4020-F2011-HW14Solut - 1 MSE 4020 HW14-SOLUTION Problem 1(a&(b A n" N = C n" log A logN = logC logN = $ n" log A logC From given

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Unformatted text preview: 1 MSE 4020 HW14-SOLUTION 12/04/2011 Problem 1. (a) & (b) ! A n " N = C # n " log ! A + logN = logC # logN = $ n " log ! A + logC From given picture, we can extract the data listed in the table below, N(cycles) 10 5 10 6 10 7 10 8 5 ¡ 10 8 σ A (ksi) 43.8 35.7 28.7 23.2 21.0 log(N) 5 6 7 8 8.699 log( σ A ) 1.6415 1.5527 1.4579 1.3655 1.3222 Fitting the data of log(N) vs. log( σ A ), we have following linear equation (and the corresponding plot): y = -11.3 x +23.54 Thus, n = 11.3 Also, logC = 23.54 ! C = 10 23.54 2 (c) The curves asked are plotted below in different colors: 3 Problem 2. According to the Weibull equation, F x ( ) = 1 ! exp ! x " # $ % & ' ( k # $ % % & ' ( ( ) ln ! ln 1 ! F x ( ) ( ) ( ) = k * ln x ( ) ! k * ln " ( ) where F x i ( ) = i ! 0.3 n + 0.4 i is the ranking index,and n is the total number of experiments (a) For A320 bolts in seawater, we have the following data, i x or N F(x) ln(N) ln(-ln(1-F(x)) 1 47780 0.12963 10.77436 -1.974458694 2 47890 0.31482 10.77666 10....
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This note was uploaded on 12/05/2011 for the course MSE 4020 at Cornell University (Engineering School).

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4020-F2011-HW14Solut - 1 MSE 4020 HW14-SOLUTION Problem 1(a&(b A n" N = C n" log A logN = logC logN = $ n" log A logC From given

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