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Unformatted text preview: Sec_3.4.qxd 284 9/27/08 1:09 PM Page 284 CHAPTER 3 Torsion Problem 3.4-19 A magnesium-alloy wire of diameter d 4 mm and
length L rotates inside a flexible tube in order to open or close
a switch from a remote location (see figure). A torque T is applied
manually (either clockwise or counterclockwise) at end B, thus
twisting the wire inside the tube. At the other end A, the rotation of
the wire operates a handle that opens or closes the switch.
A torque T0 0.2 N m is required to operate the switch.
The torsional stiffness of the tube, combined with friction between
the tube and the wire, induces a distributed torque of constant
intensity t 0.04 N m/m (torque per unit distance) acting along
the entire length of the wire. T0 = torque Flexible tube
B d A
t (a) If the allowable shear stress in the wire is allow 30 MPa,
what is the longest permissible length Lmax of the wire?
(b) If the wire has length L 4.0 m and the shear modulus of
elasticity for the wire is G 15 GPa, what is the angle of twist
(in degrees) between the ends of the wire? Solution 3.4-19 Wire inside a flexible tube d 4 mm
T0 0.2 N m
t 0.04 N m/m (b) ANGLE OF TWIST
1 (a) MAXIMUM LENGTH Lmax
Equilibrium: T tL T0
From Eq. (3-12): tmax
tL + T0
Lmax 4 m G 15 GPa
angle of twist due to distributed torque t
pGd4 T pd3tmax
16 2 angle of twist due to torque T0
GIP pd 3tmax
16 (from problem 3.4-16) 32 T0 L
pGd4 (from Eq. 3 -15) total angle of twist
16t 16T0) 1
16t 16T0) Substitute numerical values: Lmax f
4.42 m ; 16L
pGd 4 2 (tL + 2T0) ; Substitute numerical values:
2.971 rad 170°
; T ...
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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