고체역학 (Gere) — Stresses in Beams (Basic Topics): Problem 5.10-8

5.10-8 A bridge girder $AB$ on a simple span of length $L = 14 \text{ m}$ supports a distributed load of maximum intensity $q$ at mid-span and minimum intensity $q/2$ at supports $A$ and $B$ that includes the weight of the girder (see figure). The girder is constructed of three plates welded to form the cross section shown. Determine the maximum permissible load $q$ based upon (a) an allowable bending stress $\sigma_{\text{allow}} = 110 \text{ MPa}$ and (b) an allowable shear stress $\tau_{\text{allow}} = 50 \text{ MPa}$. Cross-section dimensions (from image): Top & Bottom Flanges: $450 \text{ mm} \times 32 \text{ mm}$ Web: $1800 \text{ mm} \times 16 \text{ mm}$