337_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

337_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_3.9-3.11.qxd 9/27/08 1:14 PM Page 331 SECTION 3.10 Thin-Walled Tubes Problem 3.10-6 Calculate the shear stress and the angle of twist (in degrees) for a steel tube (G 76 GPa) having the cross section shown in the figure. The tube has length L 1.5 m and is subjected to a torque T 10 kN m. t = 8 mm r = 50 mm r = 50 mm b = 100 mm Solution 3.10-6 Steel tube SHEAR STRESS G L r2 Am (50 mm)2 10 kN m 2br 2(100 mm)(50 mm) 2b 2(8 mm)(17,850 mm2) ; ANGLE OF TWIST TL GJ (10 kN # m)(1.5 m) (76 GPa)(19.83 * 106 mm4) 0.00995 rad 0.570° 2r 2(100 mm) 10 kN # m 35.0 MPa f 17,850 mm2 Lm T 2tAm t 1.5 m T Am 76 GPa. ; 2 (50 mm) 514.2 mm J 4tA2 m Lm 4(8 mm)(17,850 mm2)2 514.2 mm 19.83 * 106 mm4 Problem 3.10-7 A thin-walled steel tube having an elliptical cross 331 t section with constant thickness t (see figure) is subjected to a torque T 18 k-in. Determine the shear stress and the rate of twist (in degrees per inch) if G 12 106 psi, t 0.2 in., a 3 in., and b 2 in. (Note: See Appendix D, Case 16, for the properties of an ellipse.) 2b 2a ...
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