a 20% percent increase. Similar to previous cases, the most affected nodes are the one located in the top or mid-span point of the arch.

Conclusively, the initial assumption as to the positive effect of the rods’ re-distribution, can be considered as effective for the reduction of internal stresses, where the most benefit was seen by the aluminium crosses. Although there is an incremental increase in displacement of the upper nodes, this can still be considered to be non-critical.

Consequently, the parametric model was updated by adopting this option for future studies.

Given that it is expected that the system’s lateral resistance is provided by the arches collaborating with each other, it was decided for the proﬁle of the joints to adopt a rectangular geometry. On the other hand, resistance to out of plane forces is provided by the joints, which are also expected to distribute these forces along the arches’ rods. Therefore, as shown in Figure 4.36, the sections of the joints were varied, again symmetrically from the support to the top of the arches, with a dominant vertical dimension, which increases towards the centre of the arch.

When revising the geometry of these elements, more realistic values needed to be introduced, although ﬁnal aspects of structural design are described in Chapter 5. This was to respond to two critical objectives: stress values should be brought closer to acceptable levels, and also constructability should begin to be taken into account. Therefore a signiﬁcant increment in the cross section size was necessary.

139 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

Bar Type Joints Geometry Max. of Smax [MPa] Min. of Smin [MPa] Size (0) 223 -181 Arches Size (1) 201 -154 Size (0) 242 -240 Joints Size (1) 368 -361

Table 4.14: Extreme internal stresses in arches and joints bars with diﬀerent components sizing.

Minimum values of joints’ width (a) and maximum values for joints’ height (b) were established, as shown in Figure figure 4.36. The minimum value for (a), was defined as 150 mm based on the minimum spacing of elements that would allow the manual assembly of multiple bars, bolts and anchors wearing bulky-gear and it was increased to 300 mm at the top of the arch, where a largest section was needed. The maximum (b) size, 500 mm, was defined by a manageable weight and size (both estimated) of components needed to be lifted and installed during the unaided set-up process under severe weather conditions. Therefore, the mid-span cross size was defined by a 300 × 500 mm rectangle.

Once the support section was varied from 50×50 mm to 150×150 mm, and the mid- span section increased from 150×150 mm to 300×500 mm, a signiﬁcant reduction in the maximum and minimum stress values was observed. The values obtained with the new sizing (Size 1) are shown in Table 4.14, where they are compared to the original conﬁguration (Size 0).

Whilst the arches exhibited a moderate increase of maximum values (11%) a significant reduction was gained in the crosses’ maximum and minimal stresses (nearly 35% of the original values)

4.8.3 Variation Study on the Number of Subdivisions

In the original design, each arch was divided into 16 segments [Chapter 3], with the bars as continuous elements. Additionally, the new strategy proposed arches as assembled elements, with bar segments fastened to the aluminium joints.

In order to ease the construction procedure, a reduction in the number of joints was explored from points of view of structure and a construction.

From a structural perspective, the rigid aluminium joints play a key role: they deﬁne the shape of the arch as well as transmit vertical loads to the bars and therefore provide the entire system a resistance to out-of-plane loads. They also provide the net of bracing cables with ﬁxing points over the surface.

As shown in Figure 4.19, vertical elements on the joints are subject to high bending stresses, for which it was initially believed that reducing the number of aluminium

140 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

Bar Type Number of segments Max. of Smax [MPa] Min. of Smin [MPa] 8 (9 nodes) 257 -217 11 (12 nodes) 230 -188 Arches 12 (13 nodes) 223 -181 15 (16 nodes) 206 -165 8 (9 nodes) 284 -282 11 (12 nodes) 255 -255 Joints 12 (13 nodes) 242 -240 15 (16 nodes) 214 -213

Table 4.15: Extreme internal stresses in arches with diﬀerent number of segments. joints would be responsible for the increment of bending stresses in both arches and joints. Therefore, the sensitivity of both types of components in relation to the variation of the number of crosses was assessed, using diﬀerent samples. The results are shown in Table 4.15.

The results show both elements responding to the variation in the number of components. However a bigger reduction is noticed in the joints. Assuming that the diﬀerence in stresses’ values could be uniformly distributed, then each added node is accountable for a reduction of 7.2 MPa in the Smax value of the arches’ bars, and a 10 MPa reduction in the joint’s Smax. This is a reduction of 3.2% in the case of the arches’ bars and 4.1% in the case of the crosses, based on the values from the original conﬁguration (4 m span and 12 segments). For the case of minimum negative stress values, almost identical variations in combined stresses are observed. Therefore, it can be said that arches and joints are equally sensitive to the variation on the number of components, although that variation can be considered moderate.

Another point to be observed is the effect of the presence of a joint in the mid-span point of the arch. When the results of arches with 11 and 12 segments are inspected, the arches’ highest positive stress in the 12 nodes arch presented a reduction of exactly 7.2 MPa, which is the average and expected decrease. However, the crosses in this same sample presented a more than proportional reduction, of −14 MPa, where an average reduction of 10 MPa was projected. It has already been said that upper elements are the most critically affected components in terms of stresses distribution and deformations [Fig. figure 4.19], so the presence of a node in the mid- span point (or an uneven number of nodes), should be considerate as a preferable attribute, although with a moderate benefit.

From a construction perspective, reducing the number of joints (from 16), increases the length of the bar segments. This can have diﬀerent eﬀects in the assembly procedure depending on the span of the arch. Therefore, a balanced solution for the number of joints was derived.

The length of the bars’ segments for the diﬀerent spans was inspected in Table 4.16.

141 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN Span 10.5 11.5 Arc 1 . 5 4.5 5.5 6.5 7.5 8.5 9.5 10 11 12 4 5 6 7 8 9 [m] m ihee ubro nodes of number even with h emn Length < Segment T tlLnt [m] Length otal 10.2 11.8 12.6 13.4 14.1 14.9 15.7 16.5 17.3 18.1 18.8 6.3 7.1 7.9 8.6 9.4 11 < T m 0 . 5 be4.16: able Num e f3 bars 3m of ber 3 3 3 3 4 4 4 4 5 5 5 5 6 6 6 6 7 assget egh face ihdﬀrn pn n ubro joints. of number and spans diﬀerent with arches of lengths segments Bars 0.79 0.87 0.96 1.05 1.13 1.22 1.31 1.48 1.57 1.66 1.75 1.83 1.92 2.01 2.09 0.7 1.4 9 0.63 0.71 0.79 0.86 0.94 1.02 1.18 1.26 1.34 1.41 1.49 1.57 1.65 1.73 1.81 1.88 1.1 10 Num Segmen 0.57 0.64 0.71 0.79 0.86 0.93 1.07 1.14 1.21 1.29 1.36 1.43 1.57 1.64 1.71 1.5 11 1 e fSegments of ber egh[ Length t 0.52 0.59 0.65 0.72 0.79 0.85 0.92 0.98 1.05 1.11 1.18 1.24 1.31 1.37 1.44 1.51 1.57 12 0.48 0.54 0.66 0.72 0.79 0.85 0.91 0.97 1.03 1.09 1.15 1.21 1.27 1.33 1.39 1.45 0.6 13 m ] 0.45 0.56 0.62 0.67 0.73 0.79 0.84 0.95 1.01 1.07 1.12 1.18 1.23 1.29 1.35 0.5 0.9 14 0.42 0.47 0.52 0.58 0.63 0.68 0.73 0.79 0.84 0.89 0.94 0.99 1.05 1.15 1.26 1.1 1.2 15

142 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

As an initial criterion, the convenience of a node at the mid-span point was established. Therefore, the election of the number of subdivisions began by discarding those options with an even number of nodes (uneven number of segments). It was also concluded that segments shorter than 0.5 meters should be avoided as the complex joints placed at both ends of each segment including tensile cables and membrane buckles, would be too complicated to manipulate manually or repair. Segments longer than 1.5 meters were also discarded as manipulation could also be diﬃcult under severe wind conditions. Therefore, two options were assessed to be equally feasible: 12 and 14 segments. The option with the fewer subdivisions was therefore chosen, namely, 12 segments (or 13 nodes).

4.8.4 Variation Study on the Arch’s Depth

The depth of a trussed arch mid-span provides the system with vertical load bearing to resist out- of-plane forces in the most critical zones. Based on the material self-weight and the limited aid for assembly, the maximum height of crosses, thus the arch’s depth, was restricted to a maximum of 500 mm. Due to the 13 nodes considered, each arch would require 6 diﬀerent crosses. Given that the span varies, each of these crosses, with exception of the top and the bottom elements, would need to be bespoke.

However, the uniformity of the arch depth leads some of the arches, particularly those within the smallest range of span, to be over-structured and/or aesthetically unproportioned.

Therefore, the effect of the arch’s depth variation on the performance of this particular structural typology was studied by comparing different options: a 4 m span arch with 300, 400 and 500 mm depth. For all three options, the width of mid-span cross was fixed at 300 mm. Given that all intermediate joints are already bespoke, the proportional variation of the mid-span depth will not result in a higher number of different components at this stage. The reduction of the number of components is explored in the following chapter.

Table 4.17, shows the global extreme combined stresses for bars forming arches and joints, with these three diﬀerent conﬁgurations.

In this case, a consistent reduction is observed in the variation of the component’s stresses.

For the arches, in terms of highest Smax values, the ﬁrst step of depth reduction (this is from 0.5 to 0.4 m) caused an increment of 14.1 MPa (or 6.3% with respect to the original conﬁguration), while for the Smin values, the increment was 15.8

(8.7%). In the second depth reduction step (from 0.4 to 0.3 m), the highest Smax

143 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

Bar Type Mid-span Depth [m] Max. of Smax [MPa] Min. of Smin [MPa] 0.3 248 -209 Arches 0.4 234 -193 0.5 222 -181 0.3 267 -265 Joints 0.4 258 -257 0.5 242 -240

Table 4.17: Extreme internal stresses for arches with diﬀerent mid-span depth. was increased to 11.4 MPa (8.7%), which is almost equivalent to the increment in the extreme Smin value of 11.7 MPa (6.5%).

The variation in the stresses of the crosses showed coherent results with the reduction of this attribute. Here, a 6.8% increment in both Smax and Smin global extreme values, was observed with the ﬁrst reduction, and 3.5% for the second reduction step, again for both critical values.

Therefore, the variation of this attribute, although eﬀective, can be considered to be moderate in regards to the internal stresses.

4.9 Conclusions

All the results obtained from the Finite Element models are coherent with the theoretical notions of a vierendeel form of truss.

The examination of FE results against Polar-based criteria allowed the speciﬁcation of the geometrical features for the primary structural element (a single trussed arch) with a minimum span (four meters).

The sensitivity of each geometrical attribute has also been established.

In order to better visualise how sensitive the components are to the variation of every attribute, the results were normalised using a bar chart. The graph refers to the results in the arches’ bars as they are considered the main results.

In these graphs, every iteration (series) sets a new reference value (100%) which is represented by the red bars. The geometry was consecutively updated based on the best option obtained by the previous iteration, highlighted with the symbol ‘*’.

The expected dominance of global geometry and joint’s shape, with respect to the rest of the attributes (size of section, number of subdivisions and mid-span depth) was observed.

In the case of sizing, the new version proposed resulted in a moderate increment on the arches’ bars stresses (equivalent to a 10% increment). This version was

144 CHAPTER 4. NODAL FORCES METHOD AND STRUCTURAL COMPONENTS DESIGN

Figure 4.37: Sensitivity comparison of diﬀerent geometric attributes for a single trussed arch. however chosen, due to the signiﬁcant contribution to the reduction of stresses in the aluminium joints’ bar (35% from the original version).

From a more general perspective, the scripting approach used could be applied whenever a high number of complex geometries need to be evaluated and ranked simultaneously. This approach widens the solution space, since countless options can be created, analysed and evaluated within a very short space of time.

Finally, given that a sound calculation method could be created, the geometrical attributes of a single element (with the minimal span) could be deﬁned. Further- more, the sensitivity toward the variation of each attribute was established. The same method can now be used to deﬁne the attributes of the rest of the components. This process is presented in the following chapter.

145

Chapter 5

Multi-Objective Design Process

5.1 Introduction

This chapter presents the second part of the design study for an adaptable lightweight structure in a Polar area. In the previous sections, the basic characteristics of a trussed arch were defined and a parametric method to calculate the internal stresses in arches was introduced. This chapter describes the design of the structure as a generic system, meaning that specific attributes of arches as well as the relationship between the different components are established. In the first part (Section 5.2), the initial design conditions are revised in order to both make accurate assumptions and to bring stress values closer to allowable levels. This includes: inclusion of material properties, pre-stress and span values. Secondly, geometric variations are studied in order to either allow the adaptability of the lightweight system, or to reduce the number of different components. This exercise could be defined as a multi-objective optimisation study. As in any multi-attribute problem, there are several objectives to be pursued, where some can be contradictory. As an analogy, a common engineering problem is the minimisation of a structure’s deflection and the reduction in self-weight, so a single solution that simultaneously optimises each objective is not possible. Instead, some level of optimisation (towards one of the objectives) is achievable, for which a trade-off between other attributes is necessary. In this research, the main criteria (or objectives) are lightness of the structure, adaptability of configuration and a reduced number of different components. Although it is believed that a number of Pareto optimal solutions are possible, this study will show one set of results using a polar logistic- based weighting method. A solution is called a Pareto optimal (or noninferior) if none of the attribute (or objective functions) can be modified or improved without degrading some of the other objective values [113].

147 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

There can be many ways of carrying out the optimisation of a certain attribute on a given structure, in which the components are resolved individually. However, the extreme logistical and environmental limitations of this case did not allow such a detailed solution. Instead, this multi-objective study was employed in order to enable the ‘partial-optimisation of the structure’. Where a set of pre-established values is determined for each attribute and assigned to each class of component according to their size. This study was led by three main criteria (lightness of the structure, adaptability of conﬁgurations, and reduction of the number of diﬀerent components).

Once the preconditions were reestablished, a sensitivity study was carried out, which presented in Section 5.3. This involved the deﬁnition of several variables, such as arches’ span, rods’ cross section, number of crosses, mid-span (or ridge) depth. This study pointed towards introducing a certain degree of ‘optimisation’ to the diﬀerent aspects of the structure. Therefore, some of the attributes were resolved by segmenting or grouping its values. As a results, groups of values were established for each component’s attribute according to the arches’ span, rather than singular solutions.

Whilst span variations and material properties were pre-established, the sensitivity study described in Section 5.3 was used to determine the following attributes or variables:

i) Diﬀerentiated cross sections of the arches’ bars according to span.

ii) Diﬀerentiated arch mid-span depth according to span.

iii) Uniform load condition of arches according to span and distances between arches.

Following, Section 5.4, a set of geometry-based optimisation studies were carried out with the purpose of reducing the number of diﬀerent components, in particular:

iv) Reducing the number of joints per arch according to span.

v) Reducing the number of diﬀerent scissor-joints for the whole system.

The corresponding subsections of sections 5.3 and 5.4 are later introduced. Finally, the information acquired for each set of components and its relation to the others are integrated into a generic parametric CAD model, which is presented in the Section 5.5.

148 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

5.2 Revision of pre-conditions for Sensitivity Study

The FE test described in Chapter 4 was run multiple times on single trussed arches with spans ranging from 4 m to 12 m, where external loads valid for a 1m arch- spacing were applied. From analysis of the results, some modiﬁcation of the initial pre-conditions was considered necessary in order to bring stresses within allowable and realistic levels. These modiﬁcations are as follows:

5.2.1 Material properties

Firstly, the large stresses observed in Chapter 4, suggested a change in the material properties used for the arches’ bars. This time, the use of Carbon Fibre Reinforced Polymer (CFRP) was considered, with a modulus of elasticity of 70 GPa, and a bending and tensile strength limit of 600 MPa. These values imply the use of a particular build-up of composite with a specific proportion of longitudinal fibres (at least 30 %) and the use of a particularly stiff type of carbon fibre. For a material with such characteristics and used as part of an arch, compressive strength is not usually critical, since buckling would occur before collapse. Density is kept at standard values. Poisson Modulus is 0.33 and its Shear Modulus is 50 GPa (see Chapter 4).

5.2.2 Pre-stress

Apart from the externally derived loads, a more realistic study also requires the inclusion of pre-stress derived from internal bending forces. This would be caused by the force necessary to get initially-straight bar segments to adapt to the curved shape which deﬁnes the arch. Pre-stress forces derived from bending are deﬁned by the expression:

σy⁄Iy = E⁄R

Where,

σy is bending stress

Iy is the moment of inertia

E is the modulus of elasticity

R is the radius of curvature of the arc

149 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

(a) (b) (c) (d)

Figure 5.1: Top view of a curve standardised with diﬀerent values: (a) original input curve subdivided into a number of segments (b) span values rounded to nearest 0.2m value, (c) span values rounded to the nearest 0.5m value and, (d) span values rounded to nearest 1m value.

Therefore, this value needs to be updated according to the arch’s span (deﬁning the arc’s radius) and bar’s cross section (Moment of Inertia, Iy ). It was initially decided that the value of pre-stress should be kept below one half of the bending strength, in order to allow the bars to cope with external forces. This required a careful trade-oﬀ between material resistances to external forces, since the thickness of bars (dictating the ‘Iy’ value) is inversely proportional to the σyvalue. Similarly, the largest arch’s span (this is the largest radius) would present the lowest value of pre-stress derived from bending. However, such elements would need to cope with the highest values of external forces, as their loaded areas would be the largest. Correspondingly, the smallest radiuses would be derived from the highest values of internal stress derived from bending, and the smallest values of forces derived from snow and wind.

5.2.3 Standardisation of Span Values

It was also decided that, in the case of the Union Glacier Station, the span variation would be restricted to increments of 1 m. Whilst this constraint could compromise the aesthetic aspects of the structure, it would limit the number of diﬀerent components signiﬁcantly.

Figure 5.1 shows early-stage sketches assessing the re-interpretation of the input curve with span values rounded to the nearest 1, 0.5 and 0.2 m respectively. It was then quickly understood that, given the proportion of the structures, the subtle aesthetic diﬀerence between options became irrelevant when the beneﬁt of the construction and logistics were compared. Therefore, a ‘low degree of variation’ strategy was adopted, i.e. span values derived from an architectural scheme, would be standardised and rounded to the nearest whole number of metres.

Up to this stage, the system considered only a standard height for the ridge crosses of 500 x 300 mm and for the crosses at the base of 150 x 150 mm. However, given that each arch would initially have a diﬀerent length and equal number of

150 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS subdivision (12 segments), the central joints would inherit bespoke measurements based on the arches’ length. This means that every diagonal cross joint, except ridge (or mid-span) and base ones, would require a very specific size to define the arch’s shape. The same would be true for every bar segment. The inclusion of this integer value restriction on the arches’ span [Fig. 5.1(d)] would narrow down the number of different components to 8 segment lengths, and the number of different joints to 49.

Nevertheless, in the case of a less restrictive context, where more detailed components can be handled, the original input-curve could be interpreted with a ﬁner degree of discretisation, by using smaller segment lengths to replicate the original curve with higher precision [Fig. 5.1(b) and (c)].

This restriction was ﬁnally included into the parametric model as shown in section 5.5.

5.3 Sensitivity study

As stated earlier, this multi-objective study is led by three conflicting criteria: lightness of the structure, adaptability of configurations, and reduction of the number of different components.

Whilst span variations and material properties were pre-established, the sensitivity study was used to determine the following attributes: cross sections of the arches’ bars according to span, arches’ mid-span depth according to span, and the distance between arches.

The extreme logistical and environmental limitations of this case, proposed that the structural system could only be ‘partially-optimised’. The introduction of a certain degree of ‘optimisation’ of the structural system’s attributes implied that these were resolved as groups of values. As a result, groups of values were established for each component’s attribute according to the arch span.

The maps of the values tested versus the restrictions imposed are described in Figure 5.2.

Subsection 5.3.1 explains the characteristics of the aluminium joints and why these were not considered as a variable attribute.

The ﬁrst of this set of studies, titled ‘Diﬀerentiated rod cross sections according to span’, is described in section 5.3.2. This section looks into a controlled variation of the rods’ cross-section throughout the surface in order to employ the minimum amount of material (smallest possible rod cross-sectional area) whilst keeping stresses within allowable limits according to material properties (see Chapter 4).

151 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

The second study, ‘Diﬀerentiated arch depth according to span’, is described in Section 5.3.3 and it looks at variations of the arch’s span and depth based on aesthetic as well as structural criteria.

Section 5.3.4 is dedicated to the third study titled ‘Grouping of arches attributes for the reduction of internal stresses’. In this section, the attributes of the set of arches are grouped in diﬀerent arrangements. These arrangements are compared to ﬁnd the option which brings stress values closest to an acceptable level. Section 5.3.5 explores a geometrical solution to reduce the Carbon Fibre bars’ stresses derived from bending to be applied to the whole set of arches, in order to further reduced the internal stresses on arches’ bars.

Finally, Section 5.3.6, is dedicated to the standardisation of load conditions for all the arches of the group. This study proposes a method to uniform the value of stresses afforded by arches of different span, derived from external loads applied on the membranes spanning between arches spaced at 1m (initially). As a result, the spacing between arches of different span, as well as the size of the spanning membrane pieces corresponding to each arch are defined.

5.3.1 Uniform Cross Section of Aluminium Joints

As shown in Figure 5.2, several different variations of the joint’s cross-section were tested, where the objective was to find the minimum value necessary to keep internal stresses below the material capacity. This parameter’s outputted values were identified as highly sensitive in Chapter 4, for which the detailed differentiation of the aluminium bars’ cross sections (according to the variation of the arches’ span) would be expected. Nevertheless, a unique value needed to be established, since the joints were grouped according to node position rather than span value, as described in Section 5.4. Consequently, a section of 40 mm, with a wall thickness of 5 mm was selected. This was based on that is the one of the minimum values that was commonly tested for all range of arches span, with most of the stresses values being within acceptable limits.

