Section 6 - Combined Stresses.pdf

7/25/2019 Section 6 - Combined Stresses.pdf

1/133

SECTION 6 COMBINED STRESSES

Page 1 of 133

ECCENTRIC LOADING (NORMAL STRESSES)

DESIGN PROBLEM

361. I

. I 2500 .

2 . T

= 2 . . F AISI

C1022, , 3, ?

S:

2500=

2=

52.=

=

F AISI C1022, , 52= (T AT7).

0002626

2

52,====

23 ==

( ) 423

25212

3

12

.===

512

.==

5152512

... +=+=+=

=

( )( )

++=

42252

515152

3

1250000026

.

...,

++=

3251

5152

3

1250000026

.

..,

B :

8

56250 == .

( ) 8

718751625033 ==== ..


2/133


Page 2 of 133

362. A 361 0 3000 .;

AISI 1045, , = 0.5 .

; 3. D = 2 S

.

S:

S L:

+=

1

F AISI 1045, (T AT 7).

59= 96=

4850 == .

S = 0.85

L () = 0.80

( )( ) 643248800850 ... ==

( ) 1500030002

1=+=

( ) 150003000

2

1==

5150512

... +=+=+=

+=

1

( )( )

++=

32 242

515150

3

11500

.

...

++=

3251

5150

3

11500

.

..

+=

1

( )( )

++=

32242

515150

3

11500

.

...

++=

3251

5150

3

11500

.

..

+=

1


3/133


Page 3 of 133

++

+=

32 51

5150

3

1

64032

1500

00059

1500

2

1

.

..

,,

00751

5150

3

132

..

..=

++

B :

530.= ( ) 59153033 .. ===

U = 9/16 1 5/8

363. T 362, , 3 3 .

S:

( ) 0332

1==

( ) 3332

1=+=

+=

1

( )( )

++=

32242

515150

3

11500

.

...

( ) 051

5150310

32 =

++=

...

+=

1

( )( )

++=

32242

515150

3

13

.

...

++=

3251

5150

3

13

.

..

+=

1

++

+=

3251

5150

3

1

6432

30

2

1

.

..

.

44551

5150

3

132

..

..=

++

B :

59050.=


4/133


Page 4 of 133

( ) 771515905033 .. ===

U = 5/8 1 13/16

364. A (S F. 8.3, T), SAE 1020, ,

9 . 16 3 .

. L = 3. () W = 0.75? () W ?

S:

.

T J.B. J

=

2

2

41

F SAE 1020, , ksisy 48=

61030=

T

( )111

48000

103022 21

622

1

2

=

=

=

2=

1089 ==

( ) 21610822 ===

=

( ) ( )[ ]64

68360

64

750

64

44444

..=

=

=

( ) ( )[ ] 22222 109375075044

.. ===


5/133


Page 5 of 133

312501093750

64

68360

2

4

..

.

==

( )

=

=

=

2

2

32

2

2

2

236319

1

564246

10304

31250

21648

1

1093750

16

41

.

.

.

.

+=

50

2.==

3=

16=

16

3

48===

( )( )

+

==

64

68360

50316

363191

564246

164

2

2

.

.

.

.

3

2

222715

363191

564246

16

.

.

.

+

==

B

233.=

( ) 0094123331250 ... ==

111214

00941

2162>===

.

T E

2

2

=


6/133


Page 6 of 133

( )

2

2

2

206580

31250

2163

00030.

.

,=

=

+=

( )( )3

2

4

2 22715206580

64

68360

5031620658016

..

.

.. +=

+=

8023.=

( ) 851528023750750 .... ===

T :

( ) 188125180233125031250 .... ===

1111821881251

216>==

.

U = 3 13/16 , = 2 13/16

.

F , E .

=

64

4

=

4

2

=

2504

1

4

642

4

.===

2

2

=

( )

2

2

2

13220

250

2163

00030.

.

,=

=

+=

( )( )3

2

4

2 48913220

64

503161322016

+=

+= .

..

B .


7/133


Page 7 of 133

2213.=

( ) 8052502213250250 .... ===

111268805250

216>==

.

U = 3 .

365. T 364, 15 .

S:

E E:

( )( ) 360121522 ===

16=

3=

.

64

683604

.=

21093750 .=

31250.=

2

2

=

( )

2

2

2

074370

31250

3603

00030.

.

,=

=

+=

( )( )3

2

4

2 22715074370

64

68360

5031607437016

..

.

.. +=

+=

6243.=

( ) 71826243750750 .... ===

T :

( ) 1325162433125031250 .... ===

111191

13251

216>==

.

U = 3 5/8 , = 2 5/8


8/133


Page 8 of 133

.64

4

=

4

2

=

250.=

2

2

=

k

LN

Es

e

e

( )

2

2

2

04760

250

3603

00030.

.

,=

=

+=

( )( )3

2

4

2 48904760

64

503160476016

+=

+= ..

.

B .

1583.= 3 3/16

( ) 789501583250250 .... ===

11127478950

216>==

.

U = 3 3/16 .

366. A : = 8 , = 20 . = 30

; 2024T4; = 2.6 . I

1 3/8 . D

. T

.


