Triangular spaceframe lattice, Tri-1:  (self-dual tessellation, three-way triangular outer grid

over three-way triangular inner grid)

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 ◄  Fig. 231 - Tri-1 spaceframe sliced out of the octet truss Fig. 232 - Strut diagram  ► (looking down from shove) click image to enlarge

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Fig. 232 is a diagram of the layout of the struts comprising the Tri-1 spaceframe.  By

convention the bottom (blue) grid layer is called the inner layer, and the top (red) grid layer

is called the outer layer (as though the spaceframe were enclosing an interior space).  The

diagonal struts comprising the web of the spaceframe are colored purple.  The lattice is

categorized according to the predominant polygonal shape in the pattern of the outer layer,

which in this case is the triangle.  The number following the name denotes each variation

of the basic category - hence it is called Tri-1.

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You can use Euler's equation for stable polyhedra, E = 3J - 6, to determine the stability of

the Tri-1 spaceframe by analyzing a section of it called a unit cell. A unit cell is the smallest

segment of the structure that contains all of its basic elements.  Consequently the entire

lattice can be constructed by simple repetition of the cell (called tiling the plane).  Fig. 233

is a model of the Tri-1 unit cell.  It is a rhombohedron comprised of two tetrahedra and one

 Fig. 233 - Tri-1 unit cell click image to enlarge ◄  top view side view  ► 18 = 3 ( 8 ) - 6   stable

octahedron.  The cell has 18 members, or struts, and 8 joints, or hubs.  Euler's equation

predicts that it is inherently stable.  Therefore the Tri-1 lattice is also (obviously, in this

instance, since the lattice is entirely triangulated).

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The equation presumes of course that the joints of the lattice are completely flexible, which

they are here.  A load applied perpendicularly to the plane of the spaceframe is dissipated

axially throughout the struts as tension and compression stresses.  The individual struts do

not experience any significant bending stresses.  This is directly analogous to how statically

determinate truss bridge designs with pinned joints react to a load. Like a truss deck bridge,

the spaceframe's outer grid of struts, which correspond to the top chord members of the

bridge, are subjected to compressive stresses primarily.  And the inner grid of struts, which

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 Page 135 - Building stability - Tri-1 spaceframe