5.3.2 Variations of Rod Cross-Sections According to Span.

The size of the rods’ cross section has also been described as a sensitive or responsive parameter (see Chapter 4). Therefore, the partial optimisation of this attribute according to diﬀerent span values was attempted. FE tests were ran for every other span value; that is, cases of single trussed arches of 12, 10, 8, 6 and 4 m span. In each case, several diﬀerent rod sections were tested, as shown in Figure 5.2. A linear

152 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS Diagram of the diﬀerent attributes, values and constraints assessed for the deﬁnition of components. e 5.2: Figur

153 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

Arch’s Aluminium Joints’ Bars Arches’ Bars Features OD/W T [mm] Smax[MPa] OD/W T [mm] Smax[MPa] Span 12 [m] 625 45/5 373 Depth 500 648 40/5 475 [mm] 664 35/5 640

Span 10 [m] 487 40/5 339 Depth 500 503 35/5 457 [mm] 511 30/5 650

Span 10 [m] 395 40/5 437 Depth 400 515 35/5 464 [mm] 744 30/5 461

312 40/5 259 Span 8 [m] 325 35/5 319 Depth 400 40/5 427 30/5 333 [mm] 402 25/5 523

Span 6 [m] 185 30/5 253 Depth 400 190 25/5 397 [mm] 191 22.5/5 520

228 30/5 295 Span 6 [m] 234 25/5 435 Depth 300 235 22.5 572 [mm] 235 20/5 785

Span 4 [m] 102 25/5 221 Depth 300 104 22.5 277 [mm] 105 20/5 380

Table 5.1: Sensitivity study for the deﬁnition of arches’ bars’ cross section.

154 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

Group 1 2 3 4 Span Range 12 ≤ S ≤ 10 10 ≤ S ≤ 8 8 ≤ S ≤ 6 6 ≤ S ≤ 4 OD/W T [mm] 40/5 35/5 30/5 25/5

Table 5.2: Group of arches according to span range and bars’ cross section. behaviour was assumed for the intermediate cases. Some of these results are shown in Table 5.1.

Several different rod sections were used in each span case. Largest and smallest spans were spared from being tested using maximum and minimum rod sections because the resulting values were extensively out of scope. As expected, stress values showed a highly responsive variation to this attribute (diameter of bars’ cross section). In order to restrict the number of different components, the options were narrowed down to four option of CFRP bar sections, with external diameters of 40, 35, 30 and 25 mm, all with a wall thickness of 5 mm, based on the span values (12 to 10 m, 9.99 to 8 m, 7.99 to 6 m and 5.99 to 4 m respectively). The definition of these four groups are shown in Table 5.2

In each group, the bar cross section was sized to the most critical load case (that is, the largest span), where the objective is to identify the minimum size of bar cross-section necessary to keep internal stresses below the material strength limit. This grouping strategy is further studied in section 5.3.4.

5.3.3 Variation of Arches’ Depth According to Span

Figure 5.1 and Table 5.1 show the iterations tested where the arches’ mid-span depth was increased according to the span increment. The three depth values examined were 500, 400 and 300 mm.

It could be argued that changing this attribute would increase the number of different components, particularly the number of aluminium joints and length segments, which had been rationalised to 8 and 48 variations respectively. However, the controlled variation of the mid-span depth of arches would significantly contribute to the lightness of the system, which is of benefit for both structural efficiency and architectural expression.

The results displayed in Table 5.1 are corresponding with the role assigned to this geometrical attribute in Chapter 4, this is, to the distribution of out-of-plane forces with a rather low sensitivity. In that sense, when stresses from two arches with same span, same rod section, yet diﬀerent depths are compared, a moderate diﬀerence in the resulting maximum stress (Smax) is observed. Correspondingly, the arch with the smallest depth presents slightly higher stress values and vice versa.

155 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

Given that this feature was not considered to be a highly sensitive attribute, only 3 variations were established, forming three groups, based on the arches’ span. For arches with a span between 12 m and 10 m, the maximum possible value of depth (500 mm) was assigned. For the middle range (9.99 to 6 m), joints would have a 400 mm height, whilst the smallest range (5.99 to 4 m) would be deﬁned with the minimum 300 mm height. As explained previously, all crosses were deﬁned with a uniform width of 300 mm.

5.3.4 Grouping of Arches’ Attributes for Reduction of Internal Stresses

This section looks at the deﬁnition and organisation of the diﬀerent geometric attributes explored (span, rod section and mid-span depth) based on the internal stress values in the arches’ bars.

Additionally, pre-stresses were also included at this stage. Results are represented by the value ‘Total Stress’ (St ) in the tables included from this section onwards. This value stands for the aggregate stress on the most critical bar segment, this is, the sum of the maximum value of the combined normal stresses derived from external loads (Smax) and the internal stress derived from bending (σy). Table 5.3 shows the original segmentation of values (Case A) described in the previous section: uniform values for aluminium bars, four different values of rods’ cross section (with a difference of 5 mm) and three different values of mid-span depth (with a difference of 100 mm). All arches were segmented evenly.

Although the Smax values in all cases were acceptable according to their material capacity, once the pre-stresses were included, the St values signiﬁcantly exceeded the aﬀordable limit in some cases.

Alterations to the uniform grouping strategy [Table 5.2] were then explored in order to reduce the combined internal stresses. Figure 5.3, shows how the uniform distribution of span values (Case A) was altered in Cases B and C to inﬂuence the internal stress values.

According to Figure 5.3, Case A represent the original groups of span values [Table 5.2]. In Case B, the rod section value for the Group 4 (this is arches with span ranging from 4 to 5.99 m) was further reduced from 25 to 22.5 mm. This was explored in order to reduce the high pre-bending stress observed at the lower limit of the group, this is, in arches of 4 m span.

Case C studied the eﬀect of reducing the span range of Group 1 , which originally included arches with spans between 12-10 m down, to 12-10.6 m, in order to reduce the high Smax values observed in Case A, particularly in the lower limit of the Group

156 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

Figure 5.3: Cases of values’ grouping.

1 (this is, arches of 10 m span). This reduction on the span range covered by the ﬁrst group, obviously caused the extension of the range covered by Group 3, which now included arches ranging from 8.00 to 10.59 m span)

The results of this are shown in Tables 5.4 and 5.5 for Cases B and C respectively. For all case wall thickness is preserved as 5 mm.

In each span range (or group), the trussed arch with the largest span presented the lowest σy value and the highest Smax value. Every pair of maximum and minimum span values in each group (12 m and 10 m for Group 1, 9.99 m and 8 m for Group 2, 7.99 m and 6 m for Group 3 and, 5.99 m and 4 m for Group 4) show signiﬁcant variations. In each case (either A, B or C) and in each pair of limiting values, the sample with the largest span presented the highest Smax value, whilst the arch with smallest span, presented the highest σy value.

The resultant values of aggregated stress St are generally excessive in comparison to the material capacity. In several cases, the pre-condition of keeping pre-stress under the target limit of 30% of the material capacity is largely exceeded. In some cases, the normal stress value is equivalent to nearly 85% of the allowable stress limit.

Although the modifications of some of the attributes or parameters (cases B and C respectively) in one the span groups, presented consistent results, they proved not only insufficient, but also reduced the performance of some groups. For case B, the reduction of the bar’s section in Group 4, effectively reduced the high level of pre- stress (21% for the case of a 4 m arch span and 14% for the case of a 5.99 m arch), which was expected, however it also provoked a large increment in the value of Smax.

Similarly, the alteration proposed in Case C, caused the expected reduction in σy

157 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

Attributes’ Segmentation (CASE A) Group Span [m] Depth [mm] Rod Section (OD) [mm] Min Max 500 40 10 12 σ [MPa] 320 267 1 y Smax [MPa] 339 475 St [MPa] 659 741 400 35 8 9.99 σ [MPa] 350 280 2 y Smax [MPa] 319 464 St [MPa] 669 744 400 30 6 7.99 σ [MPa] 400 300 3 y Smax [MPa] 253 333 St [MPa] 653 633 300 25 4 5.99 σ [MPa] 500 333 4 y Smax [MPa] 221 435 St [MPa] 721 768

Table 5.3: Internal stresses according to grouping of arches’ attributes Case A.

CASE B Group Span [m] Depth [mm] Rod Section (OD) [mm] Min Max 500 40 10 12 σ [MPa] 320 267 1 y Smax [MPa] 339 475 St [MPa] 659 741 400 35 8 9.99 σ [MPa] 350 280 2 y Smax [MPa] 319 464 St [MPa] 669 744 400 30 6 7.99 σ [MPa] 400 300 3 y Smax [MPa] 253 333 St [MPa] 653 633 300 22.5 4 5.99 σ [MPa] 397 263 4 y Smax [MPa] 277 572 St [MPa] 674 834

Table 5.4: Internal stresses according to grouping of arches’ attributes, Case B.

158 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

CASE C Group Span [m] Depth [mm] Rod Section (OD) [mm] Min Max 500 40 10.6 12 σ [MPa] 264 267 1 y Smax [MPa] 377 475 St [MPa] 641 741 400 35 8 10.59 σ [MPa] 350 231 2 y Smax [MPa] 319 516 St [MPa] 669 748 400 30 6 7.99 σ [MPa] 400 300 3 y Smax [MPa] 253 333 St [MPa] 653 633 300 25 4 5.99 σ [MPa] 500 333 4 y Smax [MPa] 221 435 St [MPa] 721 768

Table 5.5: Internal stresses according to grouping of arches’ attributes, Case C. on the lower limit of Group 1 (from 320 MPa for arches of 10 m span to 264 MPa for arches of 10.6 m span). However, this eﬀect is irrelevant when the increment in internal stresses is considered in both, Groups 3 and 4. Therefore, this can also be interpreted as an ineﬀective alternative. Case A was therefore still considered the closest option towards a ‘pareto’ optimal solution, although Stotal values were still above acceptable limit.

The fact that σy is derived from geometric parameters and, on the other hand,

Smax results from the external loads, oﬀered the possibility of deﬁning a geometry based solution, provided that combined normal stresses were below the material mechanical limit for all ranges. This solution in described in the following section.

5.3.5 Geometry-based Method to reduce Pre-stress in Arches

There is an inverse relation between pre-stress and radius of curvature, given by the previously deﬁned expression:

E σ = I y y R

Assuming that the span, as well as values of Iy and E are ﬁxed, the minimisation of pre-stress can be achieved by controlling the radius of the curvature of the arches’ segments. That is, the curvature of the bar segments between two joints.

159 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

Figure 5.4: Angle between an arc’s segments according to diﬀerent level of curvature.

As Figure 5.4 shows, the arch is originally defined with a radius of X. The level of curvature can be measured by a scale of angles ranging from a fully curved bar defined by an angle of 180°, and at the other extreme, by a discretised arch formed by straight bar segments with infinite radius of curvature, with segments positioned at kink angle θ. Correspondingly, the curved arch would present a full pre-stress whereas kinked segments would have zero bending-induced stress.

Given that pre-stress is deﬁned by the arch radius, it is then possible to ﬁnd a compromise solution; this is an arch formed by segments with a certain degree of pre-stress, induced by segments with radius of curvature R2 and angle ε

There are multiple possible solutions to determine its value of R2. Figures 5.5 and

5.6 present two equivalent geometry-based solutions to determine R2, and therefore to control the pre-stress by decreasing the curvature of the arch’s segments.

Assuming that the objective is to determine the value of R2, and variables known are:

R1 is the radius of the original arc

α is the angle deﬁned by radius of the original arc segment

ε is the assigned kink angle between two bent arc segments

160 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

Figure 5.5: First geometry-based method for controlling the curvature of an arc’s bar segments.

161 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

By trigonometry, β, the angle determined by the radius of the kinked arc’s segment can be found by:

β = ε + α − 180◦

Additionally, C, the straight distance between nodes (or chord) can be determined by the expression:

α C = 2R sin 1 2 or

β C = 2R sin 2 2

Once that C and β are known it is possible to determine R2, by substitution of C:

C R2 = β 2 sin 2

α R1 sin 2 R2 = β sin 2

R sin α R = 1 2 2 sin(ε+α−180◦) 2

The same expression can be used in reverse, namely, the value of the aimed pre-stress can be established a-priori and consequently, the kink angle ε can be determined.

Similarly, the following ﬁgure shows a second approach for the case of 50% pre-stress reduction:

162 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

Figure 5.6: Second geometry-based method for controlling the curvature of an arc’s bar segments.

Given that:

γ R sin γ = R sin 1 2 2 then,

sin γ R2 = R1 γ sin 2

When required, this percentage of reduction can be adjusted.

Table 5.6 shows the revised results of segregated arches with a 50% reduction in pre-stress values.

Given that the results for St values above are still beyond acceptable limits in several cases, a further reduction in the pre-stresses, this time 90%, was applied [Table 5.7].

It can be seen from Table 5.7 that no value exceeds the allowable limit, and so Case A with 90% of pre-stress reduction was chosen as the best alternative. The geometric values obtained from this study could then be integrated into the parametric model.

163 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

Attributes’ Segmentation with 50% Pre-Stress Segmentation (Case A) Group Span [m] Depth [mm] Rod Section (OD) [mm] Min Max 500 40 10 12 σ [MPa] 160 133 1 y Smax [MPa] 339 475 St [MPa] 499 608 400 35 8 9.99 σ [MPa] 175 140 2 y Smax [MPa] 319 464 St [MPa] 494 604 400 30 6 7.99 σ [MPa] 200 150 3 y Smax [MPa] 253 333 St [MPa] 453 483 300 25 4 5.99 σ [MPa] 250 167 4 y Smax [MPa] 221 435 St [MPa] 471 602

Table 5.6: Internal Stresses according to grouping of arches’ attributes, Case A, with 50% of pre-stress reduction.

Group Attributes’ Segmentation with 90% Pre-Stress Segmentation (Case A) Group Span [m] Depth [mm] Rod Section (OD) [mm] Min Max 500 40 10 12 σ [MPa] 32 27 1 y Smax [MPa] 339 475 St [MPa] 371 501 400 35 8 9.99 σ [MPa] 35 28 2 y Smax [MPa] 319 464 St [MPa] 354 492 400 30 6 7.99 σ [MPa] 40 30 3 y Smax [MPa] 253 333 St [MPa] 293 363 300 25 4 5.99 σ [MPa] 50 33 4 y Smax [MPa] 221 435 St [MPa] 271 468

Table 5.7: Internal Stresses according to grouping of arches’ attributes, Case A, with 90% of pre-stress reduction.

164 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

connectionlinesurfacesegmentarea2 Gap

Area 3

Area 2

S S

Area 1

Surface Segment Span 3 Span 1

Span 2

Figure 5.7: Deﬁnition of a ‘Surface Segment’ and ‘Gap’.

5.3.6 Uniform Load Condition of Arches’ Loaded Area

The distance between two consecutives arches, named the ‘Gap’, was the next geometrical attribute that needed to be deﬁned.

Once the construction possibilities were studied, this deﬁnition could also be reviewed. As Chapter 6 will detail, the tunnel’s membrane is expected to be constructed from a series of fabric strips hung from the arches and inter-connected [Figure 5.7]. By this principle, each arch, depending on its span, ‘contributes’ to the system with external loads applied over its particular area. This loaded area equals the span of the arch multiplied by 1m, initially. Thus, external forces acting on each arch were calculated as the distributed wind and snow forces applied over the loaded area.

Accordingly, the definition of ‘Gap’ can now be specified as the sum of two consecutive fabric segments’ half-widths. Thus, it should be considered that for the first and last arches, the width of the fabric segment can only be half of what has been established.

As stated in Chapter 4, the distance between arches was initially set as 1 m for all spans (ranging from 4 to 12 m). However, the relationship between the loaded area and the discretised arches’ attributes requires a deeper inspection.

The reduction of the span possibilities to integer values, as well as the discretisation of related attributes, particularly rod section and arch’s mid-span depth, implies

165 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS that some of the arches are not using their full load bearing material capacity (600 MPa), whilst others, generally the arches at the top limit of each span group, will be under a higher loading state (see Table 5.7).

This section devises a method to rectify this discrepancy, proposing a solution by which all arches are subjected to the same external forces in correspondence to the maximum capacity that the arch could provide. By doing this the number of arches used can be reduced.

A uniform load condition can be achieved by regulating the loaded area. Given that the span is pre-ﬁxed, it is the width of each membrane section that can be adjusted, so that all arches have to withstand the same load. As a result of this adjustment, in most of the cases, the distance between arches can be increased and consequently the number of arches employed can be reduced.

The adjustment of the loaded area in each segment (distinguished by Depth and Rod Section), was carried out using proportional factoring, where the optimal usable area can be found as follows:

Given that:

S is the span of the arc [m]

Smax is the maximum combined normal stress applied on each arch span [MPa]

0 Smax is the maximum combined normal stress possible to be applied on each arch span [MPa],

L is the length of the arc [m] where,

0 Smax = σb − σy and

L = π × Radius

Area is the original loaded area corresponding to each arch span [m2]

Area0 is the maximum loaded area possible to be deﬁned for each arch span [m2]

W idth is the width of Area0 [m]

166 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

It is then possible to state that:

Area = L×1 m

Additionally,

0 Area = L×W idth

Since a linear relation can be established between the areas and combined normal stresses, it is possible to state that:

Area Smax 0 = 0 Area Smax

By replacement of Area0 and Area ,

L×1 m Smax = 0 L×W idth Smax

S0 W idth = max × 1 m Smax

This approach is explained in Figure 5.8. This logic proposes that the membrane’s width can be increased along with the spans within every group, given that the pre-stress is reduced at every step of span increment, therefore more load bearing capacity is ‘available’ to be dedicated to external forces.

In Figure 5.8, pre-set attributes are highlighted in red, values inherited from a previous step are highlighted in blue, and the inﬂuence of one attribute over another is represented by black ﬂow-charts.

The diagram [Fig. 5.8] explain this ﬁrst approach using two span groups as an example. The ﬁrst span group ’Group A’ is formed by arches which span ranges between 8 and 9.99 m. The second group, ‘Group B’ is formed by arches ranging from 6 to 7.99 m.

The diagram begins establishing the preconditions for group A, which are highlighted in red. It is known that span can vary only by integer numbers, so the elements forming this group can only be arches with 8, 9 and 9.99 m span. The maximum possible mid-span (or ridge) depth is 500 mm for this group. Given that this approach looks to minimise the number of diﬀerent arches’ components, this value

167 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS is common for all three arches of the group, so it is highlighted with blue values and ﬂows in the diagram.

Given this two pre-conditions, span and mid-span depth (represented with black ﬂows), the cross-section of the arch’s bars can then be deduced. The size of the rod section is deﬁned based on the pre-condition than pre-stress should be no higher than the 50% of the material bending capacity ( or σy ≤ 300 MPa). The cross section is calculated considering the most critical case of pre-stress within the group, this is, the arch with smallest span (8 m). The cross section (O/ ) is then calculated as A.

This value A is then inherited by the rest of the arches of this group, for the aim of this approach is to have a minimum number of arches’ components. As an inherited value, the rod diameter is represented by blue colour in Figure 5.8.

The width value of the loaded area assigned to each arch need to be defined individually. The definition of this value (loaded area width) is started by the smallest arch of the group, this 8 meter span. The width is influenced by the already defined bar’s cross section, span, and mid-span depth, as shown in the diagram by black flow-chart. Given than pre-stress is already using half of the material capacity (300 out of 600 MPa). The ‘available’ capacity of the material (300 MPa) would only allow this distance to be calculated as the minimum, this is X m. X is calculated so the St value (equivalent to the addition of σy and Smax) is not higher to material capacity (σb = 600 MPa). In the case of the structure proposed for Glacier Union Station, load were calculatedfor a loaded area’s with equivalent to 1 m, being this the minimum value.

The next step in the diagram determines the maximum width of the area for a 9 m span arch. Mid-span depth and bars’ cross section has been inherited from the previous step. Given than the radius of curvature is slightly smaller than the previous case (8 m) and the rod section is the same, the pre-stress (σy) is consequently lower than 300 MPa. Therefore, the available material’s capacity to be dedicated to dead, 0 snow and wind derived stresses (Smax) is then higher than 300 MPa (given by: 0 Smax = σb–σy). Therefore, the distance for the 9 m arches can be slightly increased from X to X0 m. By repeating this procedure, the width for the largest arch of Group A (9.99 m) is deﬁned. Similarly, the load area’s width for this last arch, 00 0 equivalent to X m, is expected to be larger than X m, given that pre-stress (σy) is even smaller.

For the second group, Group B, the distance of the arches is deﬁned in the same way. The preconditions for the deﬁnition of the rod’s cross section for this group are: a minimum span of 6 m and a maximum mid-span depth of the arch of 400 mm. According to Figure 5.8, the minimum width value is calculated as Y for the

168 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

Material Bending Capacity 600 MPa Span [m Midspan Depth [mm] Rod Section (OD) [mm] Min Max 500 40 10 12 σy [MPa] 32 26.67 Smax [MPa] 338.74 474.6 Stotal [MPa] 370.74 501.27 0 Smax [MPa] 568 573.33 Width [m] 1.67 1.2 400 35 8 9.99 σy [MPa] 35 28 Smax [MPa] 319 464 Stotal [MPa] 354 492 0 Smax [MPa] 565 572 Width [m] 1.77 1.23 400 30 6 7.99 σy [MPa] 40 30 Smax [MPa] 253 333 Stotal [MPa] 293 363 0 Smax [MPa] 560 570 Width [m] 2.2 1.71 300 25 4 5.99 σy [MPa] 50 33 Smax [MPa] 221 435 Stotal [MPa] 271 468 0 Smax [MPa] 550 567 Width [m] 2.4 1.3

Table 5.8: Internal stresses and adjusted distance between two arches given a uniform load condition. smallest sample, this is 6 m span. This value is increased to Y 0 for the 7 m span sample and to Y 00 to the largest arch of the group (7.99 m span)

Table 5.8 and 5.9 shows the resulting membrane widths and ‘adjusted loaded areas’ for each arch’s span, respectively.

