


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
threedimensional 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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to Knowhere 

Page 119
 Building stability  Lattice action 