9/133


Page 9 of 133

S:

A (2024T4), 47=

o30 =

o30=

( )

o30+=

o30 ==

=2

2

=

12

3

=

222

3066

o==

o301

=

21 +=

2

30630

oo +=

18

62

47===

.

8=

37518

31 .==

20=

2

30630

oo +=


10/133


Page 10 of 133

( ) ( )( )2

3751

302086

3751

30818

.

.

oo+=

0483147524 2 = ..

8

7

58775 = .

274

8

31

8

75

.==

T, 8

75= ,

8

31=

367. A 15 . 2= 50,000 . A = 8 .

( 1= 0). S I

3 . T . S

.

S:

U C1020, , = 48

S F

+=

21

2

50000502 === ,

8=

3=

00030,=

2

=

( )( ) 360121522 ===


11/133


Page 11 of 133

( ) ( )

( )( )

( )( )

+

00030

503

2

36028

1503

482 ,

F S M, 3

E F.S. S A. P, T B2, . 640,

WF S .T W360 51,

= 6450 2= 10 2

= 355 = 14

= 148 = 5.83

= 1.41 1084= 338.8 4

S,

( ) ( )

( )

( )( )

( )( )

+833800030

503

2

360

835

2

148

110

50348

2 .,

.

084748 .

T I W14 34 . (E )

= 10 2

= 14

= 5.83

= 338.8 4

368. T 367, 1= 50,000 .

S:

U C1020, , = 48

3=

00030,=

( )( ) 360121522 ===

T P

( )111

48

0003022 21

22

1

2

=

=

=

,

50000501 === ,


12/133


Page 12 of 133

C J.B. J F

==

2

2

14

1

=

2

2

1

41

( )

( )

000304

36048

1

50348

2

2

,

2

254951

15048

.

F S M, 3E F.S. S A. P, T B2, . 640,

WF S .

T W310 21,

= 2690 2= 4.17

2

= 117 = 4.61

S,

( )

2614

254951174

150

48

.

..

( )

2614

254951174

15048

.

..

84748 .

C JB J F

111178614

360


13/133


Page 13 of 133

CHECK PROBLEMS

369. A , F. 191, T, 10 7

. . I 1 .

6 .,

?

S:

+=

10=

102

67 =+=

32

6==

( )( ) 212612 ==

( )( ) 43

3612

612 ==

+=

( )( )( )29

36

31010

12

10.=+=

370. A (6061T6) C, ( F.

8.4, T). O T ( T

AT 1): = 1 1/16 , = 17/32, = 1/8, = 1/8. T 2 3/8 .

. () F = 3 ,


14/133


Page 14 of 133

( )? () A

?

S:

AA 6061T6, 40= (T AT 3)

S F. 8.4, (C) T

+=

+=

1

F T AT 1 (T)

( ) +=

( ) ( ) 22

22

1212

+++=

06251.=

531250.=

1250.=

1250.=

93750125006251 ... ===

F 1 :

( ) ( ) ( )

+

+=+

221

( )( ) ( )( )[ ] ( )( )

( )( )12505312502

1250

1250937502

93750125012509375012505312501

...

...

.....

+

+=+

401601 .=

66090401600625112 ... ===


15/133


Page 15 of 133

339102

125040160

21 .

.. ===

192150401602

937501250

21 ..

.. =+=+=

( ) += ( )( ) ( )( ) 21836012500625112501250531250 ...... =+=

( ) ( ) 22

22

1212

+++=

( )( )( )( )( )

( )( )

( )( )( ) 42

22

2

020630192150937501250

12

937501250339101250531250

12

1250531250

....

.....

..

=+

++=

401601 .==

77662401603752 ... =+=

.

13

3

40===

( )( )

+==

020630

4016077662

18360

113

.

..

.

2182180 == .

. 40==

( )( )

+==

020630

4016077662

18360

140

.

..

.

6726720 == .

371. A C (F. 8.5 T) , ASTM

A2758 . T

12 . . T

: = 3 ., = 6 ., = 5 ., = == 1 . D = 6

.


16/133


Page 16 of 133

S: 3=

6=

5=

1===

( ) ++=

( )( ) ( )( ) ( )( ) 21211165131 =++=

F 1 :

( )

+

+

=

2221

( ) ( )( ) ( ) ( )( )

+

+

=

2

1613

2

6116

2

115121

58321 .=

41735832612 .. ===


17/133


Page 17 of 133

( )

417058322

116

2211 .. =

+=

+=

=

91722

14173

22 .. ===

08322

15832

21 .. ===

( )( ) 2

32

32

3

121212

+++

++=

( )( )( )( )( )

( )( )( )( )( )

( )( )( )( )( )2

32

32

3

08321512

1541701161

12

1161917213

12

13... +++

++=

4

9253 .=

F ASTM A2758 A C S

60=

106

60===


18/133


Page 18 of 133

+=

1

58321 .==

58314583212 .. =+=

( )( )

+= 9253

583258314

12

1

10 .

..

7891278912 ,. ==

372. I (366), = ., = 2 ., = 2 ., = 18 ., = 60. T A B B

; AISI C1020, . W = 3

?

S:

R P. 366.