For the purpose of this design study, only variations on the W idth values are of interest. In this regard, although in some cases the rectiﬁcation of the maximum allowed distances between arches revealed marginal diﬀerences to the original 1m value, in some others, a substantial increment can be achieved by this method.

Given that a linear behaviour can be assumed for intermediate spans, the W idth values in these cases can be deﬁned by simple interpolation. Table 5.10 shows the list of W idth values for each span.

This approach, along with the restriction on span variation (see section 5.2.1) controls the number of diﬀerent membrane segments as components, provided that

169 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

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170 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

Material Bending Capacity 600 MPa Span [m Midspan Depth [mm] Rod Section (OD) [mm] Min Max 500 40 10 12 σy [MPa] 32 26.7 Smax [MPa] 3389 474 Stotal [MPa] 371 501 0 Smax [MPa] 568 573 Area’ [m2] 16.7 14.4 400 35 8 9.99 σy [MPa] 35 28 Smax [MPa] 319 464 Stotal [MPa] 354 492 0 Smax [MPa] 565 572 Area’ [m2] 14.16 12.3 400 30 6 7.99 σy [MPa] 40 30 Smax [MPa] 253 333 Stotal [MPa] 293 363 0 Smax [MPa] 560 570 Area’ [m2] 13.2 13.68 300 25 4 5.99 σy [MPa] 50 33 Smax [MPa] 221 435 Stotal [MPa] 271 468 0 Smax [MPa] 550 567 Area’ [m2] 9.6 7.8

Table 5.9: Internal stresses and assigned loaded area according to arches’ spans given a uniform load condition.

Span [m] 12 11 10 9.9 9 8 7.99 7 6 5.99 5 4 Width [m] 1.2 1.43 1.67 1.23 1.5 1.77 1.71 1.95 2.2 1.3 1.81 2.4

Table 5.10: List of adjusted membrane’s segments widths according to span values.

171 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

Variation 1st Arch Span [m] 2nd Arch Span [m] 1 4 4 2 4 5 3 5 5 4 5 6 5 6 6 6 6 7 7 7 7 8 7 8 9 8 8 10 8 9 11 9 9 12 9 10 13 10 10 14 10 11 15 11 11 16 11 12 17 12 12

Table 5.11: List of possible sequences of two consecutives spans with ±1meter of variation.

each span is associated to a deﬁned polygon, which is deﬁned by two consecutive arches and the curve’s chords, measured as the shortest distance between them. This polygon was highlighted with blue lines in Figure 5.7.

It is believed that surfaces can be implemented from a sequence of arches (thus a sequence of fabric polygons) whose span varies progressively, that is, adjoining arches’ spans should vary by ±1 meter or remain the same. Therefore, a set of membrane polygons could be pre-deﬁned, and assigned accordingly to each arch. It is believed that a variation of ±2 m between adjacent arches is rather unlikely to be found in this type of design, given that this would imply the use of input curves with a rather high level of curvature. The implementation of such case would present no other diﬃculty other than reducing the width assigned to arches, which implies the production of a bespoke membrane section.

As Figure 5.7 explains, the geometry of each membrane piece is inﬂuenced by the next arch’s span. Given that these two elements can vary by either ±1, each span can be associated to 2 or 3 diﬀerent variations, as shown by Table 5.10. Thus, there are 17 possible variations of fabric segment for the whole system. It should be taken into account that once connection strips are sewn onto the fabric, membrane segments cannot be turned around and re-used, therefore reciprocate sequences cannot be implemented with the same membrane piece. Therefore, this table is only valid for the fabrication process. When construction process is included the list should include reciprocate sequences, for which the number of variations is doubled.

172 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

Finally, one interesting aspect of considering membrane segments as a component associated to the structural performance, is that other approaches can be created to respond to diﬀerent objectives using the same discretising method. As an example, Figure 5.9 shows an approach in which the objective is to provide a uniform W idth value within each segment. Such an approach could be used to improve aesthetics or to overcome limitations to the fabrication of membrane. Similarly to Figure 5.8, preconditions are highlighted in red, in this case these are the span values within each group (Group A or B) and the maximum mid-span depth for the smallest arch of each group. Based on these precondition, the value of the rod section is calculated for the smallest sample of the group based on that σy should be equal or less than 300 MPa for each sample. Thus, O/ is equivalent to A for an 8 m arch.

Assuming that σy uses nearly 50% of the material bending capacity, the membrane width is calculated for the smallest arch of the group, based on that St should be no higher than 300 MPa and a maximum mid-span depth of a given value (this diagram uses 500 as an example). The value of the membrane width is inherited from the ﬁrst sample to the rest of the arches of the group, which is equivalent to X for Group A and Y for Group B. A uniform loaded area’s width for all arches implies that the load applied on every arch are not uniform, therefore components of each arch need to be adjusted individually to meet the constraints imposed by the material capacity. In this sense, at every step of span increment the pre-stress is controlled by adjusting the value of the rod section (which can be assumed to be smaller as the span increases), and the value of Smax’ is controlled, to be smaller than 300 MPa, by adjusting the mid-span depth of each arch.

5.4 Geometry-based Studies for the Reduction of Com- ponents

This section looks at the reduction of the number of different physical components. In particular, the reduction of the number of crosses for the whole system was studied. Tensile membranes and cables are expected to play a key role for the lateral resistance of the system which is characterised by high deformability. As mentioned earlier, the whole system requires 49 different crosses [Table 5.12]. This includes 13 nodes on each arch, 3 different mid-span (or ridge) crosses, and all the supports being identical. Given that supports are resolved with anchorages rather than joints, it can be stated that the whole system involves 48 joints.

173 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

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TTT

Figure 5.9: Coordination of attributes for the uniformity of distance between arches.

174 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

Pairs of Middle Pair of Joints at Anchor- Single Single Single 15° and ages at Joint at Joint at Joint at 105°, 30° Span Number 0° and 90° [300 90° [400 90° [500 and 120°, [m] of Joints 180° x x x 45° and [150 x 300mm] 300mm] 300mm] 135°, 60° 150mm] and 150°, 75° and 165° 4 5 5 1 5 6 5 7 5 8 1 1 5 49 9 5 10 5 11 1 5 12 5

Table 5.12: Number of diﬀerent aluminium joints.

The reduction of the number of joints according to the span of the arches, is considered highly beneﬁcial for the reduction of weight of the structure and to simplify the construction process. However, the alteration of the number of joints per arch presented two challenges: i) the triangulation of the tensile cables should not be disrupted, ii) the number of diﬀerent types of joints would be even higher.

The following two sections are dedicated to the studies carried out to resolve these two problems.

For the geometric studies, in the first instance, the possibility of reducing the number of crosses in the arches, again using a ‘grouping according to span’ criteria, was surveyed, and described in Section ??. As in the previous cases, the number of crosses was reduced using a grouping strategy. Although this attribute showed a moderate influence on the structural performance of the single arches, four different segments were established in order to maximise the reduction.

This was followed by the development of a method to reduce the number of scissors- shaped joints throughout the whole range of the arches using a reductive approach, which described in Section ??.

175 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

5.4.1 Reduction of the Number of Nodes per Arch Group

As presented in Chapter 3, they system achieves a continuous net of triangulating bracing cables by lacing two consecutives arches in a zigzagging fashion, using the cross-joints as nodes from where the cables can be fastened. It is expected that this method contributes to simplify the assembly process and also to avoid long bracing elements whose high tension level would be diﬃcult to keep constant. The alteration on the number of nodes in the arches (originally 13 nodes for all type of arches) challenges the continuity of the triangulation.

After several trials it was established that the continuity of the cables’ triangulation could be assured if the variation of the number of nodes did not exceed ±1 unit between consecutives arches. Higher orders of variation would simply disrupt the triangulation. A generic example is shown in Figure 5.10.

This type of diagrams serve a 2D test of the continuity of the lacing on a set of arches with variable span. Arches are numbered by the position from inside towards outside, for example, Arch 1 correspond to the arch with the smallest span placed at the centre of the group, while Arch 5 correspond to the outer arch. The direction of the lacing follows a clockwise direction, unless otherwise is indicated. Node position should also be read in the same direction, as it will be later shown.

Although the variation of this attribute, this is number of joints per arch, would contribute to decreasing the total number of joints required for the implementation of a given scheme, it would, on the other hand, increase the number of different components, this time to 61 different units. Once again, a precise number of aluminium joints would be 60, given that anchorages (Nodes A in the figure) will be resolved differently. Figure 5.11, shows all the variation conforming this group of 61 different crosses. According to this figure, Group 1 includes 15 variations, Group 2 includes 24 variations, Groups 3, 12 variations, and Group 4 with variations.

Diﬀerent approaches for triangulation arrangements with variation of the number of nodes were tested. Firstly, the convenience of the original subdivision arrangement was questioned, and other approaches were tested.

Chapter 3 already highlighted the differences between ‘equal-length’ and ‘equal- angle’ subdivisions schemes. Figure 5.12 shows the effect of these two subdivision schemes on the cable’s lacing. For the purpose of understanding these figures, the lacing was started from the first node on the inner arc, in a clockwise direction.

Consequently, the triangulation of a set of arcs with diﬀerent numbers of subdivision was studied.

The introduction of a notation that expresses the basic sequence of lacing turns out necessary for the understanding of the following examples. The original lacing

176 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

Figure 5.10: Triangulation of a set of arches with cases of variation on the number of nodes of 2 units. scheme proposes that the lacing between two arches starts at the ﬁrst node on Arc

0, from now on called n(0,0), and it fastened at the second node on the second arch, this is n(1,1) in Arc 1. The lacing continues from this last node to the node in the third position on Arc 1, and from there to the node in the fourth position in Arc 1, and so on. This original sequence of lacing between two consecutives arcs is called

‘from n(i,j) to n(i+1,j+1)’. The first aspect studied, was the confirming the relevance of beginning the lacing from the inner arch toward the outer one. As Figure 5.13 and 5.14 show, the triangulation can be affected by node where the lacing starts from. In Case 1, the starting point is the first node (n(0,0)) in the first arc (9 segments), whilst in the second case, the triangulation starts from the first node (n(1,0)) in the second arc (10 segments). In both cases, although continuity is preserved, the mesh becomes progressively disfigured, due to the increasing distance between segments of consecutives arches. This effect would be structurally dysfunctional. Some other strategies were then tested. In Figure 5.15 (Case 3), the last segment of the lacing are completed by altering the sequence ‘n(i,j) to n(i+1,j+1)’, to ‘n(i,j) to n(i+1,j+2)’ for the last two nodes. In Figure 5.16 (Case 4), the direction of the second lacing (between arc 1 and 2) was inverted. These methods proved to be unsuccessful. In the last case in particular, the method turns out trivial as the lacing between the last two arcs (Arc 2 And 3) is not updated, this is, the lacing between arcs 2 and 3 was still done in the clockwise direction. Figure 5.17 (Case 5), provides a continuous triangulation where every last step of the lacing sequences are ‘n(i,j) to n(i+1,j)’. Although geometrically correct, the triangulation again becomes disfigured.

177 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS Figur 5.11: e ubro ieetauiimjitwe ieetae ubro rhs oe codn osa segment. span to according nodes arches’ of number diﬀerentiated when joint aluminium diﬀerent of Number

178 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

Figure 5.12: Two examples of nodes lacing with diﬀerent subdivision approaches: (a) equal angle-distance and (b) equal linear distance.

Figure 5.13: Lacing of a set of arcs with increasing number of subdivision starting from the ﬁrst arc (Case 1).

Figure 5.14: Lacing of a set of arcs with increasing number of subdivisions starting from the second arc (Case 2).

179 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

Figure 5.15: Lacing of a set of arcs with increasing number of subdivisions with last lacing step altered to ‘n(i,j) to n(i+1,j+2)’ (Case 3).

Figure 5.16: Lacing of a set of arcs with increasing number of subdivisions with the second sequence inverted (Case 4).

180 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

Figure 5.17: Solution A. Lacing of a set of arcs with increasing number of subdivisions with last lacing step altered to ‘n(i,j) to n(i+1,j)’ (Case 5).

Further trials included combinations of some of these operations. Figure 5.18 (Case 6), represents a case in which all the lacing sequences are inverted from the second lacing sequence onwards. Although continuous, the same problem encountered in Figure 5.13 is inherited. Finally, Figure 5.19 (Case 7) shows a case, where although only the second lacing sequence is inverted (lacing between arcs 1 and 2), the third sequence (lacing between arc 2 and 3) continues the triangulation with the original left to right direction.

Cases 5 and 7 are more feasible options and these were tested in 3D. In this test, a larger number of arcs were placed, with the number of segments varying according to the span, and some consecutive arcs presented the same number of segments. The condition of variation on the number of segments on consecutive arches was restricted to ±1.

The 3D grammar was then based on the number of subdivisions of each arc, rather than the position of the arc in the sequence. This means that for the 3D interpretation of case 5, the following logic was used: all the lacing sequences start with the same clockwise direction, with bracing between consecutive arcs following the ‘n(i,j) to n(i+1,j+1)’ logic. If there is either a positive or negative variation on the number of nodes in the second arc (this is the second arc of the sequence present n + 1 or n − 1 nodes), the last lacing segment jumps from node n(i,j) (on the ﬁrst arch) to the node n(i+1,j) on the second arc, in other words, a ‘n(i,j) to n(i+1,j)’ sequence is used for the last segment. Based on Figure 5.20, the lacing method of Case 5 proved feasible, although presented some irregularities on one side of the vault.

For the 3D interpretation of Case 7, whenever a ‘n(i,j) to n(i+1,j±1)’or a ‘n(i,j) to n(i+1,j)’situation between two consecutives arcs is followed by a ‘n(i,j) to n(i+1,j±1)’

181 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

Figure 5.18: Lacing with an increasing number of nodes with the sequence inverted from second arch onwards. (Case 6).

Figure 5.19: Solution B for continuous lacing with an increasing number of nodes (Case 7).

182 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

(a) (b)

(c)

Figure 5.20: Three dimensional test of solution A in an arbitrary set of arches: (a) top view, (b) left side view and (c) right side view.

183 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

(a) (b)

(c)

Figure 5.21: Three-dimensional test of solution B in an arbitrary set of arches: (a) top view, (b) left side view and (c) right side view. case, this second lacing sequence inverts its direction (this means, it starts from 180° and runs to 0°) and the subsequent lacing will continue the triangulation from the original direction (this is from 0° to 180°). The sequence then starts again. This means that if the fourth lacing again presents ±1 nodes, then its lacing direction is inverted. For example, if the following lacing sequences are found: ‘n(i,j) to n(i+1,j)’, ‘n(i,j) to n(i+1,j±1)’, ‘n(i,j) to n(i+1,j±1)’ and ‘n(i,j) to n(i+1,j±1)’; or ‘n(i,j) to n(i+1,j±1)’, ‘n(i,j) to n(i+1,j±1)’, ‘n(i,j) to n(i+1,j)’ and n(i,j) to n(i+1,j±1)’, in both cases the direction of the second and fourth lacings are inverted. This method also proved viable, and is shown in Figure 5.21.

A second approach to the problem of continuous triangulation with variable number of nodes (±1) was also explored. This time, arches were classiﬁed generically either as odd or even according to their number of nodes. Whilst in most of the cases triangulation was possible, some scenarios needed to be dis-allowed, speciﬁcally, cases where there was no node in the centre of the arch [114].

The ﬁrst early study, shown in Figure 5.22, consisted of a scheme where the triangulation departs from the central node on the ﬁrst odd arch (in this case, arc number

184 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

(a) (b)

Figure 5.22: Three-dimensional test of lacing scheme starting from central node toward both sides: (a) top view, and (b) side view.

2). The triangulation continues symmetrically in both directions, bottom and top, in an ‘every-other node’ fashion. The process is interrupted when an ‘even to even’ situation is encountered and stops, due the lack of a central node to converge into. The logic proposes to search for the next odd arc’s central node and resume the triangulation from there, again in both directions. In the ﬁgures, red lines are used to identify evenly subdivided arcs, and black for the odd ones.

A solution for the discontinuity of the lacing was found by varying the number of nodes on some of the even arcs, speciﬁcally in arcs 8 and 12. This variation should be made considering the fundamental restriction of a maximum varation of ±1 number of nodes between consecutives arcs. Figure 5.23 shows the case where Arc 8 has been subdivided into 12 segments (added +1 nodes), and Arc 12 into 10 segments (11 nodes). Figure 5.24 shows a case where Arc 8 has instead been subdivided with −1 nodes, this is 10 segments. Alhough both cases seemed to resolve the problem, the ﬁrst case appears to render a smoother surface. The ammended lacing were highlighted in black.

The use of this particular solution requires some reﬂection on the eﬀect of other attributes of the system, given that it would be necessary to induce some distorsions in the multi-value segmentation established. For example, if Arc 8 was the case of a 9 m span arch, therefore subdivided into 11 segments (with 12 nodes) as the above example presents, then a 400 mm midspan (or ridge) depth, and a rod section of 35 mm diameter would be required [see section 5.2.2]. If the number of subdivisions on the curve is increased to +1, a total of 12 segments. Arches with 12 segments correspond to Group 4 (spans range from 10 to 12 m), whith a midspan depth of 500 mm and a 40 mm diameter cross-section. Therefore, an inconsistency in the attributes grouping will be produced.

185 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

(a) (b)

Figure 5.23: Three-dimensional test of a lacing method starting from a central node and where speciﬁc even-divided arcs have altered the number of node to n + 1: (a) top view, (b) left side view.

(a) (b)

Figure 5.24: Three-dimensional test of a lacing method starting from a central node and where speciﬁc even-divided arcs have altered the number of node to n − 1: (a) top view, (b) left side view.

186 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

If the geometry of the arc is updated according to the discussed values, the result would be an arch with 500 mm depth and 9m span, but then a new set of intermediate joints would be needed. If this distortion was omitted, the result would also imply the inclusion of a new set of intermediate crosses for an arc with 12 segments, but a 400 mm depth arc and a 9 m span, which would otherwise not exist. Given that none of the options avoid increasing the number of diﬀerent components, then it is suggested to ommit the update of the arc depth and preserve the shape of the arch instead.

From observing the previous cases, general rules were identiﬁed allowing the assessment of the triangulation’s continuity for any given set of arcs. Thus, failing cases can be corrected, and lacing using this method becomes a possibility.

The exercise consisted of a brute-force approach, where all the possibilities of combinations of evenly and oddly subdivided arcs were listed, up to 4 arcs. Higher sequences were discarded as they quickly become impractical to be solved by simple inspection (number of combinations equals to 2n , with n as the number of arcs). The sequences were grouped according to the condition of the lacing starting from a central node or not. The list started with the simplest sequences containing 2 arcs and then increased to up to 4.

Once the listing was made, failing patterns were identified. Two basic failure arrays were found. The first one, ‘Basic Failure 1’ was present when two evenly subdivided arcs were place consecutively. The second failing pattern, ‘Basic Failure 2’, was found when sequences which start from a central node, have an evenly divided arc located in an odd position, or when a lacing that does not start from a central node has an evenly subdivided arc placed in an even position. In both cases, the ‘even arc’ would be preceded by an oddly divided arc. The list of combinations and identified failing patterns are shown in Table 5.13.

In order to integrate these criteria into the parametric model, this process was then translated into a ﬂow chart [Fig. 5.25]. By checking this routine a number times, the process could be summarised in a much simpler expression, which is shown in Figure 5.26. This last version examines and assesses the position of even arcs, and is valid for sequences with any number of arcs.

The symbolling for Table 5.13 is given by:

O Arc subdivided with an odd number of nodes

E Arc subdivided with an even number of nodes

B.F.1 Basic failure type 1

B.F.2 Basic failure type 2

187 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

@ Opposite option does not exist

5.4.2 Reduction on the Number of Diﬀerent Joints

The high number of diﬀerent joints was identiﬁed as the second paradigm derived from the arcs’ segmentation strategy that needed attention. In order to have a better understanding of this problem it was necessary to establish the total variation in the sizes of the joints. Such information is available from the parametric model [see Section 5.3].

Table 5.14, shows the angles between the joints’ bars (angle α◦ in Figure 5.27) for all the possible arches in the case of a surface where spans have been rounded to values of 0.5 m. Table 5.15 shows the study of the blades length for the same case.

Limiting values were identiﬁed from these tables. If length values are inspected, the maximum length is 583 mm, whilst the minimum is 285 mm. Values for the support nodes are dismissed, as they are not expected to be implemented with aluminium crosses, but with anchorages. Therefore the variation in length for the whole group is 297.4 mm. Values were then put into seven groups, which were allocated crosses with 50 mm variations. The joints included in each group can be identiﬁed in Table 5.14 according to the assigned colour.

Consequently, this grouping allows the whole surface to be constructed using seven diﬀerent crosses, each with a length adaptability of 50 mm. This means that each cross should be able to be adapted by up to 25 mm at each end. An early scheme of this idea is shown in Figure 5.27.

When these results were inspected according to their angular variation, a maximum of 5 variations per group were found, particularly in groups 2 and 4, as shown in Table 5.16. This implies that each of the joints proposed above should have the possibility to be positioned at different angles. The number of different options would then range from only two positions (cross 7), to five different positions (cross 2 and 4). Given the proximity of some of these values, a tolerance of 2 degrees was imposed, which further reduced the number of angular options required, to a maximum of three, again for group 2 and 4. These last values are shown in Table 5.17.

Figure 5.28 shows an early study for the design of a cross which allows the adaptation of the length of its blades, as well its angle. This design is further implemented in Chapter 6.

