Solution Manual for Shigleys Mechanical Engineering Design
11th Edition Author:Budynas / All Chapters 1 - 20 / Full
Complete A+ Study Guide Latest Version
, 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 = 2 Ans.
=1.43 0.85C
0.953
1-10 (a) X1 + X2:
x1 + x2 =X1 + e1 + X 2 + e2
error =e =C x1 + x2 3 - C X1 + X 2 3
=e1 + Ans.
(b) X1 - X2: e2
x1 - x2 =X1 + e1 - C X 2 + e2 3
e =C x1 - x2 3 - C X1 - X 2 3 =e1 - e2 Ans.
(c) X1 X2:
x1x2 =C X1 + e1 3 C X 2 + e2 3
e =x1 x2 - X1 X 2 =X1e2 + X 2e1 + e1e2
”X e + / e
e X XX
= + 2 Ans.
e1
1 2 2 1 1 2∣X X ∣
1 2J
Shigley’s MED, 11th edition Chapter 1 Solutions, Page 1/12
, (d) X1/X2
: x1 X1 + e1 ∣ X1+1 e/1 X1 ∣
x =X + e X=
2 2 2 2 1+ e2 X 2 J
-1 /
/ e e ”1
2- the / 1+ e X / 1- e2 ”1+ e1 - e2
1+ 2 n e1 1 1 1+
∣ 1+ e2 X 2 ∣ ”∣ ∣
∣ ∣ X X ∣∣
X2 J 2 J 1J X2 X1 X 2
J
x1
Thus, e = X1 X1 / e2 Ans.
- ”
e1
x X - X ∣X X ∣
2 2 2 1 2J
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
32 C10003 25 C 10 3 3
ơ= ⟶ = ⟶ d =1.006 Ans.
S ud 3 2.5
1-12 in
nd 11
Table A-17: d 4 in Ans.
= n =S = 25 C 10 3 3
1000
32 =4.7
9
Ans.
ơ C 3
3
u C1.253
Factor of
safety:
Shigley’s MED, 11th edition Chapter 1 Solutions, Page 2/12
, 1-13 (a)
x f fx f x2
60 2 120 7200
70 1 70 4900
80 3 240 19200
90 5 450 40500
100 8 800 80000
110 12 1320 145200
120 6 720 86400
130 10 1300 169000
140 8 1120 156800
150 5 750 112500
160 2 320 51200
170 3 510 86700
180 2 360 64800
190 1 190 36100
200 0 0 0
210 1 210 44100
Z 69 8480 1 104 600
1 k 8480
x = fi xi = =122.9 kcycles
Eq. (1- Ni =1 69
6)
Eq. (1-
7)
k
f i xi2 - N x 2 1 104 600 - 69(122.9)2
N - 1 1/ 2
sx = =∣ ∣ = 30.3 Ans.
kcycles
L 69 - 1
x - μx = x 115 122. =- 0.2607
z = - =
x115 - 9
115
(b) Eq. (1- ơˆx 30.3
5) s
x
Interpolating from Table (A-10)
Shigley’s MED, 11th edition Chapter 1 Solutions, Page 3/12
11th Edition Author:Budynas / All Chapters 1 - 20 / Full
Complete A+ Study Guide Latest Version
, 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 = 2 Ans.
=1.43 0.85C
0.953
1-10 (a) X1 + X2:
x1 + x2 =X1 + e1 + X 2 + e2
error =e =C x1 + x2 3 - C X1 + X 2 3
=e1 + Ans.
(b) X1 - X2: e2
x1 - x2 =X1 + e1 - C X 2 + e2 3
e =C x1 - x2 3 - C X1 - X 2 3 =e1 - e2 Ans.
(c) X1 X2:
x1x2 =C X1 + e1 3 C X 2 + e2 3
e =x1 x2 - X1 X 2 =X1e2 + X 2e1 + e1e2
”X e + / e
e X XX
= + 2 Ans.
e1
1 2 2 1 1 2∣X X ∣
1 2J
Shigley’s MED, 11th edition Chapter 1 Solutions, Page 1/12
, (d) X1/X2
: x1 X1 + e1 ∣ X1+1 e/1 X1 ∣
x =X + e X=
2 2 2 2 1+ e2 X 2 J
-1 /
/ e e ”1
2- the / 1+ e X / 1- e2 ”1+ e1 - e2
1+ 2 n e1 1 1 1+
∣ 1+ e2 X 2 ∣ ”∣ ∣
∣ ∣ X X ∣∣
X2 J 2 J 1J X2 X1 X 2
J
x1
Thus, e = X1 X1 / e2 Ans.
- ”
e1
x X - X ∣X X ∣
2 2 2 1 2J
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
32 C10003 25 C 10 3 3
ơ= ⟶ = ⟶ d =1.006 Ans.
S ud 3 2.5
1-12 in
nd 11
Table A-17: d 4 in Ans.
= n =S = 25 C 10 3 3
1000
32 =4.7
9
Ans.
ơ C 3
3
u C1.253
Factor of
safety:
Shigley’s MED, 11th edition Chapter 1 Solutions, Page 2/12
, 1-13 (a)
x f fx f x2
60 2 120 7200
70 1 70 4900
80 3 240 19200
90 5 450 40500
100 8 800 80000
110 12 1320 145200
120 6 720 86400
130 10 1300 169000
140 8 1120 156800
150 5 750 112500
160 2 320 51200
170 3 510 86700
180 2 360 64800
190 1 190 36100
200 0 0 0
210 1 210 44100
Z 69 8480 1 104 600
1 k 8480
x = fi xi = =122.9 kcycles
Eq. (1- Ni =1 69
6)
Eq. (1-
7)
k
f i xi2 - N x 2 1 104 600 - 69(122.9)2
N - 1 1/ 2
sx = =∣ ∣ = 30.3 Ans.
kcycles
L 69 - 1
x - μx = x 115 122. =- 0.2607
z = - =
x115 - 9
115
(b) Eq. (1- ơˆx 30.3
5) s
x
Interpolating from Table (A-10)
Shigley’s MED, 11th edition Chapter 1 Solutions, Page 3/12
