LOCAL & ITERATIVE
Wax bridge structures
Tutors: Shajay Bhooshan Vishu Bhooshan David Reeves Students: Jurij LiÄ?en Sujitha Sundraraj Ke Wang
CONTENTS CHAPTER 1
- Material experimentation
CHAPTER 2 - Rules of construction
CHAPTER 3
- Geometry experimentation, self supporting structures
CHAPTER 4 - Digital solutions
CHAPTER 5
- Final model construction
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Local & Iterative
AA DESIGN AND RESEARCH LAB - WORKSHOP 1 Tutors: Shajay Bhooshan Vishu Bhooshan David Reeves Students: Jurij LiÄ?en Sujitha Sundraraj Ke Wang
WORKSHOP BRIEF The task of the workshop was to construct the lightest and strongest structure that could span 1,5m using any material capable of deposition. The two materials suggested were wax and sodium acetate.
Architectural Association School of Architecture, London, November 2015
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CHAPTER 1
- Material experimentation
The material used was white beeswax. After some experimentation with other kinds of wax we discovered that beeswax works best. It is easier to melt and control and it provides for better cohesion. The material was bought in beads.
Additional equipment needed were syringes of different sizes. The syringes used for water were bigger size (100 - 150 ml) and equipped with a needle for better accuracy and higher pressure.
Syringes for wax deposition were smaller and did not require the usage of a needle.
Heating and melting the wax using wax heaters. The heaters use an indirect heating method that prevents the wax from boiling.
Using syringes to deposit the wax and cooling it down with cold water.
The simultaneous deposition and cooling allows for creation of first simple geometries.
CHAPTER 1
- Material experimentation A catalogue of initial experiments. The experiments were oriented towards discovering the properties of wax and learning about the technique of deposition. The material proved difficult and brittle in the case of cantilevering geometries.
01 2D Cantilever structure: 3 vertexes, 2 edges
02 1D structure: 2 vertexes, 1 edge
03 2D structure broken: 3 vertexes, 2 edges
Triangulation
04 3D tower structure: 7 vertexes, 9 edges
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2D line at an angle: 2 vertexes, 1 edge
07 2D Simple frame: 6 vertexes, 5 edges
Triangulation
08 3D Cantilever structure: 12 vertexes, 21 edges Triangulation
31 cm Triangulation
09 27 cm 3D Cantilever structure: 18 vertexes, 32 edges
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CHAPTER 2
- Rules of construction Experimenting with the material and trying to span using cantilevered structures, we discovered that having vertexes with higher valency improves the structural properties. The Furthermore triangulating shapes assure that the geometry is structurally stable. Different options were explored that use triangulation and create high valency values. We were looking at an algorithmic approach that would be based around simple rules and could generate a stable, self supporting structure. Starting with a simple triangle we add a point in the desired direction of growth. The point is connected to the closest two existing points. This creates a triangle that serves as a base for further growth. In the case of the structure becoming unstable a new rule is applied. A secondary point is added to support the growing geometry.
Direction of collapse
Growth direction
01
Added triangle
02
03
04
Add a support
Direction of collapse
05
8
06
Add a support
Local & Iterative
Step 1
Step 2
Step 3
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CHAPTER 2
- Rules of construction The two dimensional system of triangulation was expanded into tetrahedron based growth. The growth begins with a single tetrahedron. In the next step a point is added in the desired direction of growth perpendicular to the centre of one of the faces. The point is connected to its three closest neighbours and forms a new tetrahedron. The resulting tetrahedron is used for further growth.
Starting with a single tetrahedron.
01
Growth by adding another tetrahedron. 02
03
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01 growing on the same face
02 growing on two faces
03 growing on random faces
04 growing on two faces
05 growing on the face with highest y value
06 growing on the face with the highest z value
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CHAPTER 3 - Geometry experimentation, self supporting structures
CHAPTER 3 - Geometry experimentation, self supporting structures The structure grows in one direction and is supported by adding weight at the back to prevent collapse.
Top view of the model
Perspective view of the model
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Local & Iterative DIAGRAM OF THE GEOMETRY
Added weight for support Growth direction
The structure grows in one direction and is supported by adding weight at the back to prevent collapse.
GROWTH SIMULATION
01
02
03
04
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CHAPTER 3 - Geometry experimentation, self supporting structures The structures grow from two sides simultaneously. Two branches start as cantilevers and merge into one at the top which transforms the structure into an arch.
The merging point balances out the cantilevering branches and they start acting as an arch.
Top view of the model GROWTH SEQUENCES
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Perspective view of the model
Local & Iterative DIAGRAM OF THE GEOMETRY
Growth direction Growth direction
The structure grows from two starting points simultaneously. The two branches merge with a single vertex.
