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where c  d .
D
In the design calculating (5.11) or (5.12) are substituted into
(5.10) and we obtain respectively:
- for a circular cross section:

16M
D  3 x ; (5.13)
   

- for a ring section:

16M
D  3 x , (5.14)
  1 c  4 

where the value c should be predetermined in advance

5.5 Deformations and displacements in torsion.
Calculation for the hardness

In torsion the cross-sections of a rod return relatively to each
other around its longitudinal axis at a certain angle, i.e. behave like
thin and hard disks that impaled on the rod axis and elastically
linked. These displacements are called the angle of twist   x .
The deformation measure in torsion is the variable value in the
angle of twist per unit length - linear (relative) angle of twist:
d
   x  .
dx
After differentiating the expression (5.7) and taking into
account the equation (5.1), we obtain the differential equation of
displacements of the second order

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