Spaceframe lattices



Two single layer grids can also be stacked on top of each other so

that the grid pattern of one layer is staggered relative to the grid of

the other layer (Fig. 227).  The joints of one grid are aligned with

the center points of the polygons of the other grid like dual

tessellations.  As a result the web elements, or struts, form oblique

angles with the grids they span between.  Fig. 228 following

shows an example of two staggered, single layer, three-way grids

click to enlarge

that are connected together with struts to form a completely

Fig. 227 - Staggered

triangulated lattice structure, or spaceframe.  In this particular

three-way grids

spaceframe, all of the struts making up the grid and web of the


lattice are of equal length.  Each facet, or face, of the lattice is an equilateral triangle.

As a structural framework it is commonly referred to as a Tri-1 spaceframe, or octet truss.





Fig. 228 -Tri-1 spaceframe

(octet truss)

overhead view  ►

(static demonstration model)

click image to enlarge


One of  the first practical uses of the octet truss lattice was a man-carrying kite invented


by Dr. Alexander Graham Bell in 1907. This lattice was also


popularized later by R. Buckminster Fuller as the isotropic

vector matrix, or IVM.  Readers of the prior lesson on

geometry will recognize it as a space filling of tetrahedra

and octahedra in the ratio of two to one respectively.


◄  Fig. 229 - Cygnet tetrahedral kite (Bell, 1907)

click image to enlarge


It is also identical to the FCC crystal lattice structure presented in the previous lesson on

crystallography.   The Tri-1 spaceframe can be cut out of the FCC crystal lattice by slicing

it parallel to the 111 plane.   Two other basic spaceframe lattices can be sliced out of the


octet truss also.  One is a two-way square lattice, called


the Square-2 spaceframe, which is a slice taken parallel

to the 100 plane.  The other is a two-way rectangular
lattice, Rec-2, which is sliced parallel to the 110 plane


Fig. 230 - Slicing the octet truss (blue) to reveal the Tri-1

(purple), Square-2 (red), and Rec-2 (green) spaceframes


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Page 134 - Building stability - Spaceframe lattices

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