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,

plate_action.gif

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

roof.gif

house.gif

roof.gif

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

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