Question

A stepped steel shaft shown below is subjected to 10 N-m torque. If the modulus of rigidity is 80 GPa, the strain energy in the shaft in N-mm is

• A. 4.12
• B. 3.46
• C. 1.73
• D. 0.86

Answer 1

The correct option is C 1.73

$U_{torsion}=\frac{1}{2}{T}_1{\theta }_1+\frac{1}{2}{T}_2{\theta }_2$
$=\frac{T_1}{2}\left(\frac{T_{1}L}{G{J}_1}\right)+\frac{T_2}{2}\left(\frac{T_{2}L}{G{J}_2}\right)$
$=\frac{T^{2}L}{2G{J}_1}+\frac{T^{2}L}{2G{J}_2}(As{T}_1=T_2=T)$
$=\frac{T^{2}L}{2G{J}_1}(\frac{1}{J_1}+\frac{1}{J_2})=\frac{(10\times 1000{)}^2\times 100}{2\times 80\times 1000}$ $\left[(\frac{32}{\pi \times (50{)}^4}+\frac{32}{\pi \times (25{)}^4})\right]$

$=\frac{{10}^8\times 100\times 32}{2\pi \times 80\times 1000}[\frac{1}{(50{)}^4}+\frac{1}{(25{)}^4}]$
$=1.73N-mm$