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In the cross-sectional plane (also in the plane of the
longitudinal sections) shear stresses appear from torsion. Recall
that
M M
  x  x . (1.23)
max
W 2W
 z
Thus, at the points of the rod plane stress state occurs.
Therefore, to assess the strength you must use one of the theories
of strength. The main tension is determined by the formula
1 2 2
       4  .
max
min 2
For example, according to the third theory the condition of
strength takes the form
2
2
 III        4    . (1.24)

екв 1 3
Substituting formulas (1.22) and (1.23) in the condition
(1.24), we obtain
2
M  M 2 M III
 III  z x  зв    , (1.25)

екв
W W
z z
where the combined moment for the third theory
2
2
M III  M  M ,
зв z x
in the case of spatial bending of the torsion
2
2
2
M III  M  M  M .
зв y z x
When using four (energy) theory the condition of strength
takes the form
2
M  0,75M 2
 IV  z x    ,

екв
W
z
and the use of theory Mora
1  M 1 
2
2

 M  z  M  M    ,
екв z x
2 W 2W
z z
 
where, we recall rate   p .
 
c

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