03-01ChapGere.0018 - Torsion Tube Tube A T Fixed plate End...

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Problem 3.4-2 A circular tube of outer diameter d 3 5 70 mm and inner diameter d 2 5 60 mm is welded at the right-hand end to a fixed plate and at the left-hand end to a rigid end plate (see figure). A solid circular bar of diameter d 1 5 40 mm is inside of, and concentric with, the tube. The bar passes through a hole in the fixed plate and is welded to the rigid end plate. The bar is 1.0 m long and the tube is half as long as the bar. A torque T 5 1000 N ? m acts at end A of the bar. Also, both the bar and tube are made of an aluminum alloy with shear modulus of elasticity G 5 27 GPa. (a) Determine the maximum shear stresses in both the bar and tube. (b) Determine the angle of twist (in degrees) at end A of the bar. Solution 3.4-2 Bar and tube 198 CHAPTER 3
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Unformatted text preview: Torsion Tube Tube A T Fixed plate End plate Bar Bar d 1 d 2 d 3 T UBE d 3 5 70 mm d 2 5 60 mm L tube 5 0.5 m G 5 27 GPa 5 1.0848 3 10 6 mm 4 B AR d 1 5 40 mm L bar 5 1.0 m G 5 27 GPa ( I p ) bar 5 p d 1 4 32 5 251.3 3 10 3 mm 4 ( I p ) tube 5 p 32 ( d 3 4 2 d 2 4 ) T ORQUE T 5 1000 N ? m (a) M AXIMUM SHEAR STRESSES Bar: Tube: (b) A NGLE OF TWIST AT END A Bar: Tube: f A 5 f bar 1 f tube 5 0.1474 1 0.0171 5 0.1645 rad f A 5 9.43 8 f tube 5 TL tube G ( I p ) tube 5 0.0171 rad f bar 5 TL bar G ( I p ) bar 5 0.1474 rad t tube 5 T ( d 3 / 2) ( I p ) tube 5 32.3 MPa t bar 5 16 T p d 1 3 5 79.6 MPa Tube A T Bar A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Institute of Technology.

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