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 2 E
    , (5.19)
кр 2 пц

where  – proportional limit of the material of the rod.
пц
Inequality (5.19) defines the condition that must satisfy the rod
flexibility for Euler's formula was applicable:

  E  . (5.20)
пц
Equal sign in this condition corresponds to the marginal
flexibility  , while reducing it Euler’s formula becomes
гр
inapplicable. We see that the rod marginal flexibility is its
physical and mechanical properties, depending on the elastic
modulus and the coasts of proportionality. For example, rods,
made of mild steel St3, with modulus of elasticity
E  2 10 МПа 5 and boundary proportionality   200МПа
пц
limit flexibility

  3,142 2 10 200 100 5  ,
гр
i.e. for steel St3 Euler’s formula applies when   100 . Thus, for
materials from other mechanical properties limit flexibility will
have other values.
With the decrease of rod flexibility the critical tension increases,
and if the flexibility is lower than limit, the critical stress exceeds
the limit of proportionality. Then, in practical calculations we use
empirical formulas obtained by experimental studies. In
particular, we should apply the formula proposed by Jasinski:

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