Shigley’s MED, 10th edition Chapter 5 Solutions, Page 1/52
Chapter 5
5-1 Sy = 350 MPa.
MSS:
σ1 −
σ3 = Sy /n ⇒ ( )1 3
yS
n
σ σ
= −
DE: ( ) ( )
1/2 1/22 2 2 2 2
3A A B B x x y y xy
σ σ σ σ σ
σ σ σ σ τ′ = − + = − + +
yS
n
σ
= ′
(a) MSS:
σ1 = 100 MPa,
σ2 = 100 MPa,
σ3 = 0
350 3.5 .
100 0
n Ans= =
−
DE: 2 2 1/2 350
(100 100(100) 100 ) 100 MPa, 3.5 .
100
n Ans
σ ′ = − + = = =
(b) MSS:
σ1 = 100 MPa,
σ2 = 50 MPa,
σ3 = 0
350 3.5 .
100 0
n Ans= =
−
DE: 2 2 1/2 350
(100 100(50) 50 ) 86.6 MPa, 4.04 .
86.6
n Ans
σ ′ = − + = = =
(c)
2
2100 100
, ( 75) 140, 40 MPa
2 2
A B
σ σ  
= ± + − = − 
 
1 2 3140, 0, 40 MPa
σ
σ σ= = = −
MSS: 350 1.94 .
140 ( 40)
n Ans= =
− −
DE: ( ) 1/2
2 2 350
100 3 75 164 MPa, 2.13 .
164
n Ans
σ  ′ = + − = = = 
(d)
2
250 75 50 75
, ( 50) 11.0, 114.0 MPa
2 2
A B
σ σ − − − + 
= ± + − = − − 
 
1 2 30, 11.0, 114.0 MPa
σ σ
σ= = − = −
MSS: 350 3.07 .
0 ( 114.0)
n Ans= =
− −
DE: 2 2 2 1/ 2
[( 50) ( 50)( 75) ( 75) 3( 50) ] 109.0 MPa
σ ′ = − − − − + − + − =
350 3.21 .
109.0
n Ans= =
(e) ( )
2
2100 20 100 20
, 20 104.7, 15.3 MPa
2 2
A B
σ σ + − 
= ± + − = 
 

Shigley’s MED, 10th edition Chapter 5 Solutions, Page 2/52
1 2 3104.7, 15.3, 0 MPa
σ
σ
σ= = =
MSS: 350 3.34 .
104.7 0
n Ans= =
−
DE: ( ) 1/222 2
100 100(20) 20 3 20 98.0 MPa
σ  ′ = − + + − =
 
350 3.57 .
98.0
n Ans= =
______________________________________________________________________________
5-2 Sy = 350 MPa.
MSS:
σ1 −
σ3 = Sy /n ⇒ ( )1 3
yS
n
σ σ
= −
DE: ( )1/22 2 y y
A A B B
S S
n
n
σ σ σ σ σ
σ
′ = − + = ⇒ = ′
(a) MSS: 1 3
350
100 MPa, 0 3.5 .
100 0
n Ans
σ
σ= = ⇒ = =
−
DE: 2 2 1/2
350 3.5 .
[100 (100)(100) 100 ]
n Ans= =
− +
(b) MSS: 1 3
350
100 , 100 MPa 1.75 .
100 ( 100)
n Ans
σ
σ= = − ⇒ = =
− −
DE:
( ) 1/222
350 2.02 .
100 (100)( 100) 100
n Ans= =
 − − + −
 
(c) MSS: 1 3
350
100 MPa, 0 3.5 .
100 0
n Ans
σ
σ= = ⇒ = =
−
DE: 1/22 2
350 4.04 .
100 (100)(50) 50
n Ans= =
 − + 
(d) MSS: 1 3
350
100, 50 MPa 2.33 .
100 ( 50)
n Ans
σ
σ= = − ⇒ = =
− −
DE:
( ) 1/222
350 2.65 .
100 (100)( 50) 50
n Ans= =
 − − + −
 
