Limitations of Euler's theory

The general expression of bucking load for the long column as per Euler’s theory is given as,

P = Π ²E I / L²

σ = Π ²E / (Le / k) ²

We know that, Le / k = slenderness ratio

Limitation 1: The above formula is applied only for long columns

Limitation 2: As the slenderness ratio decreases the crippling stress increases. Consequently if the slenderness ratio reaches to zero, then the crippling stress reaches infinity, practically which is not possible.

Limitation 3 : if the slenderness ratio is less than certain limit, then crippling stress is greater than crushing stress ,which is not possible practically. Therefore, up to limiting extent Euler’s formula is applicable with crippling stress equal to crushing stress.