03-02ChapGere.0025 - T B 5 T 0 L A I PB L B I PA 1 L A I PB...

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228 CHAPTER 3 Torsion Problem 3.8-7 A stepped shaft ACB is held against rotation at ends A and B and subjected to a torque T 0 acting at section C (see figure). The two segments of the shaft ( AC and CB ) have diameters d A and d B , respectively, and polar moments of inertia I PA and I PB , respectively. The shaft has length L and segment AC has length a . (a) For what ratio a / L will the maximum shear stresses be the same in both segments of the shaft? (b) For what ratio a / L will the internal torques be the same in both segments of the shaft? ( Hint: Use Eqs. 3-45a and b of Example 3-9 to obtain the reactive torques.) Solution 3.8-7 Stepped shaft B T 0 A C I PA d A d B I PB a L S EGMENT AC : d A , I PA L A 5 a S EGMENT CB : d B , I PB L B 5 L 2 a R EACTIVE TORQUES (from Eqs. 3-45a and b) (a) E QUAL SHEAR STRESSES (Eq. 1) Substitute T A and T B into Eq. (1): t AC 5 t CB Ê or Ê T A d A I PA 5 T B d B I PB t AC 5 T A ( d A / 2) I PA Ê t CB 5 T B ( d B / 2) I PB T A 5 T 0 ¢ L B I PA L B I PA 1 L A I PB ;
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Unformatted text preview: T B 5 T 0 L A I PB L B I PA 1 L A I PB or ( L 2 a ) d A 5 ad B (b) E QUAL TORQUES T A 5 T B or L B I PA 5 L A I PB or ( L 2 a ) I PA 5 aI PB or a L 5 d A 4 d A 4 1 d B 4 Solve for a / L : a L 5 I PA I PA 1 I PB Solve for a / L : a L 5 d A d A 1 d B L B I PA d A I PA 5 L A I PB d B I PB or L B d A 5 L A d B B T A C d A d B a L T A T B Problem 3.8-8 A circular bar AB of length L is fixed against rotation at the ends and loaded by a distributed torque t ( x ) that varies linearly in intensity from zero at end A to t at end B (see figure). Obtain formulas for the fixed-end torques T A and T B . A t ( x ) t T B T A B L x 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 Institute of Technology.

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