If the input curve is discretised by arches which spans are integer values, as in the case proposed for Union Glacier Station, there is no reduction in the number

188 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS t e e e e e e e Aliv Aliv Aliv Aliv Aliv Aliv Aliv Assessmen ailed (B.F.2) ailed (B.F.2) ailed (B.F.2) ailed (B.F.2) ailed (B.F.2) ailed (B.F.1) ailed (B.F.1) ailed (B.F.1) ailed (B.F.1) ailed ( B.F.1) F F F F F F F F F F ailed (B.F.1 and 2) ailed (B.F.2 and 1) ailed (B.F.1, 1 and 1) F F ailed ( B.F.2, 1 and 1) F F @ @ @ @ @ @ @ th E E E E E E E E O O O O O O O O 4 Arc rd E E E E E E E E E E O O O O O O O O O 3 Arc Does Not Start from Central Node nd E E E E E E E E E E O O O O O O O O O O O 2 Arc Lacing st E E E E E E E E O O O O O O O O O O O O O 1 Arc t e e e e e e e e e e Aliv Aliv Aliv Aliv Aliv Aliv Aliv Aliv Aliv Aliv Assessmen ailed (B.F.1) ailed (B.F.2) ailed (B.F.1) ailed (B.F.1) ailed (B.F.1) ailed (B.F.2) ailed (B.F.1) ailed (B.F.2) ailed (B.F.1) ailed (B.F.1) F F F F F F F F F F Brute-force test for the lacing of four arcs. th E E E E O O O O 4 Arc @ @ @ @ @ @ @ @ rd E E E E E E E E O O O O O O O O able 5.13: 3 Arc T Starts from Central Node nd E E E E E E E E E E O O O O O O O O O O 2 Arc Lacing st E E E E E E O O O O O O O O O O O O O O 1 Arc 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 Sequence

189 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS Figur 5.25: e lwcatfrnds aigcniut assessment. continuity lacing nodes’ for chart Flow

190 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

Figure 5.26: Simpliﬁed ﬂow chart for nodes’ lacing continuity assessment.

Figure 5.27: Scheme for an adaptable aluminium joint.

191 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS Depth Segmen Span No 12 11 10 9 8 7 6 5 4 3 2 1 0 de [mm] [m] ts 212 309 401 478 536 571 583 571 536 478 401 309 212 T 12 be5.14: able 11.5 212 309 401 478 536 571 583 571 536 478 401 309 212 212 309 401 478 536 571 583 571 536 478 401 309 212 500 11 12 lmnu on’ a’ eghacrigt ieetsasruddt ers . m. 0.5 nearest to rounded spans diﬀerent to according length bar’s joint’s Aluminium 10.5 212 309 401 478 536 571 583 571 536 478 401 309 212 212 309 401 478 536 571 583 571 536 478 401 309 212 10 212 295 371 432 475 497 497 475 432 371 295 212 9.9 212 295 371 432 475 497 497 475 432 371 295 212 9.5 212 295 371 432 475 497 497 475 432 371 295 212 11 9 212 295 371 432 475 497 497 475 432 371 295 212 8.5 Length 212 295 371 432 475 497 497 475 432 371 295 212 8 400 7.99 212 303 384 447 487 500 487 447 384 303 212 [mm] 212 303 384 447 487 500 487 447 384 303 212 7.5 212 303 384 447 487 500 487 447 384 303 212 10 7 212 303 384 447 487 500 487 447 384 303 212 6.5 212 303 384 447 487 500 487 447 384 303 212 6 5.99 212 286 350 397 421 421 397 350 286 212 212 286 350 397 421 421 397 350 286 212 5.5 300 212 286 350 397 421 421 397 350 286 212 9 5 212 286 350 397 421 421 397 350 286 212 4.5 212 286 350 397 421 421 397 350 286 212 4

192 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS 4 90 90 90 90 89.6 89.5 89.8 89.8 89.5 89.6 90 90 90 90 4.5 89.6 89.5 89.8 89.8 89.5 89.6 9 5 90 90 90 90 300 89.6 89.5 89.8 89.8 89.5 89.6 90 90 90 90 5.5 89.6 89.5 89.8 89.8 89.5 89.6 90 90 90 90 5.99 89.6 89.5 89.8 89.8 89.5 89.6 6 90 74 74 90 80.9 76.6 74.7 73.7 74.7 76.6 80.9 90 74 74 90 6.5 80.9 76.6 74.7 73.7 74.7 76.6 80.9 7 10 90 74 74 90 80.9 76.6 74.7 73.7 74.7 76.6 80.9 90 74 74 90 7.5 80.9 76.6 74.7 73.7 74.7 76.6 80.9 [ ° ] 90 74 74 90 7.99 80.9 76.6 74.7 73.7 74.7 76.6 80.9 400 8 90 90 Angle 81.5 77.2 75.1 74.2 73.8 73.8 74.2 75.1 77.2 81.5 90 90 8.5 81.5 77.2 75.1 74.2 73.8 73.8 74.2 75.1 77.2 81.5 9 11 90 90 81.5 77.2 75.1 74.2 73.8 73.8 74.2 75.1 77.2 81.5 90 90 9.5 81.5 77.2 75.1 74.2 73.8 73.8 74.2 75.1 77.2 81.5 90 90 9.9 81.5 77.2 75.1 74.2 73.8 73.8 74.2 75.1 77.2 81.5 10 90 63 63 90 75.2 68.2 64.7 62.2 61.9 62.2 64.7 68.2 75.2 90 63 63 90 10.5 75.2 68.2 64.7 62.2 61.9 62.2 64.7 68.2 75.2 12 11 90 63 63 90 500 75.2 68.2 64.7 62.2 61.9 62.2 64.7 68.2 75.2 90 63 63 90 11.5 75.2 68.2 64.7 62.2 61.9 62.2 64.7 68.2 75.2 12 90 63 63 75 90 75.2 68.2 64.7 62.2 61.9 62.2 64.7 68.2 Angle between aluminium joints’ bars according to diﬀerent spans values, with a span values rounded to nearest 0.5 m. ts [m] [mm] de 0 1 2 3 4 5 6 7 8 9 10 11 12 No Span Segmen able 5.15: Depth T

193 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

Group 1 2 3 4 5 6 7 Number of angular variations 01 05 03 04 03 04 02 90 75.2 76.6 68.2 74.7 74 62.2 89.6 77.2 75.1 74.2 73.7 61.9 Lists of variations [°] 89.6 89.5 89.8 64.7 73.8 81.5 89.8 63 81.5 90

Table 5.16: Variations of angle between joints’ bars found in each length group.

Group 1 2 3 4 5 6 7 Number of angular variations 01 03 03 03 02 02 01 90 75 77 68 75 74 62 Lists of variations [±1ř] 90 89 75 65 63 82 89

Table 5.17: Reduced variations of angle between joints in each length group with a tolerance of ±1ř imposed.

(a) (b)

Figure 5.28: Early model of a adaptable joint (Model 4): (a) two blades, (b) blades placed at 89°, (c) blades placed at 75° and (d) blades placed at 68°.

194 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS 4 212 286 350 397 421 421 397 350 286 212 5 9 212 286 350 397 421 421 397 350 286 212 300 212 286 350 397 421 421 397 350 286 212 5.99 6 212 303 384 447 487 500 487 447 384 303 212 7 10 212 303 384 447 487 500 487 447 384 303 212 [mm] 212 303 384 447 487 500 487 447 384 303 212 7.99 400 8 212 295 371 432 475 497 497 475 432 371 295 212 Length 9 11 212 295 371 432 475 497 497 475 432 371 295 212 9.9 212 295 371 432 475 497 497 475 432 371 295 212 10 212 309 401 478 536 571 583 571 536 478 401 309 212 12 11 500 212 309 401 478 536 571 583 571 536 478 401 309 212 12 212 309 401 478 536 571 583 571 536 478 401 309 212 ts [m] [mm] de 0 1 2 3 4 5 6 7 8 9 10 11 12 No Span Segmen Depth Aluminium joint’s bar’s length according to diﬀerent spans values, with a span values rounded to nearest 1.00 m. able 5.18: T

195 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS T be5.19: able nl ewe lmnu ons asacrigt ieetsasvle,wt pnvle one onaet10 m. 1.00 nearest to rounded values span a with values, spans diﬀerent to according bars joints’ aluminium between Angle Depth Segmen Span No 12 11 10 9 8 7 6 5 4 3 2 1 0 de [mm] [m] ts 68.2 64.7 62.2 61.9 62.2 64.7 68.2 75.2 90 75 63 63 90 12 75.2 68.2 64.7 62.2 61.9 62.2 64.7 68.2 75.2 500 90 63 63 90 11 12 75.2 68.2 64.7 62.2 61.9 62.2 64.7 68.2 75.2 90 63 63 90 10 81.5 77.2 75.1 74.2 73.8 73.8 74.2 75.1 77.2 81.5 9.9 90 90 81.5 77.2 75.1 74.2 73.8 73.8 74.2 75.1 77.2 81.5 90 90 11 9 81.5 77.2 75.1 74.2 73.8 73.8 74.2 75.1 77.2 81.5 90 90 Angle 8 400 80.9 76.6 74.7 73.7 74.7 76.6 80.9 7.99 90 74 74 90 [ ° ] 80.9 76.6 74.7 73.7 74.7 76.6 80.9 90 74 74 90 10 7 80.9 76.6 74.7 73.7 74.7 76.6 80.9 90 74 74 90 6 89.6 89.5 89.8 89.8 89.5 89.6 5.99 90 90 90 90 89.6 89.5 89.8 89.8 89.5 89.6 300 90 90 90 90 5 9 89.6 89.5 89.8 89.8 89.5 89.6 90 90 90 90 4

196 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS of diﬀerent components, due to the marginal diﬀerence in the size of both sets of components [Tables 5.18 and 5.19].

Therefore, by grouping the different attribute’s values (or by the partial-optimisation of attributes) it has been possible to reduce the number of components, specifically to six joints plus one standard anchorage, to cover all of the ranges of joints required by the proposed surface, for at least two different degrees of span standardisation: 1 and 0.5 m. Additionally, each of these joints could eventually be adapted in length, angular position, or be replaced, allowing the surface to modify its shape. This segmentation method based on the joint’s length and angle can be implemented in the parametric model to identify the type of joint required at each node, as is demonstrated in Chapter 6.

With respect to the arches’ bars, the method presents no major complications for their deﬁnition. Table 5.20 lists all of the possible lengths for a surface with span values standardised to 0.5 m (24 types in total, considering twelve types for upper bars and twelve types for lower bars). Given that the proposed system has only four diﬀerent bar cross sections, they can easily be cut to size, and in the case of replacement or repair, spare standard bars can be transported to site and cut according to Table 5.20. The length of the arches’ bars is also an attribute than can be read using Rhino’s graphic programming tools, and therefore the quantity of each type of bars required by a surface can be obtained, as described in Chapter 6.

Finally, the case of an arc whose number of subdivisions has been changed by ±1 unit was also revised. Table 5.22, shows the length of the joints’ diagonals and the angle between diagonals for the example previously given: a 9 m span and 400 mm deep arch which is required to alter its number of subdivision to +1, i.e. to 12 nodes. As highlighted by the colour attribute of Table 5.21, all the nodes from this particular arc can be implemented using one element of the previously deﬁned set. It is then assumed that other cases of alteration can be also resolved similarly. Given that the segment’s length in such a case is also uniform, this case represented a satisfactory outcome.

5.5 Parametric Model

The speciﬁed attributes were ﬁnally integrated into a single parametric model and their discretised values are summarised in Table 5.22.

As a general description, the model requires a single input consisting of a native CAD NURBS curve drawn on the ground-plane and oﬀset from the x-axis, which should be derived from the architectural scheme design. This curve should be deﬁned within the limits that the system allows for the arches’ spans, that is, the distance

197 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS Depth Segmen Span Segmen 12 11 10 9 8 7 6 5 4 3 2 1 [mm] [m] ts t T be5.20: able 1.62 1.62 1.62 1.62 1.62 1.62 1.62 1.62 1.62 1.62 1.62 1.62 12 1.55 1.55 1.55 1.55 1.55 1.55 1.55 1.55 1.55 1.55 1.55 1.55 11.5 egho pe abnFbebr,acrigt pnwt pn one onaet05mvalue. m 0.5 nearest to rounded spans a with span to according bars, Fibre Carbon Upper of Length 1.49 1.49 1.49 1.49 1.49 1.49 1.49 1.49 1.49 1.49 1.49 1.49 500 11 12 1.42 1.42 1.42 1.42 1.42 1.42 1.42 1.42 1.42 1.42 1.42 1.42 10.5 1.35 1.35 1.35 1.35 1.35 1.35 1.35 1.35 1.35 1.35 1.35 1.35 10 1.47 1.47 1.47 1.47 1.47 1.47 1.47 1.47 1.47 1.47 1.47 9.9 1.40 1.40 1.40 1.40 1.40 1.40 1.40 1.40 1.40 1.40 1.40 9.5 1.33 1.33 1.33 1.33 1.33 1.33 1.33 1.33 1.33 1.33 1.33 11 9 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 1.25 8.5 1.18 1.18 1.18 1.18 1.18 1.18 1.18 1.18 1.18 1.18 1.18 Length 8 400 1.30 1.30 1.30 1.30 1.30 1.30 1.30 1.30 1.30 1.30 7.99 [mm] 1.22 1.22 1.22 1.22 1.22 1.22 1.22 1.22 1.22 1.22 7.5 1.14 1.14 1.14 1.14 1.14 1.14 1.14 1.14 1.14 1.14 7 10 1.07 1.07 1.07 1.07 1.07 1.07 1.07 1.07 1.07 1.07 6.5 0.987 0.987 0.987 0.987 0.987 0.987 0.987 0.987 0.987 0.987 6 1.09 1.09 1.09 1.09 1.09 1.09 1.09 1.09 1.09 5.99 1.17 1.17 1.17 1.17 1.17 1.17 1.17 1.17 1.17 5.5 0.911 0.911 0.911 0.911 0.911 0.911 0.911 0.911 0.911 5 300 9 0.824 0.824 0.824 0.824 0.824 0.824 0.824 0.824 0.824 4.5 0.738 0.738 0.738 0.738 0.738 0.738 0.738 0.738 0.738 4

198 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

Nodes Length of Joints’ Diagonals [mm] Angle between Diagonals [°] Cross Type 0 and 12 212 90 1 1 and 11 289 82 2 2 and 10 359 77.7 3 3 and 9 418 75.5 4 4 and 8 463 74.4 5 5 and 7 491 73.9 6 6 500 73.7 6

Table 5.21: Length of joint’s bars and angle between joint’s bars with number of nodes altered in +1 units for evenly-divided arcs.

Group 1 2 3 4 Span range 12 ≤ S ≤ 10 10 ≤ S ≤ 8 8 ≤ S ≤ 6 6 ≤ S ≤ 4 Arch’s mid-span 500 400 300 depth [mm] Arch’s bar rod section 40/5 35/5 30/5 25/5 (OD/WT) [mm] Number of 12 11 10 9 subdivision Span [m] 12 11 10 9.9 9 8 7.99 7 6 5.99 5 4 Width [m] 1.2 1.43 1.67 1.23 1.5 1.77 1.71 1.95 2.2 1.3 1.81 2.4

Table 5.22: Set of resulting attributes and values.

199 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS of the curve to the x-axis should be no less than two metres and no larger than six metres. The curve is then automatically mirrored to produce the footprint of the surface.

At this point, arches are then automatically placed at the corresponding distance, which is done with the aid of a C# component integrated into the graphic model.

By using this component, the ﬁrst arch is located at one end of the curve. Once the ﬁrst point in known, it is stored in a list. A second point is placed at a distance S (= 0.01 m) along the curve. The diameter (distance between the curves) is then rounded up and assessed. This means that the code checks the gap between the previous and the proposed arch does not exceed the value assigned to that particular pair of arches. If this condition is not met, a further point at a Sn+1 distance is located and the gap is re-assessed. Once the condition is exceeded, an arch is placed at the previous Sn distance and the operation is repeated until placing the next arch. The C# code source can be found in C.

With the arches defined, the rest of the attributes are assigned using programming components offered by Grasshopper®. Finally, the membrane was modelled using a formfinding method enabled by Kangaroo Physics® [115].

Figures 5.29, 5.30 and 5.31 show three examples of surfaces created from a NURBS curve (shown in red) using the parametric deﬁnition based on the methodology derived in this chapter.

200 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

(a)

(b)

(c)

Figure 5.29: First example of the parametric model applied on a curve: (a) isometric view, (b) top view and, (c) side view.

201 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

(a)

(b)

(c)

Figure 5.30: Second example of the parametric model applied on curve: (a) isometric view, (b) top view and, (c) side view.

202 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

(a)

(b)

(c)

Figure 5.31: Third example of the parametric model applied on a curve: (a) isometric view, (b) top view and, (c) side view.

5.6 Conclusions

This set of studies has proved the structural feasibility of the proposed system. Furthermore, the objective of conceiving a lightweight system of reduced number of

203 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS components, whilst still allowing geometric adaptability has also been demonstrated.

The contradiction of a controlled optimisation of the structural system, whilst keeping the number of diﬀerent components to a minimum, can be resolved with a discretising strategy of the system’s geometric attributes, which is the grouping of each attributes value. This has been called partial optimisation of the structure.

The knowledge acquired in the previous chapter relating to the level of sensitivity of each attribute facilitated the assessment required to determine the level of grouping (or number of groups) at each step.

The early restriction on span variations to integers is perhaps the key step that enabled the rest of the study to be carried out with a similar discretising criteria.

The controlled differentiation of carbon fibres proved to be particularly complex. Due to the high sensitivity of this attribute, it involved numerous sets of variables to be assessed simultaneously, resulting in a large number of iterations. In this sense, the FEM-CAD software tool developed eased the process significantly.

However, it should also be recognised that even though the results obtained previously, via the manual assessment of FE models (nearly 80 for this stage), were not completely precise and were ﬁnally discarded, they did help to narrow down the range of values to be later re-tested with the software, which made this second round of tests simpler. It was estimated that if all the involved values for every attribute would have been automatically tested, nearly 4 million FE models would have been produced. Given that a range of useful values for every attribute could be determined, around 200 iterations were output and only some of them were ﬁnally used.

On the other hand, the method developed to reduce the pre-stress showed how a structural question can be resolved with a geometry-based approach.

The normalisation of loaded areas demanded clear coordination between all attributes. As a result, the number of arches employed could be reduced, although the width of membrane pieces needed to be differentiated according to each pair of consecutive arches. However, the number of different membrane pieces did not vary significantly when compared to the original scheme. Apart from reducing the number of components, it showed that this method can be used to tackle different problems.

The study for reducing the number of subdivisions of arches, whilst preserving the cables’ triangulation, offered the opportunity to explore the geometric problem under different approaches. The chosen solution could be increasingly simplified and reduced using pseudo-codes, until a simple pattern could be found and was later applied to the parametric model.

204 CHAPTER 5. MULTI-OBJECTIVE DESIGN PROCESS

The method for reducing the number of crosses, demonstrated that attributes can also be grouped across the different span values groups. This is, joints can be also grouped by their node-position based on their length. The tolerance embedded in the joints could absorb the increase in the number of components produced by the differentiated mid-span depth and the differentiated number of nodes, from which, the number of elements could be significantly reduced from 61 to 7.

Finally, given that all structure’s attributes have been pre-deﬁned in this chapter, the resulting parametric model could be deﬁned by using standard Grasshopper applications.

Next chapter oﬀers a ﬁnal round of complementary studies where the architectural and constructional feasibility of the system is assessed.

205

Chapter 6

Complementary Studies

6.1 Introduction

This chapter is dedicated to the development of the construction system in more detail, where the main objective is to test its architectural and constructional feasibility. The second section is dedicated to a study of different configurations. As a result, options and limitations are established and auxiliary components are defined. The third section deals with the definition of the system elements, which includes the basic components, namely: set of carbon fibre bars, aluminium joints, membrane sections, anchorages, and some of the auxiliary components identified in the first section (rigid supporting arches and interstitial membranes). A proposal is then made for an assembly sequence, considering the resources available in the Union Glacier scenario. And finally, a set of examples are produced to show how the system could be applied in the case of the Union Glacier station.

6.2 Study for Variable Conﬁgurations

One of the initial objectives of the study was to overcome the main constraint of the original version, this is the limited span of the arches. This new version has proven the structural soundness of a range of options which allow for versatile uses. The second step of the architectural study consisted of defining different possible configurations. The original scheme proposed that a side opening in tunnels was possible [Chapter 3]. This possibility was re-studied, this time with the objective to enable the aggregation of two perpendicular tunnels. As with the original scheme proposal, the inclusion of rigid boundary trussed arches was necessary. As described in Chapter 3, these boundary arches provide the whole

207 CHAPTER 6. COMPLEMENTARY STUDIES

(a) (b)

(c)

Figure 6.1: Two membrane tunnels meeting perpendicularly: (a) top view, (b) perspective view and (c) side view. system with lateral resistance. In this case, boundary arches are used at both ends of a tunnel, as well as at the side of the tunnel where the lateral void is embedded. In the original scheme, these rigid arches were designed with a cross section which was opposite to the one from the ﬂexible arches, this is, a minimum cross section at the ridge a larger cross section at the base. This geometry was initially replicated in this study.

In the diagrams shown in Figure 6.1, the rigid boundary arches are coloured red, whilst flexible arches are shown in blue. A central axis is also defined, which provided a set of central points with the minimum height for the new rotated flexible arches.

The choice of geometry on the boundary arches was made in the belief that, as an isolated rigid element, such shape would help to provide additional lateral resistance, although no further analysis was carried out to verify such a principle.

Apart from the boundary arches, this example also revealed the need to deﬁne a set of connecting membranes, from now on called ‘interstitial membranes’.

The option of a vault containing a lateral void presented a series of new questions: i) should a special joint be designed for the connection points between the supporting arch and the set of perpendicular ﬂexible arches?, and ii) should the set of rotated ﬂexible arches then be assessed in terms of their span and corresponding attributes

208 CHAPTER 6. COMPLEMENTARY STUDIES

(a) (b)

(c)

Figure 6.2: Three units meeting together: (a) top view, (b) perspective view and (c) side view.

