273_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

273_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_3.4.qxd 9/27/08 1:09 PM Page 267 267 SECTION 3.4 Nonuniform Torsion Problem 3.4-2 A circular tube of outer diameter d3 70 mm and inner diameter d2 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 d1 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 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 27 GPa. Tube Fixed plate End plate Bar T A (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. Tube Bar d1 d2 d3 Solution 3.4-2 Bar and tube TORQUE T 1000 N m (a) MAXIMUM SHEAR STRESSES Bar: t bar Tube: t tube 16T 79.6 MPa ; pd3 1 T(d3/2) 32.3 MPa (Ip) tube ; TUBE d3 70 mm Ltube 0.5 m (Ip) tube p4 (d 32 3 d2 (b) ANGLE OF TWIST AT END A 60 mm G 27 GPa Bar: fbar 4 d2) Tube: ftube 1.0848 * 106 mm4 TL bar G(Ip) bar TL tube G(Ip) tube A d1 40 mm (Ip) bar 4 pd1 32 Lbar 1.0 m G 251.3 * 103 mm4 27 GPa bar tube A BAR 0.1474 rad 9.43° ; 0.0171 rad 0.1474 0.0171 0.1645 rad ...
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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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