One of the main deliverables for the design project was a CAD model used to understand the structure and how it handled stresses. Though the original goal was to use SketchUp for a visual model, then Visual Analysis for the structural analysis, difficulties with circular geometry in SketchUp led to the decision to switch to Autodesk Inventor for both purposes. After a lot of geometry with the known dimensions, a model could be developed. Due to time constraints and very limited experience with the software, the structure was made as one whole part, as opposed to many different parts with constraints between each one to more properly illustrate the real structure in Brussels. To start, the first thing to be modeled in the CAD, as we did with the physical model, was the central beam. The beam has a diameter of 10.8 ft and the height was determined by the height of the structured added to the depth that the beam goes underground for support.
Now that the central beam was constructed, we can build the pavilion on the ground plane with the beam in the center.
After the pavilion was added, the three spheres that sit on the central beam could be added to their proper locations. Because of the designated length of the central beam, the center of the top sphere is the same point as the center of the top of the beam.
Now that the above-ground portion of the center beam of the structure was completed, the next step was to add the other eight spheres. To determine the location of the spheres, I constructed a cube with the side length necessary, determined by the length between two spheres plus two times the radius as roughly 154 feet. Then in SketchUp, I rotated the cube on two different axes to make the bottom three spheres and the top three spheres on two planes. From there, I multiplied the length by a combination of the sines and cosines of the necessary angles (45 and 35.3) and determined the correct point in space for the centers of all the spheres in the model.
Once the spheres were in place, the rods that connect them were next. These rods are 9.8 feet in diameter and in real life they may contain stairs, escalators, etc. but in the model they are solids. From the centers of the spheres, I drew the proper size circle, then swept the drawing along the path of the rotated cube.
Now the entire above-ground portion was completed besides the bipods, next up was to handle the support for the central beam. According to our research, there were 59 57' bipods that were built concentrically around the central mast. All we knew about the placement of these piles was that the furthest piles were 38' from the center of the building. Using proportions of the circumferences of four equally spaced circles drawn from the central beam, we placed 8 piles concentrically 17.6' from the center, 12 piles concentrically 24.4' from the center, 18 piles concentrically 31.2' from the center, and the remaining 21 piles 38' from the middle. These piles were then extruded 57' below the ground plane.
The geometry of the bipods was a much greater challenge. Information about the dimensions of these were scarce, and there weren't many good pictures of them either. Eventually however, we were able to determine the extremes of the sub-structures and analyze the entire bipods from there. In the model, I started with three rectangular prisms with dimensions matching the max height and length of the bipods.
I then made two drawing planes on the faces of the rectangles and drew the shape of the bipods from there.
The pile caps were another difficult part of the model in terms of research potential. The diameter of the pile cap under the pavilion, and the depth of 6.5' were the only known variables. The final product includes potential pile caps based on the information that we had but do not necessarily reflect the actual structure properly.
There are only two remaining elements to the structure: the piles under the bipods and the diagonal beams. Research yielded that the piles under the bipods maintained the same angle with the vertical as the bipods and that they went to the same depth as the central piles. Using this information, the piles were built under one bipod using sweep commands, then rotated in a pattern to the other two bipods as well.
The last element to add is the diagonal beams. These beams have a diameter of 10.8', the same as the central beam. Once a circle was constructed at the intersection of the linear beams in one corner, the circle was swept from one corner to the opposite one for both of the remaining three instances.
Now that the visual part of the model is complete, we can use Inventor to test the structure. The only force that we really have to deal with here is gravity, so I'll apply that force to the structure.
As for constraining the model, realistically there would be many more joints where the piles end, but with the limitations of the program, the only constraints made fixed the bottom of the pile caps in place.
Once the simulation was run, we can see exactly how well the structure stands.
