고체역학 (Beer) — Pure Bending: Problem 4.191

*4.191 For a curved bar of rectangular 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 \(\sigma_r\) 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 surface.)