A uniformly tapered aluminum-alloy tube AB of circular cross section and length L is fixed against rotation at A and B, as shown in the figure. The outside diameters at the ends are dA and dB = 2dA. A hollow section of length L/2 and constant thickness t = dA/10 is cast into the tube and extends from B halfway toward A. Torque To is applied at L/2.
(a) Find the reactive torques at the supports, TA and TB. Use numerical values as follows: dA = 2.5 in., L = 48 in., G = 3.9 ( 106 psi, T0 = 40,000 in.-lb.
(b) Repeat (a) if the hollow section has constant diameter dA.
(a)

(b)

Transcribed Image Text:

Fixed against rotation Fixed against d(x) B rotation TB 1 constant TA To dA Fixed against Fixed against B rotation 7,1 A | rotation TB To