Analyzing the stability of an entire three-dimensional 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.

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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 three-dimensional structures to be sure that a common sense notion

of what a structure requires for stability agrees with reality.

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 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.
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Plate action

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Thus far we have modeled the stability of three-dimensional 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 four-sided 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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 Page 120 - Building stability - Plate action