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3
J   hb . (5.33)
t
Stresses in the middle of the shorter side of the rectangle are
defined by the formula
   . (5.34)
max
Coefficients  ,  and  depend on the ratio of sides of the

rectangle h and are selected from tables.
b
The distortion of a rectangular cross-section of the rod in
torsion is described by the equation
 k z k y 
 8 h 2 (  )1 k (  )1 2 sh sin k  z
u( y, z)    zy  3  3 h b cos  .
  k k ch k h b 
 b 2  


In numerical calculations the first two terms of the series
sufficiently are taken into account.
Expressions for W and J of different cross-sections can be
к к
found in the references and used for practical calculations.

5.9 Rational form of cross section

From all the sections that have the same moment of resistance
to the torsion, a rational section is a section which area is the
smallest, i.e. that section of the rod, which contains the least
amount of material. The rationality of a sectional form is usually
estimated by dimensionless characteristic  which is called the
t
specific moment of resistance
W
  к .
к 3
F

Table 5.1

101