Triangular spaceframe lattice, Tri-1:
(self-dual tessellation, three-way triangular outer grid |
over three-way triangular inner grid) |
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 |
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 |
◄ Fig. 231 - Tri-1 spaceframe |
sliced out of the octet truss |
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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. |
. |
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 ► |
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18 = 3 ( 8 ) - 6 stable |
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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). |
. |
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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to Knowhere |
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Page 135
- Building stability - Tri-1 spaceframe |
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