고체역학 (Gere) — Stresses in Beams (Basic Topics): Problem 5.9-6

5.9-6 A steel pipe is subjected to a quadratic distributed load over its height with the peak intensity \(q_0\) at the base (see figure). Assume the following pipe properties and dimensions: height \(L\), outside diameter \(d = 200 \text{ mm}\), and wall thickness \(t = 10 \text{ mm}\). Allowable stresses for flexure and shear are \(\sigma_a = 125 \text{ MPa}\) and \(\tau_a = 30 \text{ MPa}\). (a) If \(L = 2.6 \text{ m}\), find \(q_{0,max} \text{ (kN/m)}\), assuming that allowable flexure and shear stresses in the pipe are not to be exceeded. (b) If \(q_0 = 60 \text{ kN/m}\), find the maximum height \(L_{max} \text{ (m)}\) of the pipe if the allowable flexure and shear stresses in the pipe are not to be exceeded.