FRAME # 640263 KATHRYN RANDALL-DZERDZ
â€œBased on the geometric rigidity of the triangleâ€? (Ching 2008, ch.2.16), original designs depicted a vertically elongated triangular-based pyramid. The three vertical members were to be supported periodically with horizontal beams to reduce buckling of the flexible balsa wood structure. This tower was designed to taper towards to its apex to ensure the stability and integrity of the structure in the area where it encounters the greatest moment (the base). As the tower increases in height, it is subjected to greater lateral loads, and must increase in taper (Vassigh 2008). Many natural structures taper, such as the limbs of trees or animals. This form in the natural environment has occurred naturally over time in response to forces that could disrupt the stability of the organic structure.
Figure 1. Concept sketch.
Figure 2. Top view of base.
Additionally, the triangular shape suited this exercise as it only has three sides, allowing for the most efficient use of material to create the “tallest tower” while providing it with strength.
At the foundation of the structure, the vertical members were affixed at right-angles to the horizontal base. Connecting parallel vertical members with another beam to prevent buckling (see previous page), created a square; a shape “easily transformed...with minimal force” (Maths in the City 2011). Therefore, extra supports were added to the structure, creating triangles at each join, to reinforce the foundation of each vertical member.
Figure 4. Reinforced foundation structure.
Figure 3. Corner joint in base.
Figure 5. (above) Cross-bracing. Figure 6. (right) Fixed joint.
Upon construction, it was found that the flexible balsa wood required additional bracing to the long, vertical members to prevent them from buckling under their own weight (dead load). The material, while lightweight, was subject to lateral forces the higher the structure grew, and became increasingly difficult to keep upright. Many remaining quadrilaterals were reduced into triangles, by applying crossbracing affixed at major joints. Figure 7. Cross-bracing (diagram).
Figure 8. Constructed structure.
The flexible balsa wood structure was easily deformed under slight vertical or lateral forces. Vertical forces caused longer, unsupported members to buckle (the longer the unreinforced member, the greater the buckling). Lateral forces caused horizontal movement of the members, and some temporary deformation of the structure, but short, horizontal bracing prevented major buckling in many members.
Figure 9. Vertical and lateral deformation of structure; blue: direction of force, red: deformed structure.
The footing of a structure ensures a stable and secure foundation by spreading the load of the building across the soil and transferring this load to the earth. It is the part of the structure that is in contact with the soil/bare ground at the “lowest part of [the]... foundation” (Ching 2008). The type of footing used depends on the construction, weight, and requirements of the building and the soil composition. (Australian Building Inspection Services 2013). An example of a footing method is pole construction where posts are placed into pre-drilled holes and backfilled with concrete (fig.10). Figure 10. Pole construction.
Australian Building Inspection Services 2013, Footing. Available: http://www.abis.com.au/footing [2013, 12 August].
Ching, F. 2008, “Foundation Systems” in Building Construction Illustrated, ed. F. Ching, 4th edn, John Wiley and Sons Incorporated, Hoboken, New Jersey. Ching, F. 2008, “The Building” in Building Construction Illustrated, ed. F. Ching, 4th edn, John Wiley and Sons Incorporated, Hoboken, New Jersey. Maths in the City 2012, 17 October-last update, The strength of triangles - Bloomsbury tour. Available: http://www.mathsinthecity.com/sites/strength-triangles-bloomsbury-tour [2013, 11 August]. Vassigh, S. 2008, Interactive Structures - Visualising Structural Behaviour, 2.0th edn, John Wiley & Sons.