Question

A Stepped steel shaft is subjected to a clockwise torque of 10 Nm at its free end. Shear modulus of steel is 80 GPa. The strain energy stored in the shaft is

• A. 1.73 Nmm
• B. 2.52 Nmm
• C. 3.46 Nmm
• D. 4.12 Nmm

Answer 1

The correct option is A 1.73 Nmm



$SE=U_1+U_2={\int }_0^{L_1}\frac{T^{2}dx}{2G{I}_{p1}}+{\int }_0^{L_2}\frac{T^{2}dx}{2G{I}_{p2}}$


$=\frac{T^2{L}_1}{2G{I}_{p1}}+\frac{T^2{L}_2}{2G{I}_{p2}}=\frac{T^{2}L}{2G}[\frac{1}{I_{p1}}+\frac{1}{I_{p2}}]$

$=\frac{{10}^2\times 0.1}{2\times 80\times {10}^9}[\frac{32}{\pi (0.025{)}^4}+\frac{32}{\pi (0.05{)}^4}]\times 1000$

= 1.73 Nmm.