03-01ChapGere.0023

# 03-01ChapGere.0023 - d A(The prismatic bar is made of the...

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Solution 3.4-7 Shaft with four gears SECTION 3.4 Nonuniform Torsion 203 t allow 5 10,000 psi T BC 51 11,000 lb-in. T AB 52 8000 lb-in. T CD 51 7000 lb-in. (a) S OLID SHAFT Required d 5 1.78 in. d 3 5 16 T max p t allow 5 16(11,000 lb-in.) p (10,000 psi) 5 5.602 in. 3 t max 5 16 T p d 3 (b) H OLLOW SHAFT Inside diameter d 0 5 1.0 in. U NITS : d 5 inches or d 4 2 5.6023 d 2 1 5 0 Solving, d 5 1.832 Required d 5 1.83 in. 10,000 5 56,023 d d 4 2 1 10,000 psi 5 (11,000 lb-in.) ¢ d 2 ¢ p 32 [ d 4 2 (1.0 in.) 4 ] t max 5 Tr I p Ê t allow 5 T max ¢ d 2 I p C D A B 8,000 lb-in. 19,000 lb-in. 4,000 lb-in. 7,000 lb-in. 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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Unformatted text preview: d A ? (The prismatic bar is made of the same material, has the same length, and is subjected to the same torque as the tapered bar.) Hint : Use the results of Example 3-5. Solution 3.4-8 Tapered bar AB T T A B L d B d A T APERED BAR (From Eq. 3-27) P RISMATIC BAR f 2 5 TL G ( I P ) A f 1 5 TL G ( I P ) A ¢ b 2 1 b 1 1 3 b 3 ≤ Ê b 5 d B d A A NGLE OF TWIST S OLVE NUMERICALLY : b 5 d B d A 5 1.45 or 3 b 3 2 2 b 2 2 2 b 2 2 5 f 1 5 1 2 f 2 Ê b 2 1 b 1 1 3 b 3 5 1 2 T T A B L d B d A Problems 3.4-8, 3.4-9 and 3.4-10 A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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