Question

Four identical hollow cylindrical columns of mild steel support a big structure of mass 50,000 kg. The inner and outer radii of each column are 30 and 60 cm respectively. Assuming the load distribution to be uniform, calculate the compressional strain of each column.

Answer 1

Mass of the big structure, M $=$ 50,000 kg
Inner radius of the column, r $=$ 30 cm $=$ 0.3 m
Outer radius of the column, R $=$ 60 cm $=$ 0.6 m
Young’s modulus of steel, $Y=2\times {10}^{11}Pa$

Total force exerted, $F=Mg=50000\times 9.8N$

Stress = Force exerted on a single column $=50000\times \frac{9.8}{4}=122500N$
Young’s modulus, $Y=\frac{Stress}{Strain}$

Strain $=\frac{\left(F/A\right)}{Y}$
Where,
Area, $A=\pi (R^2-r^2)=\pi \left(\right(0.6{)}^2-\left(0.3{)}^2\right)$

Strain $=122500/\left[\pi \right((0.6{)}^2-(0.3{)}^2)\times 2\times {10}^{11}]=7.22\times {10}^{-7}$

Hence, the compressional strain of each column is $7.22\times {10}^{-7}$.