고체역학 (Gere) — Stresses in Beams (Basic Topics): Problem 5.5-20

5.5-20 A cantilever beam AB of an isosceles trapezoidal cross section has a length \( L = 0.8 \text{ m} \), dimensions \( b_1 = 80 \text{ mm} \) and \( b_2 = 90 \text{ mm} \), and height \( h = 110 \text{ mm} \) (see figure). The beam is made of brass weighing \( 85 \text{ kN/m}^3 \). (a) Determine the maximum tensile stress \( \sigma_t \) and maximum compressive stress \( \sigma_c \) due to the beam’s own weight. (b) If the width \( b_1 \) is doubled, what happens to the stresses? (c) If the height \( h \) is doubled, what happens to the stresses?