Monday, July 13, 2009

Stress Trajectories Wind on Dome

As discussed in my report on rads, this image shows the schematic stress trajectories of wind in a dome shaped structure:

Source: Structures, D.L. Schodek

To explore the possibilities of adjusting the structure to the specific wind trajectories, i've made some sketches as seen below.

In the first sketch, I took one side of the trajectories (could be tension or compression). I distributed 9 points evenly along each line. I connected the points and created a Delaunay triangulation (red lines upper part). The lowerpart is the Voronoi diagram, based on the Delaunay triangulation. By connecting the points, we see that two additional line-sets are created. They look like the two sides of stress trajectories, but are not the same. This is because I distributed the points evenly and not accourding to the other side of the stress trajectories.

To check how this tesselation would work in 3d, I sketched the same lines onto a plastic dome shape. But distributed the points at the crossings of the two sides of stress trajectories. This causes a symmetrical image again. except that the thicker lines should resist to compression and the other set, to tension. I elongated the lines in order to get an enclosing structure. The way to close the structure can be more dense or adjusted in an other way.

Then I copied this line-set into illustrator, to get it more clear. The green lines, which appear when connecting the points, become clear ellipses.

I'm curious how this set-up would respond to forces at this point. Since I'm doubting if they can transfer the self weight of the building. We probably need to add an other line-set..

Focus on the Continued Research

I mentioned in the report a number of ideas for possible proposals. For this particular research subject, as described in the previously posted abstract, my interest goes out to one main directions:

"IDEA: If a column free dome is the starting point, we could divide the dome structure in two shells, one resisting the wind loads, and one taking the deadweight of the structure. We could design the “deadweight shell” by distributing points onto the dome shape, and connect the points applying a Voronoi algorithm, in order to get a framework as light as possible, while at the same time being one integrated entity. The wind-shell could be constructed out of a frame following the stress trajectories due to wind loads (one main direction). The one shell should be connected to the other in a way, which is parametrically predefined."

To discuss this a bit further, I want to comment that, wind load is a tricky load case to use as a shape giver. Since it moves around and the force flow caused by the wind on the structure, very much depends on the shape of the structure itselves. To use this principle, we should at least stay to one type of shape of the structure.

Let's assume that we use a dome structure as a model. Based on the adaptive qualities of rads to their loadcases, we could consider to optimize the dome to one main wind direction. And make the dome able to rotate towards the wind direction. Other wise, the structure would collapse, as soon as the wind changes its direction. An other solution could be to over-dimension the structure of the dome in order to make it strong enough to stand wind form all directions, but in this case,this is not our aim, since we want to create a light structure which is as much optimized as possible to its surroundings.

The issue of two cooperating shells: In radiolarians we see that they have to deal with 2 kinds of load cases in general: 1) the distibuted pressure of the water surrounding them, and 2)Impact loads caused my predators or other objects in their environment. This way of dealing with both different types of forces, made them able to develop efficiently. The fine tesselation of their shells withstand the evenly distibuted pressure of the water. While the Impact forces are counter acted by the arm of spines connected to the shells.

If we want to translate this principle to a dome shaped structure, we first have to define our load case. The distributed loading acting on a building is it's selfweight, magnified by gravity. The impact force encountered by a building structure is wind force, although its partly distibuted.

The big question is: How can we integrate this into one structure?

Impact forces and distributed loads acting on radiolarian shell

Deeper Research Radiolarians

I've been working to get a bit deeper in the radiolarian principles.. Via this link you can find a report of my work done. This report is my way to archive my findings for my own process. And its also a way to share it with my colleagues Michela and Peter and all others who are interested in the subject.

you can download the radiolaria report via THIS link