Fig. P4.158 and P4.159
4.158 A beam of unsymmetric cross section is subjected to a couple $M_y$ acting in the horizontal plane xz. Show that the stress at point A of coordinates y and z is
$$\sigma_A = \frac{zI_z - yI_{yz}}{I_yI_z - I_{yz}^2}M_y$$
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.
4.159 A beam of unsymmetric cross section is subjected to a couple $M_z$ acting in the vertical plane xy. Show that the stress at point A of coordinates y and z is
$$\sigma_A = \frac{yI_y - zI_{yz}}{I_yI_z - I_{yz}^2}M_z$$
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 $M_z$ the moment of the couple.
