고체역학 (Gere) — Stresses in Beams (Basic Topics): Problem 5.5-28

5.5-28 A foot bridge on a hiking trail is constructed using two timber logs each having a diameter \( d = 0.5\text{ m} \) (see figure a). The bridge is simply supported and has a length \( L = 4\text{ m} \). The top of each log is trimmed to form the walking surface (see Fig. b). A simplified model of the bridge is shown in Fig. b. Each log must carry its own weight \( w = 1.2\text{ kN/m} \) and the weight (\( P = 850\text{ N} \)) of a person at mid-span (see Fig. b). The cross-section is shown in Fig. c, where the flat top subtends a central angle of \( 90^\circ \). (a) Determine the maximum tensile and compressive stresses in the beam (Fig. b) due to bending. (b) If load \( w \) is unchanged, find the maximum permissible value of load \( P_{\max} \) if the allowable normal stress in tension and compression is \( 2.5\text{ MPa} \).