5. (20 points). Solve for the rotation and vertical displacement at the joint of the beam assembly below. For each frame element, assume E = 30 x 106 psi, I = 50 in', and A = 5 square inches. 3/3 lb./in, horizontal length 100" 30o Bonus: a. (5 points) Show that for a beam with constant vertical load h, constant El, and both ends fixed against displacement and rotation, the displacement in natural coordinates is hLed 384EI 1 - 262 + 64 (2) b. (5 points) Show that the moment for the same case is hLe2 M({) = 24 - 1 (3) Hint: there are several approaches to this. One is to solve the differential equation and apply the boundary conditions