Chapter_1_solutions(2)

(d) X1/X2:

x1X1 e1X1 1 e1X1 x2X2 e2X2 1 e2X2

1

1 e1X1 e2e2 e2e1 e2 e1

11 then 111

X2 X2X1 X2 X1X2 1 e2X2

xXX ee

Thus,e 1 1 1 1 2 Ans.

x2X2X2 X1X2

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x1

= 2.645 751 311 1 1-11 (a)

X1 = 2.64 (3 correct digits) x2

= 2.828 427 124 7

(3 correct digits) X2 = 2.82

x1 + x2 = 5.474 178 435 8 e1 = x1 X1 = 0.005 751 311 1 e2 = x2 X2 = 0.008 427 124 7 e = e1 + e2 = 0.014 178 435 8 Sum = x1 + x2 = X1 + X2 + e = 2.64 + 2.82 + 0.014 178 435 8 = 5.474 178 435 8 X1 = 2.65, X2 = 2.83 (3 digit significant numbers) (b)

e1 = x1 X1 = 0.004 248 688 9 e2 = x2 X2 = 0.001 572 875 3 e = e1 + e2 = 0.005 821 564 2 Sum = x1 + x2 = X1 + X2 + e = 2.65 +2.83 0.001 572 875 3 = 5.474 178 435 8 ______________________________________________________________________________

3

16 1000 25 10 S

1-12 d 0.799inAns. 3

2.5 dnd

in Ans. Table A-17: d = 78

Factor of safety: n

S

25 103 161000 3.29Ans.

n

78

3

______________________________________________________________________________ 1-13 Eq. (1-5):

R = Ri= 0.98(0.96)0.94 = 0.88

i 1

Overall reliability = 88 percent Ans.

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