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5 STABILITY OF COMPRESSED RODS

In engineering calculations the conditions of strength and
stiffness are usually supplemented by the stability condition,
which involves maintaining the original shape of structure
equilibrium or its individual elements under a given load.
Physical indication of stable or unstable form of equilibrium is
the behavior of loaded elastic system when it deals with the
deviation from the equilibrium by some small amount. If the
system is deflected from equilibrium, after elimination of the
reasons that caused this deviation, returns to its original position,
then the equilibrium is stable. If the deviation does not
disappeared and continues to grow, the equilibrium is unstable.
The load at which a stable equilibrium becomes unstable is called
critical.

5.1 Stable and unstable elastic equilibrium of
compressed rod

Under the influence of compressive load that is gradually
growing, rod passes through three forms of equilibrium: stable,
unstable and indifferent. Obvious certain analogy between the
resistance and the resistance of the elastic position is absolutely
solid.
In a state of stable equilibrium is heavy ball at the bottom of the
spherical recess (fig.5.1 a). When deflecting the ball from the
original position it after a certain number of vibrations returns to
its original state. Compressed rod is in stable equilibrium if
gripping force P does not exceed a critical value P . If a
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straight rod is deflected by the application of the external
transverse force, it will return to original shape under the
influence of internal forces of elasticity after removing the cause
of the deviation.
Ball on a horizontal flat surface (fig.5.1, b) is in a state of
indifferent equilibrium, because any of its position will be equally
stable. Equilibrium shape of compressed rod is indifferent when
gripping force reaches a critical value. In this condition the rod

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