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03-01ChapGere.0017 - AB L 1 G I p AB 5 2 12,000 lb-in(30...

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Nonuniform Torsion Problem 3.4-1 A stepped shaft ABC consisting of two solid circular segments is subjected to torques T 1 and T 2 acting in opposite directions, as shown in the figure. The larger segment of the shaft has diameter d 1 2.25 in. and length L 1 30 in.; the smaller segment has diameter d 2 1.75 in. and length L 2 20 in. The material is steel with shear modulus G 11 10 6 psi, and the torques are T 1 20,000 lb-in. and T 2 8,000 lb-in. Calculate the following quantities: (a) the maximum shear stress max in the shaft, and (b) the angle of twist C (in degrees) at end C . Solution 3.4-1 Stepped shaft SECTION 3.4 Nonuniform Torsion 197 L 1 d 1 T 1 T 2 L 2 B C d 2 A d 1 2.25 in. L 1 30 in. d 2 1.75 in. L 2 20 in. G 11 10 6 psi T 1 20,000 lb-in. T 2 8,000 lb-in. S EGMENT AB T
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Unformatted text preview: AB L 1 G ( I p ) AB 5 ( 2 12,000 lb-in.)(30 in.) (11 3 10 6 psi) ¢ p 32 ≤ (2.25 in.) 4 t AB 5 ` 16 T AB p d 1 3 ` 5 16(12,000 lb-in.) p (2.25 in.) 3 5 5365 psi S EGMENT BC T BC 5 1 T 2 5 8,000 lb-in. (a) M AXIMUM SHEAR STRESS Segment BC has the maximum stress (b) A NGLE OF TWIST AT END C f C 5 f AB 1 f BC 5 ( 2 0.013007 1 0.015797) rad f C 5 0.002790 Ê rad 5 0.16 8 t max 5 7600 psi 5 1 0.015797 rad f BC 5 T BC L 2 G ( I p ) BC 5 (8,000 lb-in.)(20 in.) (11 3 10 6 psi) ¢ p 32 ≤ (1.75 in.) 4 t BC 5 16 T BC p d 2 3 5 16(8,000 lb-in.) p (1.75 in.) 3 5 7602 psi L 1 d 1 T 1 T 2 L 2 B C d 2 A A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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