forces
bearing on them and how the internal forces are distributed within them.
That is, 
they
exhibit plate action as opposed to the lattice action we just covered.
The equation 
describing the stability of pure plate structures is: 
. 
E = 3 F  6
where E = edges 
F = faces 
. 
Notice
that, in terms of plate action, this equation asserts that the cube plate
structure just 
pictured
in Fig. 203 is stable. But the cube lattice structure is not
stable. Why is this so? 
. 
Pure
plate structures are entirely composed of rigid plates that are joined
together edge to 
edge
with flexible hinge joints. These edges are called shear lines
because the internal 
stresses
generated by an external load are distributed over the surface area of
the plates, 
which are
then concentrated as shear forces along the entire length of the edges
where the 

plates are joined. This shear force consists of a pair of
equal, 

parallel forces acting in opposite directions with no distance 
between them, as shown in the animation to the left. Note 
how pressing on the opposite vertices of the cube plate 
structure causes the plates to shear past each other when 
there is no hinge pin, or pinge, to resist this stress.
Normally 
the pinges of the structure resist this shearing when they are 
positioned between the plates. The pinges, plus the rigidity

(demonstration model) 
of
the plates enables the structure to achieve a state of stable 
Fig. 204  Plates of a cube 
equilibrium so that it resists shear failure when loaded. Due 
shearing past each other 
to
the hinge able nature of this joint the plates do not


experience bending moments when the structure is loaded at 

its
vertices. Therefore pure plate structures are statically
determinate, although the static 
analysis
techniques are considerably more complex than those for trusses, or even
lattices. 
. 
The
following images show building sections that are modeled as plate
structures. Each is 




a) 9 = 3 ( 5 )  6 
*b) 9 = 3 ( 5 )  6 
*c) 12 = 3 ( 6 )  6 
d) 8 < 3 ( 5 )  6 
stable 
stable 
stable 
unstable 
click image to enlarge 
Fig. 205  Plate stability analysis of structures
(static demonstration models) 

* Note:
for modeling purposes, all panels lying in the same plane are counted as
one plate 
. 
analyzed
for its stability as a pure plate structure using E = 3 F  6. Note
that most of the 
models
are stable except d), a square pyramid peaked roof. It is
undoubtedly rigid since 
. 
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Page 121
 Building stability  Plate action 

