its shape will not distort easily.  Despite this, for it to qualify as a stable pure plate structure, the internal forces induced by an externally applied load must be distributed throughout the structure as shear forces acting between the plates.  However, as shown by the animation to the right, pushing down on the apex of the pyramid creates a thrusting force that tries to tear the edges apart rather than force them to shear past one another.  Therefore, although Fig. 206 - Instability it is rigid, the pyramid is not a stable plate structure. of a square pyramid

.

 Exercise: Construct plate structures like those shown in Fig. 205.  Empirically examine them
 for the presence of shear forces by removing one or two pinges and then squeezing the
 model by pressing on opposite vertices. Analyze their stability with the equation E = 3 F- 6.

.

It is useful at this time to look again at box girders and analyze their stability as plate

structures.  The inherent stability imparted to the box girder structure by joining the plates

together edge to edge is revealed by plate analysis.

 *a)   9 = 3 ( 5 ) - 6 *b)  12 = 3 ( 6 ) - 6 *c)  12 = 3 ( 6 ) - 6 click image to enlarge Fig. 207 - Plate stability analysis of box girders    (static demonstration models)

* Note: for modeling purposes, all panels lying in the same plane are counted as one plate

.

Of course box girders are comprised of steel plates that are welded or riveted together edge

to edge.  Therefore, structurally speaking, they do not qualify as pure plate structures since

their joints are not flexible.  Neither do buildings that have wood or metal shear panels

fastened to their exterior frameworks for resistance to shear forces acting on them.  For that

matter, the structural members of building frameworks are normally fixed to their supports

and each other so that their joints are not flexible, as is required of pure lattice structures.

Nevertheless, we made this excursion into stability theory - planar, lattice, and plate - to

show the basic structural dynamics operating in complex building systems comprised of

elements of two-dimensional planes, three-dimensional lattices, and plate structures.  The

actual forces acting on buildings are much more complex than these simple models suggest

as will be shown in the next section on forces and reactions in buildings.

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 Page 122 - Building stability - Plate action
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