The shortcoming of the Euler's column failure theory or Limitation of Euler's Formula:

• The general expression of buckling load for the long column as per Euler's theory is given as,

i.e (since I=Ak^2)

The stress at failure =, according to formula stress at failure will be high when the slenderness ratio is small. But the stress at failure cannot be greater than the crushing stress for the column material.

• When the slenderness ratio is less than a certain limit, Euler's formula gives a value of the crippling load even greater than the crushing load, which is not practically possible.

Rankine's column crippling theory

• It has been shown that Euler’s formula is valid for long column having l/k ratio greater than a certain value for a particular material. Euler’s formula does not give a reliable result for short column and length of column intermediate between very long to short.
• An empirical formula has been proposed by Rankine for columns of all lengths. The proposed formula is

Where P = crippling load

Pc = crushing load = fc × A

A is the area and fc is the ultimate crushing stress

Pe = crippling load by Euler’s formula