In Galileo’s Dialogues Concerning Two New Sciences there is a passage where he describes the relationship between cross sectional area and bending stiffness.
It’s a fairly straightforward principle, and highlights the concept behind my favorite type of structural system; the space frame. The strength of a space frame comes from creating rigid cells that spread material over a greater cross section than if that same amount of material was used in a solid block.
Initially, space frames were only used for flat or arc based geometries because the components could be standardized, but parametric modeling and digital fabrication have reduced the need to limit the number of unique parts. This has made it possible to explore more complex forms that have the potential to be tuned for specific purposes. Space frames tend to require a lot of pieces so their use is limited to situations where their structural efficiency outweighs the complexity of constructing them. We’re interested in finding opportunities to use them for more typical floors, walls, and roofs or other loading bearing systems at scales smaller than the long span roof structures of convention centers and airports.
In graduate school, I became fascinated with trying to find ways to develop a space frame joint that had a large degree of formal flexibility. One approach was to have a joint that was physically flexible with a range of adjustability through the use of ball and socket joints. The other approach was to have a joint that was digitally flexible by using a family of unique parts customized for the angles at each joint.
More recently this research has continued with the idea of a digitally flexible system where the adjustability is handled within the parametric model, but now instead of the struts and connectors being separate pieces that are fastened together, the entire system is bent from one sheet of material. The starting point of the design was reducing the overall number of pieces. This evolved into a process of using as much of a sheet of material as possible without decreasing its spanning area. There is very little material that is not used within the structure, unlike the previous folded version with cut sheets which used less than half the starting sheet.
Folding patterns into material has been used to increase the stiffness of material and give it a defined form, but the footprint of the material tends to shrink because of the folding. In this approach, the material footprint stays the same, but the depth is increased by creating a series of cuts, producing sets of arms which are then folded together to create rigid tetrahedrons.
We previously shared this research, but at the time we weren’t able to easily test the system with full-scale fabricated pieces. Recently, we returned to this research and were able to cut out the prototypes shown above with our CNC router. We’re using aluminum composite material for the prototypes. This material has two aluminum skins, separated by a core which is typically polyethylene. The advantage to this material is that it can be scored through the first aluminum skin and almost all the way through the core and then the parts can be easily and cleanly folded by hand. A challenge has been how the arms are attached to each other. The first attempt used three screws to hold them arms together at each overlap, but we’re now exploring a single piece of hardware that clamps a set of arms against the opposing sheet. Again a driver with these connections is to reduce the number of pieces as much as possible.
The next step is to begin prototyping instances of this system that has varying depths within a sheet and also trying to deform a sheet of cells into taking on more complex forms similar to what is shown below.