Chapter 12, Problem 12.1P

Determine the internal resisting torque in the shaft shown at A, B, and C. Show the free-body diagrams.

To determine

The externally resisting torque in the shaft at points A, B, and C

Answer to Problem 12.1P

   $4\text{ k-}in.$

   $13\text{ k-}in.$

   $31\text{ k-}in.$

Explanation of Solution

Given Information:

The shaft and torque acting on it are shown in the figure below:

Let internal resisting torque at $A=T_a$, at $B=T_b$ and at $C=T_c$

Cutting a section at A, take the free body diagram from the left bearing to point A

At point A, for equilibrium the summation of torques must be zero $\sum T=0$

   $\begin{array}{l}4\text{ k-}in\mathrm{..}+T_a=0\\ T_a=-4\text{ k-}in.\end{array}$

At point B, the free body diagram from the left bearing

For equilibrium, the summation of torques must be zero $\sum T=0$ at point B

   $\begin{array}{l}4\text{ k-}in.+9\text{k-}in.+T_b=0\\ T_b=-13\text{ k-}in.\end{array}$

At point C, the free body diagram from the left bearing

For equilibrium, the summation of torques must be zero $\sum T=0$ at point C

   $\begin{array}{l}4\text{ k-}in.+9\text{k-}in.+18\text{k-}in.+T_b=0\\ T_b=-31\text{ k-}in.\end{array}$

Conclusion:

At point A, the internal resisting torque is $4\text{ k-}in.$ and it acts in the clockwise direction when viewed from the left bearing.

At point B the internal resisting torque is $13\text{ k-}in.$ and it acts in the clockwise direction when viewed from the left bearing.

At point C the internal resisting torque is $31\text{ k-}in.$ and it acts in the clockwise direction when viewed from the left bearing