고체역학 (Beer) — Analysis and Design of Beams for Bending: Problem 5.27

5.27 Determine (a) the magnitude of the counterweight \(W\) for which the maximum absolute value of the bending moment in the beam is as small as possible, (b) the corresponding maximum normal stress due to bending. (Hint: Draw the bending-moment diagram and equate the absolute values of the largest positive and negative bending moments obtained.) Note: This problem refers to Figs. P5.26 and P5.27. From the figure: Beam \(AB\) has a total length of 4 m with supports at \(A\) and \(B\). Concentrated loads of 8 kN act downward at points \(C\) (1 m from \(A\)) and \(E\) (3 m from \(A\)). A counterweight \(W\) provides an upward force at point \(D\) (2 m from \(A\)). The beam cross-section is a W310 × 23.8 rolled-steel shape.