고체역학 (Gere) — Stresses in Beams (Basic Topics): Problem 5.7-8

5.7-8 A cantilever beam AB having rectangular cross sections with varying width \(b_x\) and varying height \(h_x\) is subjected to a uniform load of intensity \(q\) (see figure). If the width varies linearly with \(x\) according to the equation \(b_x = b_B x/L\), how should the height \(h_x\) vary as a function of \(x\) in order to have a fully stressed beam? (Express \(h_x\) in terms of the height \(h_B\) at the fixed end of the beam.)