03-02ChapGere.0030

03-02ChapGere.0030 - N # m 2 I PS 5 p 32 ( d 2 4 2 d 1 4 )...

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Steel sleeve S Brass core B d 1 d 2 Problem 3.8-12 The composite shaft shown in the figure is manufactured by shrink-fitting a steel sleeve over a brass core so that the two parts act as a single solid bar in torsion. The outer diameters of the two parts are d 1 5 40 mm for the brass core and d 2 5 50 mm for the steel sleeve. The shear moduli of elasticity are G b 5 36 GPa for the brass and G s 5 80 GPa for the steel. Assuming that the allowable shear stresses in the brass and steel are t b 5 48 MPa and t s 5 80 MPa, respectively, determine the maximum permissible torque T max that may be applied to the shaft. ( Hint: Use Eqs. 3-44a and b to find the torques.) Solution 3.8-12 Composite shaft shrink fit SECTION 3.8 Statically Indeterminate Torsional Members 233 Steel sleeve T T Brass core d 1 d 2 d 1 5 40 mm d 2 5 50 mm G B 5 36 GPa G S 5 80 GPa Allowable stresses: t B 5 48 MPa t S 5 80 MPa B RASS C ORE ( ONLY ) S TEEL SLEEVE ( ONLY ) G B I PB 5 9047.79 N # m 2 I PB 5 p 32 d 1 4 5 251.327 3 10 2 9 m 4 G S I PS 5 28,981.2
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Unformatted text preview: N # m 2 I PS 5 p 32 ( d 2 4 2 d 1 4 ) 5 362.265 3 10 2 9 m 4 T ORQUES Total torque: T 5 T B 1 T S Eq. (3-44a): 5 0.237918 T Eq. (3-44b): 5 0.762082 T T 5 T B 1 T S (CHECK) A LLOWABLE TORQUE T BASED UPON BRASS CORE Substitute numerical values: T 5 2535 N ? m A LLOWABLE TORQUE T BASED UPON STEEL SLEEVE S UBSTITUTE NUMERICAL VALUES : T 5 1521 N ? m S TEEL SLEEVE GOVERNS T max 5 1520 N # m Ê 5 2(80 MPa)(362.265 3 10 2 9 m 4 ) 50 mm T S 5 0.762082 T t S 5 T S ( d 2 / 2) I PS Ê T S 5 2 t S I PS d 2 5 2(48 MPa)(251.327 3 10 2 9 m 4 ) 40 mm T B 5 0.237918 T t B 5 T B ( d 1 / 2) I PB Ê T B 5 2 t B I PB d 1 T S 5 T ¢ G S I PS G S I PB 1 G S I PS ≤ T B 5 T ¢ G B I PB G B I PB 1 G S I PS ≤ T B T B T S T S 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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