Euler's formula for long column- Strength of Material

Euler’s theory:

• This theory is valid only for long columns only.
• This theory is valid only when slenderness ratio is greater or equal to critical slenderness ratio.
• For any slenderness ratio above critical slenderness ratio, column fails by buckling and for any value of slenderness ratio less than this value, the column fails in crushing not in buckling.

Euler’s critical load formula is,

`e = (pi^2*EI)/l^2`

• Euler’s formula is applicable when, Crushing stress ≥ Buckling stress

For mild steel,

E = 2 × 105 N/mm2

σcr = 330 N/mm2

 λ ≥ 80 N/mm2

• When slenderness ratio for mild steel column is less than 80, the Euler’s theory is not applicable.