Eco Sphere Design
Eco Sphere - A Dodecahedron Tensegrity Structure
Below is some draft text for integrating with the Concept section (also still in development) and other parts of the below text for this section on Design. Drawings and illustrations are missing from the text below. Also this page will be developed into a series of Design Pages that are connected by Wiki Trail? and which will serve as an index to many other pages that will go into details on the components, layout and construction details. The Design section is about how to build the Eco Sphere with links to pages with indepth HOWTO information and DIY support.
The Eco Sphere Concept section is to introduce the ideas and concepts that explain what the Eco Sphere is about and Why we propose this type of structure - including benefits. The Concept section will also be a series of linked pages that will link to other pages for indepth information, discussion and learning.
This is an initial draft text (illustrations missing) by Ed:
Buckminster Fuller asked: "What's the minimal structure that can support a weight and oppose horizontal forces, that uses compression and tension, but experiences no torque?" His answer to (his own) question was: The Dodecahedron!
What is a tensegrity? Fuller explained, "Tensegrity describes a structural-relationship principle in which structural shape is guaranteed by the... continuous, tensional behaviors of the system and not by the discontinuous exclusively local compressional member behaviors" (Quote from http://www.angelfire.com/mt/marksomers/133.html)
In other words, the tensegrity concept diverges from traditional construction design in that that the structure's shape is defined by a continuity of members in tension, like a spider web. Compression members (structural elements carrying weight by "squashing" force rather than being pulled on) are placed here and there to "stretch-out" or support any variety of cable or net-like arrangements, but are not the defining elements for the form.
Why tensegrity design? Tension is the most efficient use of construction material in resisting force. James Gordon pointed out in "The New Science of Strong Materials or Why You Don't Fall Through the Floor" that mankind is the only species on the earth, other than ants, that build their shelter using compression structures.
At least the ants build in a stout cone form. We stack a series of identical weighty floors on top of columns. When the wind blows or the earth shakes, the heavy mass at the top acts like a pendulum to bend the columns and twist them off of the floor beams they support.
In traditional Western home construction, the critical structural role of exterior sheeting is to transmit torque through the beams and columns to the foundation (with many, many nails) to resist this twisting and bending and, hopefully, keep the whole structure from tipping over like dominoes. It takes enormous amounts of material and effort to handle this torque. And as soon as nature exceeds the building's design criteria, the rigid structure cracks up like egg shells.
In a tensegrity structure, the columns don't need to be rigidly connected to the tensile web. The columns (or compressions members) simply stretch out a stable web of tension members. And when compression members are isolated from resisting torque, they are much less prone to buckling and can, therefore, be made from much smaller and lighter materials. Non-rigid connections are simpler and can require much less material and labor to construct than rigid connections. Utilizing the flexibility and stability of a tensile web with non-rigid connections gives the structure an inherent ability to slightly flex in resisting force, like an animal's body, which results in dispersion and sharing of the load, and thereby makes the structure vastly more robust and resilient than a conventional rigid structure.
The Eco Sphere Tensegrity Picture a dodecahedron (bear with me, it should be easier to imagine as we progress). Think of the edges of the 12-sided dodecahedron shape as a mesh of wires (like a fishnet) made up of 12 pentagons. How would you stretch out this mesh to show its dodecahedral form?
I think this view is about the best way to see it. (I've made the faces solid here so the resulting shape is discernable.)
The arrows shown are the main forces needed to pull the wire mesh into tension and make the dodecahedron shape.
Notice that this orientation is different than the typical views we see of dodecahedrons. Usually, we see it oriented with a flat face on top, where here we have an edge on top. There are three pairs of these edges, each in the pair on symmetrically opposite sides of the shape. Isn't it neat that the direction of the red, yellow, and orange arrows align to each of the perpendicular X,Y & Z axis of the Cartesian coordinate system? (This is the cubic form inherent in the dodecahedron geometry that makes it so convenient to build a house in. You'll see this come out in a moment.)
If we suspended this form from an exterior frame (interesting concept to pursue) and all of the pulling forces were exactly equal, would the wire mesh retain this form? In any case, were going to add a few more pulling forces to the mesh in a moment since we're not expecting to construct a structure that has zero tolerance for variation in forces.
Here is the profile you will see if you look straight on to any of the six outer edges, from the top, bottom, or any side of the dodecahedron. (If I hadn't shown the shaded panels, you would see right through the pentagons.) This is an illustration of the cubically symmetric form of the dodecahedron geometry.
Now here it is with a transparent membrane over the wire mesh. (If someone would like to help with some web programming, maybe we could animate this? There are all kinds of neat ways to look at this transparent form. I can generate multiple image files or an avi...)
Okay, now that we know where we need to apply outward force to stretch out the wire mesh that defines the shape of our Tensegrity structure, recall that these outward forces are supplied by compression members in a Tensegrity.
Again, isn�t it convenient that the outward forces needed are aligned straight on with each other and are all perpendicular, just like the walls and floors of a house are typically perpendicular? Because of this, we can replace each of the six sets of opposing arrows with one internal compression member. At one end of each compression member we might have some kind of an arrangement to extend the length just a bit once in place to apply the outward force to tension the mesh.
Here is a half-section view to start with, again for the sake of visual simplicity.
And here is the whole Chicago.
Here I�ve changed some wire mesh members to compression members, shown in black. As alluded to earlier, they will take some compression to retain the shape of the triangular sections at the ends of the orange columns. They will also resist bending forces, since the top set will support a plant leaf canopy, and the bottom a Sola Roof water reservoir. (Will we need additional compression members in the same location at the ends of the yellow and red members?)
There will also be a floor supported by the pair of red members and at each of the yellow members. Thus, they will be acting as both compression members and beams (called beam-columns). Tension in the outer �mesh� will support the resulting vertical loads at the ends of the yellow, red, and black beam-columns.
So, we have beam-columns applying initial tension to the tension mesh and then increasing the tension as they take floor load, which, in turn, applies additional compression back to the beam-columns themselves as well as the other compression members. This is called a second order effect and makes for some interesting engineering in determining the magnitude of the various forces as they will actually balance out in the overall structure under various loading conditions; and in designing the beam-columns for the various types of stresses they will need to endure.
The members acting in compression and/or bending (shown in red, orange, yellow, and black) are shown as rectangular tubes here for simplicity. In the actual construction, they will be made from 3D open web lattices that dismantle.
Each of the two orange columns are pinned to the ground at the Footing Vertices, which are located below grade. The lower black Base Vertices are located at the finish grade elevation and are giving further support to the structure. Alternatively, the structure can be built without excavation with the Sola Roof water reservoir above grade and supported with additional bracing to the interior and to the ground.
The Sola Roof water reservoir can be subdivided into separate volumes of water with different uses. Since the structure is very light, the water mass is also the anchor for the structure so that it is secured to the ground by the weight of this liquid reservoir system.
The envelope would be constructed as a double layer that creates a cavity space for the Bubble Tech? and the Liquid Solar systems. The envelope is entirely a transparent fabric and can be folded into a small volume package.
The plant leaf canopy at the top level will use an aeroponic culture system. Plants are also grown vertically within the transparent, flexible covering of the Eco Sphere.
Richard says, he has ��been thinking about using a wire net to form a lightweight tension floor system. This will take some further explanation but with our collaborative team these and other details will be documented as we go � our design goal is to get a good picture of the main structural elements of the project and to consider how the double layer transparent envelope is attached to the tensegrity frame.�
Here, we further explore the interior vertical arrangement of living spaces and plant growing areas.