Question

A solid circular shaft tapers uniformly from $100mm$ to $20mm$ over a length of $500mm$ is hanged vertically as shown:



If the self weight of shaft is $78.5kN/m^3$ and modulus of elasticity, $E=2.1\times {10}^{5}MPa$ then the elongation of shaft due to its own weight is _______ $\times {10}^{-5}mm$. (Answer correct upto two decimal places).

• A. 2.18

Answer 1

The correct option is A 2.18

$\lambda =78.5kN/m^3$

$E=2.1\times {10}^{5}N/m{m}^2$

Elongation of shaft,

$\delta =\frac{\lambda l^2}{6E}[1+\frac{2d_1}{d_2}]$

$\delta =\frac{78.5\times {0.5}^2}{6\times 2.1\times {10}^8}\times [1+\frac{2\times 20}{100}]\times {10}^{3}mm$

$\delta =2.18\times {10}^{-5}mm$