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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
nd = = 1.43 Ans.
0.85(0.95)
2
1-10 (a) X1 + X2:
x1 + x2 = X1 + e1 + X 2 + e2
error = e = ( x1 + x2 ) − ( X1 + X 2 )
= e1 + e2 Ans.
(b) X1 − X2:
x1 − x2 = X1 + e1 − ( X 2 + e2 )
e = ( x1 − x2 ) − ( X1 − X 2 ) = e1 − e2 Ans.
(c) X1 X2:
x1x2 = ( X1 + e1 )( X 2 + e2 )
e = x1x2 − X1 X 2 = X1e2 + X 2e1 + e1e2
e e
Xe +X e =X X 1 + 2 Ans.
1 2 2 1 1 2
Shigleỵ’s MED, 10th edition Chapter 1 Solutions, Page 1/12
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X1 X2
Shigleỵ’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 X 2 + e2 X 2 1+ e2 X 2
−1
e e 1+ e X e e e e
1− 1+ 1+ −
2
1+
2 then
1 1 1
1−
2 1 2
X2 X2 1+ e2 X 2 X1 X2 X1 X2
x X X e e
Thus, e= 1
− 1
1
1
− 2
Ans.
x2 X2 X 2 X1 X2
1-11 (a) x1 = = 2.645 751 311 1
X1 = 2.64 (3 correct digits)
x2 = = 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 (1000) 25 103 ( )
1-12 = = d = 1.006 in Ans.
nd d3 2.5
Table A-17: d = 1 14 in Ans.
Factor of safetỵ: n=
S
=
( )
25 103
= 4.79 Ans.
32 (1000)
Shigleỵ’s MED, 10th edition Chapter 1 Solutions, Page 1/12
SOLUTION MANUAL
, www.konkur.in
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
nd = = 1.43 Ans.
0.85(0.95)
2
1-10 (a) X1 + X2:
x1 + x2 = X1 + e1 + X 2 + e2
error = e = ( x1 + x2 ) − ( X1 + X 2 )
= e1 + e2 Ans.
(b) X1 − X2:
x1 − x2 = X1 + e1 − ( X 2 + e2 )
e = ( x1 − x2 ) − ( X1 − X 2 ) = e1 − e2 Ans.
(c) X1 X2:
x1x2 = ( X1 + e1 )( X 2 + e2 )
e = x1x2 − X1 X 2 = X1e2 + X 2e1 + e1e2
e e
Xe +X e =X X 1 + 2 Ans.
1 2 2 1 1 2
Shigleỵ’s MED, 10th edition Chapter 1 Solutions, Page 1/12
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X1 X2
Shigleỵ’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 X 2 + e2 X 2 1+ e2 X 2
−1
e e 1+ e X e e e e
1− 1+ 1+ −
2
1+
2 then
1 1 1
1−
2 1 2
X2 X2 1+ e2 X 2 X1 X2 X1 X2
x X X e e
Thus, e= 1
− 1
1
1
− 2
Ans.
x2 X2 X 2 X1 X2
1-11 (a) x1 = = 2.645 751 311 1
X1 = 2.64 (3 correct digits)
x2 = = 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 (1000) 25 103 ( )
1-12 = = d = 1.006 in Ans.
nd d3 2.5
Table A-17: d = 1 14 in Ans.
Factor of safetỵ: n=
S
=
( )
25 103
= 4.79 Ans.
32 (1000)
Shigleỵ’s MED, 10th edition Chapter 1 Solutions, Page 1/12
