고체역학 (Gere) — Shear Forces and Bending Moments: Problem 4.5-35

4.5-35 A compound beam (see figure) has an shear release just to the left of C and a moment release just to the right of C. A plot of the moment diagram is provided below the beam for applied load P at B and triangular distributed loads w(x) on segments BC and CD. First, solve for reactions using statics; then plot axial force (N) and shear force (V) diagrams. Confirm that the moment diagram is that shown below. Label all critical N, V, and M values and also the distance to points where N, V, and/or M are zero. Given from diagram: Segments: \(AB = L/2\), \(BC = L/2\), \(CD = L/2\). Supports: Pin at \(A\), Roller at \(B\), Roller at \(C\), Roller at \(D\). Loading: Concentrated load \(P = \frac{w_0 L}{2}\) at point \(B\). Triangular distributed loads: On \(AB\): intensity \(w_0\) at \(A\) decreasing to \(0\) at \(B\). (Based on typical problem variations leading to the provided BMD). On \(BC\): intensity \(w_0\) at \(B\) decreasing to \(0\) at \(C\). On \(CD\): intensity \(w_0\) at \(C\) decreasing to \(0\) at \(D\). Releases: Shear release at \(C^-\) (\(V_{C^-} = 0\)), Moment release at \(C^+\) (\(M_{C^+} = 0\)).