고체역학 (Gere) — Shear Forces and Bending Moments: Problem 4.5-29

4.5-29 A beam of length \( L \) is designed to support a uniform load of intensity \( q \) (see figure). If the supports of the beam are placed at the ends, creating a simple beam, the maximum bending moment in the beam is \( qL^2/8 \). However, if the supports of the beam are moved symmetrically toward the middle of the beam (as shown), the maximum bending moment is reduced. (a) Determine the distance \( a \) between the supports so that the maximum bending moment in the beam has the smallest possible numerical value. Draw the shear-force and bending-moment diagrams for this condition. (b) Repeat part (a) if the uniform load is replaced with a triangularly distributed load with peak intensity \( q_0 = q \) at mid-span (see Fig. b).