UNDULATING PANELS
Faramarz Manteghi | Instructor: Mary Polites | Washington State University | Fall 2013
10”
Primary Objective The aim of the project was to fix the problems with the previous components and with the respect to the intial intention that is to be capable of bearing and distributing the vertical loads through out the whole system. in order to achieve this goal I tried simplifying the geomtery into a module made out of a strip of paper which with series of folds could forms a geometry that can be self-supporting. I used the Crescent Museum Board, which is thicker than a normal (20lb) of paper, to gives the stifness to the component. However, this component was not be able to support a vertical load and it bent from the edges as demonstrated.
1/2”
1/2” 1” 1 1/8”
1” 3 5/8”
1” 63º
1/2” 1 1/8”
1”
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3 1/8”
Primary Objective
1 1/2”
1/2” 1/2”
1” 1/2” 1 1/2”
The aim of the project was to 3 5/8” refine the geometry of the previous component into a more selfsupporting. I rotated the component 180° and combined the two components together from their square base. This method led me to have two vertical members that can act as structural elements.
Applied Techniques In terms of the applied techniques in this project, I used series of cutting, scoring, subtracting surfaces, and straight folding techniques and glued them together which were to derive a three-dimensional component out of a single two-dimensional template cut from a flat sheet of paper.
1”
1”
Stress Analysis Scan and Solve has been used for these analysis. from top to bottom diagrams show the Tension, Compression, and Displacement towards different components and systems. Where red is the danger zone and blue is the safe zone.
1 and >
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Fig.6.1: Indicates that the Combination “c� is the most stable combiniation among the rest.
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Fig.6.1
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Linear Growth For the aggregation of the components I experimented two linear growth pattern one was along the XY plane and the other one was along the YZ plane. Due to the orientation of the components and the way of neighboring with one another the whole system generates large amount of surfaces that can be overlap with one another through panel to panel connections and let the system to grow in XY direction. On the other hand this gives the capability of stacking on top of each other as well and because of its stability which is proven through the Scan and Solve analysis and even a smaller modules you can eleminate some of the components while aggregating them which creates varity of random void spaces through out the system.
Linear Growth Another fact that helps this system to grow easily in a linear fashion is the abstract geomtery related to it which is a inverse truncated pyramid that provide 5 faces to work with.
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Component Optimization Having a system based on two intersecting truncated pyramid gives a limited option in terms of the growth possibilities for this system in addition to excessive use of material. Therefore, for solving the issue with using too much material, I simplified the component itself into a trapezoid which can rotate 90° and intersect with another trapezoid and creates the same truncated pyramid without using too many joining panels. And lastly, for developing the growth possibilities and finding different variation by using the new component, I manipulated the geometry of the trapezoid in a fashion that I kept the Hypotenuse and top side length constant and change the side angles. However, there were some constraints that needed to be taken into account. Some of which are: 1) Material thickness; you cannot have angles less than a certain number which is in a direct relation with the material thickness and its connection. 2) angles range should be in between 90° and X which is been discussed above.
1/n 1/n 1/n
α>X
α
Case Studies To further my knowledge of structural performance, lateral connectivity, and edge to edge connection I researched about the following three case studies.
1) DRAGONFLY Done in collaboration with Buro Happold Engineers, for the Sci-Arc Gallery in 2007, was an experiment in hybrid pattern-formation and structural feedback loops in a canopy structure. The project was set up in order to elicit a variety of heterogeneous behaviors in response to its asymmetrical shaping environment and extreme cantilever. The design process iteratively generated structural mutations based on support conditions for the extreme cantilever while using boundary conditions to interrelate overall form, cell shape, and band width. To achieve the cantilevered condition, EMERGENT and Happold used fully parametrized fabrication process. What does this mean is to link the two process of three-dimensional computer model and two-dimensional CAD templating together in the modeling environment.
