3_ch 02 Mechanical Design budynas_SM_ch02

3_ch 02 Mechanical Design budynas_SM_ch02 -...

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8 Solutions Manual Instructor’s Solution Manual to Accompany Mechanical Engineering Design 2-10 To plot σ true vs. ε , the following equations are applied to the data. A 0 = π (0 . 503) 2 4 = 0 . 1987 in 2 Eq. (2-4) ε = ln l l 0 for 0 L 0 . 0028 in ε = ln A 0 A for L > 0 . 0028 in σ true = P A The results are summarized in the table below and plotted on the next page. The last 5 points of data are used to plot log σ vs log ε The curve fit gives m = 0.2306 log σ 0 = 5 . 1852 σ 0 = 153 . 2 kpsi Ans. For 20% cold work, Eq. (2-10) and Eq. (2-13) give, A = A 0 (1 W ) = 0 . 1987(1 0 . 2) = 0 . 1590 in 2 ε = ln A 0 A = ln 0 . 1987 0 . 1590 = 0 . 2231 Eq. (2-14): S y = σ 0 ε m = 153 . 2(0 . 2231) 0 . 2306 = 108 . 4 kpsi Ans. Eq. (2-15), with S u = 85 . 5 kpsi from Prob. 2-9, S u = S u 1 W = 85 . 5 1 0 . 2 = 106 . 9 kpsi Ans. P L A ε σ true log ε log σ true 0 0 0.198 713 0 0 1000 0.0004 0.198 713 0.0002 5032.388 3.69901 3.701 774 2000 0.0006 0.198 713 0.0003 10064.78 3.52294 4.002 804 3000 0.0010 0.198 713 0.0005 15097.17 3.30114
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