341_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

# 341_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 335 335 SECTION 3.10 Thin-Walled Tubes Solution 3.10-11 Square aluminum tube THICKNESS t BASED UPON SHEAR STRESS t T 2tAm UNITS: t in. t)2 Outer dimensions: 2.0 in. G 4 106 psi T 3000 lb-in. u allow u 0.01 rad/in. 12 0.01 rad/ft Let b Centerline dimension J (b 4tA2 m Lm t) Lm 4t(b 4(b psi 13 in. 3 0.0915 in. T GJ T 3 Gt(b UNITS: t in. b t 10t(2 4(b t) t(b psi t)3 T Gu rad/in. 3000 lb-in t)3 t(2.0 in. t) G (4 * 106 psi)(0.01/12 rad/in.) 9 10 2.0 in. Am lb-in. 0 outer dimension 2 T 2t t)2 THICKNESS t BASED UPON RATE OF TWIST 4500 psi allow T 3000 lb-in. 2(4500 psi) 1 Solve for t: t 2.0 in. t(b in. b t)2 t(2.0 in. 3t(2 T 2t tAm Solve for t: 4 t) t) t(b t)3 t t)3 9 0 0.140 in. ANGLE OF TWIST GOVERNS tmin Problem 3.10-12 A thin tubular shaft of circular cross section (see figure) with inside diameter 100 mm is subjected to a torque of 5000 N m. If the allowable shear stress is 42 MPa, determine the required wall thickness t by using (a) the approximate theory for a thin-walled tube, and (b) the exact torsion theory for a circular bar. 0.140 in. ; 100 mm t ...
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