In order to achieve this goal, each member was accurately described, including material thickness, scored seams, and bolt holes, in CATIA. They were also digitally labeled with with pertinent information, such as location and bending angle. the bands were then automatically unfolded as the computer model evolved structurally and formally. On final iteration, these templates were arranged with RhinoNest on a four-byeight-foot aluminum sheet and then cut using a CNC router. They were also digitally labeled with with pertinent information, such as location and bending angle. the bands were then automatically unfolded as the computer model evolved structurally and formally. On final iteration, these templates were arranged with RhinoNest on a four-byeight-foot aluminum sheet and then cut using a CNC router.
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Dragonfly is ruled by a different set of parameters, including gravity and seismic loads, specific suport locations and the quality of those supports, flat material inrecements, and buckling failure.
Dragonfly uses folding for structural performance and lateral connectivity, employing the depth of the band to span. Folding is treated as an operative language for this project as well as focusing on the cells construction as their unit. The material constraint in this project makes folding so effective constructionally. They used Aluminum plates for this project and edge to edge connections.
2) MANIFOLD MANIFOLD, develops a honeycomb system that adapts to diverse performance requirements through modulating the system’s inherent geometric and material parameters.
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3) HAPPY BOX ARCHITECTURE
Conclusion
Participate in a 800 square foot addition to a house in Charlotte,NC. Material Constraint: 1- From constrained by twisted standing-seam metal roofing, plywood subtrate, and sheet rock. 2- Minimal custom componentry used as templates for roof joists. 3- Sphere-mapping allows for percise mathching of standing-seam metal edges with underlying substrate, minimizing the amount of flashing.
All of these three case studies are applicable to my component construction process. Especially the Happy Box Architecture project which they have used plywood as their material and the bird’s mouth cut to connect and control each roof component. I believe with combining the last two project techniques I can figure out how to connect my components in order to get to the global aggregation upon a warped surface.
Aggregation Possibilites After reasearching on aformentioned case studies, one solution to experiment the variation within this component is to redfine the geometry based on the length of the hypotenuse.
Constant Hypotenuse
These three configurations are samples of the component’s potentials in terms of the aggregation process. The applied methods of joining these components are through lateral connectivity and edge to edge connection. I used the hypotenuse as the connecting member. Shorter Hypotenuse
Longer Hypotenuse
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Assembly I applied the finger joints connection. The intention was not to use any mechanical or adhesive connections, employing only the precision of a Laser Cutter to define built-in connection details.
Material Constraints • 1/8” Basswood is rigid and provides a relatively consistent material thickness, allowing the Finger Joints connection. • The material thickness causes the edges to be compromised which is not suitable.
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sio
res mp
Co α)
in(
/s =t
L
T
α t
T * sin(α)+ t * cot(α)
Finger Joints Connection
Tension
Conclusion • There are limitations in this sort of planar (XY)-(YZ) aggregation. • Losing the purpose of eliminating the redundancy of the materials. • Losing the integrity of the desired material property (rigidity). • Lack of potential for spatial distribution. • One of the possibilities for this form is to be used as a canopy. With these limitations this form will lose its potential and purpose as a structural entity and for the next step the component itself has to change in a way that the system of the new component serves the aforementioned purpose.
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X
Component Redefinition
Y Y= SIN(X)
After the last experiment, I went back to the egg crate structure and instead of the linear abstracted geometry I drew out the curvilinear abstracted from the form. After studying the form I realized that we can apply a sine function to our curvilinear form and go from there. Since the sine graph is one of the stable curvature forms I intended to instead of creating a wall with a linear based geometry (last experiment) study and design a wall with curvature based geometry. The ratio between amplitude and the cycle of the curve that has been used for the purpose of this experiment is 1’ to 4’. Y The next step would be to create a vertical element from the same curve. In order to do that I just rotated the base curve 90° and extruded it along the horizontal curve. This step gave me the initial form of the wall, afterwards, I chose wood as the main material and experimented different thicknesses and their structural capacity in terms of bearing vertical loads and their deflections range.
1’ 2’
Y
X
X
Stress Analysis Scan and Solve has been used for these analysis. from top to bottom diagrams show the Tension, Compression, and Displacement towards different components and systems. Where red is the danger zone and blue is the safe zone.
