Chapter 4.10, Problem 191P

For a curved bar of rectagular cross section subjected to a bending couple M, show that the radial stress at the neutral surface is

${\sigma }_r=\frac{M}{Ae}=\left(1-\frac{r_1}{R}-\ln \frac{R}{r_1}\right)$

and compute the value of σ_r for the curved bar of Concept Applications 4.10 and 4.11. (Hint: consider the free-body diagram of the portion of the beam located above the neutral suface.)

Fig. P4.191