*Prob. 4.7-6. As illustrated in Fig. P4.7-6, a composite shaft

AC is made by shrink-fitting a titanium-alloy sleeve of

length L₁ = 4 ft over segment BC of a 6-ft-long aluminum-

alloy rod. This makes a three-component shaft, which is fixed

+4₂=4₂

P4.7-6

against rotation at ends A and C. The shear moduli are G₁ =

G₂ = 6 x 10³ ksi and G₁ = 4 x 10³ ksi, respectively, and the

diameters and d₁ = d₂ = (d), = 2 in., and (d.), = 2.5 in. (a)

Using the Displacement Method, determine the angle of ro-

tation at B.. produced by an applied torque T₂ = 50 kip-in.

(b) Determine the maximum shear stress (T) in the alu-

minum segment AB, (T) in the aluminum core segment

BC, and (max) in the titanium sleeve BC.