고체역학 (Beer) — Pure Bending: Problem 4.151

4.151 Solve Prob. 4.150, assuming that the couple \( M_0 \) acts in a horizontal plane. 4.150 A beam having the cross section shown is subjected to a couple \( M_0 \) that acts in a vertical plane. Determine the largest permissible value of the moment \( M_0 \) of the couple if the maximum stress in the beam is not to exceed \( 12\text{ ksi} \). Given: \( I_y = I_z = 11.3\text{ in}^4 \), \( A = 4.75\text{ in}^2 \), \( k_{\min} = 0.983\text{ in} \). (Hint: By reason of symmetry, the principal axes form an angle of \( 45^\circ \) with the coordinate axes. Use the relations \( I_{\min} = Ak_{\min}^2 \) and \( I_{\min} + I_{\max} = I_y + I_z \).)