Page 92 - 4749

d d
M  G   2 dF  GJ ,
x 
dx dx
F
or
d M
 x , (5.7)
dx GJ

where J   2 dF – the polar moment of inertia of the cross-
 
F
section; product GJ – the cross-sectional hardness in torsion.

The dependence (5.7) expresses the Hooke's law in torsion.
Substituting the expression for d dx in the formula (5.6)
M
  x  . (5.8)

J

The maximum tangential stresses will get when    (fig.
max
5.6)
M
  x , (5.9)
max
W

J 
where W  – the polar moment of resistance.


max

Figure 5.6
92