03-02ChapGere.0014

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Problem 3.7-2 A motor drives a shaft at 12 Hz and delivers 20 kW of power (see figure). (a) If the shaft has a diameter of 30 mm, what is the maximum shear stress t max in the shaft? (b) If the maximum allowable shear stress is 40 MPa, what is the minimum permissible diameter d min of the shaft? Solution 3.7-2 Motor-driven shaft SECTION 3.7 Transmission of Power 217 d 12 Hz 20 kW f 5 12 Hz P 5 20 kW 5 20,000 N ? m/s T ORQUE P 5 2 p fT P 5 watts f 5 Hz 5 s 2 1 T 5 Newton meters (a) M AXIMUM SHEAR STRESS t max d 5 30 mm T 5 P 2 p f 5 20,000 W 2 p (12 Hz) 5 265.3 N . m (b) M INIMUM DIAMETER d min t allow 5 40 MPa d min 5 0.0323 m 5 32.3 mm Ê 5 33.78 3 10 2 6 m 3 d 3 5 16 T p t allow 5 16(265.3 N . m) p (40 MPa) 5 50.0 MPa Ê t max 5 16 T p d 3 5 16(265.3 N . p (0.030 3 Problem 3.7-3 The propeller shaft of a large ship has outside diameter 18 in. and inside diameter 12 in., as shown in the figure. The shaft is rated for a maximum shear stress of 4500 psi. (a) If the shaft is turning at 100 rpm, what is the maximum horsepower that can be transmitted without exceeding the allowable stress?
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