334_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

334_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_3.9-3.11.qxd 328 9/27/08 1:14 PM Page 328 CHAPTER 3 Torsion Thin-Walled Tubes Problem 3.10-1 A hollow circular tube having an inside diameter of 10.0 in. and a wall thickness of 1.0 in. (see figure) is subjected to a torque T 1200 k-in. Determine the maximum shear stress in the tube using (a) the approximate theory of thin-walled tubes, and (b) the exact torsion theory. Does the approximate theory give conservative or nonconservative results? 10.0 in. 1.0 in. Solution 3.10-1 Hollow circular tube APPROXIMATE THEORY (EQ. 3-63) 1200 k-in. T t1 2 2pr t approx 6314 psi 2p(5.5 in.)2(1.0 in.) ; 6310 psi EXACT THEORY (EQ. 3-11) T 1200 k-in. t 1.0 in. r radius to median line r 5.5 in. d2 outside diameter d1 inside diameter t2 T (d2/2) IP Td2 p 4 2a b 1d2 32 4 d1 2 16(1200k-in.)(12.0 in.) p [(12.0 in.)4 12.0 in. (10.0 in.)4] 6831 psi 10.0 in. t exact ; 6830 psi Because the approximate theory gives stresses that are too low, it is nonconservative. Therefore, the approximate theory should only be used for very thin tubes. Problem 3.10-2 A solid circular bar having diameter d is to be replaced by a rectangular tube having cross-sectional dimensions d 2d to the median line of the cross section (see figure). Determine the required thickness tmin of the tube so that the maximum shear stress in the tube will not exceed the maximum shear stress in the solid bar. t t d d 2d ...
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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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