Data: d = 500 mm

Calculate : k

Radius of gyration (K): The radius of gyration of a given area about any axis is the distance from the given axis at which the area is assumed to be concentrated without changing the MI about the given axis.

$K=\sqrt{\frac{I}{A}}$

Where, I = Moment of Inertia $(mm)^{2}$ A = Cross Sectional Area $(mm)^{2}$ K = Radius of Gyration. $(mm)^{2}$

Application: It is used in Euler’s formula to determine buckling load on long column.

$K=\sqrt{\frac{I}{A}}$

$\mathrm{K}=\sqrt{\frac{\frac{\pi \mathrm{d}^{4}}{64}}{\frac{\pi \mathrm{d}^{2}}{4}}}$

$\mathrm{K}=\sqrt{\frac{\frac{\pi \times \mathrm{500}^{4}}{64}}{\frac{\pi \times \mathrm{500}^{2}}{4}}}$

$\mathrm{K}=\sqrt{\frac{3.068 \times 10^{9}}{196.35 \times 10^{3}}}$

$\mathrm{K}=125 \mathrm{mm}$