고체역학 (Gere) — Applications of Plane Stress: Problem 8.4-9

8.4-9 A simple beam with a rectangular cross section (width, 90 mm; height, 300 mm) carries a trapezoidally distributed load of 20 kN/m at A and 15 kN/m at B on a span of 4.2 m (see figure). Find the principal stresses \(\sigma_1\) and \(\sigma_2\) and the maximum shear stress \(\tau_{\text{max}}\) at a cross section 0.6 m from the left-hand support at each of the locations: (a) the neutral axis, (b) 50 mm above the neutral axis, and (c) the top of the beam. (Disregard the direct compressive stresses produced by the uniform load bearing against the top of the beam.)