(e) MSS: 1 3
350
0, 100 MPa 3.5 .
0 ( 100)
n Ans
σ σ= = − ⇒ = =
− −
DE:
( ) ( ) 1/22 2
350 4.04 .
50 ( 50)( 100) 100
n Ans= =
 − − − − + −
 
______________________________________________________________________________
5-3 From Table A-20, Sy = 37.5 kpsi

Shigley’s MED, 10th edition Chapter 5 Solutions, Page 6/52
5-6 Note: The drawing in this manual may not be to the scale of original drawing. The
measurements were taken from the original drawing.
(a)
σA = 25 kpsi,
σB = 15 kpsi
MSS:
4.37" 1.50 .
2.92"
OB
n Ans
OA
= = =
DE:
5.02" 1.72 .
2.92"
OC
n Ans
OA
= = =
(b)
σA = 15 kpsi,
σB = − 15 kpsi
MSS:
2.66" 1.25 .
2.12"
OE
n Ans
OD
= = =
DE:
3.05" 1.44 .
2.12"
OF
n Ans
OD
= = =
(c)
2
220 20
, ( 10) 24.1, 4.1 kpsi
2 2
A B
σ σ  
= ± + − = − 
 
MSS: 3.25" 1.34 .
2.43"
OH
n Ans
OG
= = = DE: 3.46" 1.42 .
2.43"
OI
n Ans
OG
= = =
(d)
2
212 15 12 15
, ( 9) 17.7, 14.7 MPa
2 2
A B
σ σ − + − − 
= ± + − = − 
 
MSS: 2.67" 1.16 .
2.30"
OK
n Ans
OJ
= = = DE: 3.06" 1.33 .
2.30"
OL
n Ans
OJ
= = =
(e) ( )
2
224 24 24 24
, 15 9, 39 kpsi
2 2
A B
σ σ − − − + 
= ± + − = − − 
 
MSS: 3.85" 0.96 .
4.00"
ON
n Ans
OM
= = = DE: 4.23" 1.06 .
4.00"
OP
n Ans
OM
= = =
______________________________________________________________________________

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Download Shigley’s MED Solution Manual Chapter 5 Failures Resulting from Static Loading and more Lecture notes Mechanical Systems Design in PDF only on Docsity!

Chapter 5

5-1 S

= 350 MPa.

MSS: σ 1

− σ 3

= S

/ n ⇒

1 3

S

σ σ

DE:

1/2 1/

2 2 2 2 2

A A B B x x y y xy

σ σ σ σ σ σ σ σ σ τ

S

(a) MSS: σ 1

= 100 MPa, σ 2

= 100 MPa, σ 3

σ = 0, σ = −11.0, σ = −114.0 MPa

MSS:

n = = Ans

DE:

2 2 2 1/ 2

σ [( 50) ( 50)( 75) ( 75) 3( 50) ] 109.0 MPa

n = = Ans

(e)

, 20 104.7, 15.3 MPa

A B

σ σ

1 2 3

σ = 104.7, σ = 15.3, σ =0 MPa

MSS:

n = = Ans

DE:

2 2 2

σ 100 100(20) 20 3 20 98.0 MPa

n = = Ans

______________________________________________________________________________

5-2 S

= 350 MPa.

MSS: σ

− σ

= S

/ n ⇒

1 3

S

σ σ

DE:

2 2 y y

A A B B

S S

σ σ σ σ σ

(a) MSS:

2 2

n = = Ans

(d) MSS:

1 3

100, 50 MPa 2..

σ = σ = − ⇒ n = = Ans

DE:

n = = Ans

( e ) MSS:

1 3

0, 100 MPa 3..

σ = σ = − ⇒ n = = Ans

DE:

2 2

n = = Ans

______________________________________________________________________________

5-3 From Table A-20, S y

= 37.5 kpsi

DE:

2 2 2

σ 24 24 24 24 3 15 35.4 kpsi

n = = Ans

______________________________________________________________________________

5-4 From Table A-20, S y

= 47 kpsi.

