고체역학 (Gere) — Stresses in Beams (Basic Topics): Problem 5.5-8

5.5-8 A freight-car axle $AB$ is loaded approximately as shown in the figure, with the forces $P$ representing the car loads (transmitted to the axle through the axle boxes) and the forces $R$ representing the rail loads (transmitted to the axle through the wheels). The diameter of the axle is $d = 82\text{ mm}$, the distance between centers of the rails is $L$, and the distance between the forces $P$ and $R$ is $b = 220\text{ mm}$. Calculate the maximum bending stress $\sigma_{\text{max}}$ in the axle if $P = 50\text{ kN}$.