고체역학 (Gere) — Stresses in Beams (Basic Topics): Problem 5.6-19

5.6-19 Determine the ratios of the weights of four beams that have the same length, are made of the same material, are subjected to the same maximum bending moment, and have the same maximum bending stress if their cross sections are (1) a rectangle with height equal to twice the width, (2) a square, (3) a circle, and (4) a pipe with outer diameter \(d\) and wall thickness \(t = d/8\) (see figures).