272_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

272_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_3.4.qxd 9/27/08 266 1:09 PM Page 266 CHAPTER 3 Torsion Nonuniform Torsion T1 Problem 3.4-1 A stepped shaft ABC consisting of two solid d1 circular segments is subjected to torques T1 and T2 acting in opposite directions, as shown in the figure. The larger segment of the shaft has diameter d1 2.25 in. and length L1 30 in.; the smaller segment has diameter d2 1.75 in. and length L2 20 in. The material is steel with shear modulus G 11 106 psi, and the torques are T1 20,000 lb-in. and T2 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 d2 T2 B A C L1 L2 Stepped shaft SEGMENT BC T2 TBC 16 TBC d2 L1 1.75 in. 30 in. L2 p(1.75 in.)3 TBCL2 G(Ip)BC fBC 2.25 in. 16(8,000 lb-in.) pd3 2 tBC d1 8,000 lb-in. 20 in. 7602 psi (8,000 lb-in.)(20 in.) (11 * 106 psi) a p b (1.75 in.)4 32 0.015797 rad 6 G 11 10 psi T1 20,000 lb-in. T2 8,000 lb-in. (a) MAXIMUM SHEAR STRESS Segment BC has the maximum stress max SEGMENT AB TAB T2 tAB ` fAB TABL1 G(Ip)AB pd3 1 ; (b) ANGLE OF TWIST AT END C T1 16 TAB 7600 psi 12,000 lb-in. ` 16(12,000 lb-in.) p(2.25 in.)3 ( 5365 psi 12,000 lb-in.)(30 in.) (11 * 106 psi) a 0.013007 rad C p b (2.25 in.)4 32 C AB BC 0.002790 rad ( 0.013007 0.16° ; 0.015797) rad ...
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