(mid-span depth, rod section, number of subdivsions and gap). These problems were later inspected and are explained in Section 6.3.5.

Following this, the aggregation of three and four units were examined. However, considering that the results from the global geometry study (Chapter 4) suggested that the geometry originally employed did not provide the most efficient performance, this option was revised at this stage. A new version of the element was then included, this time with a uniform section, which proved to be a more efficient configuration, and from a construction point of view, it is also provides a simpler geometry.

Figure 6.2 shows a version how three tunnels meet using the revised geometry for the supporting arches.

Evidently, the interstitial membrane in this case turns out to be more complex. This is proposed to be resolved using a cable pulling from the centre of this membrane element to the top of each rigid arch. The alternative option of using a central pole to sustain these membranes, although feasible, was discarded based on architectural grounds.

A second version of this case is shown in Figure 6.3, where an almost synclastic

209 CHAPTER 6. COMPLEMENTARY STUDIES

(a) (b)

(c)

Figure 6.3: Three units meeting at the same point using a synclastic membrane: (a) top view, (b) perspective view and (c) side view. geometry is used for the interstitial membranes, for which the inclusion of a three- pinned joint arch is necessary (highlighted in green).

If these two options (anticlastic interstitial membranes supported by cables and synclastic membranes using boundary arches) are contested in terms of their fabrication and feasibility of construction, then the ﬁrst approach turns out to be the most eﬃcient, given that it does not require the inclusion of more rigid elements. Following this principle, the aggregation of four units was then studied as shown in Figure 6.4.

Finally, aggregations using ﬁve or more rigid arches to produce non-perpendicular conﬁgurations were also studied, one of these examples is shown in Figure 6.5. Many other options of aggregation can be created.

An additional benefit of including a rigid component is that it can also serve as a reinforcing element, either for long tunnels, or more complex configurations, such as the lateral voids earlier presented. For the first case, the specification of when this component should be inserted cannot be easily predicted, as it depends on many variables of a different nature (such as architectural scheme, span, nearby bifurcations and others). A recommendation for these values is found in the next section, where this component is specified. The following section also describes the geometry of the rigid arch when used as a support element for lateral voids.

210 CHAPTER 6. COMPLEMENTARY STUDIES

(a) (b)

(c)

Figure 6.4: Set of four units meeting at the same point: (a) top view, (b) perspective view and (c) side view.

(a) (b)

Figure 6.5: Four diﬀerent units meeting on a non-orthogonal conﬁguration: (a) top view and (b) perspective view.

211 CHAPTER 6. COMPLEMENTARY STUDIES

Examples of these potential uses are shown in Figure 6.6.

(a) (b)

Figure 6.6: Rigid arch being used as reinforcement element for long tunnels and lateral voids: (a) top view and (b) perspective view.

The example above, shows that the boundary supporting arches also enable the attachment of standard elements such as ﬂexible membranes, as shown in Figure 6.6 and the case of the Jotabeche Station (Chapter 3), or rigid modules, i.e. Igloo Satellite Cabins© (see Chapter 2), that can be used for more sensitive purposes, such as sleeping units.

However, when examined in more detail, some conflicts in the connection of perpendicular membranes can be identified. Figure 6.7 shows two membranes meeting perpendicularly with some voids being created at the intersection. These can however be resolved with standard methods, for example, using overlapping flaps.

Finally, it can also be said that with the inclusion of these last sets of components (boundary arches, interstitial membranes for the aggregation of 2, 3, 4 or 5 units, and terminal curved panels), the possibilities for a given conﬁguration are vast. Certainly, the inherent rules of the system’s construction grammar, such as maximum and minimum span, adjacency and progression rules, and the inclusion of rigid supporting arches for endings, long or complex conﬁgurations, come to control the global geometry of a design using this construction system.

In Section 6.5, some of the options portrayed in this section are used to generate a proposal for the Union Glacier Station.

212 CHAPTER 6. COMPLEMENTARY STUDIES

Figure 6.7: Conﬂict between two membranes pieces meeting perpendicularly.

6.3 Components Deﬁnition

This section resumes the design process carried out in order define some of the system’s components identified during this research, given that most of them cannot be procured from standard commercial products. Although some of these components, namely joints and bars, have already been specified in terms of dimensions, materiality and number of variations, a more detailed description is necessary to demonstrate the feasibility of the system.

6.3.1 Carbon Fibre Bars

Chapter 5 defined the carbon bar segments in terms of material properties, outer and inner diameter, and length variations. In Chapter 4, twelve length variations were identified, according to each possible arch span. These twelve versions were divided into four groups, each of them with a different circular rod diameter: 40 mm for arches of 10-12 m span (Group 1), 35 mm for arches of 8 - 9.99 m span (Group 2), 30 mm for arches of 6 - 7.99 m span (Group 3), and 25 mm for arches of 4 - 5.99 m span (Group 4). In all cases, the thickness of tube considered was 5 mm.

The number of different bar segments can be increased by increasing the number of subdivisions in some of the arches. The effect of this alteration, regarding the required number of different scissors joints, was already studied in Chapter 5, however the effect on number of different bars’ segments, also needs to be included.

The fact that, in certain cases, evenly subdivided arches might need to increase the number of subdivisions by one to allow the continuity of the triangulating bracing cables (see Chapter 5), while keeping the span depth, implies that another set of twelve new length variations should be included. Table 6.1 explains this statement.

Therefore, a total of 36 different bar segments were defined. This correspond to the 24 original types of bars identified in Chapter 5 plus the twelve types identified in Table 6.1. It is possible for this attribute to be identified and labelled in the

213 CHAPTER 6. COMPLEMENTARY STUDIES

Original number of Altered number Span Original bar Modiﬁed bar subdivisions of subdivisions [m] segment segment (number of (+1 segments) length length segments) [m] [m] 12 1.57 1.45 12 13 11 1.44 1.33 10 1.31 1.21 11 N/A 7.99 1.26 1.14 10 11 7 1.1 1.00 6 0.94 0.86 9 N/A

Table 6.1: Variation in upper bars’ length in altered arches. parametric model, which facilitates the segment’s production. It can also eventually serve as a guideline in case a replacement is needed on site, in which case bar segments can be cut to size from standard length bars.

Figures 6.8 and 6.9 show an example of this application.

6.3.2 Angled Bar Connections

The connection between bar segments is an aspect that needs to be addressed independently. The bars are designed to be connected at the location of the joints. Given that the cross joints are designed to provide certain tolerance in their bars’ rotation angle and length, the kink between bars is required to be resolved with an independent element.

Figure 6.10 shows an early study for an aluminium attachment ring, where a kink connection can be inserted. The carbon ﬁbre bar segments are fastened to each end of this kinked connection with locking pins. One of these aluminium rings protrude from each of the four extremities of the scissor-shaped joint.

A sketch of these rings is shown in Figure 6.11.

Alternatively, a second version of this element can be obtained by joining the locking pin to the protruding connection and considering the connection ring as an independent element, as sketched in Figure 6.12.

Whilst this aluminium ring can then be uniform for all types of connections, the angled connectors need to be designed for each of the carbon ﬁbre variations. Therefore, as ﬁgure 6.13 shows, three variations are needed, considering altered cases.

A sketch showing the assembly sequence is given in Figure 6.14.

214 CHAPTER 6. COMPLEMENTARY STUDIES

Figure 6.8: List of the bars’ length on a surface output by the parametric model for two subsequent arches with the same span.

The final version of a proposal for this element is shown in Figure 6.15., and the first option was implemented, given than this version offers a simpler fabrication and assembly procedure.

6.3.3 Aluminium Crosses

The number and type of diﬀerent crosses on a given surface can be identiﬁed by the parametric model. Figure 6.16 shows an example of this application. Here two lists are generated: one identifying the angle between scissors-joints’ bars and a second list inspecting the crosses in an arch according to their length-based type. A second result is shown in Figure 6.17, where a diagram was produced identifying the same arch’s joints by colour according to their length-type.

The original design of the aluminium joints (see Chapter 3) was revised and updated in order to enable this components to: i) support the bar segments, ii) deﬁne the cross section of the arch at each node for which length and angle are adaptable iii) provide a node for the continuous lacing cable between two arches and iv) provide a hook from which the heavy duty strips (attached to membrane segments) can be winched and tensioned from (see Chapter 3). Figure 6.18 and 6.19, show early design sketches for the new version of this component. The second version was ﬁnally adopted.

215 CHAPTER 6. COMPLEMENTARY STUDIES Figur 6.9: e iga ftebr’lnt nasraeotu yteprmti oe.Iae .Bak. A. Image: model. parametric the by output surface a in length bars’ the of Diagram

216 CHAPTER 6. COMPLEMENTARY STUDIES

Figure 6.10: Sketch of an aluminium ring attached to a joint.

Figure 6.11: Sketch of a set of pieces for an aluminium ring.

217 CHAPTER 6. COMPLEMENTARY STUDIES

Figure 6.12: Second proposal for an aluminium ring set.

Figure 6.20, shows an early stage design of the full cluster of pieces required to be part of this solution.

Figure 6.21 shows the final version of this component’s design. As can be seen in the sequence, the round section (40/5 mm OD/WT) defined for this element needed to be replaced by a rectangular-section component. This modification it not expected to affect the performance of this component significantly, although further testing would be necessary to prove such statement.

Another key aspect of this component’s design to be further studied consists on the structural feasibility of the threaded connection joining the rings and crosses. It should be considered that this particular element, the thread, is subject to high bending moments, which are characteristic of the Vierendeel form of truss (see Chap- ter 5). In this sense, the reduced cross-section area of this element is particularly critical, which makes it susceptible to collapse.

The separation of these elements, angled bar holder, ring and aluminium cross’s bars, is justiﬁed by the necessity of reducing the number of components to the minimum possible, for which an assemblable set of bar holders with diﬀerent angle options (Figure 6.15), and a set of aluminium crosses (Figure 6.21) and standard rings can be joined with a single standard aluminium ring.

Evident solutions to this problem would consists on the inclusion of diagonal truss element (earlier ruled out), the enlargement of the cross section of the threaded connections, or the further improvement the element’s design in order to reinforce such connection point (either with an embedded solution or an additional reinforcing

218 CHAPTER 6. COMPLEMENTARY STUDIES

Option A Option B

γ α. . For arches within Group 1, 40mm 40mm with 40mm OD bar's rod section.

m m

m m and 13 subdivisions. 0 0

4 4

β. η. For arches within Group 1,

40mm 40mm with 40mm OD bars' rod section, and 12 subdivisions m m m m 0 0 4 4

χ. ι. For arches within Group 2, 35mm

40mm with 35mm OD bars' rod section, and 11 subdivisions. m

m m 5 m 3 5 3

κ. δ. For arches within Group 3, 30mm

40mm with 30mm OD bars' rod section,

m m and 11 subdivisions. m m

0 0 3 3

. ε λ. For arches within Group 3, 30mm

40mm with 30mm OD bars' rod section, and 10 subdivisions.

m m m 0 m 0 3 3

µ. φ. For arches within Group 4, 25mm

40mm with 25mm OD bars' rod section, and 9 subdivisions.

m m m m 5 2 5 2

Note: This option would allow a single standard Note: This option would require three type of rings ring to be employed for all types of angled connections, to be employed (50, 40, 30mm OD), but it would be easier to as all version are designed with 40mm OD in the central segment. manufacture as all sections are uniform.

Figure 6.13: Study of variations for angled connectors.

219 CHAPTER 6. COMPLEMENTARY STUDIES

Figure 6.14: Assembling sequence of an aluminium ring, angled connection, carbon-ﬁbre bars and scissor-shaped joint.

Figure 6.15: Model of an aluminium ring and angled connection. Image: A. Bak.

220 CHAPTER 6. COMPLEMENTARY STUDIES

Figure 6.16: Lists of an arch’s joint typiﬁed their length and angle produced by the Grasshopper model.

221 CHAPTER 6. COMPLEMENTARY STUDIES Figur 6.17: e ufc ihauiimjit dnie yclusacrigt eghbsdtp.Iae .Bak. A. Image: type. length-based to according colours by identiﬁed joints aluminium with Surface

222 CHAPTER 6. COMPLEMENTARY STUDIES

Figure 6.18: First version of an aluminium joint.

Figure 6.19: Second version of an aluminium joint.

223 CHAPTER 6. COMPLEMENTARY STUDIES

Figure 6.20: Sketch of a scissor-shaped joint connected to the membrane.

224 CHAPTER 6. COMPLEMENTARY STUDIES

Figure 6.21: Model of a scissor-shape joint. Image: A. Bak. component). However, further analysis and physical testing turns out necessary at this point.

6.3.4 Membrane Patterning and voids

As stated in Chapter 5, it is possible to obtain the membrane cutting pattern from the parametric model by using standard formﬁnding applications. In this case, the application used was Daniel Piker’s engine Kangaroo. Although this is not an accurate modeling exercise it oﬀers a good idea of the component’s geometry.

For this particular case, each membrane segment is expected to be hung from the arches’ scissors-joints using a series of heavy duty ratchet straps and metal cam-lock buckles (see Chapter 3). The original version of the structure’s design proposed that each segment include a polyester strap sewn along its central axis, from where adjustable bands and buckles were placed. This concept was conserved. Consequently, the number of belts and buckles included in the band attached to the fabric piece should be equal to the number of scissor joints contained in the

225 CHAPTER 6. COMPLEMENTARY STUDIES

Figure 6.22: Sketch of connection between consecutives membrane pieces. corresponding arch. Additionally, the membrane segments can be ﬁxed to the ground by attaching them to the anchorages.

The joining of consecutive fabric segments is proposed to be achieved with heavy duty zipper connections. Waterproof materials are readily available and are widely used by tent manufacturers. Additional protection can be achieved with the inclusion of a fabric ﬂap. The connection of these elements is illustrated in Figure 6.22.

Although the fabric is expected to be implemented with a certain degree of isotropic pre-stress, and the edge cables to have a prescribed tension force, a level of ﬂexi- bility is also expected. Therefore, by pre-tensioning the membrane, a curved edge spanning between the support points will naturally be introduced, thereby, lifting

226 CHAPTER 6. COMPLEMENTARY STUDIES

Figure 6.23: Example of a set of membrane cutting pattern obtained from the parametric model. Image: A. Bak. the membrane oﬀ the ground. The curve of the edge cable can be decreased by increasing the cable force, and reciprocally, decreasing the tension force of the cable would enlarge this indentation.

A common solution for the closure of the surface consists of attaching a ﬂap along the external face of the membrane segment to cover this curved edge and protect the interior. This fold can be easily be pulled down to the ground with auxiliary tent pegs and cables.

The uniformity of the membrane segments has already been discussed in Chapter 5. Although there are only 8 different possible arches, the fact that each segment of membrane is defined in relation to the neighbouring spans and their specific widths, then there are 17 possible variations of membrane polygons (see Chapter 5).

Additionally, the heavy-duty straps sewn into the membrane pieces must contain the corresponding number of connections (ratchet straps and metal buckles). In some cases (evenly-subdivided arches), such number could have been increased (by one node). Therefore, it is less likely that this element can easily be reused in the case that the surface is to be reconﬁgured. Instead, membrane pieces are considered semi-bespoke components.

An example of membrane pattering obtained from the parametric model is showed in Figure 6.23.

Customised openings can be allowed by assessing the level of curvature of each fabric polygon forming the membrane and identifying the zones with suitable curvature. Areas with higher curvature are subject to lower tension forces than ﬂat zones, therefore curved zones can be considered to be more suitable for regular incisions [58]. This option conﬁrms the semi-bespoke character of the membrane strips.

Figure 6.24 shows a map of the membrane where the level of curvature is assessed. The areas with low degree of curvature, therefore unsuitable for the placement of voids, are highlighted in yellow, and the areas subject to less tension forces are shown in blue and red.

227 CHAPTER 6. COMPLEMENTARY STUDIES

Figure 6.24: Assessment of surface curvature. Image: A. Bak.

6.3.5 Rigid Boundary Arches

The definition of rigid-arch elements was partially discussed in Section 6.2. Rigid boundary arches were defined as trussed metal elements, whose function is to provide the system with lateral resistance and to support flexible arches when a lateral void is required.

The first function refers to cases requiring intermediate support for long configurations of tunnels, or for end panels. The size of this element was restricted to only two options: 6 and 4 meter spans. The second option is considered to serve as a connection element for perpendicularly attached units, in which case a lateral opening is produced. Only one configuration is allowed (a 3 m x 2.1 m arch). Larger spans needed to be disregarded, due to restrictions in assembling and transportation capacity. An aluminium alloy is proposed with similar properties to that used for the joints.

The segmentation of the 6 m and 4 m arches were studied, based on the weight and sizes of the sections, for which two diﬀerent cross sections were considered: 40 mm OD, wall thickness of 2.5 mm, with a linear weight of 0.795 kg/m (Case A), and 50 mm OD, wall thickness of 3 mm, with a linear weight of 1.196 kg/m (Case B) [Tables 6.2 and 6.3]. The composition of the arch was simpliﬁed from its original version to perpendicular crosses, with a uniform section of 400 x 400 mm [Fig. 6.25].

The structural performance of the elements was not tested, as it does not contribute to the development of the design method, since features could eventually be modiﬁed without altering the resulting surface. Instead, options were assessed based on the building and logistical constraints. Arches with components longer than two meters were discarded as they could present diﬃculty for their manipulation on site. Similarly, arches heavier than 50 kg were also dismissed on safety grounds and

228 CHAPTER 6. COMPLEMENTARY STUDIES

Se gm e nt Le n g th

56 7 ,7 mm 400 mm

400 mm

0,4 m Radius Radius 0,4 m

Figure 6.25: Section and proﬁle of a rigid arch.

6 m Span Arch Expression Case A Case B Linear weight 0.795 1.2 WL [kg⁄m ] Inner arcs WI = (π × 3) × WL × 2 15 22.5 weight (WI ) [kg] Outer arcs Wo = (π × 3.4) × WL ∗ 2 23.5 25.5 weight (Wo) [kg] Crosses (WC ) WC = 0.5657 × WL × 2 0.89 1.353 [kg] Number of 5 6 7 5 6 7 Segments (nc) Total weight WT = [W I + Wo + (nc × W c)] 27.9 28.8 29.7 54.9 56.21 57.6 [kg] Segment LS = (π × 3.4/nc) 2.13 1.78 1.53 2.13 1.78 1.53 Length [m] Segment WS = (W T /nc) 5.59 4.8 4.24 11 9.37 8.22 Weight [kg]

Table 6.2: Study for diﬀerent subdivision options of a 6 m rigid arch.

229 CHAPTER 6. COMPLEMENTARY STUDIES

4 m Span Arch Expression Case A Case B Linear weight 0.795 1.2 WL [kg⁄m ] Inner arcs WI = (π × 3) × WL × 2 9.99 15 weight (WI ) [kg] Outer arcs Wo = (π × 3.4) × WL ∗ 2 12 16.9 weight (Wo) [kg] Crosses (WC ) WC = 0.5657 × WL × 2 0.89 1.35 [kg] Number of 5 6 7 5 6 7 Segments (nc) Total weight WT = [W I + Wo + (nc × W c)] 26.4 27.3 28.2 38.7 40 41.4 [kg] Segment LS = (π × 3.4/nc) 1.51 1.25 1.08 1.51 1.25 1.08 Length [m] Segment WS = (W T /nc) 5.29 4.55 4.03 7.73 6.67 5.91 Weight [kg]

Table 6.3: Study for diﬀerent subdivision options of a 4 m rigid arch. limited transportation capacity. Conﬁgurations including components lighter than 5 kg were preferable in order to ease the manual assembly procedure. Therefore, using aluminium tubes of 40 mm OD (Case A) with seven segments seemed the most suitable option for the 6 m version of the boundary arches, whereas for the 4 m span model, the option using six subdivisions, and same cross section (Case A) was chosen.

A solution to divide the boundary arches into a set of practical components is shown in Figure 6.26.

With respect to the ﬁrst case of use of boundary arches, (this is as an intermediate support for long membrane tunnel), a rule to determine the frequency with which rigid arches should be introduced remains hard to deﬁne, due to the high number of variables involved. However, it was estimated that for a given set of arches where any arch with a span larger than 8 m is found, then a 6 m supporting arch should be used every 10 m. If only arches with spans smaller than 8 m are employed, then either a 4 m or 6 m rigid arch should be used every 12 m. These conditions impose a relevant restriction for any architectural scheme.

Finally, regarding to the use of boundary arches as supporting element for lateral openings, the shape of the rigid arch for this case was constrained to assimilate the proﬁle of the Igloo Satellite Cabin®, which in the case of the Glacier Union Station, is meant to be attached to the main tunnel and employed as sleeping or service

230 CHAPTER 6. COMPLEMENTARY STUDIES

Figure 6.26: Proposal for assembling of rigid arches.

Figure 6.27: Rigid arch designed for perpendicular intersections with flexible arches. units. As earlier mentioned, this defines a profile 3 m wide and 2.1 m high [Fig. 6.27], which can also be assembled from a reduced number of segments.

Additionally, the introduction of a lateral opening using a boundary arch presents a series of challenges. The first is related to the geometry of the spanning arches being supported by this arch. Figure 6.28 shows two possibilities for the geometry of the spanning arches intersecting a boundary arch. In Option 1, the spanning arches are defined as quarter-circular, with one end on the floor and the other end located off the ground at the centre of the boundary arch (see left-hand-side of Figure 6.28). In Option 2, the element consists of half of an arch, defined by an origin point on the ground and the mid-span point, where it is interrupted by the intersecting boundary arch (see right-hand-side of Figure 6.28).

Whilst the second option oﬀers the advantage that fewer new element types are required, there are several aspects that make it inconsistent with the structural

231 CHAPTER 6. COMPLEMENTARY STUDIES

Rigid Supporting Arch Rigid Supporting Arch

Flexible Arch Flexible Arch

Option 1 Option 2

Figure 6.28: Cases of spanning arches supported by a lateral boundary arch.

