Solutions Manual for Complex Variables and Applications (9th Edition) by James Ward Brown and Ruel V. Churchill – Complete Worked Solutions, Analytical Explanations, and Mathematical Problem Derivations

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SOLUTION MANUAL

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Chapter 1

Problems 1-1 through 1-6 are for student research. No standard solutions are provided.

1-7 From Fig. 1-2, cost of grinding to 0.0005 in is 270%. Cost of turning to 0.003 in is
60%.
Relative cost of grinding vs. turning = 270/60 = 4.5 times Ans.


1-8 CA = CB,

10 + 0.8 P = 60 + 0.8 P 0.005 P 2

P 2 = 50/0.005 P = 100 parts Ans.


1-9 Max. load = 1.10 P
Min. area = (0.95)2A
Min. strength = 0.85 S
To offset the absolute uncertainties, the design factor, from Eq. (1-1) should be

1.10
n Ans.
1.43
2
d 0.85 0.95


1-10 (a) X1 + X2:
x1 x2 X1 e1 X2 e2
error e x1 x2 X1 X2
e1 e2 Ans.
(b) X1
X2:
x1 x2 X1 e1 X2 e2
Ans.
(c) X1 X2: e x1 x2 X1 X2
e1 e2

x1x2 X1 e1 X2 e2


e x1x2 X1 X 2 X1e2 X 2e1 e1e2
e e
Xe X X 1 2 Ans.
e X

Shigley’s MED, 10th edition Chapter 1 Solutions, Page 1/12

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1 2 2 1 1 2
 X1 X2




Shigley’s MED, 10th edition Chapter 1 Solutions, Page 1/12

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(d) X1 /X2 :
x X e X 1 e X
1 1 1 1 1 1

x2 X2 e2 X2 1 X2
e2
1
e e 1 e X e e e e

1 2
2
1 then 1 1
1 1
1 2
1 1 2


X2 X2 1 e2 X 2 X1 X2 X1 X2
x X X e e


Thus, e2 1 1 1 1 Ans.
x2 X2 X2 X2
X1


1-11 (a) x1 = 7 = 2.645 751 311 1
X1 = 2.64 (3 correct digits)
x2 = 8 = 2.828 427 124 7
X2 = 2.82 (3 correct digits)
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 Checks
(b) X1 = 2.65, X2 = 2.83 (3 digit significant numbers)
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 Checks


S 32 25 103
1000
1-12 d 1.006 Ans.
in
nd d 2.5
3


Table A-17: d = 1 14 in Ans.
S 25 103
Factor of safety: n Ans.
4.79
32 1000


Shigley’s MED, 10th edition Chapter 1 Solutions, Page 1/12