03-02ChapGere.0023

03-02ChapGere.0023 - A LLOWABLE TORQUE BASED UPON SHEAR...

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Problem 3.8-5 A stepped shaft ACB having solid circular cross sections with two different diameters is held against rotation at the ends (see figure). If the allowable shear stress in the shaft is 6000 psi, what is the maximum torque ( T 0 ) max that may be applied at section C ? ( Hint: Use Eqs. 3-45a and b of Example 3-9 to obtain the reactive torques.) Solution 3.8-5 Stepped shaft ACB 226 CHAPTER 3 Torsion A 0.75 in. 6.0 in. 15.0 in. 1.50 in. B C T 0 d A 5 0.75 in. d B 5 1.50 in. L A 5 6.0 in. L B 5 15.0 in. t allow 5 6000 psi Find ( T 0 ) max R EACTIVE TORQUES (from Eqs. 3-45a and b) (1) (2) A LLOWABLE TORQUE BASED UPON SHEAR STRESS IN SEGMENT AC (3) Combine Eqs. (1) and (3) and solve for T 0 : (4) Substitute numerical values: ( T 0 ) AC 5 3678 lb-in. 5 1 16 p d A 3 t allow ¢ 1 1 L A d B 4 L B d A 4 ( T 0 ) AC 5 1 16 p d A 3 t allow ¢ 1 1 L A I PB L B I PA 5 1 16 p d A 3 t allow T A 5 1 16 p d A 3 t AC t AC 5 16 T A p d T B 5 T 0 ¢ L A I PB L B I PA 1 L A 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: A LLOWABLE TORQUE BASED UPON SHEAR STRESS IN SEGMENT CB (5) Combine Eqs. (2) and (5) and solve for T : (6) Substitute numerical values: ( T ) CB 5 4597 lb-in. S EGMENT AC GOVERNS N OTE : From Eqs. (4) and (6) we find that which can be used as a partial check on the results. ( T ) AC ( T ) CB 5 L A L B d B d A ( T ) max 5 3680 lb-in. 5 1 16 p d B 3 t allow 1 1 L B d A 4 L A d B 4 ( T ) CB 5 1 16 p d B 3 t allow 1 1 L B I PA L A I PB 5 1 16 p d B 3 t allow T B 5 1 16 p d B 3 t CB t CB 5 16 T B p d B 3 A d A L A L B d B B C T T B T A A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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