2

6

+=

+=

2

6

F AISI C1020, , 48= .

16

3

48===

50.=

2=

18=

o60=

( )( )

( )

( )( )

+=

2

250

60186

250

6016

.

.

5745740 == .

373. T 1= 2.1 ; = 0.5 ., = = = 2 ., =

18 .; AISI 1040, (10% ). T

2 A; 2 0 ,


19/133


Page 19 of 133

. F = 1.5 S ,

2? A .

S:

50.=

2===

18=

121 .=

= 0 ( ) 21 +=++

++

+=

21

= 0 = 1

= 0 2=

F 02 = :

( )( ) 1910

2182

0122.

.=

++

+=

90911910121 ... ===

02 ==

( ) +==

( )( )

++

++=

21

02 =


20/133


Page 20 of 133

( ) ( )( )[ ] =

++

++= 823

2182

0122218.

.

L 22 =

2823. +=

( ) ( )[ ]( )2

2 128212182

2122218

+=

++

++= ..

.

( )2

2 9108232

82312821

..

...+=

++=

2

823. =

( )2

2 9102

82312821

.

...=

+=

250 .==

F SAE AISI 1040 C D (10% W)

85=

54=

( ) ( )( ) 94585054 .. ===

+=

++

+==

( )( )( )

( )( )

( )( )

( )( )

++

++

=250

50

3

1

1910

945

85

250

50

3

1

112821

51

85 2222

.

..

..

...

.

78532 .=

376. A , = 12 . , 10. , 40, (=

10.75 ., = 10.02 ., = 3.67 .,= 11.908 2., = 160.7

4

.,= 29.9

3

.). T = 15 .; = 3; AISI C1015, . ()

U , () .

() J S ,

. () D . () S

.


21/133


Page 21 of 133

S:

F AISI C1015, .

545.=

61=

( ) 530615050 ... ===

7510.=

0210.=

12=

673.=

290811 .=

407160 .=

3929 .=

3=

.

A ()

( )( ) 288121222 ===

120578673

288


22/133


Page 22 of 133

( )( )

( )

=

000304

578545190811

2

21

,

...

0991

.

=

=2

15=

( )

2929

152

==

.

21 +=

20993

545 +=

.

.

8632486324 ,. ==

.

V : = , =

02

=

=

( )

=

=

2

+=

A = 0.80

( )( )( ) 7420800850530 .... ===

++

+=

( ) ( )

2529081929

15

7420

5450 .

...

.=

++==

2523

545.

.=

6740746 == .

.

S F

+=

21

2

=


23/133


Page 23 of 133

3545

929

07160.

.

.===

( )( )

( )9635

673

35451522

..

.==

( )( )

1138200716000030

3

2

288

2 .., ==

2520

90811

3.

.==

+=

21

2

( ) 113820963512520545 .... +== 50022522 ,. ==

.

6740 .

377. A (367) 14. 193., I ( =

56.73 . ., = 15.5 ., = 15.710 ., = 2402.4 4., = 930.1

4., = 4.05 .). T , 40 . ,

(1= 0) . F = 12 . = 4,

2?

S:

U :

+=

21

2

442402 . ==

00030,=

12=

506. ==

( )( ) 960124022 ===


24/133


Page 24 of 133

148=

4= 27356 .=

7572

515

2.

.===

F C1020, , ,

48=

( )( )

( ) ( )( )

+==

4240200030

4

2

460

506

757121

7356

448

2 .,

.

.

.

( ) 1130802210705048 ... += 90010491042 ,. ===

378. A 14. 193., I (= 56.73

. ., = 15.5 ., = 2402.4 .4, = 930.1 .4, = 4.05 ., = 40

.). I 2 = 4 . ( 1=

0), 4? F = 15.71 .

S:

U :

+=

21

2

2=

27356 .=

4=

85572

7115

2.

.===

054. ==

00030,=


25/133


Page 25 of 133

41930 . ==

( )( ) 960124022 ===

4=

48=

( )( )( ) ( )( )

+==

1930000304

2960

054855741

7356448 22

2

.,

..

.

)22 181740554010705048 ... += 8806888682 ,. ==

379. T 378, 1= 0.5 2.

S:

12

2

2

21 +

+==

21 50 .=

( )7356

5018174055401

73564

48 22

2

.

...

.

++=

) 222 00881401817405540101763012 .... ++=

222 1817400097670026444012 ... +=

B T :

56682 .= 283450 21 .. ==

380. T (SAE 080) ( )

, = 2 ., = .,

. S T (

), . () W ?

E. () W = 3 ?


26/133


Page 26 of 133

S:

F SAE 080, ksisy 40=

()

T

.

()

313

3

40.===

R :

==

( )( )250313

..

=

313.=

T:

2= , 50.=

( ) ( ) ( ) 275125050250 .... =+=+=

( ) ( )

+

+=

22

11

( ) ( ) ( ) ( )

+

+=

2

5025050502

2

1502507511

.......

678601 .=

3214167860212 .. ===

( ) ( ) 571405022

132141

2

12 ... ===

428602

5067860

21 .

.. ===

( ) ( ) 2323

1212

+++=

( )( )( )

( )( )( )2

32

3

4286050212

5025714050250

12

50250..

