Polymorf - Knowhere - Lattice action

The sloped plane of the roof must also be stabilized with some sort of bracing to keep the

trusses from tipping over (braces are indicated by blue pinges).

Combining all of these planes together gives an
idealized model of a completely stabilized
house framework complete with bracing.

Fig. 201 - Stable skeletal framework of a house ►
(static demonstration model)

Lattice action

Thus far our stability analysis of a home's framework has treated the structure as though it

was comprised of discrete triangulated planes in order to simplify the stability analysis.

This approach is similar to treating polyhedra as though they are assemblies of discrete

planar faces, which of course they are. However, we can also do a stability analysis of the

entire three-dimensional structure by using another equation Euler devised for polyhedra:

M = 3 ( J ) - 6 where M = members

J = joints

Lets apply it to the house framework you just studied. For example, the stabilized cube has

a total of 18 members (12 edges plus 6 diagonal braces) and 8 joints. Substituting these

values into Euler's equation gives 18 = 3 ( 8 ) - 6, confirming that it is stable.


a) stabilized cube	b) stabilized roof	c) stabilized house
18 = 3 ( 8 ) - 6	12 = 3 ( 6 ) - 6	24 = 3 ( 10 ) - 6
stable	stable	stable
click image to enlarge
Fig. 202 - Analyzing the stability of idealized lattice frameworks with M = 3 ( J ) - 6

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