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a)

b)

Figure 2.4.

The geometric aspect. According to Bernoulli’s hypothesis
(see point1.8), it can be argued that all longitudinal fibers of a rod
between two arbitrary cross sections are the same longer, i.e.
  const .
x
The physical aspect. The deformation is the reason for
appearing the stress. As the deformation between any sections is
distributed evenly, then, according to the hypothesis, normal
stresses are also distributed evenly, i.e. there is a uniform stress
state:
  const . (2.4)
x
According to the equations (2.4) and (2.3) we obtain

N   dA   , A
x x x
A
hence

N
  x . (2.5)
x
A
Thus, during the central tension and compression of a rod with
constant cross dimensions in an arbitrary cross-section there are

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