342_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

342_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_3.9-3.11.qxd 336 9/27/08 1:14 PM Page 336 CHAPTER 3 Torsion Solution 3.10-12 Thin tube (b) EXACT THEORY t Ip T 5,000 N m d1 inner diameter 100 mm t is in millimeters. 50 mm + p [(50 + t)4 2 (50)4] (5,000 N # m)(50 + t) p (50)4] [(50 + t)4 2 t 2 (5000 N # m)(2) (p)(42 MPa) 5 * 106 mm3 21p Inner radius Solve for t: 50 mm r2 42 MPa r4) 1 (50 + t)4 (50)4 50 + t Average radius r1 p4 (r 22 42 MPa allow r Tr2 Ip t 7.02 mm ; Outer radius 50 mm t Am The approximate result is 5% less than the exact result. Thus, the approximate theory is nonconservative and should only be used for thin-walled tubes. r2 (a) APPROXIMATE THEORY t T T 2tAm 42 MPa T 2t(pr 2) 2pr 2 t 5,000 N # m 2p a 50 + t2 bt 2 or t a 50 + t2 b 2 5,000 N # m 2p(42 MPa) Solve for t: t 6.66 mm ; 5 * 106 mm3 84p ...
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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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