03-02ChapGere.0024

# 03-02ChapGere.0024 - 1 L A I PB ≤ A LLOWABLE TORQUE BASED...

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Problem 3.8-6 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 43 MPa, 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 3.8-6 Stepped shaft ACB SECTION 3.8 Statically Indeterminate Torsional Members 227 B T 0 A 450 mm C 225 mm 20 mm 25 mm d A 5 20 mm d B 5 25 mm L A 5 225 mm L B 5 450 mm t allow 5 43 MPa 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 5 150.0 N . m 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 A 3 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
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Unformatted text preview: 1 L A I PB ≤ 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 5 240.0 N . m 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 5 150 N . m 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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