Question

The compound shaft shown is built-in at the two ends. It is subjected to a twisting moment T at the middle. What is the ratio of the reaction torques $T_1$ and $T_2$ at the ends?

• A. $\frac{1}{16}$
• B. $\frac{1}{8}$
• C. $\frac{1}{4}$
• D. $\frac{1}{2}$

Answer 1

The correct option is A $\frac{1}{16}$

At the joints,

${\theta }_1={\theta }_2$

$\Rightarrow \frac{T_1{L}_1}{G{J}_1}=\frac{T_2{L}_2}{G{J}_2}$ $[J=\frac{\pi }{32}{d}^4]$

$\frac{T_{1}L}{G\frac{\pi d^4}{32}}=\frac{T_{2}L}{\frac{G\pi (2d{)}^4}{32}}$

$or\frac{T_1}{T_2}=\frac{1}{16}$