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 M   M  M  M  0. (5.25)
A
x
B
4. The geometric aspect of problem is that the total angle of
twist of the rod is zero:
    0 . (5.26)
1 2
5. The physical aspect of the problem. According to the formula
(5.17) we obtain:
M l  M l
x
  1 1  A 1 ; (5.27)
1
GJ GJ
 
M l  M  M l
x
  2 2  A 2 . (5.28)
2
GJ GJ
 
6. Synthesis. Substitute the expressions (5.27) and (5.28) in the
condition (5.26) and take into account (5.25), we have:
M l M l
M  2 ; M  1 .
A B
l  l l  l
1 2 1 2
Static indetermination is disclosed.

5.8 Torsion of noncircular cross-section rod

The problem of torsion of noncircular profile rod is solved by
the theory of elasticity. In pure torsion in the cross-sections of rods
only tangential stress occurs, just as in torsion of a circular cross-
section of the rod. The largest tangential stress, angle of twist and
potential energy of deformation can be calculated using the
formulas that are similar in the structure to the formulas (5.10),
(5.17) and (5.23), but the replacement of J and W to J and W :
  t t
M
  x , (5.29)
max
W
к
M l
  x , (5.30)
GJ
к
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