Wax bridge structures | AADRL | Shajay Bhooshan | Workshop-I

LOCAL & ITERATIVE wax bridge structures

Tutors: Shajay Bhooshan Dave 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

2

Local & Iterative

AA DESIGN AND RESEARCH LAB - WORKSHOP 1 Tutors: Shajay Bhooshan Dave 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 matrials sugested were wax and sodium acetate.

Architectural Association School of Architecture, London, November 2015

3

CHAPTER 1

- Material experimentation

The material used was white beeswax. After some experimantation with other kinds of wax we discovered that beeswax works best. It is easier to melt and control and it provides for beter cohesion. The material was bought in beads.

Aditional equipment needed were syringes of different sizes. The syringes used for water were bigger size (100 - 150 ml) and equiped with a needle for beter 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 simultaneus 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 prooved difficult and brittle in the case of cantilevering geometries.

01 2D Cantilever structure: 3vertexes, 2 edges

02 1D structure: 2 vertexes, 1edge

03 2D structure broken: 3vertexes, 2 edges

Triangulation

04 3D tower structure: 7 vertexes, 9 edges

6

Local & Iterative

05

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

7

CHAPTER 2

- Rules of construction Experimenting with the material and trying to span using cantilevered structures, we discovered that having vertxes with higher valency improves the structural properties. the Furthermore triangulating shapes assuree that the geometry is structuraly 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 stucture becoming unstable a new rule is applied. A secondary point is added to support the growing geometry.

Direction of colapse

Growth direction

01

Added triangle

02

03

04

Add a support

Direction of colapse

05

8

06

Add a support

Local & Iterative

Step 1

Step 2

Step 3

9

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 center 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

10

Local & Iterative

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

11

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

14

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

15

CHAPTER 3 - Geometry experimentation, self supporting structures The structures grow from two sides simultaneusly. 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 cantelivering branches and they start acting as an arch.

Top view of the model GROWTH SEQUENCES

16

Perspective view of the model

Local & Iterative DIAGRAM OF THE GEOMETRY

Growth direction Growth direction

The structure grows from two starting points simultaneusly. The two branches merge with a single vertex.

GROWTH SIMULATION

01

02

03

04

17

CHAPTER 3 - Geometry experimentation, self supporting structures Growing in two directions simultaneusly balances the structure and makes it self supporting.

Top view of the model

18

Perspective view of the model

Local & Iterative DIAGRAM OF THE GEOMETRY

Growth direction

Growth direction

Growing in two directions simultaneusly balances the structure and makes it self supporting.

GROWTH SIMULATION

01

02

03

04

19

CHAPTER 3 - Geometry experimentation, self supporting structures Introducing a four sided pyramid as the base allows for four directional simultaneous growth. The structure is symetrical and self supporting.

Top view of the model

20

Perspective view of the model

Local & Iterative DIAGRAM OF THE GEOMETRY Growth direction

Growth direction

Growth direction

Growth direction

Growing in four directions simultaneusly balances the structure and makes it self supporting.

GROWTH SIMULATION

01

02

03

04

21

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 eacho other and their branches merge togehter to create a larger entity.

Top view of the model

Perspective view of the model

22

Local & Iterative DIAGRAM OF THE GEOMETRY

Three self suporting 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

23

CHAPTER 4 - Digital solutions

CHAPTER 4 - Digital solutions A catalogue of possible solutions that would allow for spaning the 1,5m distance.

3 points, Growing in 3 directions

01

02

03

04

05

06

07

26

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

27

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 gravitiy 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

32

Local & Iterative

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

33

CHAPTER 5 - Final model construction The top view illustrates how four individual nodes start growing independently. As time progresses they start to infuence and attract each other and gradualy fuse to form a single continious structure.

01: day one, 9.57 PM

02: day two, 3.57 PM

03: day two, 5.15 PM

34

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

35

CHAPTER 5 - Final model construction

vertex 7 vertex 5 vertex 6

vertex 4

vertex 3

vertex 2

vertex 1

36

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 modeling 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

37

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

38

Local & Iterative

39

CHAPTER 5 - Final model construction Final model picture.

40

Local & Iterative

41

Verts: 202 202 202 Edges: 607 607 0 Faces: 790 790 0 Tris: 790 790 0 UVs: 2368 2368 0

Archiectural Association School of Architecture, London, November 2015