고체역학 (Gere) — Stresses in Beams (Basic Topics): Problem 5.8-13

5.8-13 A square wood platform is $2.4\text{ m} \times 2.4\text{ m}$ in area and rests on masonry walls (see figure). The deck of the platform is constructed of $50\text{ mm}$ nominal thickness tongue-and-groove planks (actual thickness $47\text{ mm}$; see Appendix G) supported on two $2.4\text{ m}$ long beams. The beams have $100\text{ mm} \times 150\text{ mm}$ nominal dimensions (actual dimensions $97\text{ mm} \times 147\text{ mm}$). The planks are designed to support a uniformly distributed load $w$ ($\text{kN/m}^2$) acting over the entire top surface of the platform. The allowable bending stress for the planks is $17\text{ MPa}$ and the allowable shear stress is $0.7\text{ MPa}$. When analyzing the planks, disregard their weights and assume that their reactions are uniformly distributed over the top surfaces of the supporting beams. (a) Determine the allowable platform load $w_1$ ($\text{kN/m}^2$) based upon the bending stress in the planks. (b) Determine the allowable platform load $w_2$ ($\text{kN/m}^2$) based upon the shear stress in the planks. (c) Which of the preceding values becomes the allowable load $w_{\text{allow}}$ on the platform? Hints: Use care in constructing the loading diagram for the planks, noting especially that the reactions are distributed loads instead of concentrated loads. Also, note that the maximum shear forces occur at the inside faces of the supporting beams.