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278_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

278_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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272 CHAPTER 3 Torsion Solution 3.4-7 Shaft with four gears allow 10,000 psi T BC 11,000 lb-in. T AB 8000 lb-in. T CD 7000 lb-in. (a) S OLID SHAFT Required d 1.78 in. ; d 3 16 T max pt allow 16(11,000 lb-in.) p (10,000 psi) 5.602 in. 3 t max 16 T p d 3 (b) H OLLOW SHAFT Inside diameter d 0 1.0 in. U NITS : d inches or d 4 5.6023 d 1 0 Solving, d 1.832 Required d 1.83 in. ; 10,000 56,023 d d 4 1 10,000 psi (11,000 lb-in.) a d 2 b a p 32 b [ d 4 (1.0 in.) 4 ] t max Tr I p t allow T max a d 2 b I p Problem 3.4-8 A tapered bar AB of solid circular cross section is twisted by torques T (see figure). The diameter of the bar varies linearly from d A at the left-hand end to d B at the right-hand end. For what ratio d B / d A will the angle of twist of the tapered bar be one-half the angle of twist of a prismatic bar of diameter
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