33_ch 03 Mechanical Design budynas_SM_ch03

33_ch 03 Mechanical Design budynas_SM_ch03 -...

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46 Solutions Manual • Instructor’s Solution Manual to Accompany Mechanical Engineering Design Ratio of torques T sq T rd = 2( b t ) 2 t τ all π ( b t ) 2 t τ all / 2 = 4 π = 1 . 27 Twist per unit length square: θ sq = 2 G θ 1 t t τ all ± L A ² m = C ³ ³ ³ ³ L A ³ ³ ³ ³ m = C 4( b t ) ( b t ) 2 Round: θ rd = C ± L A ² m = C π ( b t ) π ( b t ) 2 / 4 = C 4( b t ) ( b t ) 2 Ratio equals 1, twists are the same. Note the weight ratio is W sq W rd = ρ l ( b t ) 2 ρ l π ( b t )( t ) = b t π t thin-walled assumes b 20 t = 19 π = 6 . 04 with b = 20 t = 2 . 86 with b = 10 t 3-34 l = 40 in, τ all = 11 500 psi, G = 11 . 5(10 6 ) psi, t = 0 . 050 in r m = r i + t / 2 = r i + 0 . 025 for r i > 0 = 0 for r i = 0 A m = (1 0 . 05) 2 4 ´ r 2 m π 4 r 2 m µ = 0 . 95 2 (4 π ) r 2 m L m = 4(1 0 . 05 2 r m + 2 π r m / 4) = 4[0 . 95 (2 π/ 2) r m ] Eq. (3-45): T = 2 A m t τ = 2(0 . 05)(11 500) A m = 1150 A m Eq. (3-46): θ (deg) = θ 1 l 180 π = TL m l 4 GA 2 m t 180 π = m (40) 4(11 . 5)(10 6 ) A 2 m (0 . 05) 180 π = 9 . 9645(10
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