고체역학 (Gere) — Stresses in Beams (Basic Topics): Problem 5.5-29

5.5-29 A steel post (\(E = 200 \text{ GPa}\)) having thickness \(t = 3 \text{ mm}\) and height \(L = 2 \text{ m}\) supports a stop sign (see figure), where \(s = 310 \text{ mm}\). The height of the post \(L\) is measured from the base to the centroid of the sign. The stop sign is subjected to wind pressure \(p = 0.95 \text{ kPa}\) normal to its surface. Assume that the post is fixed at its base. (a) What is the resultant load on the sign? (See Appendix E, Case 25, for properties of an octagon, \(n = 8\).) (b) What is the maximum bending stress \(\sigma_{\max}\) in the post? (c) Repeat part (b) if the circular cut-outs are eliminated over the height of the post. Numerical properties of post: \(A = 373 \text{ mm}^2\), \(c_1 = 19.5 \text{ mm}\), \(c_2 = 18.5 \text{ mm}\), \(I_y = 1.868 \times 10^5 \text{ mm}^4\), \(I_z = 0.67 \times 10^5 \text{ mm}^4\).