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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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336 CHAPTER 3 Torsion Solution 3.10-12 Thin tube T 5,000 N m d 1 inner diameter 100 mm allow 42 MPa t is in millimeters. r Average radius r 1 Inner radius 50 mm r 2 Outer radius 50 mm t A m r 2 (a) A PPROXIMATE THEORY or Solve for t : t 6.66 mm ; t a 50 + t 2 b 2 5,000 N # m 2 p (42 MPa) 5 * 10 6 84 p mm 3 42 MPa 5,000 N # m 2 p a 50 + t 2 b 2 t t T 2 tA m T 2 t ( p r 2 ) T 2 p r 2 t 50 mm + t 2 (b) E XACT THEORY Solve for t : t 7.02 mm The approximate result is 5% less than the exact result. Thus, the approximate theory is nonconserv-
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