고체역학 (Beer) — Analysis and Design of Beams for Bending: Problem 5.29

5.29 Knowing that \(P = Q = 480 \text{ N}\), determine (a) the distance \(a\) for which the absolute value of the bending moment in the beam is as small as possible, (b) the corresponding maximum normal stress due to bending. (See hint of Prob. 5.27.) Hint from Prob. 5.27: Draw the bending-moment diagram and equate the absolute values of the largest positive and negative bending moments obtained. Given values from Figure P5.29: Beam \(AB\) with pin support at \(A\) and roller support at distance \(a\) from \(A\). Load \(P = 480 \text{ N}\) at point \(C\), where \(AC = 500 \text{ mm}\). Load \(Q = 480 \text{ N}\) at point \(D\), where \(CD = 500 \text{ mm}\). The total length of the beam is not explicitly given, but point \(D\) appears to be the second load point. Based on the contiguous "500 mm" dimension lines, the loads are at \(x = 0.5 \text{ m}\) and \(x = 1.0 \text{ m}\) from \(A\). Cross-section: width \(b = 12 \text{ mm}\), depth \(h = 18 \text{ mm}\).