Question

A hollow cylindrical column of steel supports a load of $12,000 \,kg$. The inner and outer radii of the column are $20 \,cm$ and $30 \,cm$ respectively. Assuming the load distribution to be uniform, calculate the value of compressional strain in terms of $10^{-6}$ of the column. (Take Young's modulus of steel $=2 \times 10^{11} Pa , \pi=3.14, g =9.8\, m / s ^{2}$ )

Answer 1

Area of cross-section of the cylindrical column,
$a =\pi\left( r _{2}^{2}- r _{1}^{2}\right)=\pi\left(0.3^{2}-0.2^{2}\right)=0.05 \pi m ^{2}$
Mass supported on the column, $M=12,000\, kg$
Therefore, compressional force on the column,
$F = Mg =12,000 \times 9.8=117600\, N$
Compressional strain,
$\frac{l}{L} =\frac{F}{a Y}$
$=\frac{117600}{0.05 \pi \times 2 \times 10^{11}}$
$=\frac{117600}{3.14 \times 10^{10}} $
$=3.7452 \times 10^{-6} $
$=3.75 \times 10^{-6}$
....(Rounding off to $2$ decimal places.)