고체역학 (Gere) — Stresses in Beams (Basic Topics): Problem 5.6-20

5.6-20 A horizontal shelf $AD$ of length $L = 1215 \text{ mm}$, width $b = 305 \text{ mm}$, and thickness $t = 22 \text{ mm}$ is supported by brackets at $B$ and $C$ (see part a of the figure). The brackets are adjustable and may be placed in any desired positions between the ends of the shelf. A uniform load of intensity $q$, which includes the weight of the shelf itself, acts on the shelf (see part b of the figure). (a) Determine the maximum permissible value of the load $q$ if the allowable bending stress in the shelf is $\sigma_{\text{allow}} = 8.5 \text{ MPa}$ and the position of the supports is adjusted for maximum load carrying capacity. (b) The bookshelf owner decides to reinforce the shelf with a bottom wood plate $b/2 \times t/2$ along its entire length (see figure part c). Find the new maximum permissible value of the load $q$ if the allowable bending stress in the shelf remains at $\sigma_{\text{allow}} = 8.5 \text{ MPa}$.