(Solved): Problem 2: 25 points The compound beam shown in Figure \( 2.1 \) has an internal hinge at point \( ...

Problem 2: 25 points The compound beam shown in Figure \( 2.1 \) has an internal hinge at point \( B \). It is fixed (clamped) at point \( C \) and supported by a roller at point \( A \). The length of each segment is shown in the figure. The beam is carrying a distributed load on segment \( A B \) and a concentrated load at point \( \mathrm{E} \). Take \( 4 w_{1}=2 w_{2}=8 \mathrm{kip} / \mathrm{ft} \). a) Determine the support reactions at points \( A \) and \( C \). b) Calculate the internal resultant loadings (normal and shear forces and bending moment) at point \( D \) and at the midpoint of segment \( B E \). c) If the cross-section of the beam is as shown in Figure 2.2, calculate the location of the centroid \( C \) with respect to the bottom of the cross-section and the moment of inertia about the centroidal axis \( x \).