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system (deformation compatibility equation). The number of
additional equations equals to the degree of static uncertainty. The
essence of deformation of the compatibility elements of the system
is that during deformation rod breaks, their disconnects from each
other, or unpredictable by the scheme displacements of one part of
the construction compared with the other do not occur.
Consider the sequence of expansion of static uncertainty, for
example, the rod rigidly fixed from both sides (fig.2.13 a).
1. Determine the degree of static uncertainty.
There are two unknown reactions in jamming R and R , and
A B
the static equation can be made only one X  0 , as all forces are
directed along a straight line (the other two equations in this case
are trivial). Thus, the rod is once statically undetectable.
2. Form an equivalent system. Reject the "extra" neck (neck
without which the rod is geometrically unchanged), for example,
lower resistance, and replace its effect on the rod by unknown
force R (fig.2.13, b).
A
3. Consider the static aspect of the problem. The equation of
equilibrium of the rod is:
X  R  P  R  0. (2.38)
B A
4. Consider the geometric aspect of the problem (make a
deformation compatibility equation). The required force should be
such that the equivalent system behaves as real. To make the
equation of deformation compatibility we must imagine the rod in
a deformed form and directly from the picture (geometrically) to
establish the relationship between the deformations of different
parts of the rod. In this case, the total length of the rod can vary, so
we get a condition:

l     0. (2.39)
l
1 2
5. Consider the physical aspect of the problem. According to
Hooke's law (2.11) we find the absolute elongation of each rod
part:
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