Page 112 - 4749

or
1 M z   x
 , (6.10)
 EJ
z
2
where J  y dF – axial moment of inertia relative to the
z 
F
neutral axis of bending.
The relation (6.10), which is called Hooke's law under bending,
establishes a link between stress and deformation degree of a beam
– the curvature of the neutral layer 1/.
The product EJ is called the hardness of the cross-section of
z
the beam under bending.
Substituting (6.10) into the formula (6.9), we obtain
M
  z y . (6.11)
x
J
z
The maximum normal deformations can be found with the
formula
M
  z , (6.12)
x max
W
z
J
where W  z – axial sectional moment of resistance
z
y
max
relative to the neutral axis.
Fig. 6.8 shows the curves of stresses symmetrically (fig. 6.8, a)
and asymmetrically (fig. 6.8, b) with respect to the neutral axis of
the cross-section of the beam.

112