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Unformatted text preview: Sec_3.8.qxd 316 9/27/08 1:13 PM Page 316 CHAPTER 3 Torsion Problem 3.8-15 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
G 3.9 106 psi, T0 40,000 in.-lb.
(b) Repeat (a) if the hollow section has constant diameter dA.
t constant TB T0 dA Fixed against
rotation B 2.5 in., L dB L
(a) TA A Fixed against
rotation B L
2 dA TB T0
dA Fixed against
rotation dB L
(b) Solution 3.8-15
Solution approach-superposition: select TB as the redundant (1° SI )
TA1 A B ϕ1(same results for parts a & b) T0
2 A 81GpdA f1 4 2.
389 See Prob. 3.4-13 for results
for w2 for Parts a & b B
TB L 608T0L f2a 3.868 f2a 3.057 T0 L
Gd A 4
Gd A 4 T0L
GdA 4 48 in., ...
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- Fall '11