03-03ChapGere.0003

03-03ChapGere.0003 - torque T at the free end and by a...

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Problem 3.9-4 A stepped shaft of solid circular cross sections (see figure) has length L 5 0.80 m, diameter d 2 5 40 mm, and diameter d 1 5 30 mm. The material is steel with G 5 80 GPa. Determine the strain energy U of the shaft if the angle of twist is 1.0°. Soluton 3.9-4 Stepped shaft 238 CHAPTER 3 Torsion d 2 d 1 T T L 2 L 2 d 1 5 30 mm d 2 5 40 mm L 5 0.80 m G 5 80 GPa (steel) f 5 1.0 85 0.0174533 rad S TRAIN ENERGY (Eq. 1) Also, (Eq. 2) U 5 T f 2 5 8 T 2 L p G ¢ 1 d 2 4 1 1 d 1 4 U 5 a T 2 L 2 GI P 5 16 T 2 ( L / 2) p Gd 2 4 1 16 T 2 ( L / 2) p Gd 1 4 Equate U from Eqs. (1) and (2) and solve for T : S UBSTITUTE NUMERICAL VALUES : U 5 1.84 J U 5 T f 2 5 p G f 2 32 L ¢ d 1 4 d 2 4 d 1 4 1 d 2 4 Ê f 5 radians T 5 p G d 1 4 d 2 4 f 16 L ( d 1 4 1 d 2 4 ) Problem 3.9-5 A cantilever bar of circular cross section and length L is fixed at one end and free at the other (see figure). The bar is loaded by a
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Unformatted text preview: torque T at the free end and by a distributed torque of constant intensity t per unit distance along the length of the bar. (a) What is the strain energy U 1 of the bar when the load T acts alone? (b) What is the strain energy U 2 when the load t acts alone? (c) What is the strain energy U 3 when both loads act simultaneously? Solution 3.9-5 Cantilever bar with distributed torque L T t G 5 shear modulus I P 5 polar moment of inertia T 5 torque acting at free end t 5 torque per unit distance L T t 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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