....

..+++

=

459.0 inI=


27/133


Page 27 of 133

+=

678601 .==

67860.==

( )( )

+=590

67860678607511313

...

..

9416.=

COPLANAR SHEAR STRESSES

381. T 5 . T

SAE 1020, . T = 5000 ., = 3 ., = 0, = 5 .;

= 3. D D

3 .

S:0=

F SAE 1020, .

48=

60.=

3=


28/133


Page 28 of 133

2

12

21

5

+=

212 =

21 2 =

[ ] = 0 ( ) ( ) ( ) ( ) +=+ 2222 21

0=

3=

3=

5=

5=

21 2 =

( )( ) ( ) ( )( ) ( )36055532324 22 +=+ o

2530 2 =

6

52 =

3

5

6

522 21 =

==

2

4

=

=

60.==


29/133


Page 29 of 133

=

60.

2

1

2

21

560

+

=.

( )

2

2

1

22

4

5

5

3

5

3

4860

+

=.

2

2

1

2

78540

17782

69

.

.

.

+

=

B .

8

56250 == .

F , t.

=

=

( )

852

5

5

62503

5

5

5

3

52

1

222

122

..

=

+

=

+

=

==

6250

852

3

48

.

.=

4

12850 == .

382. T 383, = 30.


30/133


Page 30 of 133

S:

2

1

1

2

2

1120

52

5

+=

o

2

1

1

2

21 60

52

5

+

+=

o

[ ] = 0 ( ) ( ) ( ) ( ) +=+ 2222 21

( )( ) ( ) ( )( ) ( )36305530532324 22 +=+ oo ( ) 1514151257652130 2 ... +=+=

30

1514152

.+=

4720502

.. +=

94401

47205022 21

... +=

+==

=

60.==

=

60.

2

1

1

2

21 60

52

560

+

+

=

o.


31/133


Page 31 of 133

( )

2

2

1

22

4

605

5944012

5

594401

3

4860

++

+

+

=

o..

.

2

212

7854.0

60cos944.0

121944.0

1

6.9D

DD

+++

+

=

o

B . 6410.=

S 8

56250 == . ( 381).

F t.

2

12

609440

1219440

1

+++

+=

o..

13253606250

9440121

6250

94401

2

12

..

.

.

.=

+++

+=

o

=

==

6250

13253

3

48

.

.=

16

5313250 == .

383. D , , F

= 1500 . = 18 . = 0. L ,

, 6, ; SAE 1020, ,

; = 2.5 . T

. T :

.


32/133


Page 32 of 133

S:o0= , 6==

( ) 362

1==

41

+=

=

F SAE 1020, , 48= .

52.=

60.=

( )

5211

52

486060.

.

..====

( ) +=14

( ) ( ) 3185134 1 += .( )

+=

637501

.

( )750

252

4

5163750.

...+=+

+=

2

4

1 =


33/133


Page 33 of 133

=

2

4

1

750252

5211

..

.

+

=

16

1168750 == .

==

750

252

52

48 .

.

.

+

=

68750

75068750

252

219

.

..

.

.

+

=

16

5=

384. T 383, = 45.

S:

5211.= , 219.=


34/133


Page 34 of 133

o

454

24

1

2

21

2

+

+=

( ) ( ) ( ) 3184551334 1 +=+= o.

( )

+=

6265201

.

( ) ( ) o

454

516265202

4

5162652022

2

....

++

+

+=

( )

+++

+=

614062501406250

6265202

2..

.

2812508437506

07030

2

2.

.. ++

+=

=

2

2

12

4

1

281250843750607030

5211

++

+

=

...

.

5940.=

59375032

19.==

2213281250593750

843750

593750

593750607030

2

12

...

.

.

.. =

++

+=

=

=219.

593750

2213219

.

.. =

int 2815.0=

4

1= .

385. T (381) SAE 1020 , ,

. SAE 1022 , . T .,

= 2 ., = 6 ., = 4 ., = 0. F 5 .


35/133


Page 35 of 133

S:

P, SAE 1020, (T AT 7)

65=

135

65===

=

( )( ) 3152

1

4

313 .=

=

R, SAE 1022, (T AT 7)

54=

8105

54.===

774

4

4

3

810

4

2

2

.. =

=

=

774.=

F 381.

2

12

21

5

+=

21 2FF =

( ) ( ) =+ 21 222

( )( )( ) ( ) ( )652252222 22 =+

.. 625 2 =

2402 .=

( ) 48024021 .. ==

( ) ( )22

22774

5480 .. =

+=

lbskipsF 173,9173.9 ==


36/133


Page 36 of 133

386. T 385, = 90.

S:

774.=

51

+=

21 2 =

( ) ( ) ( ) =+ 2222 21

( )( )( ) ( ) ( )[ ]452252252222 22 =+ ...

=225

0402 .=

0801 .=

5080774

+== ..

00017,=


37/133


Page 37 of 133

387. T AISI 1020 , , I (AISI

1020, ) AISI C1015,

. T I .,

., = 8.5 ., = 11.5 . = 4.5 ., = 4 . F 2= 0,

1 = 2.5 .

