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determines the value of the principal stress on the principal area.
We previously supposed about its existence.
It is easy to prove that all three roots of (3.10) are valid. They
are denoted by ,  ,  , and indexes are assigned so that the
1 2 3
condition      .
1 2 3
If as a result of the equation solution (3.10) we find the
principal stresses  ,  ,  , then, substituting each of the found
1 2 3
values in any two equations (3.8) and using the geometric ratio
l 2  m 2  n 2  1, we can determine the direction cosines of the
respective principal areas.

3.4 Classification of stress states

Depending on the number of principal stresses that are not
equal to zero, distinguish linear, plane and volumetric stress state
at a point (table. 3.1).

Table 3.1
Stress state at a point
Volumetric Plane Linear
  ; 0   ; 0   0   ; 0   ; 0   0   ; 0   ; 0   0
i j k i j k i j k
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