03-02ChapGere.0016

03-02ChapGere.0016 - order that the splice can transmit the...

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Problem 3.7-6 A tubular shaft being designed for use on a construction site must transmit 120 kW at 1.75 Hz. The inside diameter of the shaft is to be one-half of the outside diameter. If the allowable shear stress in the shaft is 45 MPa, what is the minimum required outside diameter d ? Solution 3.7-6 Tubular shaft SECTION 3.7 Transmission of Power 219 d 5 outside diameter d 0 5 inside diameter 5 0.5 d P 5 120 kW 5 120,000 W f 5 1.75 Hz t allow 5 45 MPa T ORQUE P 5 2 p fT P 5 watts f 5 Hz I P 5 p 32 [ d 4 2 (0.5 d ) 4 ] 5 0.092039 d 4 T 5 newton meters M INIMUM OUTSIDE DIAMETER d min 5 110 mm Ê d 3 5 0.0013175 m 3 Ê d 5 0.1096 m 0.092039 d 4 5 (10,913.5 N . m)( d ) 2(45 MPa) t max 5 Td 2 I P Ê I P 5 Td 2 t max 5 Td 2 t allow T 5 P 2 p f 5 120,000 W 2 p (1.75 Hz) 5 10,913.5 N . m Problem 3.7-7 A propeller shaft of solid circular cross section and diameter d is spliced by a collar of the same material (see figure). The collar is securely bonded to both parts of the shaft. What should be the minimum outer diameter d 1 of the collar in
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Unformatted text preview: order that the splice can transmit the same power as the solid shaft? Solution 3.7-7 Splice in a propeller shaft d d 1 S OLID SHAFT H OLLOW COLLAR 5 p t max 16 d 1 ( d 1 4 2 d 4 ) T 2 5 2 t max I P d 1 5 2 t max d 1 ¢ p 32 ≤ ( d 1 4 2 d 4 ) I P 5 p 32 ( d 1 4 2 d 4 ) t max 5 T 2 r I P 5 T 2 ( d 1 / 2) I P t max 5 16 T 1 p d 3 Ê T 1 5 p d 3 t max 16 E QUATE TORQUES For the same power, the torques must be the same. For the same material, both parts can be stressed to the same maximum stress. (Eq. 1) M INIMUM OUTER DIAMETER Solve Eq. (1) numerically: Min. d 1 5 1.221 d Ê or ¢ d 1 d ≤ 4 2 d 1 d 2 1 5 ∴ T 1 5 T 2 Ê p d 3 t max 16 5 p t max 16 d 1 ( d 1 4 2 d 4 ) d d 1 T T 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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