Rigid Supporting Arch

Flexible Arch

 b c d e Figure 6.29: Spanning arches intersecting a boundary arch at irregular intervals. grammar proposed. These include the mid-span depth possibly needing to be larger than necessary, and discrepancies in the cable triangulation rule would be found due to an irregular number of joints. If the ﬁrst option was employed, then more coherent features can be expected. Thus, mid-span depth and the number of subdivisions should be assumed according to the rules deﬁned, namely, they are determined by their span and adjacency rules.

Another aspect to be considered in this situation is the irregular frequency at which spanning arches are placed, which is dependent of their span (see Chapter 5). The intersection of arches and a perpendicularly placed boundary arch should also take into account the irregular interval and angles at which the boundary arches would be intersected by the spanning arches according to the uniform load condition adopted. Figure 6.29 shows a sketch of such problem, where the a set of spanning arches are placed at irregular distances (a, b, c, d and e), perpendicularly to a boundary arch.

In order to simplify this situation, it was decided that spanning arches intersecting a boundary arch should have a uniform span. Figure 6.30 shows an early study of this proposal, using arches of 4 m span.

A signiﬁcant challenge imposed by this operation is the resolution of a joint that permits these two types of elements to be assembled together. The principle of this problem is that the boundary arch should replicate the actions of the ground, receiving and supporting the set of four spanning bars in a common point. Each spanning arch intersects the rigid arch at a diﬀerent angle from both, side and front directions of the rigid arch. Therefore such a joint should be allowed to rotate in both directions. The design of such an element was not achieved during the time of

232 CHAPTER 6. COMPLEMENTARY STUDIES

Figure 6.30: Front and back view of an intersection between a boundary arch and a set of 4 m span spanning arches.

Supporting Arch

Membrane Bracing Cables

Anchors (a) (b)

Figure 6.31: Proposal for a membrane cover as an ending element: (a) side view and (b) front view. this study, but it is believed that with further modelling and prototyping, multiple solutions could be found.

6.3.6 Ending of tunnels

According to the cases described in Chapter 2, there are two solutions that could be implemented to end the tunnels, ﬂexible membranes [Fig. 6.31] or a set of rigid panels forming a shell [Fig. 6.32].

If a fabric membrane is used, this would require the inclusion of bracing cables, where the most efficient configuration would be a triangulated net to provide the stability characteristic lacking in these types of elements. Additionally, these cables should be pulled down and fixed to the ground by means of anchorages. In Figure 6.31, cables are highlighted in green. Although this triangulated surface would behave similarly to a rigid surface, it is expected that some additional tension force would be induced to the rest of the membrane structure. On the other hand, the use of rigid panels instead of a flexible membrane would provide a more robust ending solution. Both solutions have already been implemented in remote areas (see Chapter 2), so no further analysis was considered necessary.

233 CHAPTER 6. COMPLEMENTARY STUDIES

Figure 6.32: Rigid curved panels as a closing element.

6.3.7 Anchorages

The function of this element is to provide a support point to the ﬂexible arches as well as to help the structure to resist uplift from the wind. Given that the global geometry of the arches remains similar to its original version, no major modiﬁcations were needed for this element [see Chapter 3].

6.4 Assembly sequence

This section describes a sequence for the structure’s assembly. Given that all components have already been described in terms of materiality, function and dimensions, this section will focus purely on the building sequencing.

The logistical and environmental conditions existing in Glacier Union were taken into account in this proposal. In this regard, it is expected that the assembly could be done without the assistance of any type of electrical power tools. If arches larger than six meter span are involved, the aid of an aerial work platforms is needed to complete the upper part of the arches and to deploy and ﬁx some of the components (cables and membrane strips).

There are multiple options for aerial platforms. The most sophisticated ones include the use of a small-size scissor lifts. The smallest versions of this type of machinery can be powered by diesel or electric batteries, and their minimal weight is estimated at 588 kg [116, 117]. Therefore, the possibility of transporting this element is a critical aspect for its use.

Lighter and simpler options for aerial access can be found in the maintenance and small building industry. Examples of feasible options are double telescopic ladders [118], combinations of aluminium painting trestles and planks, combinations of

234 CHAPTER 6. COMPLEMENTARY STUDIES heavy-duty leaning and stepladders [119], tripod or orchard ladders [120], baker scaﬀold towers [121] and mobile scaﬀold mono towers [122], amongst others.

Aluminium crosses can be adjusted and mounted oﬀ-site. If the transportation capacity allows, the carbon-ﬁbre bars can also be installed, so arches can be formed and transported to site ready for installation. This is described In Figure 6.33.

The assembly of the structure can be described by the following list of activities and ﬁgures:

i) Marking the location of arches on-site and installing anchorages [Fig. 6.34].

ii) Assembling and installing the ﬁrst boundary arch. If the larger version of this element is used (6 m), upper segments would need to be lifted and assembled with the aid of an aerial platform. Figure 6.35 shows the limit for un-aided assembly. Components are designed to be lifted by one person (weighting approximately. 4.8 kg). Figure 6.36 shows a complete version of this element.

iii) Attaching the membrane piece to the arch [Fig. 6.37]. This step is valid for only one of the boundary arches of a given tunnel (either the ﬁrst, or the last one) and is done using the metal hangers provided by the aluminium joints and the heavy duty straps-buckles connections (shown in orange). The membrane piece is required to be installed clasped using temporary fabric Velcro® stripes.

iv) Erecting flexible arches. The installation of these arches can be done by assembling the components from bottom to top. Similarly, for heights above two metres, the installation would need to be assisted. Figure 6.38 shows the case of an eight metre span arch being assembled. Due to the lightness of arches, it is also advisable to first construct them on the ground, allowing their instalment can be carried out quicker. Figure 6.39 shows a completed flexible arch.

Figure 6.40 shows the installation of the corresponding membrane segment onto the arch. Similarly to the case of rigid supporting arches, fabric pieces are connected to the arch using the heavy duty straps and buckles provided (shown in orange). Again, fabric pieces are installed collapsed using temporary fabric Velcro® strips (shown in red).

235 CHAPTER 6. COMPLEMENTARY STUDIES

(a) (b)

(c)

Figure 6.33: Sequences for the preparation of crosses: (a) Crosses are adjusted to corresponding length and angle position. Aluminium rings are installed in the cross’s extremities, (b) corresponding kinked aluminium connector are installed and ﬁxed, and (c) bar segment can be installed and ﬁxed to the connectors. Image: A. Bak.

236 CHAPTER 6. COMPLEMENTARY STUDIES

Figure 6.34: Marking the location of arches on site and installing anchorages.

Figure 6.35: Boundary arch assembling.

Figure 6.36: Boundary arch completed.

237 CHAPTER 6. COMPLEMENTARY STUDIES

Figure 6.37: Boundary arch with membrane piece attached.

Figure 6.38: Assembling arches from bottom to top.

Figure 6.39: Completed ﬂexible arch.

Figure 6.40: Installation of membrane segments.

238 CHAPTER 6. COMPLEMENTARY STUDIES

Figure 6.41: Flexible arch reinforced with lateral cables.

Figure 6.42: Installation of bracing cables between two arches.

v) Temporary reinforcement. Arches should be temporarily reinforced with lateral cables [Figure 6.41].

vi) Lacing between arches. Bracing cables are installed from the mid-span point of the arches towards the sides. In Figure 6.42, the starting point for the lacings are highlighted with red arrows. The lacings should be done by stepping outside the segment covered by the cables. Again, additional assistance would be required in order to reach such points.

As earlier proposed, the triangulation is done by lacing the cables through the voids provided by the aluminium crosses. It is particularly important to ﬁx the cables on at least 5 points along each arch using wire rope clips, to ensure a minimum level of stress. Figure 6.43, shows an aluminium cross with all of the component (rings, angled connector, carbon ﬁbre bars, heavy-duty strap and cables) installed.

239 CHAPTER 6. COMPLEMENTARY STUDIES

Figure 6.43: Aluminium scissor joint with all components connected. Image: A. Bak.

240 CHAPTER 6. COMPLEMENTARY STUDIES

Figure 6.44: Progression of arches instalment.

Figure 6.45: Direction for the membrane piece’s deployment.

vii) Completing the structure. The remaining arches are installed by repeating the same process [Figure 6.44]. This sequence should be completed until the next rigid arch is installed.

viii) Deploying the membrane pieces. This should be done from the inside and starting from the last segment towards the ﬁrst rigid arch of the sequence [Figures 6.45 and 6.46].

Zipping the two first membrane segments together from the inside would imply the need to unwrap them by removing the temporary Velcro® straps. The first membrane piece is extended to the reach the zip connection provided by the second fabric piece, which should be left hanging. This implies adjusting the lifting equipment to fit inside the vault. Once this is completed, it is required that at least one person steps outside the covered segment (next to the second arch) in order to button the protective flap cover along the extended membrane segment.

ix) Thermal insulation, ﬂooring, internal divisions and service installations, can be added at a second stage using standard procedures.

241 CHAPTER 6. COMPLEMENTARY STUDIES

Figure 6.46: Progression of membrane segments deployment.

242 CHAPTER 6. COMPLEMENTARY STUDIES

Figure 6.47: Handmade sketch of side view of an early design scheme.

Figure 6.48: Side view of early design scheme with basic type of components recognise by colour.

6.5 Examples of Possible Applications for the Glacier Union Case

A proposal for a speculative design of a research station in Union Glacier was produced based on the requirements described in Chapter 1 and the system proposed in this study. Laboratories and storage units are expected to be implement using adapted shipping containers.

Figures 6.47 to figure 6.50 show some early sketches of a proposal for the Glacier Union Research Station. In Figures figure 6.48 and figure 6.50 the basic type of components are recognised by colours.

The scheme was then revised using the parametric CAD deﬁnition and CAD tools and a second version was produced which is implemented using the components speciﬁed in this chapter as well as the rules stablished. Figure 6.51 show the architectural plan for the proposal, and Figures 6.52 to 6.54 show some captions of the digital model.

Figure 6.55 and 6.56 identify the type of bars used in one part of the scheme according to their length, using the colour values speciﬁed in Figure 5.2.

243 CHAPTER 6. COMPLEMENTARY STUDIES

Figure 6.49: Handmade sketch of plan diagram for an early design scheme.

Figure 6.50: Top view of early design scheme with basic type of components recognised by colour, boundary arches in red and ﬂexible arches in blue.

244 CHAPTER 6. COMPLEMENTARY STUDIES

Figure 6.51: Architectural plan for a design scheme.

Figure 6.52: Isometric view of design scheme.

245 CHAPTER 6. COMPLEMENTARY STUDIES

Figure 6.53: Isometric view of design scheme.

Figure 6.54: Isometric view of design scheme.

246 CHAPTER 6. COMPLEMENTARY STUDIES

Figure 6.55: Bar types identiﬁed according to length using colour code, side view.

Figure 6.56: Bar types identiﬁed according to length using colour code, perspective view.

6.6 Conclusions

This chapter has provided the basic solutions to demonstrate the feasibility of the construction system proposed in terms of architectural requirements, fabrication and construction. This has involved options for diﬀerent conﬁgurations, the design of key components, as well as the proposal for an assembly sequence.

As in any design eﬀort, there is no clear limit marking the end of the design process. Nevertheless, a satisfactory level to demonstrate is believed to have been achieved.

There are some components whose solution or definitions were not addressed, either because they consisted of standard or already tested items (such as membrane flaps, closing membrane covers, inner thermal insulation layer, flooring and inner division panels), their design did not vary from the original scheme (anchorages), or their complexity required further study (such as joints for intersecting arches, interstitial membranes and voids used for windows). Based on the multiple examples presented in Chapter 2 and Chapter 3, it is believed that solutions of this level of complexity are achievable in all cases.

Finally, the variety of techniques involved in this chapter, ranging across scripting software tools, digital modelling, manual sketching and 3D printing, evidenced the experimental nature of this study.

247

Chapter 7

Conclusions

7.1 Introduction

This thesis has been dedicated to the recognition of lightweight structures as a design ﬁeld in their own right.

The development of such a narrative involved three main steps: i) the description of the research scope and the characterisation of Antarctic and Subantarctic lightweight structures, ii) the formulation and validation of an original design problem, and iii) the development of a design-based method to solve such a problem.

The actions carried out during these three stages can be summarised as following: i) Description of the research scope and the characterisation of Antarctic and Sub- antarctic lightweight structures:

In the first chapter, a description of the characteristics of Antarctic constructions and of their quick evolution during their 100 year history was presented. This introductory synopsis was necessary due to the lack of academic material relating to this field. Types of Antarctic structures were identified and classified by their scale and also by the mode of use (permanent, seasonal or temporary), which is a key characteristic of Polar facilities. It was seen that seasonal infrastructure is characterised by hard maintenance and inefficient design and use of energy resources.

Chapter 2 was concerned with the documentation of medium and small minimal- weight structures which have been designed for Antarctic and Subantarctic contexts in particular. Some cases described were used as permanent structures (such as the US South Pole Dome), others as seasonal shelters (such as the Teniente Arturo Parodi Station), and others as itinerant dwellings (such as the Aonikenk dwellings). The descriptions were mainly from a structural perspective. A particular classiﬁca- tion of structural surfaces (proposed by Martin Bechthold) was used. This approach enabled the clear description and categorisation of each of the cases found. As a

249 CHAPTER 7. CONCLUSIONS result, a fascinating array of Polar lightweight structures was documented, where the majority corresponded to hybrid schemes. Examples of diﬀerent materiality, assembly strategies and geometrical patterns were also found.

Arguably some of the most interesting cases corresponded to the group of vernacular constructions that were used for now extinct indigenous inhabitants of the Sub- antarctic and Patagonian regions. The lightness and variety of these structures constitutes remarkable examples of the smart use of materials and structural eﬃciency in some of the most extreme environments. The fact that these sets of structures have remained unstudied and excluded by most of the literature concerned with vernacular constructions is a surprising fact. Though it can perhaps be explained by the rapid extinction of the Aonikenk, Selk’nam, Yamana and Kaweshkar communities, which resulted in very scarce study material. Also the most descriptive texts have not been published in English nor translated to other languages, leaving these cases practically excluded from the best-known literature.

Therefore, the novel nature of this literature study, has not only helped to provide this research with a general background, but it is also a fundament contribution to the statement that Polar lightweight design is a valid ﬁeld of research.

This ﬁrst stage concluded by presenting the brief for a new seasonal station for the University of Magallanes’ Antarctic Division in the area of Union Glacier. Such a structure should host a variable number of staﬀ members and should comply with the strict environmental policy, logistic limitations and rough weather conditions seen in the Antarctic. In addition to these practicalities, this station should also promote an innovative architectural approach. ii) Formulation and validation of a design problem:

Based on that opportunity, this research suggested that lightweight structures could be used in Polar environments in a larger, more permanent and more innovative fashion than currently seen. It was also suggested that the periodic variation in the use of seasonal infrastructure oﬀered the chance to explore the conception of a structural system which would allow a certain degree of adaptability in its conﬁguration.

Such a task demonstrated how restrictions derived from such a context (eﬃcient performance, minimal weight, adaptable conﬁguration, reduced number of physical components, and feasible assembly procedure) can drive a novel design process, and in doing so promote the expansion in the research and use of Polar lightweight structures.

The ﬁrst step towards validating this problem comprised of a review of existing examples of small-scale constructions that by some means have addressed the problem

250 CHAPTER 7. CONCLUSIONS of adaptability with a controlled number of components. A set of singular cases, deﬁned as semi-modular systems, were found and brieﬂy described. iii) The development of a design-based method:

The design process commenced by presenting an early scheme for a generic structural surface, a hybrid structure, as was previously developed by the author. According to the author’s interpretation of M. Bechthold’s surfaces’ categorisation, this scheme could be classiﬁed as a hybrid rigid structure, more speciﬁcally, as a truss-like shell where the characteristic single curvature is overcome by the use bracing cables and membrane segments between independent arches of variable span, for which attributes of a gridshell are also present.

This scheme was outlined in terms of its basic geometrical properties, components and limitations. This surface was considered suitable to be further explored and implemented as a semi-modular system enabled by low-tech construction techniques. Consequently, Chapter 4 was dedicated to the development of a design methodology.

The first step took care of the definition of the geometry of the main structural component, this is, a trussed arch. In this study, defined as a sensitivity study, different versions of the arch were contested based on their structural behaviour combined with logistic criteria.

A sensitivity study was carried out, using FE models in combination with logistical criteria, to determine the basic geometrical characteristics of the main structural component, that is, a trussed arch. Finally, the option with minimal structural depth at the support points and maximum depth in the mid-span zone was chosen due to both, construction and structural eﬃciency. The same criteria were used to determine the initial value and role of diﬀerent geometric attributes such as the cross section of bars, number of subdivisions, mid-span depth, and geometry of aluminium joints.

The second part of this design process was devoted to the description of the geometrical attributes for the whole array of components (with trussed arches at integer intervals ranging from 4 to 12 m span) as well as their options for variations and the relationship between them. This was done through a multi-objective study, where three goals were considered, namely minimal self-weight, minimal number of diﬀerent components and variable conﬁguration.

The set of studies that were in this chapter can be listed as follows:

1. Sensitivity study to determine the attributes of the trussed arches. Attributes were partially-optimised, meaning that geometrical attribute values were grouped by ranges. These included the cross section size of carbon-ﬁbre bars and depth of the truss at mid-span. Other attributes were designed with uniform

251 CHAPTER 7. CONCLUSIONS

attributes at this stage, including the size of arches at the support points, the number of subdivisions (aluminium joints) and the aluminium bar cross- section. Additionally, and in order to bring internal stress values to acceptable levels, a geometry-based method was created to allow the reduction of pre- stress. This solution was homogenously applied to all versions of ﬂexible arches, resulting in less-stressed collections of components.

2. Control of the number of different components. The study of the variations in length and angle between the crosses’ bars allowed the definition of a strategy to significantly reduce the number of different joints from 61 types to 7. It was observed that most of the different joints would vary only by a few millimetres from others. The solution then developed a design concept for a joint which would tolerate a length variation of 50 mm, meaning only 7 types would be needed. Each of these variations would need to adopt a minimum of two, and a maximum of four different positions (angle between the two aluminium bars). Both adaptations (in length and angle) needed to be manually operable.

3. Reduction of number of joints. This study used a geometry-based approach to determine the possibility of reducing the number of aluminium joints whist preserving the continuity of the bracing cables’ triangulation. This was only possible due to this attribute being defined as low-sensitivity according to the characterisation carried out in Chapter 4 and the low value stresses achieved in Chapter 5. The rules for such an operation were determined via an exhaustive study, from where solutions for failing sequences could be derived, resulting in a straight forward method. As a result, the number of different nodes (or arches’ subdivisions) was reduced to 4 different values.

4. Regulation of the distance between arches. The grouping of different attributes led to each arch being subject to different load conditions. On the other hand, loads were calculated assuming a uniform distance between arches. By varying the distance between arches, the load condition throughout the array of arches could be normalised. This adjustment did not imply an increase in the number of components, as membrane pieces were previously considered to be a semi- bespoke component, with 17 different variations identified.

The chapter concluded with the introduction of a parametric CAD model which allowed such surfaces to be created from a native CAD curve. Such curves outline the station footprint, and should be derived from the architectural scheme. Examples of applications of the Grasshopper® deﬁnition were shared.

Once the system grammar was resolved, the next chapter was dedicated to the study of other aspects of the system related to the assessment of the system’s

252 CHAPTER 7. CONCLUSIONS architectural, construction and logistical feasibility. This included diﬀerent options for aggregations of surfaces, design solutions for key components and a proposal for assembly sequence.

As in the ﬁrst study, proposals for aggregations of two perpendicular tunnels, as well as arrangements for the aggregations of three and four units were produced. The geometrical operations revealed the need to include a rigid element into the system. A trussed rigid supporting arch was then considered. This element was also introduced as a reinforcement component for cases of very long tunnels.

In the second part of this chapter, solutions were oﬀered for the implementation of key components, namely:

1. Arches’ bar segments. Bars consisted of standard carbon fibre bars. The length-based groups were identified by the parametric model. A total of 36 types were identified.

2. Aluminium scissor joints. Node types can also be labelled and accounted for by the scripting tool embedded in the Grasshopper® deﬁnition. Identiﬁcation of the type is based on the length of the joint’s blades. Additionally, the design process for a scissor-shaped joint digital prototype was also explored.

3. Rigid arches. Versions of a mountable rigid arch were also deﬁned, these included three variations: 3 x 2.1, 6, 4 and meter spans.

4. Membrane pieces. A solution for membrane formﬁnding was also presented, which is done using Rhinoceros© applications as well as a solution for connections of adjacent membrane sections.

5. Terminal elements. Proposals for ending elements were outlined including rigid panels and ﬂexible membranes.

Although anchorages are also considered a key component, the solution proposed in the initial scheme was not varied, as it was considered to be suﬃciently resolved.

This ﬁnal chapter concluded with examples of applications of the designed system for the implementation of the Glacier Union Station.

