[1] (40 points) For the problem shown in figure (1), the tapered torsional member with radii 3ro and ro at the two ends, is being torqued by a constant force po per unit length of the member. The force is being transmitted through a belt fixed at the outer radius, such that the torque being applied at a given position x along the length will be directly proportional to the radius at that point.
\(T(x) = F(x) r(x)\)
Given: ro = 5 cm, L = 1 m, E = 200 GPa, G = 25GPa, po = 10 \frac{kN}{m}
(a) Since the radius is not constant (but the force is), the torque at a point is not constant. Find the function T(x). Then evaluate the angle of twist at the right end of the bar (x = L). The left end of the bar is fixed. (Use 1 element) [15 points]
Fixed, \(\phi = 0\)
\(w = 0, \theta = 0\)
(b) The applied force also leads to bending of the beam (assume cantilever boundary conditions). Evaluate the slope and deflection at the right end. (Use 1 element)
(Hint: What is the bending stiffness of the member?) [15 points]
