2_ch 01 Mechanical Design budynas_SM_ch01

2_ch 01 Mechanical Design budynas_SM_ch01 - µ l 2 cos θ W...

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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 Frst experience with a Fgure of merit. •±ormulate fom to re²ect larger Fgure 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. X F V = F 1 sin θ W = 0 X F H =− F 1 cos θ F 2 = 0 ±rom which F 1 = W / sin θ F 2 =− W cos θ/ sin θ fom =− $ =− ¢ γ (volume) . = − ¢ γ ( l 1 A 1 + l 2 A 2 ) A 1 = F 1 S = W S sin θ , l 2 = l 1 cos θ A 2 = ¯ ¯ ¯ ¯ F 2 S ¯ ¯ ¯ ¯ = W cos θ S sin θ fom = − ¢ γ
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Unformatted text preview: µ l 2 cos θ W S sin θ + l 2 W cos θ S sin θ ¶ = − ¢ γ Wl 2 S µ 1 + cos 2 θ cos θ sin θ ¶ Set leading constant to unity θ ◦ fom −∞ 20 − 5.86 30 − 4.04 40 − 3.22 45 − 3.00 50 − 2.87 54.736 − 2.828 60 − 2.886 Check second derivative to see if a maximum, minimum, or point of in²ection has been found. Or, evaluate fom on either side of θ *. θ * = 54 . 736 ◦ Ans. fom* = − 2 . 828 Alternative: d d θ µ 1 + cos 2 θ cos θ sin θ ¶ = And solve resulting tran-scendental for θ *....
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This note was uploaded on 12/13/2011 for the course EML 3013 taught by Professor Shingley during the Fall '11 term at UNF.

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