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Unformatted text preview: Sec_3.9-3.11.qxd 9/27/08 1:14 PM Page 327 SECTION 3.9 Strain Energy in Torsion Problem 3.9-11 A heavy flywheel rotating at n revolutions per minute is
rigidly attached to the end of a shaft of diameter d (see figure). If the
bearing at A suddenly freezes, what will be the maximum angle of twist
of the shaft? What is the corresponding maximum shear stress in the shaft?
(Let L length of the shaft, G shear modulus of elasticity, and
Im mass moment of inertia of the flywheel about the axis of the shaft.
Also, disregard friction in the bearings at B and C and disregard the mass
of the shaft.) A d n (rpm) B
C Hint: Equate the kinetic energy of the rotating flywheel to the strain
energy of the shaft. Solution 3.9-11 Rotating flywheel
d diameter of shaft U pGd 4f2
d diameter n (force)/(length)2 IP (length)4 rpm radians KINETIC ENERGY OF FLYWHEEL L length U (length)(force) 1
2 EQUATE KINETIC ENERGY AND STRAIN ENERGY v 2pn
60 K.E. n rpm K.E. 2pn 2
60 K.E. 2n f 15d Im (force)(length)(second)2 T(d/2)
IP (length)(force) STRAIN ENERGY OF SHAFT (FROM EQ. 3-51b)
2L 2 ; f TL
GIP Eliminate T: radians per second
G MAXIMUM SHEAR STRESS
t UNITS: 2A pGd 4f2
64 L Solve for : 22 p n Im
1800 U t
2L15d A G
15d A L
2L Gd 2 n 2 ; 327 ...
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