03-01ChapGere.0019

03-01ChapGere.0019 - ( I p ) CD 5 p 32 (2.0 in.) 4 5 1.571...

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SECTION 3.4 Nonuniform Torsion 199 Problem 3.4-3 A stepped shaft ABCD consisting of solid circular segments is subjected to three torques, as shown in the figure. The torques have magnitudes 12.0 k-in., 9.0 k-in., and 9.0 k-in. The length of each segment is 24 in. and the diameters of the segments are 3.0 in., 2.5 in., and 2.0 in. The material is steel with shear modulus of elasticity G 5 11.6 3 10 3 ksi. (a) Calculate the maximum shear stress t max in the shaft. (b) Calculate the angle of twist f D (in degrees) at end D . Solution 3.4-3 Stepped shaft 24 in. 24 in. 24 in. A B C D 2.5 in. 12.0 k-in. 9.0 k-in. 9.0 k-in. 3.0 in. 2.0 in. G 5 11.6 3 10 3 ksi r AB 5 1.5 in. r BC 5 1.25 in. r CD 5 1.0 in. L AB 5 L BC 5 L CD 5 24 in. T ORQUES T AB 5 12.0 1 9.0 1 9.0 5 30 k-in. T BC 5 9.0 1 9.0 5 18 k-in. T CD 5 9.0 k-in. P OLAR MOMENTS OF INERTIA
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Unformatted text preview: ( I p ) CD 5 p 32 (2.0 in.) 4 5 1.571 in. 4 ( I p ) BC 5 p 32 (2.5 in.) 4 5 3.835 in. 4 ( I p ) AB 5 p 32 (3.0 in.) 4 5 7.952 in. 4 (a) S HEAR STRESSES (b) A NGLE OF TWIST AT END D f D 5 f AB 1 f BC 1 f CD 5 0.02937 rad f D 5 1.68 8 Ê f CD 5 T CD L CD G ( I p ) CD 5 0.011853 rad f BC 5 T BC L BC G ( I p ) BC 5 0.009711 rad f AB 5 T AB L AB G ( I p ) AB 5 0.007805 rad t max 5 5870 psi Ê t CD 5 T CD r CD ( I p ) CD 5 5730 psi t BC 5 T BC r BC ( I p ) BC 5 5870 psi t AB 5 T AB r AB ( I p ) AB 5 5660 psi A B C D 2.5 in. 12.0 k-in. 9.0 k-in. 9.0 k-in. 3.0 in. 2.0 in. A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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This note was uploaded on 09/20/2009 for the course COE 3001 taught by Professor Armanios during the Spring '08 term at Georgia Tech.

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