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dM
x   m   x . (5.1)
dx
Thus, the derivative of the twisting moment on the abscissa of
a cross-section equals to the intensity of distributed moment load,
taken with the opposite sign.
Considering the analogy in the equations (5.1) and (2.1), we
come to the conclusions that are similar to those obtained in the
central tensile:
1) at a section where   0m x  the function M decreases, and
x
vice versa;
2) at a section that is free of distributed moment load, twisting
moment does not change;
3) at a section that loaded by evenly distributed load the
twisting moment varies linearly.
In the general case:

M   m   x dx C , (5.2)
x 
where C – the integration constant, which is found from the
boundary conditions.

5.3 Torsional stress of the circular cross-section rod

In the general case the torsion of the rod of an arbitrary cross-
section Bernoulli’s geometry hypotheses are not used; cross
sections are distorted. When distortions are absent (round or
circular cross sections), or if they are the same in all cross-sections
and can freely occur such torsion is called clean.
Experimental study of torsion of circular cross-section rod gives
the following results:
- Rod cross-sections in torsion are flat and orthogonal to the
axis of the rod;
- Distance between cross-sections does not change;

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