7.2 Contributions to Knowledge

There are two principal results achieved from this research. The ﬁrst part, based on the literature, was able to produce a descriptive collection of 12 minimal weight constructions designed for Subantarctic and Antarctic contexts. The description of

253 CHAPTER 7. CONCLUSIONS each case focused on the materiality used, assembly sequence, and its structural scheme. A brief description of the historical context and programmatic scheme of each project was also included. Finally, the array of structures was organised according to their structural system, based on a classification proposed by M. Bechthold. The author’s own secondary classification, based on the geometry of the surfaces was also introduced. The second result is the design of a generic lightweight structure. This comprises a hybrid system, featuring aspects of vault-like and gridshell systems. The system’s main components are flexible trussed arches of variable spans (variations consisting of integer values between 4 and 12 m), formed by carbon-fibre bars and aluminium joints. Arches are interconnected by two bracing systems: tensile membranes and an array of bracing cables. Vaults are constrained at intervals and at the ends by rigid mountable arches. The design process was able to balance three conflicting objectives, adaptable configuration, reduced number of components and low-tech assembly sequence. The resulting system is characterised by the possibility of progressively varying the size of flexible arches in units (ranging from 4 to 12 m span), achieving an adaptive morphology. Solutions were proposed for several vaulted units to be aggregated in different arrangements. Although arches were partially optimised (in terms of the cross-section of carbon fibre bars, mid-span depth, number of subdivisions, and distance between arches), which implied a diversification of geometrical attributes, it was possible to significantly reduce the number of different elements. These consisted of three types of carbon fibre bar sections, seven different types of scissor-shaped aluminium joints, one type of anchorage, three types of rigid arches, and seventeen different membrane pieces. Using principles of parametric design with a low tech approach, design solutions for these key elements were offered and an assembly choreography was proposed. It can finally be stated that both of these results are equally relevant for the purpose of this research.

7.3 Theoretical implications

The diversity of cases and the clear inﬂuence of environmental and logistical constraints derived from Antarctic and Subantarctic contexts in each of the structures portrayed in the ﬁrst part of this research enables the recognition of a singular paradigm.

254 CHAPTER 7. CONCLUSIONS

Furthermore, this study has also demonstrated that polar and subpolar scenarios do not only motivate the search for innovative design solutions, technologies and methods, but they have also been the natural response of native inhabitants to the extreme conditions of the Subantarctic region, who developed advanced construction technologies.

The diversity of approaches encountered with this study also supports the appeal from Antarctic scientiﬁc communities to conceive polar and subpolar regions as complex and varied scenarios, rather than the white empty canvases commonly pictured.

During this research it was found that no formal academic effort in the field of architectural and/or engineering has been previously made to portray such projects from a common perspective. This study is therefore, the first step towards a formal acknowledgement of such a paradigm.

The concept of ‘Polar Lightweight Structures’ was successfully tested in the second part of the research. Here, a novel problem was formulated, which dealt with the concept of an adaptable construction system, ruled by conditions of minimal weight, controlled number of different components, and a low-tech assembly procedure. The resulting system not only offers a feasible technical solution, but also an architectural tectonic tool capable of blending into the landscape or responding to the unique form of seasonal use experienced by Polar structures. This design represents a step forward in what has been done so far in the Polar context, in terms of architectural expression (as a larger and more complex design have been enabled), and also structural optimisation (where the concept of ’partial optimisation’ can offer a response to the use of parametric design tools in polar contexts.

Although eﬀorts were made to structure and systematise the design process, it is evident that the speciﬁcity of the problem does not allow the generalisation of the method to be employed, as in other cases of structural systems. In terms of parametric design environments, this method could not be translated into a generic design process. As an example, human assessment was constantly involved in the decision of how many values each geometric parameter of the structure should be divided into.

It is believed by the author that more eﬀort should be made to integrate design and engineering disciplines into Polar scientiﬁc communities, which is particularly valid for the Antarctic and Subantarctic cases. This research has provided a framework for this relating to Lightweight design.

255 CHAPTER 7. CONCLUSIONS

7.4 Limitation of this study

Limitations were encountered at diﬀerent stages of this research, involving aspects such as the collection of evidence of a rather undocumented topic, the development of a design methodology, and restrictions for post-design testing.

One of the main challenges encountered was the definition of a valid research methodology. This was particularly evident for the second part of the study (consisting of a design-based study). Although a clear research problem was formulated (the feasibility of conceiving an adaptable lightweight structure with a limited number of different components), the method of solving such a problem was undefined. It was only after a design scheme was introduced (a double curvature shell approach to a trussed system) that this problem could be broken down into a series of specific questions, and a suitable methodology (a multi-objective optimisation study) could then be identified and applied.

In contrast, the first part of the study, referring to the identification and characterisation of Antarctic and Subantarctic lightweight structures, could be planned and carried out with a clearer perspective. One of the key actions of this exercise was the identification of suitable categories of lightweight structures, which in this case was as proposed by M. Bechthold. As discussed in Chapter 2, the selection of this approach was based on Bechthold’s idea of using the structural behaviour as the primary parameter, independently of the overall shape, materiality, or scale. This approach enabled the successful assimilation between such diverse structures as vernacular dwellings and modern portable tents.

Once the methodologies were established for each part of the study (the characterisation of Antarctic lightweight structures and the design path of an adaptable lightweight system), diﬀerent challenges needed to be overcome.

For the ﬁrst part, the main challenge was the lack of academic literature in this topic, for which the material presented here was collected from a diverse range of sources, including interviews, websites, photographs and magazines articles. The description of the diverse array of vernacular structures turned out to be much more complex than initially expected. The literature on this topic, mostly by Hispanic authors (i.e. catholic missionaries), was particularly challenging to re- interpret for engineering/architectural purposes. Very limited evidence of these vernacular structures remains. That which does includes replicas reproduced by local museums in the Chilean and Argentinian Patagonian regions. Similarly, a fraction of the US South Pole Dome is now exhibited in a small private museum. Given the limited resources for this research, these samples could not be visited and documented ﬁrst hand. In other cases, such as the Admundsen-Scott Expedition Tent, original hand-

256 CHAPTER 7. CONCLUSIONS made sketches produced by Ian-Liddell were found with the collaboration of Buro Happold librarians, although it was not possible to establish where the original tent is now. This is a clear reflection of how little research has been done in this regard. As for the second part of the research, related to the design study of an adaptable lightweight structure, even though an architectural scheme was defined and a set of questions or tasks were specified, difficulties encountered were related to the method used for the structural analysis of numerous different digital models. The sensitivity study to define the basic characteristics of a trussed arch was carried out by comparing the results obtained from different models where one parameter was varied at the time (attributes defined included the rod section, mid-span depth, and the number of segments). The manual and individual production of these models proved tedious, time-consuming and was susceptible to involuntary errors. Every time an error was identified, correction was needed at different stages of the process, which could involve the production of a new CAD model, recalculation and reintroduction of nodal forces, re-assignment of materiality to each bar, redefinition of load cases or other parameters. It is believed that nearly 50 models were produced during this stage. This manual method was also used for the first part of the multi-objective study presented in Chapter 5. In this section, attributes of the whole set of arches (ranging from 4m to 12m) were studied in variation, with the objective to reduce the weight of the structure or conceived an aesthetic result (by differentiating the rod sections and the arches mid-span depth according to the span of each arch). Similar to the previous stage, this method proved laborious and unstable. Nearly It is estimated than another 450 models were produced at this stage . When the final principal results were collected and compared, some inconsistencies were found. Thorough revision of the models revealed that some erroneous values were induced, some of them at an early stage. The consequence of this was that models would create more conservative results than necessary (ranging from approximately 10 to 30 % of the results finally used, depending on the case). The manual correction of the models would have been similarly inefficient. As a result, a second method was introduced, by which the process was automated by scripting within the parametric environment provided by Grasshopper®. This tool not only avoided inaccuracies in the calculation of nodal forces found in the manual method, but also allowed for the quick production of multiple models, and therefore the detailed comparison of many individual attributes. Another limitation of the research was the impossibility of physically testing the results obtained. Whilst calculations and assumptions were thoroughly set-up, the novel and extreme scenario proposed cannot be fully portrayed by digital models. Therefore full-scale prototypes tested in-situ could have provided valuable infor-

257 CHAPTER 7. CONCLUSIONS mation to several aspects of the project, for instance, relating to the structural behaviour of carbon ﬁbre bars under severe low temperatures, or the eﬃciency of the assembly sequence proposed. These tests could not be undertaken due to the limited budget.

Reflections can also be made regarding the system attributes. Although the versatility of the system was reasonably investigated, limitations on the modification the system’s typology are acknowledged. As an example of this, the possibility of revising the geometry of the arches towards a more efficient configuration such as a funicular shape (rather than a generic semi-circumference) was considered. This would be done for two reasons: to provide a more efficient structural performance, and also because a funicular profile could reduce the unusable space defined by a semicircle. However, the modifications of this attribute require the modification of many of the grammar’s conditions already established, such as: distribution of crosses, mechanical behaviour of bars and aluminium crosses, and the triangulation of nodes, which are dependent of that particular geometry. As pointed out by Harding et al., the creation of sub-optimal solutions and the locked geometry, is a common limitation of parametrically designed models, and they require much more complex parametric definitions to be overcome[69].

A final limited aspect of the system is its capacity to adapt and perform in different scenarios, for instance being transported and relocated to another site in Antarctica. Elements have been designed according to the critical load conditions of a particular site. Whilst architecturally adaptable, the use of the same system in other contexts would require the revision of external load conditions (wind and snow), from which components would need to be redefined. Thanks to the second method implemented, modifications could be undertaken much more fluently, although the same components could not be reused in a more demanding environment.

7.5 Future work

There are several topics suggested by this research that should be further explored.

From the theoretical domain, perhaps the most interesting aspect still to be investigated is the opportunity to further study the structural behaviour of Subantarctic dwellings. The fact that a fascinating array of lightweight structures has remained unaddressed by literature dedicated to vernacular tents or dwellings in general is surprising, as they represent remarkable examples of smart use of minimal materials in one of the harshest environments. The multiple variations according to the geographical habitats reﬂects the complexities of the topic. Such a study, would imply the collection of historic documents, graphical recordings, and the consequent

258 CHAPTER 7. CONCLUSIONS reproduction using physical and digital models to enable further structural analysis. This last action could be done by using advanced finite element tools or state-of- the-art parametric applications to study the membrane and active bending element behaviour present in most of the cases. Another novel prospect suggested by the first study, is the production of academic literature regarding the many different approaches attempted by polar designers for the implementation of lightweight structures. In contrast to the many ongoing endeavours to document and comprehend the heritage of Arctic constructions (i.e. the work done by the Swedish Royal Institute of Technology’s Division of History of Science, Technology and Environment ) [123], Antarctica design lacks of any formal attempt to track the evolution of its built environment. One of the most critical aspects faced by Polar designers is the impossibility to easily test materials and designs in the real context. In that respect, there are many lessons from previous experiences that could guide future attempts. Knowledge and technologies developed by Antarctic lightweight structures could certainly be employed in other less-demanding environments. Hence, the importance of producing reliable technical material in this field. With respect to the second part of the research, there are also topics of interest that have been suggested. An example is the opportunity to further comprehend the behaviour of carbon-fibre components as a primary structural material in Polar climates, which has not yet been investigated. As discussed, there are several examples of small-scale commercial tents using carbon fibre bars that are annually brought to Antarctica. Examples of load-bearing elements using composites in a larger scale are to be found in sailing-sport equipment, such as mast and booms. In the context of this research in 2012, this topic was explored by the University of Bath’s Civil Engineering Masters student, Alberta De Nardi, who looked into the behaviour of carbon fibre bars under bending loads in cold environments. De Nardi designed and carried out a small-scale experiment where small rods of carbon fibre were progressively loaded in bending, immersed in a solution of liquid nitrogen solution and ethanol to force the temperature to be at -90 °C, to simulate Antarctic conditions. By varying the proportion of ethanol De Nardi was able to allow the temperature to be set to different levels. This represents an example of what could be further investigated. Another topic of interest is the prototyping of the components created as part of this thesis. The level of detail achieved in the design of arches and their most complex elements, namely the aluminium joints, makes this design suitable for full-scale prototyping. As earlier discussed, in-situ testing would be a major contribution to the validation of the material’s performance, assembly sequence, and the adaptive quality of the system.

259 CHAPTER 7. CONCLUSIONS

As for the particular parametric model presented in this research, it is believed by the author that solutions can be achieved to allow alternatives to the geometrical optimisation of the system (such as allowing the inspection of funicular shapes of arches, or an asymmetrical shape in the case where a predominant wind direction is known, or a combination of both, among others) by exploring more complex parametric deﬁnitions. Also, other geometrical operations, such as conﬁgurations curved on-plan, could be explored.

As discussed Section 7.4, it is not possible to consider the application of the same method as a generic action tool over for the partial-rationalisation of other structural systems . However, it is possible to consider a tool that enables the generic aggregation of elements. Given that the attributes of the physical components were speciﬁed and the system’s grammar was established, it is possible to conceive a scripting tool (for example, a Grasshopper component) to implement a structural surface out of a simple NURBS curve, using the elements described in this study.

Regarding the sensitivity study method developed, this also oﬀers an interesting assessment approach that can be employed in early stages by designers, where countless options can be quickly generated, evaluated, analysed and either discarded or taken forward. Such an approach could present an innovative interface between early conceptual design and structural analysis stages.

7.6 Final comments

It can finally be stated that the aims and objectives of this research, which are to demonstrate the validity of Polar Lightweight design and the development of a novel design method based on polar-constraints, have been satisfactorily achieved. Polar Lightweight design has been defined and addressed from different perspectives. The creation of a narrative has demanded careful combinations of research methods derived from both theoretical and technical domains. The two outputs obtained from this research are on one hand, the structural characterisation of a fascinating array of Antarctic and Subantarctic lightweight structures, and on the other hand, a semi-modular lightweight system whose design is based in the strict environmental and logistical constraints imposed by one particular Antarctic scenario. Both results contribute equally to the recognition of the polar lightweight system as a valid design paradigm.

It is enthusiastically believed by the author that this thesis can oﬀer a robust and motivating framework for future researchers from a varied range of disciplines (engineers, designers, historians and others), or for whoever is interested in what can be distinctively called Polar Lightweight Structures.

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[77] T. d’Estree Sterk, 2003, “Using Actuated Tensegrity Structures to Produce a Responsive Architecture,” ACADIA22: Connecting Crossroads of Digital Discourse, pp. 84–93.

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[81] A. Agkathidis, 2009, Modular Structures in Design and Architecture, 2nd ed., BIS Publishers.

[82] P. Serrano, A. Veliz, and J. Bak, 2009, “The Jotabeche Glacier Monitoring Station: An environmentally sustainable proposal for buildings in extreme environments,” Ciudad y Arquitectura, nÂ°139, pp. 56–64.

[83] A. Veliz, P. Serrano, and J. Bak, “Research Facilities in Extreme Environment A low-tech approach to Innovative Building Technologies,” in Proceedings of the 9th ACUNS International Student Conference on Northern Studies and Polar Regions, 2-5 October 2009. Whitehorse: Association of Canadian Universities for Northern Studies, W. A. o. C. U. f. N. Studies, Ed. Whitehorse: Whitehorse: Association of Canadian Universities for Northern Studies, 2009, pp. 187–195.

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[87] I. Hwang, 1998, VERB NATURES (Actar’s Boogazine), architectu ed., Actar.

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[91] J. Bak, 2006, “Sistema Constructivo para Eventos Geográﬁcos en Isla Navarino,” Ph.D. dissertation, Valparaiso: University of Technology Federico Santa Maria.

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[95] D. J. Wickersheimer, 1976, “The Vierendeel,” Journal of the Society of Architectural Historians., vol. 35, no. 1, pp. 54–60.

[96] Civil Engineering Portal Contributors, 2007, “What are the Characteristics of Vierendeel Ginder?, Civil Engineering Portal.” [Online]. Available: http://www.engineeringcivil.com/what-are-the-characteristics-of- vierendeel-girder.html [Accessed: 2015-02-03]

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[100] J. Schutz, jan 1998, “Properties of composite materials for cryogenic applications,” Cryogenics, vol. 38, no. 1, pp. 3–12. [Online]. Available: http://www.sciencedirect.com/science/article/pii/S0011227597001021

[101] R. Reed and M. Golda, jan 1994, “Cryogenic properties of unidirectional composites,” Cryogenics, vol. 34, no. 11, pp. 909–928. [Online]. Available: http://www.sciencedirect.com/science/article/pii/0011227594900779

[102] Sapa Proﬁles UK, 2015, “Properties of aluminium, Aluminiumdesign.net.” [Online]. Available: http://www.aluminiumdesign.net/why-aluminium/ properties-of-aluminium/ [Accessed: 2015-05-28]

[103] a. Hurlich, 1963, “Low Temperature Metals,” Chemical Engineering, pp. 311– 325.

[104] Key to Metals AG, 2001, “Properties of Aluminum Alloys at Cryogenic and Elevated Temperatures, Total Material. The worlds most comprehensive materials database.” [Online]. Available: http://www.totalmateria.com/ page.aspx?ID=CheckArticle{&}site=ktn{&}NM=23 [Accessed: 2015-05-28]

[105] O. Senkov, “High Strength Aluminum Alloys for Cryogenic Applications,” in Metallic Materials with High Structural Eﬃciency, S. A. Senkov, Oleg N., Miracle, Daniel B., Firstov, Ed. Springer Netherlands, 2004, no. DECEMBER 2003, pp. 151–162. [Online]. Available: http://books.google.com/books?id= uzcZU3EZAo8C{&}pgis=1

[106] M. Evernden, 2013, ([email protected]), “Information on Carbon Fibre Bars,” Email to J. Bak ([email protected]).

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[111] ——, 2003, “DS/EN 1991-1-3: 2003.”

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[114] P. Shepherd, “Files,” ([email protected]).

[115] D. Piker, 2013, “Kangaroo: Form ﬁnding with computational physics,” Architectural Design, vol. 83, no. 2, pp. 136–137.

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272 Appendix A

Prospects on a Formﬁnding Method using Surface Evolver and Parametric CAD Tools

(Note: This text corresponds to an extract of the Transfer Report submitted by the author in 2011 in order to obtain a doctoral candidature in the Department of Architecture and Civil Engineering at the University of Bath)

This chapter discusses the creation of a parametric formﬁnding method for minimal surfaces based on the geometric constraints previously given: implementation of minimal surfaces with diﬀerent Gaussian curvatures, variation of edge condition, control of the number of the surface’s components and volume. Physical parameters like loads derived from external forces and mechanical properties of materials are expected to be implemented in further steps.

The development of such a method requires the comprehension and integration of two very diﬀerent 3-D digital modelling tools: a mathematical software, Surface Evolver, and a CAD design tool, Rhino, assisted by C-Sharp scripting in Grasshop- per.

A.1 The Surface Evolver

Surface evolver is a mathematical software tool developed by Kenneth A. Brakke from Susquehanna University [1]. The software works with the minimization of diﬀerent energies, like tension or others, on surfaces subject to constraints, using a gradient method. Basic examples are soap ﬁlms, which are minimal surfaces as they minimize the area constrained to frames, and soap bubble clusters which do

273 APPENDIX A. PROSPECTS ON A FORMFINDING METHOD USING SURFACE EVOLVER AND PARAMETRIC CAD TOOLS the same subject to surrounding ﬁxed volumes in each bubble. So both, positive and negative Gaussian curvature surfaces can be obtained with Surface Evolver. Many other typologies can be also implemented on this platform.

The surfaces are defined by three arrays of geometrical components: ‘vertices’ (points in Euclidian coordinates), ‘edges’ (straight line joining two vertices), and ‘facets’ (a triangular plate defined by three oriented edges) which a listed in a text datafile.

Possible interventions during the evolution process include changes in the properties of the surfaces, or control of the behaviour of the evolution through physical and geometrical operations [2]. The basic operations that can be carried out on the surface are: iterations (one descendent gradient step of energy minimization), mesh subdivision or ‘surface reﬁnement’, and mesh relaxation or ‘equangulation’. Geometrical constraints can include ﬁxed boundaries, volumes in the case of bodies and vertices might be constrained to lie on smooth manifolds, etc.

The most used energy when operating with minimal surfaces is tension, but there are many other energies that are important in shaping liquid surfaces like gravity, elastic bending, stretching, pressure, etc.

The initial surface is specified as a text datafile that can be produced with any standard text editor, and then named with the right file extension (.fe), to be able to be opened from Evolver.

Figure A.1 shows the evolution of a catenoid using tension energy and the three mentioned operations.

The capability of running a formﬁnding process which deﬁnes a mesh from a minimal surface given geometrical and physical constraints, suggests that Surface Evolver could be a suitable tool as a design environment for the purposes of this research. However, it presents some aspects that needed to be considered, such as:

• Controlling number of components: the optimization of a surface is naturally generated by the increment on the number of vertices forming the ﬁlm. For the purposes of this study, the number of edges deﬁning the mesh, which could represent the constructive components of a system, is required to be known and relatively controlled.

• Mesh geometry: the different structural systems expected to be tested in the future might required different geometrical definition of the surface’s constructive components (panels for a monocoque shell, umbrella membrane with radial tailoring seams, air-chambers forming a pneumatic system, or any other), thus a triangular mesh might not be always the required result.

274 APPENDIX A. PROSPECTS ON A FORMFINDING METHOD USING SURFACE EVOLVER AND PARAMETRIC CAD TOOLS

(a) (b) (c)

(d) (e)

Figure A.1: Evolution of the catenoid in Surface Evolver using tension energy, using the three basic operations, (a) original cylinder; (b) cylinder after mesh reﬁnement ;(c)catenoid after area minimization; (d) catenoid after mesh reﬁnement, area minimization and mesh relaxation; (e) collapse of the unstable surface

• Interoperability: Surface Evolver is not designed to interact with any CAD tool. Thus, once a minimal surface has been found, the resulting geometry coordinates and arrays of edges and facets can only be ‘dumped’ as a text ﬁle.

• Parametric definition: The initial data file defines geometries through parametric coordinates, in this case cylindrical coordinates, which might represent a limitation for the desired variations of surfaces and interaction with other digital environments.

