Analyzing the stability of an entire threedimensional framework of
members is referred to 
as
lattice stability analysis, as opposed to the planar stability analysis we
employed for 
polygons
and trusses previously. If the lattice framework is completely
triangulated and all 
of its
joints, or hubs, are flexible, it is said to exhibit pure lattice action
and is statically 
determinate. That is, static analysis techniques, like those we
employed to analyze the 
forces
acting on truss bridges, can be used to quantify and qualify those forces.
However, 
doing a
static analysis of a lattice involves significantly more work than doing
one for a 
truss. 
. 
Referring back to the lattice calculations just presented in
Fig. 202, notice what happens 
when the
roof structure, b), is added on top of the room structure, a), to build
the entire 
house
structure, c). The resulting structure needs only 24 members to be
stable with its 10 
joints.
One might have guessed that the house needs 25 members, presuming that the
top 
face of
the cube shares its diagonal bracing strut with the one in the base of the
roof. 
Actually
this strut is altogether unnecessary, or redundant, since the room
structure and the 
roof
structure combine to stabilize each other's top and base respectively
without the need 
for any
shared brace between them. The stabilizing elements of these lattice
structures 
combine
to achieve a synergistic effect whereby the whole is not equal to the sum
of its 
parts.
Rather it exhibits a unique behavior of its own. One has to be
careful when doing 
a
stability analysis of threedimensional structures to be sure that a
common sense notion 
of what
a structure requires for stability agrees with reality. 
. 
Exercise: 1)Construct a model of the completely triangulated house
structure shown in 

Fig. 202 c). Examine its stability
with and without the extra diagonal brace in 

question to confirm it is redundant. 

. 
Plate
action 
. 
Thus far
we have modeled the stability of threedimensional polyhedra as though
they are 
lattices
comprised of rigid members, or struts, connected together end to end by
flexible 
joints,
or hubs. We have also briefly mentioned that the faces of a cube's
framework could 
click image to enlarge 
be
stabilized by using a rigid panel, or shear plate. Such a 

plate can be imagined as being a foursided polygon braced 
by
an infinite number if diagonal struts acting together to 
create the stable plate. That is, it is infinitely
triangulated 
like the blue colored plate in the image shown on the left. In 
this respect a plate does not differ from a strut in how it 
stabilizes a structure. However, plates do differ in the way 
12 = 3 ( 6 )  6 
that they are joined together as an assembly to build stable 
stable plate structure 
structures. They are joined edge to edge around their entire 
Fig. 203  Pure plate action 
perimeter but not at the vertices where their edges converge. 
As
a result plate structures differ in how they react to outside 

. 
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Building stability  Plate action 

