geometric arrangement of the members into the triangle. The triangle
then must be an |
inherently stable structure. |
|
With
that in mind let's take another look at the other polygonal shapes to see
how they |
might be
made stable. For example let's place an additional member in the
parallelogram |
so that
it joins two of its opposite joints together as shown in Fig. 122 a). This action, called |
triangulation since we are dividing the polygon into two triangular shaped
sections, makes |
|
|
|
a) square |
b) pentagon |
c) hexagon |
Fig. 122 - Stabilizing polygons by triangulation
(demonstration models) |
|
|
the
parallelogram stable and forms it into a square. Let's do the same
for the pentagon. |
First we
insert one extra member so as to form a triangle with any two adjacent
edges of |
the
pentagon as shown in Fig. 122 b)
above. This helps stabilize part of the structure but |
the
other three members can still move. We add another member forming
three triangular |
sections
in all. The pentagon is now stable also. Finally, we
triangulate the hexagon in a |
similar
manner and find that it takes a minimum of three extra members to make it
stable |
(Fig.
122 c). In each of these examples, the rigidity imparted to the polygon
is due only to |
the fact
that it was triangulated since all of its joints are hinged.
Triangulation changed |
them
from being inherently unstable to being inherently stable. |
|
Using
such hit and miss methods ancient builders eventually discovered the
principle of |
triangulation in their attempts to build stable structures. But
structural engineers do not |
like
being eaten by wolves any more than the third little pig did. So
they wisely use a |
mathematical equation, attributed to Euler, that gives a good indication if
a polygonal |
structure with flexible joints is inherently stable or not. And if
it is not stable the equation |
predicts
how many additional bracing members it takes to stabilize it: |
|
M = 2 J - 3
where M = members |
J = joints |
|
Back to
Knowhere |
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Page 79 -
Building stability - Two-dimensional stability |
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