Budynas ch01

Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)

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Chapter 1 Problems 1-1 through 1-4 are for student research. 1-5 (a) Point vehicles Q = cars hour = v x = 42 . 1 v v 2 0 . 324 Seek stationary point maximum dQ d v = 0 = 42 . 1 2 v 0 . 324 v * = 21 . 05 mph Q * = 42 . 1(21 . 05) 21 . 05 2 0 . 324 = 1368 cars/h Ans . (b) Q = v x + l = 0 . 324 v (42 . 1) v 2 + l v 1 Maximize Q with l = 10 / 5280 mi v Q 22.18 1221.431 22.19 1221.433 22.20 1221.435 22.21 1221.435 22.22 1221.434 % loss of throughput = 1368 1221 1221 = 12% Ans. (c) % increase in speed 22 . 2 21 . 05 21 . 05 = 5 . 5% Modest change in optimal speed Ans. x l 2 l 2 v x v
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2 Solutions Manual Instructor’s Solution Manual to Accompany Mechanical Engineering Design 1-6 This and the following problem may be the student’s first experience with a figure of merit. Formulate fom to reflect larger figure of merit for larger merit. Use a maximization optimization algorithm. When one gets into computer implementa- tion and answers are not known, minimizing instead of maximizing is the largest error one can make. F V = F 1 sin θ W = 0 F H = − F 1 cos θ F 2 = 0 From which F 1 = W / sin θ F 2 = − W cos θ/ sin θ fom = − $ = − ¢ γ (volume) .
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