S:

4

3=

2

1=

58.=

511.=

54.=

4=

P, AISI 1020 S, , 48=

R, AISI C1015, , ( ) 8376360 .. ==

219

52

48.

.===

1215

52

837.

.

.===

( ) ( ) 6222

1

4

3219 .. =

==

6864

3

412154

22

.. =

=

=

U

6864

3

41215

4

22

.. =

=

=

02 = ,


38/133


Page 38 of 133

22

2

32

+

=

22

2

3

54

2

4

+

=

.

52.=

=

3

2

=

3

2

+=

+

3

22

31

( )

( )

52

3

542

5223

5458

2

1.

.

..

.

+=

+

8601 .=

860

1

.

=

3

=

60052

354.

.

. ==

+

+=

32

3

1

2

122

( )6003860

23860

11

2

1

2

12 ...

+

+

=


39/133


Page 39 of 133

13891 .=

13891686 .. ==

841 .= .

388. T 387, 1= 0, 2 .

S:

686.=

3

2 +=

( )32

=

+

=

2

32

32

( ) ( )

( )

+

=

3

542

522

3

542

3

54511

2

2.

....

716702 .=


40/133


Page 40 of 133

2413

71670.

.=+=

241686 .. =

3875.=

NORMAL STRESSES WITH SHEARDESIGN PROBLEMS

389. T . L = 5 ., = 30,=1500 .; C1022, . () C

(5.1), T. () A

0.7, ()

, () . () C

.

S:

()

E. 51,6

23

= ,

<

4

3

[ ] = 0 ( ) ( ) ( ) ( ) +=+ 3392

( )( )( ) ( )( )( )2553015003301500318 . o

o

+=+

9070318 =+

39

=

3=


41/133


Page 41 of 133

907018 =+

4477.=

F C1022, , 00052,=

6

23

=

6

000524477

23

,. ==

214480 .=

S

S 2

1= , UNC, 214190 .=

()

+=

( ) 76439000527014190

4477,,.

.

.=+=

( )( )

305214190

33015003===

.

o

()

M

21222

122

200052

3052

00052

76439

2

1

+

=

+

=

,,

,

2931.=

()

O

2

1222

122

300052

3052

00052

76439

3

1

+

=

+

=

,,

,

2961.=

()

M = 39,764 .

390. F , ( ) = 3,

( ); = 2.3 , = 0, = 17

., = 1 ., = 14 .; AISI 1015, . C ()

, () , ()

.

=


42/133


Page 42 of 133

S:

+=

12

5145151

12

... +=

12 093750 .=

( ) ( ) =++ 212

( ) ( ) ( )( )173251093750514512 11 ..... =++

216511 .=

216511 .==

76670

3

32

3

..===

F AISI 4015, . 545

.=

()

M

2

122

1

+

=

( ) 75225455050 .... ===


43/133


Page 43 of 133

2

122

7522

76670

545

21651

3

1

+

=

.

.

.

.

212910 .=

22

129104

.==

40540.=

8

3=

()

5869176670

2

21651

2

21651

22

2

122

1

2

2....

=

+

+=

+

+=

=

1

=

3

54558691 ..=

210460 .=

22

104604

.==

3650.=

83=

()

27263

545

3.

.===

2

12

2726

76670

545

21651

3

1

+

=

.

.

.

.

2118740 .=

22

1187404

.==

38880.=

8

3=


44/133


Page 44 of 133

392. T 390, 2 . 1

. .

S:

+=

12

514515112

... +=

12 093750 .=

( ) ( ) 12 2093750251 .. =

12 150 .=

( ) =++ 212

( ) ( ) ( )( )173251150162 11 ... =+

213311 .=

213311 .==

76670

3

32

3

..===

F AISI 4015, . 545.=


45/133


Page 45 of 133

()

M

2

1

22

1

+

=

( ) 75225455050 .... ===

2

122

7522

76670

545

21331

3

1

+

=

.

.

.

.

212890 .=

22

128904

.==

40510.=

8

3=

()

5843176670

2

21331

2

21331

22

2

122

1

2

2....

=

+

+=

+

+=

=

1

=

3

54558431 ..=

210450 .=

22

104504

.==

36480.=

8

3=

()

27263

545

3.

.===

2

12

2726

76670

545

21331

3

1

+

=

.

.

.

.

211860 .=


46/133


Page 46 of 133

22

118604

.==

38860.=

8

3=

393. T 390, A; = 8

. T 12 . .

S:

2

22

36

+=

2

22

3

5146

+= .

7057.=

32

21

=

( )1

112 25461

70573

5142

3

2

.

.

.=

=

=


47/133


Page 47 of 133

( )

+=

3

228 21

( )( ) ( ) ( )

+=

3

51422546170572832 11

....

668201 .=

778707057

66.

. ===

+

+=

32

31

2

21

2

( ) ( ) ( )778703

32668202

3

3266820

2

22.

..

..

+

+=

35361.=

35361.==

()

2

122

1

+

=

F P 390.

21651.

=

545.=

7522.=

3=

2

122

7522

35361

545

21651

3

1

+

=

.

.

.

.

