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At certain position of the pole neutral axis will be tangent
to the cross section. If the neutral axis provides a number of
positions in the form of tangential (1 1 , 2 2 , 3 3 , 4 4 and
5 5 ) to the contour of the cross-section, the point of application
of force (1, 2, 3, 4 and 5) outlines some of the area around the
center of gravity - the core section (fig. 1.9).
Thus, the core section is an area around the center of
gravity of the cross-section, which has the feature as: if the
longitudinal force is applied in the area of the nucleus, the normal
stresses at all points of the cross-section have the same sign.
Coordinates of points on the contour of the nucleus:
i 2 i 2 y
y   z ; z   , (1.21)
я * я *
y z
н н
*
*
where y and z – segments, which cuts the neutral axis to the
н н
coordinate axes so that it is just tangent to the cross section.
Designing compressed rods (studs, pillars, columns) it
should be borne in mind that by using materials that do not work
on stretching, the point of application of force should not go
beyond of the nucleus section.

1.4 Bending with torsion

1.4.1 The rod of circular cross-section

Let the rod is loaded so that its cross-sections have two
internal power factors - bending and twisting moments (fig. 1.10).
Typical examples of this rod are the shafts of various
machines that usually undergo
simultaneous bending with
torsion.
Let consider the stress
state at a point located on the
surface of the rod. Along the
axis normal stresses act on
bending. Recall that
M
  z .
max
W
Figure 1.10 (1.22) z

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