고체역학 (Beer) — Pure Bending: Problem 4.158

4.158 A beam of unsymmetric cross section is subjected to a couple \( M_0 \) acting in the horizontal plane \( xz \). Show that the stress at point \( A \) of coordinates \( y \) and \( z \) is \[ \sigma_A = \frac{zI_z - yI_{yz}}{I_y I_z - I_{yz}^2} M_y \] where \( I_y \), \( I_z \), and \( I_{yz} \) denote the moments and product of inertia of the cross section with respect to the coordinate axes, and \( M_y \) the moment of the couple.