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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
A (a) Determine the maximum shear stresses in both the bar
(b) Determine the angle of twist (in degrees) at end A of the bar. Tube
d3 Solution 3.4-2 Bar and tube
T 1000 N m (a) MAXIMUM SHEAR STRESSES
Bar: t bar
Tube: t tube 16T 79.6 MPa
(Ip) tube ; TUBE
d3 70 mm Ltube 0.5 m (Ip) tube p4
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) 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.
- Fall '11