03-02ChapGere.0019 - Segment AB Segment BC f AC allow 5 0.06981 rad S HEAR STRESS GOVERNS d 5 53.4 mm 5 49.3 mm and d 5 0.04933 m 0.06981 5 0.4133

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Problem 3.7-10 The shaft ABC shown in the figure is driven by a motor that delivers 300 kW at a rotational speed of 32 Hz. The gears at B and C take out 120 and 180 kW, respectively. The lengths of the two parts of the shaft are L 1 5 1.5 m and L 2 5 0.9 m. Determine the required diameter d of the shaft if the allowable shear stress is 50 MPa, the allowable angle of twist between points A and C is 4.0°, and G 5 75 GPa. Solution 3.7-10 Motor-driven shaft 222 CHAPTER 3 Torsion L 1 5 1.5 m L 2 5 0.9 m d 5 diameter f 5 32 Hz t allow 5 50 MPa G 5 75 GPa T ORQUES ACTING ON THE SHAFT P 5 2 p fT P 5 watts f 5 Hz T 5 newton meters F REE - BODY DIAGRAM T A 5 1492 N ? m T B 5 596.8 N ? m T C 5 895.3 N ? m d 5 diameter At point C : T C 5 180 300 T A 5 895.3 N ? m At point B : T B 5 120 300 T A 5 596.8 N ? m At point A : T A 5 300,000 W 2 p (32 Hz) 5 1492 N ? m T 5 P 2 p f ( f AC ) allow 5 4 85 0.06981 rad I NTERNAL TORQUES T AB 5 1492 N ? m T BC 5 895.3 N ? m D IAMETER BASED UPON ALLOWABLE SHEAR STRESS The larger torque occurs in segment AB D IAMETER BASED UPON ALLOWABLE ANGLE OF TWIST
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Unformatted text preview: Segment AB : Segment BC : ( f AC ) allow 5 0.06981 rad S HEAR STRESS GOVERNS d 5 53.4 mm 5 49.3 mm and d 5 0.04933 m 0.06981 5 0.4133 3 10 2 6 d 4 From A to C : f AC 5 f AB 1 f BC 5 0.4133 3 10 2 6 d 4 f BC 5 0.1094 3 10 2 6 d 4 f BC 5 32 T BC L BC p Gd 4 5 32(895.3 N . m)(0.9 m) p (75 GPa) d 4 f AB 5 0.3039 3 10 2 6 d 4 f AB 5 32 T AB L AB p Gd 4 5 32(1492 N . m)(1.5 m) p (75 GPa) d 4 I P 5 p d 4 32 f 5 TL GI P 5 32 TL p Gd 4 d 3 5 0.0001520 m 3 d 5 0.0534 m 5 53.4 mm t max 5 16 T AB p d 3 d 3 5 16 T AB p t allow 5 16(1492 N . m) p (50 MPa) C B A 300 kW 180 kW L 1 L 2 120 kW C B A T A = 1492 N . m 1.5 m 0.9 m T B = 596.8 N . m T C = 895.3 N . m 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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