Question

If the crushing stress in the material of a mild steel column is $3300kg/c{m}^2$. Euler's Formula for crippling load is applicable for slenderness ratio equal to/greater than

• A. $40$
• B. $50$
• C. $60$
• D. $80$

Answer 1

The correct option is D $80$

In order for Euler's formula to be applicable the critical stress must not exceed the proportional limit.
Now crushing stress in mild steel
$=3300kg/c{m}^2$
$=330N/m{m}^2$
But stress at proportional limit in mild steel
$=250N/m{m}^2$
$Eule{r}^{\prime }sbucklingstress=\frac{{\pi }^{2}E}{{\lambda }^2}$
$\Rightarrow 250=\frac{{\pi }^2\times 2\times {10}^5}{{\lambda }^2}$
$\Rightarrow \lambda =88.55=89$
Thus slenderness ratio should be more than or equal to $89$ ideally. Option (d) is the most close one.