Furthermore, inherent stability in structures depends no only on the
number of structural |
 |
members used but also their placement. For example the |
polygon to the left has the minimum
number of members |
called for by Euler's equation yet it is unstable. Obviously |
then we must seek a deeper understanding of the factors |
responsible for a structure's stability other than just its
topology. |
We
must study the dynamic interplay between the internal and |
external forces a structure experiences when it is stressed. |
|
21 = 2 (12) - 3 |
◄
Fig. 125 - Unstable octagon that satisfies Euler's
equation |
. |
|
Exercise: 1) How many more members are needed to stabilize Fig. 125
? Placed where? |
|
2) Find other polygonal structures that should be stable according
to Euler's |
|
|
. |
Forces and reactions |
. |
In the
previous experiment we determined empirically that a polygon is unstable
if its |
shape is
distorted when an outside force acts on it. Newton's first law
states that an object |
that is
at rest will remain at rest provided it is not subjected to an unbalanced
force. When |
you push
on an unstable polygon the structural members move from their at rest
position |
and
deform because the total force pushing on it is greater than the
structure's ability to |
push
back and resist being deformed. If we assign a negative value to the
forces pushing |
on the
structure and a positive value to the forces resisting being pushed, then
the sum of |
the
forces do not equal zero. As a result the structure will be deformed
in the direction that |
the
excess force is pushing it. If, however, the sum of the forces
equals zero then the |
structure is stable and will not deform. |
. |
 |
For example, if you push down on the edge of a Polymorf panel that
is |
resting upright on a table it does not move downward because the |
downward acting force, or load, that you are applying to it (orange
arrow) |
is
balanced by the reaction of the upward force of the table pushing
back |
(green arrow). The harder you push down the harder the table
pushes |
back. The downward (negative) force plus the upward (positive
force) |
equals zero. We say that the forces acting on the panel are in
equilibrium |
and the panel is stable. |
◄ Fig. 126 - Pushing down on a panel
induces compressive stresses |
|
. |
Notice
that the panel is being squeezed between two forces that are external to
it. Yet it is |
not
deformed because the atoms it is made of resist being deformed.
Internal forces, |
Back to
Knowhere |
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Page 81 -
Building stability - Forces and reactions |
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