305_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

305_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_3.5-3.7.qxd 9/27/08 1:10 PM Page 299 SECTION 3.7 Transmission of Power 299 Problem 3.7-9 A motor delivers 275 hp at 1000 rpm to the end of a shaft (see figure). The gears at B and C take out 125 and 150 hp, respectively. Determine the required diameter d of the shaft if the allowable shear stress is 7500 psi and the angle of twist between the motor and gear C is limited to 1.5°. (Assume G 11.5 106 psi, L1 6 ft, and L2 4 ft.) Motor C A d B L2 L1 PROBS. 3.7-9 and 3.7-10 Solution 3.7-9 Motor-driven shaft FREE-BODY DIAGRAM L1 6 ft L2 4 ft d diameter TA 17,332 lb-in. n 1000 rpm TC 9454 lb-in. allow d 7500 psi diameter AC)allow 1.5° 0.02618 rad TB G ( 11.5 106 psi INTERNAL TORQUES TAB H T 33,000 H 2pn At point A: TA H hp n rpm T lb-ft 17,332 lb-in. TBC TORQUES ACTING ON THE SHAFT 2pnT 33,000 7878 lb-in. 9454 lb-in. DIAMETER BASED UPON ALLOWABLE SHEAR STRESS The larger torque occurs in segment AB 33,000(275 hp) 2p(1000 rpm) tmax At point B: TB At point C: TC 125 275 150 275 d3 3 pd 16TAB pt allow 16(17,332 lb-in.) p(7500 psi) 1444 lb-ft d 17,332 lb-in. 16TAB 11.77 in.3 2.27 in. DIAMETER BASED UPON ALLOWABLE ANGLE OF TWIST TA 7878 lb-in. IP TA 9454 lb-in. pd4 32 f TL GIP 32TL pGd4 ...
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