MSS: σ

− σ

= S

n = = Ans

(d) MSS:

1 3

0, 30 kpsi 1..

σ = σ = − ⇒ n = = Ans

DE:

2 2

n = = Ans

( e ) MSS:

1 3

10, 50 kpsi 0..

σ = σ = − ⇒ n = = Ans

DE:

n = = Ans

______________________________________________________________________________

5-5 Note: The drawing in this manual may not be to the scale of original drawing. The

measurements were taken from the original drawing.

______________________________________________________________________________

5-7 S

= 295 MPa, σ

= 75 MPa, σ

= − 35 MPa,

( a )

1/2 1/

2 2 2

A A B B

S

n Ans

σ σ σ σ

( b ) Note: The drawing in this manual may not be to the scale of original drawing. The

measurements were taken from the original drawing.

OB

n Ans

OA

______________________________________________________________________________

5-8 S

= 295 MPa, σ

= 30 MPa, σ

= − 100 MPa,

( a )

1/2 1/

2 2 2

A A B B

S

n Ans

σ σ σ σ

( b ) Note: The drawing in this manual may not be to the scale of original drawing. The

measurements were taken from the original drawing.

OB

n Ans

OA

______________________________________________________________________________

5-10 S

= 295 MPa,

, 40 3.8, 91.2 MPa

A B

σ σ

( a )

1/2 1/

2 2 2 2

A A B B

S

n Ans

σ σ σ σ

( b ) Note: The drawing in this manual may not be to the scale of original drawing. The

measurements were taken from the original drawing.

OB

n Ans

OA

______________________________________________________________________________

5-11 S

= 295 MPa,

, 10 30.9, 80.9 MPa

A B

σ σ

( a )

1/2 1/

2 2 2

A A B B

S

n Ans

σ σ σ σ

( b ) Note: The drawing in this manual may not be to the scale of original drawing. The

measurements were taken from the original drawing.

OB

n Ans

OA

______________________________________________________________________________

5-12 S

= 60 kpsi, S

= 75 kpsi. Eq. (5-26) for yield is

3 1

yt yc

S S

σ σ

−

( a )

1 3

σ = 25 kpsi, σ = 0 ⇒

n Ans

−

( b )

1 3

σ = 15, σ = −15 kpsi ⇒

n Ans

−

OH

n Ans

OG

( e )

, 15 9, 39 kpsi

A B

σ σ

OJ

n Ans

OI

______________________________________________________________________________

5-14 Since ε f

0.05, and S

≠ S

, the Coulomb-Mohr theory for ductile materials will be

used.

( a ) From Eq. (5-26),

1 3

yt yc

n Ans

S S

σ σ

−

( b ) Plots for Problems 5-14 to 5-18 are found here. Note: The drawing in this manual

may not be to the scale of original drawing. The measurements were taken from the

original drawing.

OB

n Ans

OA

______________________________________________________________________________

5-15 ( a ) From Eq. (5-26),

1 3

yt yc

n Ans

S S

σ σ

−

( b ) The plot for this problem is found on the page for Prob. 5-14. Note: The drawing in

this manual may not be to the scale of original drawing. The measurements were taken

from the original drawing.

OD

n Ans

OC

______________________________________________________________________________

, ( 75) 160, 35 kpsi

A B

σ σ

( a ) From Eq. (5-26),

1 3

yt yc

n Ans

S S

σ σ

−

( b ) The plot for this problem is found on the page for Prob. 5-14. Note: The drawing in

this manual may not be to the scale of original drawing. The measurements were taken

from the original drawing.

OF

n Ans

OE

______________________________________________________________________________

, 50 47.7, 157.3 kpsi

A B

σ σ

( a ) From Eq. (5-26),

1 3

yt yc

n Ans

S S

σ σ

−

( b ) The plot for this problem is found on the page for Prob. 5-14. Note: The drawing in

this manual may not be to the scale of original drawing. The measurements were taken

from the original drawing.

