고체역학 (Gere) — Stresses in Beams (Advanced Topics): Problem 6.4-9

6.4-9 A wood beam AB with a rectangular cross section (100 mm × 150 mm) serving as a roof purlin is simply supported by the top chords of two adjacent roof trusses. The beam is subjected to distributed load q acting in the vertical direction through the centroid of the purlin cross section. The top chords of the trusses have a slope \(\alpha = 27^\circ\). The purlin has length \(L = 2 \text{ m}\). Determine the permissible distributed load \(q\) based on the allowable compressive and tensile stress in the beam \(\sigma_{all} = 14 \text{ MPa}\).