03-03ChapGere.0002

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Solution 3.9-2 Copper bar SECTION 3.9 Strain Energy in Torsion 237 L d TT G 5 45 GPa L 5 0.75 m d 5 40 mm t max 5 32 MPa (Eq. 1) I P 5 p d 4 32 t max 5 16 T p d 3 Ê T 5 p d 3 t max 16 (a) S TRAIN ENERGY (Eq. 2) Substitute numerical values: (b) A NGLE OF TWIST Substitute for T and U from Eqs. (1) and (2): (Eq. 3) Substitute numerical values: f 5 0.026667 rad 5 1.53 8 f 5 2 L t max Gd U 5 T f 2 Ê f 5 2 U T U 5 5.36 J 5 p d 2 L t max 2 16 G U 5 T 2 L 2 GI P 5 ¢ p d 3 t max 16 2 ¢ L 2 G ¢ 32 p d 4 Problem 3.9-3 A stepped shaft of solid circular cross sections (see figure) has length L 5 45 in., diameter d 2 5 1.2 in., and diameter d 1 5 1.0 in. The material is brass with G 5 5.6 3 10 6 psi. Determine the strain energy U of the shaft if the angle of twist is 3.0°. Solution 3.9-3 Stepped shaft d 2 d 1 T T L 2 L 2 d 2 d 1 T T L 2 L
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