GROWTH SIMULATION
01
02
03
04
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CHAPTER 3 - Geometry experimentation, self supporting structures Growing in two directions simultaneously balances the structure and makes it self supporting.
Top view of the model
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Perspective view of the model
Local & Iterative DIAGRAM OF THE GEOMETRY
Growth direction
Growth direction
Growing in two directions simultaneously balances the structure and makes it self supporting.
GROWTH SIMULATION
01
02
03
04
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CHAPTER 3 - Geometry experimentation, self supporting structures Introducing a four sided pyramid as the base allows for four directional simultaneous growth. The structure is symmetrical and self supporting.
Top view of the model
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Perspective view of the model
Local & Iterative DIAGRAM OF THE GEOMETRY Growth direction
Growth direction
Growth direction
Growth direction
Growing in four directions simultaneously balances the structure and makes it self supporting. GROWTH SIMULATION
01
02
03
04
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CHAPTER 3 - Geometry experimentation, self supporting structures Combining multiple self supporting elements. Three identical structures start growing from three different points. Once the growth commences they attract each other and their branches merge together to create a larger entity.
Top view of the model
Perspective view of the model
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Local & Iterative DIAGRAM OF THE GEOMETRY
Three self supporting structures start growing at the same time and merge at the top to create three arches. The three remaining branches remain as cantilevers.
GROWTH SIMULATION
Growth direction
Growth direction
Growth direction
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CHAPTER 4 - Digital solutions
CHAPTER 4 - Digital solutions A catalogue of possible solutions that would allow for spanning the 1,5m distance.
3 points, Growing in 3 directions
01
02
03
04
05
06
07
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4 points, Growing in 3 directions
Local & Iterative
5 points, Growing in 3 directions
2 points, growing in 3 directions 1 point, growing in 4 directions
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CHAPTER 4 - Digital solutions A gravity simulation was used to test the shape of our structure. Using Autodesk Maya a simple mesh was drawn in plan that resembled the shape of the bridge. The mesh was transformed to an nCloth object and gravity simulation was applied. The geometry deformed over time until it remained in its most stable state. The resulting geometry was inverted and represents the ideal form that would be most efficient in carrying the loads. We compared the shape to our bridge design and adjusted its curvature accordingly.
01
02 28
Local & Iterative
03
04
06 29
CHAPTER 5 - Final model construction
CHAPTER 5 - Final model construction The construction of the final model took three days and was photographed after each round of tetrahedrons was added. The images below show the process over time.
01: day one, 11 AM
02: day one, 5.40 PM
03: day one, 9.50 PM
04: day two, 5.12 PM
05: day two, 6.15 PM
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06: day three, 12.46 PM
07: day three, 2.15 PM
08: day three, 5.28 PM
09: day three, 6.27 PM
10: day three, 7.57 PM
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CHAPTER 5 - Final model construction The top view illustrates how four individual nodes start growing independently. As time progresses they start to influence and attract each other and gradually fuse to form a single continuous structure.
01: day one, 9.57 PM
02: day two, 3.57 PM
03: day two, 5.15 PM
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04: day two, 8.03 PM
Local & Iterative
05: day three, 12.48 PM
06: day three, 2.16 PM
07: day three, 4.33 PM
10: day three, 8.58 PM
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CHAPTER 5 - Final model construction
vertex 7 vertex 5 vertex 6
vertex 4
vertex 3
vertex 2
