322_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

322_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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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. Fixed against rotation TA L — 2 A d(x) 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 ) L — 2 TA1 A B ϕ1(same results for parts a & b) T0 f1 L + TA2 L — 2 A 81GpdA f1 4 2. 389 See Prob. 3.4-13 for results for w2 for Parts a & b B ϕ2 TB L 608T0L f2a 3.868 f2a 3.057 T0 L Gd A 4 T0L Gd A 4 T0L GdA 4 48 in., ...
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