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In torsion as in other types of deformations, there are cases
when static equations are not sufficient to determine the reactions
of nodes or internal force factors. Recall that such problems are
called statically indeterminate. Their solutions are not
fundamentally different from the above mentioned statically
indeterminate problems in tension and compression (see. p.2.9).
The sequence of finding static indetermination in torsion can be
studied on the example of rod diameter D , both ends of which are
fixed (fig. 5.8).
1. Determine the degree of static indetermination. We denote
reactive moments in supporting sections through M and M .
A B
The equation of statics can be only one. Thus, the degree of static
indetermination m  2 1 1  .
2. Form the equivalent system. Reject the right fixing and its
effect on the action of rod is replaced by the action of external
moment M .
A

The equivalent
system

Figure 5.8

3. The static aspect of the problem:

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