Chapter 15, Problem 15.1P

A $\frac{1}{4}$ in.-diameter aluminum rod is bent into a circular ring having a mean diameter of $\text{125}$ in. Compute the maximum bending stress in the rod.

To determine

The maximum bending stress in the rod

Answer to Problem 15.1P

  $20\text{ ksi}$

Explanation of Solution

Given Information:

Diameter of aluminum rod, $d=0.25\text{ in}$

Mean diameter of the circular ring, $D=125\text{ in}$

Modulus of elasticity for aluminum $E=10000\text{ ksi}$

The maximum bending stress in the rod is given by

  $\begin{array}{l}{f}_b=\frac{Ec}{R}\\ f_b=\frac{10000\times \frac{d}{2}}{\frac{D}{2}}\\ f_b=\frac{10000\times \frac{0.25}{2}}{\frac{125}{2}}ksi\\ f_b=20ksi\end{array}$

Conclusion:

Therefore, the maximum bending stress in the rod is $20ksi$ .