Question

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

• A. $7.2\times {10}^{-7}$
• B. $3.78\times {10}^{-6}$
• C. $2.78\times {10}^{-4}$
• D. $3.78\times {10}^{-4}$

Answer 1

The correct option is A $7.2\times {10}^{-7}$

$\begin{array}{c}\text{Given, force applied}=500000N\\ \text{Force on each cylinder}=125000N\\ \therefore \text{Strain}=\frac{\text{Stress}}{Y}\\ =\frac{F}{AY}=\frac{125000}{\pi \left(2700\right)\times {10}^{-4}\times 2\times {10}^{11}}\\ =7.2\times {10}^{-7}\end{array}$