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03-03ChapGere.0017

# 03-03ChapGere.0017 - mm 1 t 5 50 mm 1 t 2 r 5 Average...

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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. Solution 3.10-12 Thin tube 252 CHAPTER 3 Torsion t 100 mm t 100 mm T 5,000 N m d 1 inner diameter 100 mm allow 42 MPa t is in millimeters. r 1 Inner radius 50 mm r 2 Outer radius (a) A PPROXIMATE THEORY or Solve for t : t 6.66 mm t ¢ 50 t 2 2 5,000 N . m 2 (42 MPa) 5 10 6 84 mm 3 42 MPa 5,000 N . m 2 ¢ 50 t 2
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Unformatted text preview: mm 1 t 5 50 mm 1 t 2 r 5 Average radius (b) E XACT THEORY Solve for t : 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. t 5 7.02 mm 5 5 3 10 6 21 p mm 3 (50 1 t ) 4 2 (50) 4 50 1 t 5 (5000 N . m)(2) ( p )(42 MPa) 42 MPa 5 (5,000 N . m)(50 1 t ) p 2 [ (50 1 t ) 4 2 (50) 4 ] 5 p 2 [ (50 1 t ) 4 2 (50) 4 ] t 5 Tr 2 I p Ê I p 5 p 2 ( r 2 4 2 r 1 4 ) A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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