219570 .=

22

195704

.==

50.=

2

1=

()

10235361

2

21651

2

21651

22

2

122

1

2

2....

=

+

+=

+

+=

=

1


48/133


Page 48 of 133

=

3

545102 ..=

213850 .=

22

138504

.==

420.=

16

7=

() ksisys 27.26=

2

12

2726

35361

545

21651

3

1

+

=

.

.

.

.

217420 .=

22

174204

.==

4710.=

2

1=

394. T SAE 1020, , SAE 1015,

. T = 20 , = 7 ., = 60. L ( ) 2.() D . () C

. () D

. I

? G , . (N

.)

S:

B: SAE 1020, , 48=

R: SAE 1015, , 63=


49/133


Page 49 of 133

2=

()

B.

( )( )

+= 2

4

4=

( )

3335

12

43

.==

( )( )( )

3335

276020

4

6020

2

48

.

oo+===

2751.=

4

11=

()

62

12 =

21 3 =

( ) ( ) ( )( ) ( )( )360602263 21 oo +=+ ( )( ) ( ) ( )( )( ) ( )( )( )360207602022633 22 oo +=+

1022 .=

( ) 31610233 21 .. ===

2

5

6020

5===

7749

5

6020316

5

601 ..=+=+=

2

1

22

1

+

=

63=

M. : ( ) 531635050 ... ===

2

122

531

2

63

7749

2

1

+

=

.

.

233530 .=


50/133


Page 50 of 133

22

335304

.==

6530.=

4

3=

O ,

37363

63

3.===

2

122

3736

2

63

7749

2

1

+

=

.

.

232920 .=

22

329204

.==

64740.=

4

3=

() S

( )

=

5

51.= , 48=

750.=

20=

( )

==

5

( )( )517505

6020

2

48

..

=

8060.=

8

7= 2


51/133


Page 51 of 133

A 2 7/8 .

CHECK PROBLEMS

396. () I 5/8 . , = 0, = 14 . =

2 ., = 18 .,

= 10 . () F , ,

( ).

S:


52/133


Page 52 of 133

+=

12

1822

12

+=

12 10 .=

( ) ( ) =++ 212

( ) ( ) ( )( )14102101822 11 =++ .

842531 .=

( )

52512

62504

84253

4

22

11 .

.

.====

( )

86510

62504

3

10

433 22

.

.

=

=

==

() ( )

54112865102

52512

2

2

1

222

1

2

2

...

=

+

=

+

=

( )

80418865102

52512

2

52512

22

2

1

222

1

2

2

....

=

+

+=

+

+=

()

N B, , 48= .

2

122

1

+

=

M. ; ( ) 24485050 === ..


53/133


Page 53 of 133

2

122

24

86510

48

525121

+

=

..

9141.=

O ;

71273

483

.===

2

122

7127

86510

48

525121

+

=

.

..

1232.=

397. T , .

. .

S:

+=12

12

+=

1

1

2

2

+=


54/133


Page 54 of 133

1

2

1

22

+=

11

2

2 04440750

50

182

2 .

.

.=

+=

( ) ( ) =++ 212

( ) ( ) ( )( )14102044401822 11 =++ .

49231 .=

( )

90437

7504

4923

21

1 .

.

.===

( ) ( )

269

5004

7504

2

10

2 2221.

..

=

+

=

+=

() ( )

068102692

90437

2

2

1

222

1

2

2

...

=

+

=

+

=

( )

02142692

90437

2

90437

22

2

1

222

1

2

2

....

=

+

+=

+

+=

()

2122

1

+

=

M. ; ( ) 24485050 === ..

2

122

24

269

48

904371

+

=

..

3842.=

O ;

71273

48

3 .===

2

122

7127

269

48

904371

+

=

.

..

6842.=


55/133


Page 55 of 133

398. W . ,

C1015, = 3; = 0, = 1 , = 9, = 14,= 9, = 12 .? C . C

.

S:

F , C1015, 63= .

21=

+

51951

21

..

=

+

21 7 =

o0=

( ) =++ 213

( )( ) ( ) ( )145195173 22 =++ ..

063102 .=

441707 21 .==

( )

===

2

1

7504

44170

.

.


56/133


Page 56 of 133

( )

56590

7504

44 2

.

.

=

==

2

122

1

+

=

M. ; ( ) 531635050 ... ===

2

122

531

56590

633

1

+

=

.

.

913.=

O ;

37363

63

3.===

2

1

22

3736

56590

633

1

+

=

.

.

15=

399. T 2., UNC 20 .

T = 12 , = 60, = 0; = 24 ., = 20 ., = 15 .; AISI C1137 . () W ? () W

8 . 2 .

2 . ? (S 5.9, .) () W

? () C

, , .

S:

() =

20.=

2=

= 20

( ) 22020 .=


57/133


Page 57 of 133

50=

() o60=

( ) ( )( ) o60= ( ) ( )( )2060122024 o=

30=

+=

=

=

F 2UNC2

502 .= W = 3 .

2512

52.

.==

( )

534332

34

2

.==

( )

847

53433251

25130 .

..

.=

+=

()

1423502

84750

..

.

=

+

=

+

=

16452

6012.

.

