301_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

301_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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SECTION 3.7 Transmission of Power 295 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 ± 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? d 12 Hz 20 kW Solution 3.7-2 Motor-driven shaft f ² 12 Hz P ² 20 kW ² 20,000 N ³ m/s T ORQUE P ² 2 ´ fT P ² watts f ² Hz ² s µ 1 T ² Newton meters (a) M AXIMUM SHEAR STRESS max d ² 30 mm T ² P 2 p f ² 20,000 W 2 p (12 Hz) ² 265.3 N # m (b) M INIMUM DIAMETER d min allow ² 40 MPa ² 33.78 10 µ 6 m 3 d min ² 0.0323 m ² 32.3 mm ; d 3 ² 16 T pt allow ² 16(265.3 N # m) p (40 MPa) ² 50.0 MPa ; t max ² 16 T p d 3 ² 16(265.3 N # m) p (0.030 m) 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
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