Question

A prismatic solid circular rod of diameter \( d \) is bent to introduce an offset \( s = d \) as shown. The rod is further subjected to an axial load \( P \). If the maximum longitudinal stress at a section A-B in the rod (with offset) is \( n \) times the longitudinal stress in the straight rod, the value of \( n \) (in integer) would be \(\underline{\hspace{2cm}}\). \includegraphics[width=0.5\linewidth]{image17.png}

Hint:

When a rod is bent, the longitudinal stress increases due to the bending moment, and the increase factor can be calculated based on the geometry of the system.

Answer 1

Correct Answer: 9

For a bent rod subjected to an axial load, the longitudinal stress is given by: \[ \sigma = \frac{P}{A} \] Where \( A \) is the cross-sectional area. When the rod is bent, the longitudinal stress is modified due to the bending moment. The stress is increased by a factor of \( n \), which is determined by the geometry of the rod. For the rod with an offset, the value of \( n \) is \( 9 \).
Thus, the value of \( n \) is \( 9 \).