Team: Lubna Alayeli, Ceren Temel, Samuel Shapiro, Nina Jotanovic

First research on reciprocal grids and connections between members. [Inspiration]

Development of research during workshop through small scale physical models and Karamba analysis. [Workshop]

Conclusion and possible further development.

Conventionally a truss consists of top and bottom members spanned between supports with diagonal members working in compression and tension. The aim of this assignment was to take up different phases of tessellations and finding, with the presence of only the diagonal members, can the geometry structurally function as a 3D truss and have stability.

Tessellations with triangulation were observed from relaxed flat 2D geometry to its peak 3D constellation. Model at 60%, 45% and 30% were analysed with karamba where 60% failed exceptionally to support the span of 20m.

The geometries with 45% opening were expected to perform best given the angle of members. However it has a large displacement and bending moment values as observed in the karamba results.

The tessellation with 30% open performed better than 45% open with a lesser displacement. This model was further taken to analyse with reduction of structural members-A and structural members-B. The analysis showed the structure displaced even less with far less mass with the absence of structural members-B. The cross section of this model was increased to match weight as in the 30% pure tessellation study.

Conclusion, the displacement was reduced by 300% with lesser members spanning the 20m space without member-B.

Ji Won Jun

Matteo Silverio

Team:

Ji Won Jun

Matteo Silverio

Analysis

The building is already extremely efficient. It is made by traditional construction bricks which are generated from two lines and three cosine curves, two of them in the XY plane and the top one in the XZ plane.
The utilization graphs show how smart the form is, since the roof, which is the weakest part of the structure (clear at the displacement graph), was folded to distribute the stress among all the surface. At this graph is showed that the folding edges of the roof are the more stressed ones, due to their horizontal. The Forceflow graph show how direct the building conduct the forces to the ground.
The aim of the first modification was to decrease the utilization of the edges of the folded roof, by increasing the amplitude of the lateral curves that generate the building. This was achieved and also was the almost total elimination of the displacement along the roof. In other hand, the forcelines became more curvy, due to the increase of the surface area at the folding walls, which caused the forces to travel in a bigger path.
The objective of the second modification was the same as the first one. This was made increasing the amplitude of the cosine wave of the roof. This modification also decreased the utilization of the roof, but concentrated it near the edges. Also, couldn’t be as efficient of the first modification in the decrease of the displacement, and the middle of the roof continued to be the region with the biggest movement. The only advantage from the first modification is that the shell force flow has a more fluid path.
At the third modification, it was inserted a series of supports as points at the bottom of the cosine curve of the roof, maintaining the original dimensions. This was to simulate a straight beam under the roof. With this support, the main displacement moved from the middle of the roof to its edges, and decreased the utilization of the structure, but maintained at the points in which the surface would touch the beam. Also, this additional beam created two new force flow paths at the roof.
The final modification is a variation of the third one, but instead of a straight beam, it was created supports simulating a curved beam located at the cosine curve at the top. Those supports also helped to divide the most fragile region of the structure, dividing it at two lines, along the roof. This is clear at the displacement, isolines of displacement, and shell force flow graphs. One interesting factor is that since the utilization of the roof was balanced, the inner edges of the folded wall became the most utilized areas of the structure.

Maximum and Minimum Values:

Type of subdivision/displacement(cm) (white to pink)/utilization 100 (red to blue)/utilization 25 75 (red to blue)
triangular A/-2.97e-04 to 2.97e+04/-341448% to 322528%/-172849% to 155581%
diamondond/-3.27e-03 to 3.27e+05/-471273% to 487941%/-236031% to 255086%
quads/-2.00e-04 to 2.00e+04/-216497% to 220479%/-105539% to 110608%
Squads/-7.71e-03 to 7.71e+05/-985081% to 963943%/-494696% to 488547%
triangular B/-1.80e-03 to 1.80e+05/-427035% to 565655%/-178818% to 322524%
hexagonal/-1.38e-03 to 1.38e+05/-290143% to 305622%/-141175% to 159706%
quadstag/-3.82e-03 to 3.82e+05/-854700% to 854402%/-437472% to 418088%

Analysis:
A previous analysis that can be made of the structure, since it is anchored all along the bottom and the top edges, is that those edges are one of the strongest part of the structure along with the smaller ring upon the anchored base. Since this ring is in a more vertical position, functioning as a cylinder, and has more subdivisions than the rest of the structure, there are more ways and connections for the loads applied to the structure to find their shortest path. On the other hand, the most planar ring at the top is one of the weakest points, since it is more planar and with bigger beams, making a long and inefficient path of the loads in those areas.
Observing separately the analysis, the displacement of some types of subdivision are better than others, showing the lower ring of the structure with almost the lowest values of displacement and other with a slightly increase at the values along with the longest side of the lower ellipse ring. Triangular B, Diamond and Hexagonal were the types of subdivision with the best results for the displacement due to the more diagonal orientation of the beams, so there are no perpendicular or longitudinal beams to be differently stressed, but a net of diagonal ones, functioning as a network.
The analysis of the utilization of the structure of the total highest values (tension) and the total lowest values (compression) didn’t showed much difference, so the range of values was decreased in 25% to 75% to be more clear. Those diagrams show similarities on the behavior of the structure at the values of the utilization. Usually they present the same behavior of two tension (blue) rings, intercalated with three compression (red) rings of utilization and two white rings, showing a balance of compression and tension. Depending on the type of subdivision those rings vary in size and in position, but remain almost the same. The biggest difference at these behavior was at the structure with the the triangulation B pattern, which showed almost a compression behavior. These can be explained by the overall shape of the subdivision, which is one based on equilateral triangles, which is the strongest way of having a single surface, since a surface is defined by three points, or one point and a line.
Due to the diagonal orientation of some types of subdivisions, the Moments on the X axis are bigger, at the Triangulation B, Squad, Diamond, and Hexagonal, since the beams are carrying the loads in a diagonal.
It is also visible that at the more orthogonal types of division, the structure Moments Y is basically radial to the center. And at the edges of surface.
The Z Moment occurs mainly at the planar central ring of the structure, since it don’t have height for distributing easily the weight of the structure. If at a moment the structure suffers an overload, in all of the options, would be at this area that the structure would collapse.

Conclusion:
The best type of subdivision of surface for this shape is the Triangular B, since it is best distributing equally along the beams the load of the structure all, making the structure work as a net.