===

o

( ) ksiss

s3.1216.4

2

14.23

2

2

1

2

22

1

2

2

=

+

=

+

=

( )

87231642

1423

2

1423

22

2

1

222

1

2

2

....

=

+

+=

+

+=

() F C1137, , 55=

=

558723 =.


58/133


Page 58 of 133

3042.=

M S:

50.=

( )5550312 .. =

2362.=

O ,

75313

55

3.===

2

122

1

+

=

2

122

7531

164

55

14231

+

= .

..

2692.=

400. T ., UNC ASTM

A325, ; = 26 ., = 6 ., = 4 ., = 0. T

0.6

(= , 5.8, ). W () , ()

? W = 1.5

HM ?

S:

F ASTM A325, HT, . UNC

88=

85=

( ) 51856060 === ..


59/133


Page 59 of 133

2222

2

3

6

2

4

32

+

=

+

=

832.=

()

L , A

()

L , A

( )3212

=

( ) ( ) 111

2 70750362

832

32

.

.===

+=

+

3

2

3

22 12

( )( )( ) ( ) ( )

+=

+

3

6226

3

62832707502 11 ..

7531 .=

143

7533

1 .. =+=+=

F UNC, 214190 .=

29

14190

14===

.

.

51==

B HM C.

( ) ( )2

1

2

2

21

2

1

+

+++

=


60/133


Page 60 of 133

51==

0=

29=

30.=

( ) ( )2

1

2

2

21

2

1

+

+++

==

( ) ( ) ( )2

1

22

292

5130151

2

301

51

88

+

++

= .

.

.

630630 == .

401. T , A . .

S:

21 334001 .== (3/4 UNC)

2

214190

2

.== (1/2 UNC)

( )321

1

2

2

=

( )( ) ( ) ( )[ ]362334008321419012

...

=

12 30060 .=

+=

+

3

2

3

22 12

( )( ) ( ) ( )

+=

+

3

6226

3

62832300602 11 ..

26251 .=

( ) 582126253006030060 12 .... ===

F UNC.

653

26253

1 .. =+=+=


61/133


Page 61 of 133

81633400

65.

.

.==

F . UNC,

2

1

2

2

22

323

+=

70670832

363.

. ===

( ) ( ) ( )

3671706703

582123

58212

12

2.... =

+=

6914190

3671.

.

.==

()

M. , .

() M. , .

816.=

51==

( ) ( ) ( )2

1

2

2

8162

5130151

2

301

51

88

+

++

===

..

.

.

1090091 == .

NORMAL STRESSES WITH TORSION

DESIGN PROBLEMS

402. A 70,000

., 50,000 ., 25,000 . T 3

. AISI C1030, . S

, = 3.3. C

.

S:

2

2

1

+=

= 000701 ,

363 ==


62/133


Page 62 of 133

= 32840 .=

4

2

=

22

22304

2840

.

.

==

( ) 222

5144000702

36223000070

.,

., +=+=

00025,=

+=

2

=

4

2

=

64

4

=

32

324

+=

( ) ( )3

2

2

51440007032000254

.,, ++=

14720147138313132

++= ,,

14728313101471323 ++=

,,

( )333

6548254000501616

,,===

F AISI C1030, , 0004747 ,==

2

122

1

+

=

M

( ) 50023523475050 ,... ====

2

1

2

3

2

23

50023

648254

00047

147283131014713

33

1

+

++

=

,

,

,

,,

.

B ,


63/133


Page 63 of 133

1254.=

O S

1402714273

47

3,. ====

21

2

3

2

23

14027

648254

00047

147283131014713

33

1

+

++

=

,

,

,

,,

.

B ,

1254.=

4

14=

403. T 402, 15 . D

, .

S:

18015 ==

( ) 222

63612000702

180223000070

.,

., +=+=

00025,=

+=

32

324

+=

( ) ( )3

2

2

636120007032000254

.,, ++=

798360147138313132

,,,++=

798368313101471323

,,,++=

M

2

1

2

3

2

23

50023

648254

00047

7983683131014713

33

1

+

++

=

,

,

,

,,,

.

B ,

1255.=


64/133


Page 64 of 133

O S

2

1

2

3

2

23

14027

648254

00047

7983683131014713

33

1

+

++

=

,

,

,

,,,

.

B ,

06255.=

4

15=

404. A , I II, 1 2,

, AISI 1045, . I = 8 ., = 24 ., = 20

., = 2 , . T

2.2

. T A B , Q . D

1 2.

S:

( )( ) === 40202

==+ 4021

21 =

2

22

1

11=

3232

42

2

41

1

=

42

2

41

1 248

=


65/133


Page 65 of 133

4

2

121 3

=

==+ 4021

4013

4

2

1

2 =

+

+

=

13

404

2

1

2

( )

+

=

+

=

13

120

13

340

4

2

1

4

2

1

4

2

1

4

2

1

1

2==+ =

248 =

3=

23 =+

50.=

51.=

+

=

+

==

13

1920

13

12016

16

4

2

131

4

2

1

4

2

131

4

2

1

31

1

1

( )

+

=

+

==

13

640

13

4016164

2

132

4

2

132

32

2

2

( )( )31

31

31

31

11

384851323232

====

.