OH

n Ans

OG

______________________________________________________________________________

, ( 75) 180.8, 24.2 kpsi

A B

σ σ

( a ) From Eq. (5-26),

BCM: Eq. (5-31 b ),

n Ans

−

MM: σ

≥ 0 ≥ σ

, and | σ

/ σ

| ≥ 1, Eq. (5-32 b ),

1 1

uc ut A B

uc ut uc

S S

n Ans

S S S

σ σ

− −

( e )

, ( 15) 5, 35 kpsi

A B

σ σ

BCM: Eq. (5-31 c ),

S

n Ans

MM: Eq. (5-32 c ),

S

n Ans

______________________________________________________________________________

5-20 Note: The drawing in this manual may not be to the scale of original drawing. The

measurements were taken from the original drawing.

( a ) σ

= 25, σ

= 15 kpsi

BCM & MM:

OB

n Ans

( e )

, ( 15) 5, 35 kpsi

A B

σ σ

BCM and MM:

OM

n Ans

OL

______________________________________________________________________________

5-21 From Table A-24, S ut

= 31 kpsi, S

= 109 kpsi

BCM: Eqs. (5-31), MM: Eqs. (5-32)

( a ) σ

= 15, σ

= 10 kpsi.

BCM: Eq. (5-31 a ),

S

n Ans

MM: Eq. (5-32 a ),

S

n Ans

( b), ( c ) The plot is shown below is for Probs. 5-21 to 5-25. Note: The drawing in this

manual may not be to the scale of original drawing. The measurements were taken from

the original drawing.

BCM and MM:

OB

n Ans

OA

A B

σ σ

( a ) BCM: Eq. (5-31 b ),

n Ans

−

MM: Eq. (5-32 b ),

1 1

uc ut A B

uc ut uc

S S

n Ans

S S S

σ σ

− −

( b ), ( c ) The plot is shown in the solution to Prob. 5-21.

BCM:

OL

n Ans

OK

MM:

OM

n Ans

OK

______________________________________________________________________________

5-26 S

= 36 kpsi, S

= 35 kpsi

BCM: Eq. (5-31),

( a ) σ

= 15, σ

= − 10 kpsi.

BCM: Eq. (5-31 b ),

n Ans

−

( b) The plot is shown below is for Probs. 5-26 to 5-30. Note: The drawing in this manual

may not be to the scale of original drawing. The measurements were taken from the

original drawing.

OB

n Ans

OA

______________________________________________________________________________

5-27 S

= 36 kpsi, S uc

= 35 kpsi

BCM: Eq. (5-31),

( a ) σ

= 15, σ

= − 15 kpsi.

BCM: Eq. (5-31 b ),

n Ans

−

( b ) The plot is shown in the solution to Prob. 5-26.

OD

n Ans

OC

______________________________________________________________________________

5-28 S

= 36 kpsi, S

= 35 kpsi

BCM: Eq. (5-31),

( a )

, ( 8) 16, 4 kpsi

A B

σ σ

BCM: Eq. (5-31 b ),

n Ans

−

( b ) The plot is shown in the solution to Prob. 5-26.

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Shigley’s MED Solution Manual Chapter 5 Failures Resulting from Static Loading, Lecture notes of Mechanical Systems Design

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Chapter 5

5-1 S

= S

S

DE:

S

DE:

DE:

MSS:

DE:

MSS:

DE:

MSS:

DE:

______________________________________________________________________________

5-2 S

= S

S

DE:

S S

DE:

[100 (100)(100) 100 ]

DE:

DE:

DE:

DE:

______________________________________________________________________________

DE:

______________________________________________________________________________

= S

S

DE:

S S

DE:

[30 (30)(30) 30 ]

DE:

DE:

DE:

DE:

______________________________________________________________________________

OB

OA

OD

OC

DE:

OE

OC

OG

OF

DE:

OH

OF

OJ

OI

= = = , DE:

OK

OI

OM

OL

= = = , DE:

ON

OL

______________________________________________________________________________

5-7 S

S

OB

OA

______________________________________________________________________________

5-8 S

S

OB

OA

______________________________________________________________________________

5-10 S

S

OB