333_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

333_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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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 p4 d 32 IP d diameter of shaft U pGd 4f2 64L UNITS: G d diameter n (force)/(length)2 IP (length)4 rpm radians KINETIC ENERGY OF FLYWHEEL L length U (length)(force) 1 Imv2 2 EQUATE KINETIC ENERGY AND STRAIN ENERGY v 2pn 60 K.E. n rpm K.E. 2pn 2 1 Im a b 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) U GIPf 2L 2 ; f TL GIP Eliminate T: radians per second K.E. 2pImL G MAXIMUM SHEAR STRESS t UNITS: 2A pGd 4f2 64 L Solve for : 22 p n Im 1800 p2n2Im 1800 U t tmax tmax 2pImL 2L15d A G 2pGIm n 15d A L Gdf 2L Gd 2 n 2 ; 327 ...
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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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