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 z sin y cos  M
   M      cos  z tg   y 
 J J  J
 y z  z
M cos
   sinz   y cos   ,
J cos
z

or

M cos (1.6)
   a ,
J cos
z
where a  z sin   y cos  – distance from any point to the
section neutral line. Analysis of equation (1.6) shows that the
greatest stresses occur at points of cross-section that are farthest
from the neutral line (fig. 1.4, b).
Where the cross section has two axes of symmetry (rectangular,
double-T profile) stress in the most remote from the neutral axis
points equal in magnitude and differ only in sign. Then the
condition of strength has the form
M M y
  z     , (1.7)

max
W W
z y
where W , W – moments of section modulus with respect to the
z y
axes z and y .
For design calculation of equation (1.7) can be
conveniently represented as a
M  cM
W  z y , (1.8)
 
z

where c W W – value, which are set in advance.
z y
If the cross-section of the rod has two axes of symmetry
(fig. 1.5), the formula (1.8) turns out to be unsuitable. In this case
we must be specified dimensions of cross section, and then
perform calculation. For example, a material that resists


stretching and unequal compression (     ) condition
р с
strength is of the form.

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