composite shaft AC is made by shrink-fitting a titanium-alloy sleeve of length L3 = 4 ft over segment BC of a 6-ft-long aluminum-alloy rod. This makes a three-component shaft, which is fixed against rotation at ends A and C. The shear moduli are G1 = G2 = 6 X 103 ksi and G3 = 4 X 103 ksi, respectively, and the diameters and d1 = d2 = (di)3 = 2 in., and (do)3 = 2.5 in. (a) Using the Displacement Method, determine the angle of ro- tation at B, og. produced by an applied torque Tg = 50 kip . in. (b) Determine the maximum shear stress (Tmax)1 in the alu- minum segment AB, (Tma)2 in the aluminum core segment BC, and (Tmax), in the titanium sleeve BC.
composite shaft AC is made by shrink-fitting a titanium-alloy sleeve of length L3 = 4 ft over segment BC of a 6-ft-long aluminum-alloy rod. This makes a three-component shaft, which is fixed against rotation at ends A and C. The shear moduli are G1 = G2 = 6 X 103 ksi and G3 = 4 X 103 ksi, respectively, and the diameters and d1 = d2 = (di)3 = 2 in., and (do)3 = 2.5 in. (a) Using the Displacement Method, determine the angle of ro- tation at B, og. produced by an applied torque Tg = 50 kip . in. (b) Determine the maximum shear stress (Tmax)1 in the alu- minum segment AB, (Tma)2 in the aluminum core segment BC, and (Tmax), in the titanium sleeve BC.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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a composite shaft AC is made by shrink-fitting a titanium-alloy sleeve of length L3 = 4 ft over segment BC of a 6-ft-long aluminum-alloy rod. This makes a three-component shaft, which is fixed against rotation at ends A and C. The shear moduli are G1 = G2 = 6 X 103 ksi and G3 = 4 X 103 ksi, respectively, and the diameters and d1 = d2 = (di)3 = 2 in., and (do)3 = 2.5 in.
(a) Using the Displacement Method, determine the angle of ro- tation at B, og. produced by an applied torque Tg = 50 kip . in.
(b) Determine the maximum shear stress (Tmax)1 in the alu- minum segment AB, (Tma)2 in the aluminum core segment BC, and (Tmax), in the titanium sleeve BC.
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