0.00518017
1.67454E-10 Total Dispacemepent (in)
Thickness: 10” Deflection: Min: 2.55505e-11 in Max: 3.73882e-06 in
Thickness: 2.5” Deflection: Min: 2.86225e-10 in Max: 4.35709e-05 in
Thickness: 0.75” Deflection: Min: 2.4528e-09 in Max: 0.000515618 in
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Fig. 18.1 Original surface design constrained to curvature and cantilever limits.
Fig. 18.2 Contour sections (6� apart) through the surface to define the plane of each member.
Fig. 19.1 Convert each curve with one degree of curvature to ensure that corners fall at the exteremes of each curve.
Fig. 19.2 Extrude curves 6.25� to approximate flate panels.
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Fig. 20.1 Extract curves from each cross section.
1’-4”
1’
Fig. 20.2 Redefining the vertices of curves in order to have them overlapping each other at the mid points without compromising the form and vertices.
Fig. 21.1 Front view of this system as a possible assemblage.
Fig. 21.2 Front view of this system and highlighting the median members that this system would connect through.
Fig. 21.3 Red line shows the median lines where this system would connect through.
Fig. 21.4 Median red panels shows how they connect to the adjacent memebers.
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6.72437E-05
5.98643E-11 Total Dispacemepent (in)
Fig.22.1 SNS analysis showing the stability of the system.
Half Scale Component • 300 gsm paper was used for the model. • At half scale component is 15” tall by 16” long.
• The top right image demonstrates the capability of this system to be divided into different subgroups which is beneficial for the assembly process in terms of speed, time, and cost.
• Losing the integrity of the desired material property (rigidity) due to the use of paper instead of wood. • Depth cuts weren’t strong enough to carry the self-weight of the members.
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Height : 14’
Width: 10’
Width: 2’
Width: 1’
Fig.25.1 Full scale assembly.
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Fig.26.1 Blown up detail of one set of connections
Axon and the connection details 1/8”
Varies
Varies 6”
6-1/2”
2”
R 3/8”
2-3/8” 1/8”
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One to one scale model of a sample connection of the global geometry made out of 1/8� thickness Mahogany door skin. Above pictures show the possible errors along the assembly. Due to the use of depth cut connection for the system, it’s crucial for the cuts to be at an exact distance from the top of the panels as well as their depth. In this experiment, due to unavailability of the CNC machine, the cuts were manually made and caused the noticeable bent in some of the panels.
Material Options
Material
Unit Price ($)
Volume Needed (cubic inches)
Total Cost ($)
2 x 6 x 8 #2 Pressure Treated Lumber “Hem-Fir”
7.56
40,000
262.50
1 x 6 x 8 Kiln-Dried Poplar Board “Sapwood”
17.76
40,000
1233.33
1 x 12 x 8 Acrylic Sheet - Clear Cast PaperMasked
253.30
40,000
8795.13
Pressure treated lumber, Poplar board, and Acrylic could be used to construct the full scale model. Each requires a different connection method. In this estimate labor and special connectors such as screws, bracket, and etc. are included.
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Conclusion
• The structure of this form is based on a curvature ( in this case a sin curve). Therefore, with changing the ratio between amplitude and the cycle the form would vary. • In constructing this model the width of the panels, which is one of the parameters of this project, was chose to be 6 inches. By lowering the width and extending the overlapping length of the panels the overall form of the model would be shaped in a smoother fashion. • In this experiment the 1/8” Mahogany door skin was used as the material. But different materials can apply as well. • Based on the structural analysis (SNS) of the model, wood with various thicknesses could be used in constructing this model. • The chosen connection for this model (depth cut connection) is very stable and can hold up the entire system together. • The entire assembly is held together in compression, without adhesives. • The distance between the connection’s cuts and the top/bottom of the panels are very crucial in order to maintain the structural aspect of this model. • For the future optimization of the system, studying of different connections as well as different materials would be beneficial.