46_ch 03 Mechanical Design budynas_SM_ch03

46_ch 03 Mechanical Design budynas_SM_ch03 -...

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Chapter 3 59 3-61 ω = 2 π (3000) / 60 = 314 . 2 rad/s m = 0 . 282(1 . 25)(12)(0 . 125) 386 = 1 . 370(10 3 ) lbf · s 2 /in F = m ω 2 r = 1 . 370(10 3 )(314 . 2 2 )(6) = 811 . 5 lbf A nom = (1 . 25 0 . 5)(1 / 8) = 0 . 093 75 in 2 σ nom = 811 . 5 0 . 093 75 = 8656 psi Ans. Note: Stress concentration Fig. A-15-1 gives K t . = 2 . 25 which increases σ max and fatigue. 3-62 to 3-67 ν = 0 . 292, E = 30 Mpsi (207 GPa), r i = 0 R = 0.75 in (20 mm), r o = 1 . 5in(40 mm) Eq. (3-57) p psi = 30(10 6 ) δ 0 . 75 3 ± (1 . 5 2 0 . 75 2 )(0 . 75 2 0) 2(1 . 5 2 0) ² = 1 . 5(10 7 ) δ (1) p Pa = 207(10 9 ) δ 0 . 020 3 ± (0 . 04 2 0 . 02 2 )(0 . 02 2 0) 2(0 . 04 2 0) ² = 3 . 881(10 12 ) δ (2) 3-62 δ max = 1
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