266_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

266_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_3.3.qxd 9/27/08 260 1:27 PM Page 260 CHAPTER 3 Torsion Solution 3.3-11 Construction auger d2 6.0 in. r2 3.0 in. d1 4.5 in. r1 2.25 in. G 11 T 150 k-in. IP p4 (d 32 2 (c) RATE OF TWIST (150 k-in.) u T GIP u 157 * 10 106 psi 4 d1 ) 86.98 in.4 (11 * 106 psi)(86.98 in.)4 6 rad/ in. 0.00898°/ in. ; (d) SHEAR STRESS DIAGRAM (a) SHEAR STRESS AT OUTER SURFACE t2 Tr2 IP (150 k-in.)(3.0 in.) 86.98 in.4 5170 psi ; (b) SHEAR STRESS AT INNER SURFACE t1 Tr1 IP r1 t r2 2 ; 3880 psi Problem 3.3-12 Solve the preceding problem if the shaft has outer diameter d2 150 mm and inner diameter d1 Also, the steel has shear modulus of elasticity G 75 GPa and the applied torque is 16 kN m. Solution 3.3-12 Construction auger d2 150 mm r2 d1 100 mm r1 50 mm G 75 GPa T 16 kN # m p4 (d2 d14) 32 (b) SHEAR STRESS AT INNER SURFACE 75 mm IP t1 6 39.88 * 10 mm (a) SHEAR STRESS AT OUTER SURFACE t2 Tr2 IP 4 (16 kN # m)(75 mm) 39.88 * 106 mm4 30.1 MPa ; Tr1 IP r1 t r2 2 20.1 MPa ; (c) RATE OF TWIST T 16 kN # m u GIP (75 GPa)(39.88 * 106 mm4) 0.005349 rad/m (d) SHEAR STRESS DIAGRAM 0.306°/m ; 100 mm. ...
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This note was uploaded on 12/22/2011 for the course MEEG 310 taught by Professor Staff during the Fall '11 term at University of Delaware.

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