vertex 1
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vertex 0
Local & Iterative Topology of the model: list of vertexes and faces: As part of the brief we were asked to generate a list of coordinates that represent the vertexes of our geometry and the faces/edges connecting them. This was done my modelling a polygon mesh in Autodesk Maya and extracting the coordinates. Part of the list can be seen below. v 81.806345 -20.448511 17.092989 v 73.901315 -16.578890 18.973537 v 81.353952 -13.774691 22.994780 v 80.137468 -12.047953 14.327956 v 75.876154 -18.942202 10.601535 v 31.942323 19.476808 17.092991 v 24.075853 15.529398 18.973539 v 30.984186 14.680212 24.552893 v 31.186769 10.518781 16.665127 v 74.220094 -25.271944 16.665117 v 67.554422 -20.048433 13.618256 v 71.278986 -26.203325 8.210390 v 69.022996 -18.123690 4.950005 v 62.694772 -23.974772 7.250896 v 67.657396 -25.515085 -0.000000 v 61.547418 -18.906878 0.000000 v 27.152456 15.669775 10.601541 v 22.993383 8.377504 13.618261 v 30.146886 7.614256 8.210394 v 22.351015 10.711767 4.950005 v 23.175077 2.132597 7.250896 v 27.406057 5.149023 0.000000 v 18.447267 4.288496 0.000000 v 43.346117 -24.298166 18.592524 v 48.573488 -22.350290 22.645632 v 51.716211 -27.382197 18.516230 v 50.143571 -18.522013 18.671965 v 47.675706 -13.395411 22.579191 v 41.232706 -18.588793 19.248678 v 42.578767 -18.388399 28.064758 v 39.022279 -11.274622 23.852217 v 34.220384 -18.832590 24.757170 v 33.811960 -14.132181 17.093002 v 48.320551 -23.286280 11.257232 v 30.137056 -10.904139 24.552898 v 51.715189 -15.035998 10.583547 v 56.841753 -21.699625 13.604766 v 34.326631 -5.345911 18.973555 v 26.431875 -8.998858 16.665119 v 32.909921 -8.080523 10.601550 v 54.463480 -21.419962 4.950006 v 60.332643 -15.426394 8.210395 v 28.674173 -0.832537 13.618266 v 24.436441 -6.646013 8.210388 v 58.879564 -27.502390 -0.000000 v 31.016901 -1.443339 4.950009 v 23.671892 -3.039759 0.000000 v -35.318345 -10.862528 18.671953 v -28.058103 -9.204485 13.618261 v -36.201812 -7.166147 10.601535
f 3/1/1 2/2/2 1/3/3 f 3/4/4 4/5/5 2/6/6 f 3/7/7 1/8/8 4/9/9 f 2/10/10 4/11/11 1/12/12 f 5/13/13 1/14/14 2/15/15 f 5/16/16 2/17/17 4/18/18 f 5/19/19 4/20/20 1/21/21 f 2/22/22 1/23/23 4/24/24 f 8/25/25 6/26/26 7/27/27 f 8/28/28 9/30/29 7/29/30 f 8/31/31 9/32/32 6/33/33 f 7/34/34 9/36/35 6/35/36 f 5/37/37 2/38/38 1/39/39 f 5/40/40 10/41/41 2/42/42 f 5/43/43 1/44/44 10/45/45 f 2/46/46 10/47/47 1/48/48 f 5/49/49 11/50/50 2/51/51 f 5/52/52 2/53/53 10/54/54 f 5/55/55 10/56/56 11/57/57 f 2/58/58 11/59/59 10/60/60 f 5/61/61 11/63/62 12/62/63 f 5/64/64 12/66/65 10/65/66 f 5/67/67 11/68/68 10/69/69 f 12/70/70 11/72/71 10/71/72 f 5/73/73 12/75/74 11/74/75 f 5/76/76 13/78/77 12/77/78 f 5/79/79 11/81/80 13/80/81 f 12/82/82 11/83/83 13/84/84 f 14/85/85 11/87/86 12/86/87 f 14/88/88 13/89/89 12/90/90 f 14/91/91 13/93/92 11/92/93 f 12/94/94 13/95/95 11/96/96 f 14/97/97 12/99/98 15/98/99 f 14/100/100 12/101/101 13/102/102 f 14/103/103 13/104/104 15/105/105 f 12/106/106 15/107/107 13/108/108 f 14/109/109 16/110/110 15/111/111 f 14/112/112 16/114/113 13/113/114 f 14/115/115 15/116/116 13/117/117 f 16/118/118 13/119/119 15/120/120 f 17/121/121 7/122/122 6/123/123 f 17/124/124 9/125/125 7/126/126 f 17/127/127 6/128/128 9/129/129 f 7/130/130 6/132/131 9/131/132 f 17/133/133 18/134/134 7/135/135 f 17/136/136 7/137/137 9/138/138 f 17/139/139 9/140/140 18/141/141 f 7/142/142 9/144/143 18/143/144 f 17/145/145 18/147/146 19/146/147 f 17/148/148 9/149/149 19/150/150
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CHAPTER 5 - Final model construction Topology of the final model.
Verts: 202 202 202 Edges: 607 607 0 Faces: 790 790 0 Tris: 790 790 0 UVs: 2368 2368 0
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CHAPTER 5 - Final model construction Final model picture.
0,44 m
0,35 m
0,4 m 0,46 m 0,35 m
0,5 m
1,60 m
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Local & Iterative
0,32 m
0,43 m 0,48 m 0,32 m
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Verts: 202 202 202 Edges: 607 607 0 Faces: 790 790 0 Tris: 790 790 0 UVs: 2368 2368 0
Architectural Association School of Architecture, London, November 2015