Fig. 199 - Horse barn with open Queenpost truss roof (scale visualization model) click image to enlarge

.

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).

 ◄  Fig. 200 - Bracing roof trusses to keep them from tipping over (static demonstration model)
 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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 Page 119 - Building stability - Lattice action
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