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

Page 83 - Building Stability - Forces and reactions

home   sitemap   products   Polywood   .networks   contact us   Knowhere   3Doodlings