by the
table on the end of each of the two legs also equals the downward force of
the load |
(orange
arrow). However, initially, the tensile forces being exerted by the rubber
are less |
than the
tensile stresses being induced in it by the downward force that is trying
to spread |
the legs
apart and so the rubber band stretches. That is, the forces acting
on and within the |
triangle
structure are not completely balanced and therefore the structure moves,
or |
deforms,
in the direction the greater force is pointed. As long as you
continue to increase |
the
downward pressure the legs will continue to spread apart, the rubber band
will stretch, |
and the
triangle will not achieve a state of stable equilibrium. |
|
Now, if
you hold a steady downward pressure on the apex, so that the force does
not |
increase
or decrease, you still feel an upward reaction force but the legs of the
triangle no |
longer
move (this is represented in the forgoing figure by the extreme downward
position |
of the
triangle with its legs spread apart). In that position the internal
tensile forces exerted |
by the
rubber band now equal the internal stresses induced in it by the load and
so it does |
not
continue to stretch. The triangle does not deform any more because the sum
of all the |
downward, or negative forces, is equal to, or in equilibrium with, the sum
of all the upward, |
or
positive, reaction forces. That is, the sum of the forces equals
zero. This also shows that |
the
internal strength of the weakest member of the structure (the rubber band)
must be |
equal to
or greater than the internal tensile or compressive stresses it is
subjected to for the |
structure to be stable and resist deformation. |
|
Now
replace the rubber band with a Polymorf rectangle (REC) panel for the base
and try to |
push
down on the apex. You can feel that the upward reaction force is now
significantly |
greater.
And the legs of the triangle do not spread apart. This is because
the tensile forces |
. |
|
 |
|
Fig. 129 - Demonstrating the forces and |
reactions of a stable triangle structure |
(demonstration model) |
|
|
. |
being
exerted by the material comprising the base panel matches the tensile
stresses being |
induced
in it by the downward force of your push. The harder you push the
harder the |
structure pushes back. Here again the sum of the external and
internal forces equal zero |
and the
triangle is in a state of stable equilibrium. Actually the tensile
strength of the |
plastic
in the base panel is so great that the joints will rupture before it
stretches noticeably |
causing
the triangle structure to collapse into a heap in order to reach a new
state of |
equilibrium. Try collapsing the structure yourself to see that this
is so. In doing this you are |
destructive testing the structure to empirically determine its point and
mode of failure. |
Back to
Knowhere |
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Page 83 -
Building Stability - Forces and reactions |
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