278_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

278_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: Sec_3.4.qxd 9/27/08 272 1:09 PM Page 272 CHAPTER 3 Torsion Solution 3.4-7 Shaft with four gears (b) HOLLOW SHAFT Inside diameter d0 10,000 psi allow TAB 8000 lb-in. TBC tmax 11,000 lb-in. TCD d3 a 16T UNITS: d 16Tmax pt allow Required d 16(11,000 lb-in.) p(10,000 psi) 1.78 in. 5.602 in.3 p b [d4 32 (1.0 in.)4] inches 56,023 d 10,000 ; Ip d (11,000 lb-in.) a b 2 10,000 psi pd3 d Tmax a b 2 t allow 7000 lb-in. (a) SOLID SHAFT tmax Tr Ip 1.0 in. d4 1 or d4 5.6023 d Solving, d is twisted by torques T (see figure). The diameter of the bar varies linearly from dA at the left-hand end to dB at the right-hand end. For what ratio dB/dA will the angle of twist of the tapered bar be one-half the angle of twist of a prismatic bar of diameter dA? (The prismatic bar is made of the same material, has the same length, and is subjected to the same torque as the tapered bar.) Hint: Use the results of Example 3-5. 0 1.832 Required d Problem 3.4-8 A tapered bar AB of solid circular cross section 1 1.83 in. ; B A T T L dA dB Problems 3.4-8, 3.4-9 and 3.4-10 Solution 3.4-8 Tapered bar AB ANGLE OF TWIST TAPERED BAR (From Eq. 3-27) f1 b2 + b + 1 TL a b G(IP)A 3b3 PRISMATIC BAR TL f2 G(IP)A b dB dA f1 1 f 22 or 3 3 b2 + b + 1 2 2 2 SOLVE NUMERICALLY: b dB dA 1 2 3b3 1.45 ; 2 0 ...
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