03-02ChapGere.0022 - P S HEAR STRESS IN PART CB (Eq. 1) U...

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SECTION 3.8 Statically Indeterminate Torsional Members 225 Problem 3.8-4 A hollow steel shaft ACB of outside diameter 50 mm and inside diameter 40 mm is held against rotation at ends A and B (see figure). Horizontal forces P are applied at the ends of a vertical arm that is welded to the shaft at point C . Determine the allowable value of the forces P if the maximum permissible shear stress in the shaft is 45 MPa. ( Hint: Use Eqs. 3-46a and b of Example 3-9 to obtain the reactive torques.) Solution 3.8-4 Hollow shaft with fixed ends A B C P P 200 mm 200 mm 600 mm 400 mm G ENERAL F ORMULAS : From Eqs. (3-46a and b): T B 5 T 0 L A L T A 5 T 0 L B L A B L A L B T B T A L T O A PPLY THE ABOVE FORMULAS TO THE GIVEN SHAFT A B C 600 mm 400 mm T B T A T O The larger torque, and hence the larger shear stress, occurs in part CB of the shaft. T max 5 T B 5 0.24
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Unformatted text preview: P S HEAR STRESS IN PART CB (Eq. 1) U NITS : Newtons and meters p max 5 45 3 10 6 N/m 2 d 5 d 2 5 0.05 mm Substitute numerical values into (Eq. 1): P allow 5 2710 N P 5 652.07 N . m 0.24 m 5 2717 N 5 652.07 N . m 0.24 P 5 2(45 3 10 6 N / m 2 )(362.26 3 10 2 9 m 4 ) 0.05 m 5 362.26 3 10 2 9 m 4 I P 5 p 32 ( d 2 4 2 d 1 4 ) t max 5 T max ( d / 2) I P Ê T max 5 2 t max I P d T 5 P (400 mm) L B 5 400 mm L A 5 600 mm L 5 L A 1 L B 5 1000 mm d 2 5 50 mm d 1 5 40 mm t allow 5 45 MPa U NITS : P 5 Newtons T 5 Newton meters T B 5 T 0 L A L 5 P (0.4 m)(600 mm) 1000 mm 5 0.24 P T A 5 T 0 L B L 5 P (0.4 m)(400 mm) 1000 mm 5 0.16 P 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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