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260_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 260_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_3.3.qxd 254 9/27/08 1:27 PM Page 254 CHAPTER 3 Torsion Solution 3.3-3 Lug wrench P L 9.0 in. d 0.5 in. G 11.4 (a) MAXIMUM SHEAR STRESS 25 lb 106 psi T torque acting on arm A T From Eq. (3-12): (16)(450 lb - in.) 16T tmax 3 pd p(0.5 in.)3 tmax (b) ANGLE OF TWIST From Eq. (3-15): (450 lb-in.)(9.0 in.) TL f GIP p (11.4 * 106 psi) a b (0.5 in.)4 32 P(2L) 2(25 lb) (9.0 in.) 450 lb-in. f Problem 3.3-4 An aluminum bar of solid circular cross section is twisted by torques T acting at the ends (see figure). The dimensions and shear modulus of elasticity are as follows: L 1.4 m, d 32 mm, and G 28 GPa. ; 18,300 psi 3.32° 0.05790 rad ; d T T L (a) Determine the torsional stiffness of the bar. (b) If the angle of twist of the bar is 5°, what is the maximum shear stress? What is the maximum shear strain (in radians)? Solution 3.3-4 (a) TORSIONAL STIFFNESS OF BAR d kT Ip kT kT 32 mm GI p L 1.029 G Ip 28 GPa p4 d 32 105 mm4 p 2811092a 0.0324 b 32 1.4 2059 N # m (b) MAX SHEAR STRESS AND STRAIN f T max gmax ; max 5a p b radians 180 kT f d Ta b 2 tmax Ip ; 27.9 MPa tmax G 997 10 6 radians ; ...
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