A rectangular column of 230mm x 350mm and 4M long used as a column. If one end is hinged and other is fixed, find the safe load the column can carry if FOS-2.5. use Euler’s formula. E=200Gpa

Note: Moment of Inertia of the section will be least. Before solving the problem always use effective length in the formula; which will get by using below table

Actual length of column = L, Effective length = Le

$A = 230 \times 350 \ mm^2, \ L = 4 m = 4000 \ mm, \ F.O.S = 2.5, E = 200 \ Gpa$

Effective length of column Le is $\frac{L}{\sqrt{2}} = \frac{4000}{\sqrt{2}} = 2828.42 \ mm$

($\because$ One end is hinged and other is fixed).

Now, I = Moment of inertia = $\frac{350 \times 230^3}{12} = 354.87 \times 10^6 \ mm^4$

By Euter’s formula,

Crippling load = P = $\frac{\pi^2 \ E \ I}{L^2e} = \frac{\pi^2 \times (200 \times 10^3) \times 354.87 \times 10^6}{(2828.42)^2}$

$= 87.56 \times 10^3 \ KN$

Now,

$Safe \ load = \frac{crippling \ load}{F.O.S} = \frac{87.56 \times 10^3}{2.5} = 35.02 \times 10^3 \ KN$