03-03ChapGere.0005 - f(This result agrees with Eq(3-48 of...

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Problem 3.9-7 A statically indeterminate stepped shaft ACB is fixed at ends A and B and loaded by a torque T 0 at point C (see figure). The two segments of the bar are made of the same material, have lengths L A and L B , and have polar moments of inertia I PA and I PB . Determine the angle of rotation f of the cross section at C by using strain energy. Hint: Use Eq. 3-51b to determine the strain energy U in terms of the angle f . Then equate the strain energy to the work done by the torque T 0 . Compare your result with Eq. 3-48 of Example 3-9, Section 3.8. Solution 3.9-7 Statically indeterminate bar 240 CHAPTER 3 Torsion T 0 L A L B A C I PA I PB B S TRAIN ENERGY ( FROM E Q . 3-51 B ) 5 G f 2 2 ¢ I PA L A 1 I PB L B U 5 a n i 5 1 GI Pi f i 2 2 L i 5 GI PA f 2 2 L A 1 GI PB f 2 2 L B W ORK DONE BY THE TORQUE T 0 E QUATE U AND W AND SOLVE FOR
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Unformatted text preview: f (This result agrees with Eq. (3-48) of Example 3-9, Section 3.8.) f 5 T L A L B G ( L B I PA 1 L A I PB ) G f 2 2 ¢ I PA L A 1 I PB L B ≤ 5 T f 2 W 5 T f 2 T L A L B A C I PA I PB B f Problem 3.9-8 Derive a formula for the strain energy U of the cantilever bar shown in the figure. The bar has circular cross sections and length L . It is subjected to a distributed torque of intensity t per unit distance. The intensity varies linearly from t 5 0 at the free end to a maximum value t 5 t at the support. L t t A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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