The Evolver’s data for a cataneoid is presented as following:

PARAMETER RMAX = 1.5088795 // minimum radius for height PARAMETER ZMAX = 1.0 boundary 1 parameters 1 // upper ring x1: RMAX * cos(p1) x2: RMAX * sin(p1) x3: ZMAX boundary 2 parameters 1 // lower ring x1: RMAX * cos(p1) x2: RMAX * sin(p1) x3: -ZMAX vertices // given in terms of boundary parameter 1 0.00 boundary 1 fixed

275 APPENDIX A. PROSPECTS ON A FORMFINDING METHOD USING SURFACE EVOLVER AND PARAMETRIC CAD TOOLS

2 pi/3 boundary 1 fixed 3 2*pi/3 boundary 1 fixed 4 pi boundary 1 fixed 5 4*pi/3 boundary 1 fixed 6 5*pi/3 boundary 1 fixed 7 0.00 boundary 2 fixed 8 pi/3 boundary 2 fixed 9 2*pi/3 boundary 2 fixed 10 pi boundary 2 fixed 11 4*pi/3 boundary 2 fixed 12 5*pi/3 boundary 2 fixed edges 1 1 2 boundary 1 fixed 2 2 3 boundary 1 fixed 3 3 4 boundary 1 fixed 4 4 5 boundary 1 fixed 5 5 6 boundary 1 fixed 6 6 1 boundary 1 fixed 7 7 8 boundary 2 fixed 8 8 9 boundary 2 fixed 9 9 10 boundary 2 fixed 10 10 11 boundary 2 fixed 11 11 12 boundary 2 fixed 12 12 7 boundary 2 fixed 13 1 7 14 2 8 15 3 9 16 4 10 17 5 11 18 6 12 faces 1 1 14 -7 -13 2 2 15 -8 -14 3 3 16 -9 -15 4 4 17 -10 -16 5 5 18 -11 -17 6 6 13 -12 -18

276 APPENDIX A. PROSPECTS ON A FORMFINDING METHOD USING SURFACE EVOLVER AND PARAMETRIC CAD TOOLS

Figure A.2: Initial parametric cylinder produced with ‘input’ Grasshopper deﬁnition.

A.2 Integrated geometry-based method using a Catenoid

The process of creating a common framework that permits to operate with the optimized geometry in a CAD environment entailed an in-depth study for the integration of the different tools (Surface Evolver, Grasshopper and C-Sharp), in order to overcome the limitations that the differences of languages presented. Thus, different models were developed during this research.

The model presented in this report it is based in the case of the Catenoid, and includes two different Grasshopper definitions, so-called ‘input’ and ‘output’ Grasshop- per definitions.

For the ‘input’ Grasshopper definition, the initial geometry ,in this case a cylinder, is initially parametrically defined where the number of rings, number of subdivisions and height can be customised; the radii remain fixed for this case [Fig. A.2]. As result, it produces a text file in the right format to be directly called from Evolver as a datafile, which means that it includes the arrays of Vertices (Cartesian coordinates), Edges, Faces and Boundaries [Fig A.3] in the right format and in the right order. It also can be used with arbitrary closed curves, as shown in the examples in next section.

Consequently, once the datafile is called from Surface Evolver, the formfinding process is run and the cylinder is optimised [Fig. A.4]. The number of components is preserved by uniquely operating with the reduction of tension energy and mesh relaxation. Once the surface cannot longer be reduced, a text file is obtained with the new coordinates of the catenoid.

277 APPENDIX A. PROSPECTS ON A FORMFINDING METHOD USING SURFACE EVOLVER AND PARAMETRIC CAD TOOLS

Figure A.3: Data ﬁle produced in Grasshopper with the ‘in-put’ model.

Figure A.4: Optimized Rhino catenoid using Surface Evolver.

278 APPENDIX A. PROSPECTS ON A FORMFINDING METHOD USING SURFACE EVOLVER AND PARAMETRIC CAD TOOLS

The ‘output’ Grasshopper definition permits any Surface Evolver data file to be read in again, by using a short scripting code in Grasshopper, so once the geometries have been optimised in Evolver they can be reproduced in a CAD environment. As the definition is aimed at being useful for more than one particular entry, the number of nodes and faces is required to be specified in Grasshopper using sliders, so any array of nodes can be imported in Rhino.

Horizontal, vertical and diagonals edges can be implemented separately, so the surface can be defined by different sets of edges (rings, quadrilateral or triangular mesh, columns, diagonals or combinations of them). As previously mentioned, in further phases of this research, edges are expected to define constructive elements, so this method will be of benefit when different structural systems are tested. It might also facilitate the fabrication process (i.e. definition of membrane’s tailoring seams) itself.

One of the main diﬃculties that this exercise presented was the addition of midpoints by Evolver at the centre of each quadrilateral facet, as the shape optimisation entailed the triangulation of them, thus it caused the variation on the initial number of components. This was avoided by deﬁning faces as oriented triangles in the ‘input’ model, so when Evolver executes the optimization, no more nodes (thus no more edges) are added.

Another diﬃculty that needed to be overcome to permit the interoperability between these two environments was that while arrays in Evolver are zero-based, Grasshopper series are one-based. Since Grasshopper oﬀers many options to operate with series and arrays, it was decided to adapt the entire model to the Evolver’s language.

Screen-shots of both in-put and out-put Grasshopper models are shown in Figures A.5 and A.6.

A.3 Testing Examples

This section shows the application of the model on two freeform closed curves. In each case, the ‘input’ Grasshopper definition was used to produce two very different irregular shapes, by using different values for subdivision and extrusion parameters.

279 APPENDIX A. PROSPECTS ON A FORMFINDING METHOD USING SURFACE EVOLVER AND PARAMETRIC CAD TOOLS

Figure A.5: Parametric deﬁnition for the generation of a cylinder and the suitable dataﬁle for the Surface.

280 APPENDIX A. PROSPECTS ON A FORMFINDING METHOD USING SURFACE EVOLVER AND PARAMETRIC CAD TOOLS

Figure A.6: Parametric deﬁnition for form-found geometry obtained from the Surface Evolver.

281 APPENDIX A. PROSPECTS ON A FORMFINDING METHOD USING SURFACE EVOLVER AND PARAMETRIC CAD TOOLS

A.3.1 First Optimization of an Extruded Free-Form Curve

Figure A.7: Free-form curve produced in Figure A.8: Extrusion of the free-form Rhino. curve by 14 oﬀ-settings, separation of 0.508 length units, subdivided in 20 segments using the ‘input’ Grasshopper deﬁnition.

Figure A.9: Surface reproduced in Surface Figure A.10: Surface after 290 iterations. Evolver with a triangular mesh.

Figure A.11: Optimized shape after 290 Figure A.12: New vertices reproduced iterations and 1 mesh relaxation step. in Rhino using the ‘output’ Grasshopper deﬁnition.

282 APPENDIX A. PROSPECTS ON A FORMFINDING METHOD USING SURFACE EVOLVER AND PARAMETRIC CAD TOOLS

Figure A.13: Vertices joint forming a Figure A.14: Vertices joint forming triangular mesh using Grasshopper ‘output’ a quadrilateral mesh using the ‘output’ deﬁnition. Grasshopper deﬁnition.

Figure A.15: Vertices joint forming a set Figure A.16: Vertices joint forming paral- of parallels rings using Grasshopper ‘output’ lels columns using the ‘output’ Grasshopper deﬁnition. deﬁnition.

283 APPENDIX A. PROSPECTS ON A FORMFINDING METHOD USING SURFACE EVOLVER AND PARAMETRIC CAD TOOLS

A.3.2 Second Optimization of a Cylinder with a Free-Form Section

Figure A.17: Free-form curve produced in Figure A.18: Extrusion of the second Rhino. free-form curve by 5 oﬀsetting, with a separation of 0.217 length units, subdivided in 20 segments using the ‘input’ Grasshopper deﬁnition.

Figure A.19: Surface reproduced in Figure A.20: Surface after 260 iterations. Surface Evolver with a triangular mesh.

284 APPENDIX A. PROSPECTS ON A FORMFINDING METHOD USING SURFACE EVOLVER AND PARAMETRIC CAD TOOLS

Figure A.21: Optimized shape after 210 Figure A.22: New vertices reproduced iterations and 1 mesh relaxation step. in Rhino using the ‘output’ Grasshopper deﬁnition.

Figure A.23: Vertices joint forming a Figure A.24: Vertices joint forming triangular mesh using Grasshopper-input a quadrilateral mesh using the ‘output’ deﬁnition. Grasshopper deﬁnition.

Figure A.25: Vertices joint forming parallels columns using the ‘output’ Grasshopper deﬁnition.

285 APPENDIX A. PROSPECTS ON A FORMFINDING METHOD USING SURFACE EVOLVER AND PARAMETRIC CAD TOOLS

Figure A.26: Optimized cylinder with oriented edges using surface Evolver.

A.4 Further Work Using Surface Evolver

A.4.1 Form-ﬁnding with oriented Boundaries

As figure A.26 shows, boundaries can be easily modified in their position from the datafile. For example, this was made by simply modifying the original definition of the boundaries of the regular cylinder to:

PARAMETER RMAX = 1.5088795 // minimum radius for height PARAMETER ZMAX = 1.0 boundary 1 parameters 1 // upper ring x1: RMAX * cos(p1) * 1.5 x2: RMAX * sin(p1) x3: ZMAX boundary 2 parameters 1 // lower ring x1: RMAX * cos(p1) x2: RMAX * sin(p1) * 1.5 x3: -ZMAX

This option also suggests than more than two boundaries could be deﬁned in the initial dataﬁle, so for instance tri or more axial system could be developed

A.4.2 Triple Periodic Minimal Surfaces

Minimal surfaces with crystalline structure are of particular interest for this research, both because of the Architectural possibilities that their enclosures might suggest, and also because they address the problem of replication, aggregation and transformation earlier stated.

286 APPENDIX A. PROSPECTS ON A FORMFINDING METHOD USING SURFACE EVOLVER AND PARAMETRIC CAD TOOLS

Figure A.27: Evolution of the Schwarz’ P Surface using Surface Evolver.

There is a large number of fascinating triple periodic minimal surfaces [TPMS], many of them originally discovered by Alan Schoen in his famous report for NASA ‘Inﬁnite Periodic Minimal Surface without Self-Intersection’ from 1970 [3].

In Evolver, TPMS are achieved by deﬁning and then optimising the fundamental region of the structure, which is then suitably transformed (duplicated, displaced and rotated). The fundamental regions are usually very simple due their high symmetry.

Figure A.27 shows the development of the Schwarz’ P Surface in the Evolver, one of the simplest and best-known cases of TPMS. Its fundamental region corresponds to a tetrahedron.

The upper images correspond to the fundamental section before and after its evolution. The lower images show one cubical unit cell (left) and then same unit cell repeated and four times (right).

A.4.3 Synclastic Surfaces Using other Energies

As discussed earlier, minimal surfaces are intrinsically saddle shapes. Nevertheless, there are many different ways to run formfinding processes using different energies

287 APPENDIX A. PROSPECTS ON A FORMFINDING METHOD USING SURFACE EVOLVER AND PARAMETRIC CAD TOOLS

Figure A.28: Evolution of the mound using gravity. to produce positive Gaussian curvature surfaces, the most basic ones are gravity and pressure.

Gravitational potential energy is important in shaping liquid drops lying on, hanging from, or up against ﬁxed surfaces.

Figure A.28, shows the evolution of the ‘Mound’. As any other body, the initial value of gravity is zero and body density is 1. By a simple set of operations it can be evolved to a hemisphere without gravity. The steps run in this case were:

refine edge where on_constraint 1 g 10 // perform 10 minimization iterations r // refine mesh g 10 r g 20 hessian // minimize energy by calculating second derivate matrix h e s s i a n

The same model can be used to model a drop hanging from the ceiling by setting negative gravity [Fig. A.30]. The model below was made by setting gravity to -5 and

288 APPENDIX A. PROSPECTS ON A FORMFINDING METHOD USING SURFACE EVOLVER AND PARAMETRIC CAD TOOLS

Figure A.29: Hanging mound using negative gravity turning the graphic window upside down. By evolving the surface to 50 iterations (g 50) it is possible to watch the drop fall.

An alternative method to achieve synclastic shapes is using pressure. Pressure is a force per unit perpendicular to a surface.

As explained by Brakke [2], in the evolver, pressure can operate in three diﬀerent ways:

1. “If a body has a volume constraint, then the boundary surface is unlikely to be a minimal surface. Hence, pressure is needed to counteract the desire of the surface to shrink. When there are volume constraints, the evolver automatically calculates the pressure needed.

2. A body may have a prescribed pressure. Then the appropriated force is added to the forces on the vertices when calculating the motion of the surface. This is a way of prescribing mean curvature, since pressure = surface tension * mean curvature. (Therefore, prescribed volume and prescribed pressure are not possible on the same body, at the same time).

3. The evolver can treat bodies as being made of an isothermal ideal gas that is bodies can be compressible. The pressure given is the ambient pressure outside all bodies. Each body must have a volume speciﬁed, which is the volume of the body at the ambient pressure”.

Volume constraints are of particular interest for this design-based research. The image below shows the evolution of the ‘Bubble pipe’ with prescribed pressure, using the second approach. The maximum pressure state is when the two bubbles are hemispheres, where the pressure is 2 (pressure in a sphere is equal to [2* tension/radius]). The sequence shows the increasing pressure from 1, 1.5, 2, up to 3. Iterations, subdivision and mesh relaxations are run iteratively at each stage.

289 APPENDIX A. PROSPECTS ON A FORMFINDING METHOD USING SURFACE EVOLVER AND PARAMETRIC CAD TOOLS

If the pressure is increased beyond the critical value of 2, the bubble surface might not be stable and it is likely to expand inﬁnitely if, as the pressure is too high.

A.5 Conclusions

The proposed formﬁnding method has proved successful for the generation of minimal surfaces with diﬀerent curvatures subject to physical and geometrical constraints, as well as for the integration of mathematical and CAD software tools.

Although few examples have been demonstrated, Surface Evolver offers an extraor- dinarily powerful platform to operate with well known stable minimal surfaces or to produce new ones. It is suggested that the aggregation of components with different geometrical definitions can be easily executed in the Rhino environment.

The possibility to operate with many diverse constraints suggests that this methodology can handle the incorporation of the design conditions previously deﬁned in Chapter II, for which their parameterization (or translation into quantitative attributes) turns out of radical importance. In this way, for example, external forces (like snow and wind load) or speciﬁc volume constraints could be incorporate as constraints for the design of surfaces.

From a geometrical perspective, futures challenge for this method clearly points towards the generation of more complex surfaces, which can only be achieved with a deeper comprehension on the mathematical and topological properties of minimal surfaces, as earlier suggested. Even though the work shown in this chapter is an initial exploration, the comprehension of the operatibility of very diﬀerent digital environments, rather than their usage in a traditional way, has opened an incredibly wide range of suitable possibilities to be studied and used for the purposes of this research.

A.6 References

[1] Brakke, K., 1992.The Surface Evolver. Experimental Mathematics, 1(2), pp. 141- 165. [2] Brakke K. A., 2008. Surface Evolver Manual. Version 2.30. Selinsgrove, USA: Susquehanna University. [3] Schoen, A., 1970. Inﬁnite Periodic Minimal Surfaces without Self-intersections. Washington, D. C., USA: NASA (TN D-5541)

290 APPENDIX A. PROSPECTS ON A FORMFINDING METHOD USING SURFACE EVOLVER AND PARAMETRIC CAD TOOLS

Figure A.30: Evolution of the ‘Bubble pipe’ using prescribed pressure.

291

Appendix B

Calculations of Peak Velocity Pressure

As indicated by the Danish Standard [1], the factors to be considered for Wind Load for Vaulted Roofs and Domes can be listed as:

cdir is a directional factor (1.0 can be used conservatively) cseason is a seasonal factor (1.0 can be used conservatively) vb,0 is the base value for the wind velocity (in this case set to 12.8 m/s [2])

The basic wind velocity vb can be calculated as:

vb = cdircseasonvb,0 = 12.8 m/s

Given that,

z0 is the roughness length (0.010 according to Table EC4.1 assuming terrain category I) ze is the reference height (6.00 m for the largest span) zmin is the minimum height (1 m according to Table EC4.1 assuming terrain category I) z0,II roughness length for terrain category II (0.05 m according to Table EC4.1) co is an orography factor (conservatively set to 1.0)

ρ is the air density (1.25 kg/m3 at ground level) kl is a turbulence factor (recommended value 1.0)

293 APPENDIX B. CALCULATIONS OF PEAK VELOCITY PRESSURE

The terrain factor kr is determined as

0.07 kr = 0.19 · (zl/z0) = 0.17

By this the roughness factor cr is determined

cr = kr ln(z/z0) = 1.09

The mean wind velocity vm is calculated as

vm = crcovb = 13.9 m/s

Standard deviation σv is determined

σv = krvbkl = 2.17

The turbulence intensity Iv is determined

σv Iv = = 0.16 vm

The reference mean velocity pressure qb can be calculated as follows:

1 q = ρv ²=0.12 kN/m2 b 2 m and ﬁnally, the peak velocity pressure qp is given by

1 q = (1 + 7 · I ) · · ρ · v ² = 0.25 kN/m2 p v 2 m

By reduction for missing correlation (kkr = 0.85) between windloads acting on the windward and leeward sides of the structure, the design wind pressure is determined

kkrqp = 0.21 kN/m2

References

[1]: Danish Standards Foundation, "DS/EN 1991-1-4:2007", (2007).

294 APPENDIX B. CALCULATIONS OF PEAK VELOCITY PRESSURE

[2]: C. González, “Chile triplica investigacion en la Antartica en los ultimos años” (2014), Santiago: La Tercera, 2-3.

295

Appendix C

C-sharp Component for the Placement of Trussed Arches along a NURBS Curve

///

/// This procedure contains the user code. Input parameters are provided as regular arguments, /// Output parameters as ref arguments. You don’t have to assign output parameters, /// they will have a default value. ///

private void RunScript(Curve crv1, Curve crv2, double step , ref object P, ref object D, ref object O) {

//ONLYWORKSWHENCURVEISRUNNINGALONGX-AXIS!!

//Define lists to store results List points = new List(); List < double > diameters = new List < double >() ; List originPoints = new List();

//Define variable to store new point Point3d newPoint;

//Define s as length parameter on curve

297 APPENDIX C. C-SHARP COMPONENT FOR THE PLACEMENT OF TRUSSED ARCHES ALONG A NURBS CURVE

double s = 0;

//Define lastS as the last valid length parameter double lastS ;

//Calc arc diameter double diameter = getRoundedDiameter(crv1, crv2, s, step );

//Add point at begining of curve newPoint = crv1.PointAtLength(s);

//Make sure arch has incremented diameter. newPoint.Y = diameter / 2; points.Add(newPoint); originPoints.Add( new Point3d(newPoint.X, 0, 0)); lastS = s;

//Store last diameter in list diameters.Add(diameter);

//Move along curve in small increments while (s < crv1.GetLength()) {

//Move a small step along the curve by increasing the length parameter s += 0.05;

//Get rounded diameter diameter = getRoundedDiameter(crv1, crv2, s, step);

//Check gap if gap is larger than maximum gap for the given diameter. double gap = Math.Abs(points[points.Count - 1].X - crv1.PointAtLength(s).X);

Print (" gap :␣" + gap ); if (gap > maxgap(diameter, diameters[diameters. Count - 1])) {

298 APPENDIX C. C-SHARP COMPONENT FOR THE PLACEMENT OF TRUSSED ARCHES ALONG A NURBS CURVE

Print ("Creating␣arc!"); //If gap is too large, create a arc at the last valid length parameter, lastS.

//Get last valid diameter diameter = getRoundedDiameter(crv1, crv2, lastS, step );

//Create point for arc at last valid parameter newPoint = crv1.PointAtLength(lastS);

// Make sure arch has incremented diameter. newPoint.Y = diameter / 2; points.Add(newPoint); originPoints.Add( new Point3d(newPoint.X, 0, 0));

//Add to list of diameters diameters.Add(diameter); } else { Print ("Keep␣looking!");

//If not, update lastS lastS = s; } }

P = points ; D = diameters; O = originPoints; }

// double getRoundedDiameter(Curve crv1, Curve crv2, double s, double step ) {

double diameter = crv1.PointAtLength(s).DistanceTo( crv2.PointAtLength(s));

299 APPENDIX C. C-SHARP COMPONENT FOR THE PLACEMENT OF TRUSSED ARCHES ALONG A NURBS CURVE

//Snap to nearest diameter increment return Math.Round(diameter / step) * step; }

double maxgap ( double diameter , double prevdiameter) {

double maxgap = 0; if (diameter < 4) { maxgap += 2.4 / 2; } else if (diameter < 5) { maxgap += 1.81 / 2; } else if (diameter < 6) { maxgap += 1.3 / 2; } else if (diameter == 6) { maxgap += 2.2 / 2; } else if (diameter < 7) { maxgap += 1.95 / 2; } else if (diameter < 8) { maxgap += 1.71 / 2; } else if (diameter == 8) { maxgap += 1.77 / 2; } else if (diameter < 9) { maxgap += 1.5 / 2; } else if (diameter < 10) { maxgap += 1.23 / 2; } else if (diameter == 10) { maxgap += 1.67 / 2; } else if (diameter < 11) { maxgap += 1.43 / 2; } else if (diameter <= 12) { maxgap += 1.2 / 2; }

if (prevdiameter < 4) { maxgap += 2.4 / 2; } else if (prevdiameter < 5) { maxgap += 1.81 / 2; } else if (prevdiameter < 6) { maxgap += 1.3 / 2;

300 APPENDIX C. C-SHARP COMPONENT FOR THE PLACEMENT OF TRUSSED ARCHES ALONG A NURBS CURVE

} else if (prevdiameter == 6) { maxgap += 2.2 / 2; } else if (prevdiameter < 7) { maxgap += 1.95 / 2; } else if (prevdiameter < 8) { maxgap += 1.71 / 2; } else if (prevdiameter == 8) { maxgap += 1.77 / 2; } else if (prevdiameter < 9) { maxgap += 1.5 / 2; } else if (prevdiameter < 10) { maxgap += 1.23 / 2; } else if (prevdiameter == 10) { maxgap += 1.67 / 2; } else if (prevdiameter < 11) { maxgap += 1.43 / 2; } else if (prevdiameter <= 12) { maxgap += 1.2 / 2; }

return maxgap ; } //

301