( )( )3

2

3

2

3

2

3

2

22

3842450323232

==== .

F AISI 1045, , 55= ,

22.=

O S


66/133


Page 66 of 133

2

122

1

+

=

7531

3

55

3

.===

2

122

1 11

+

=

2

12

4

2

131

4

2

12

31

137531

1920

55

384

22

1

+

+

=

.

.

2

12

4

2

131

4

2

12

31

13

251922242

22

1

+

+

=

..

.

2

122

2 21

+

=

21

2

4

2

132

2

32

137531

640

55

384

22

1

+

+

=

.

.

2

12

4

2

132

2

32

13

42622242

22

1

+

+

=

..

.


67/133


Page 67 of 133

B ,

T2

1

1 2 A2

1

1 2.268 1.820 1.25

1.25 2.372 1.730 1.37

1.37 2.398 1.714 1.401.40 2.403 1.712 1.40

U 2

121 = ,

4

312 =

B 21 > , 2

121=

2532

1231312 112 ... =

==+=

2

132 =

405. T : =

5 ., = ., = 10 . T AISI C1040, . T

= 10,000 ., 1= 10,000 ., 2= 20,000 . U

, = 2.5,

.

S:32840 .=

22 22304

2840 .. =

=

( ) 2222

15112

102230

2

.

.===

B 1F

( ) ( )( )

1142965091511500010323233

2

31

1 +=+

=+

= ,.,

B 2


68/133


Page 68 of 133

( )

333

22

8591012

10002032

32

,,

=

==

T,

( )

223

46525000204

,,

==

21 >

213 +=

332

85910111429650946525

,,,++=

1144652543740723

++= ,,

( )333

93050000101616

,,===

52.=

2

122

1

+

=

F AISI C1040, (F. AF 1) 48=

M , ( ) 24485050 === ..

2

1

2

3

2

23

00024

93050

00048

11446525437407

52

1

+

++

=

,

,

,

,,

.

952.=

O S

71273

48

3.===

2

1

2

3

2

23

71027

93050

00048

11446525437407

52

1

+

++

=

,

,

,

,,

.

952.=

03.=


69/133


Page 69 of 133

406. T , 2= 0.

S

02 =

02 = , 03 =

11429650931

+== ,

393050

,=

52.=

M , ( ) 24485050 === ..

2

1

2

3

2

3

00024

93050

00048

114296509

52

1

+

+

=

,

,

,

,

.

3=

O S

71273

48

3.===

2

1

2

3

2

3

71027

93050

00048

114296509

52

1

+

+

=

,

,

,

,

.

9972.=

03.=

CHECK PROBLEMS

407. T : =

2 ., = 4 ., = ., = 2 ., = 6 ., = 8 ., = . T

= 8000 . 1 = 8000 ., 2 = 16,000 . D

, : () A

B (= 45), () M N, () G.


70/133


Page 70 of 133

S:

B 2 :

( )( )

( )

27915

2

75000016323233

22 ,

.,===

T

( )

( )

5093

2

000164422

23 ===

,

B 1

3

2

1

1

232

+

=

.

( )

( )

5093

2

8000161633

===

( ) 8920222302230 22 ... ===

(A) 628 ===

( )( ) ( )

( ) 76440

2

2

689204800032

3

2

1 ,

.

=

+

=

A

( ) ( ) 11423452791576440509345213 ,,, =+=+= oo

M. S

( ) 629125093211423

2

2

1

2

22

1

2

2

,, =

+

=

+

=

M. N

( )

1862450932

11423

2

11423

22

2

1

222

1

2

2

,,,

=

+

+=

+

+=

O S S


71/133


Page 71 of 133

( ) ( ) ( )[ ] 6621150933114233

23

3

22

122

2

122 ,, =+=+=

A B:

( ) ( ) 92812509345279157644045 321 ,,, === oo

M. S

( )

822950932

92812

2

2

1

2

22

1

2

2

=

+

=

+

=

,

M. N

( )

6931450932

92812

2

92812

22

2

1

222

1

2

2

,,,

=

+

+=

+

+=

O S S

( ) ( ) ( )[ ] 37875093392812323322

1

222

1

22 ,, =+=+=

(B)

7574

18 .===

( )( ) ( )

( ) 77840

2

2

75789204800032

3

2

1 ,

..

=

+

=

M

5923027915778405093213 ,,, =+=+=

M. S

( )

1221650932

59230

2

2

1

222

1

2

2

,,

=

+

=

+

=

M. N

( )

4183150932

59230

2

59230

22

2

1

2

22

1

2

2

,,,

=

+

+=

+

+=

O S S

( ) ( ) ( )[ ] 009155093359230323

32 21222

122 ,, =+=+=

A N:

4062050932791577840321 ,,, ===

M. S


72/133


Page 72 of 133

( )

4031150932

40620

2

2

1

2

22

1

2

2

,,

=

+

=

+

=

M. N

( ) 606215093240620

240620

22

2

1

2

22

1

2

2

,,, =

+

+=

+

+=

O S S

( ) ( ) ( )[ ] 4801050933406203

23

3

22

122

2

122 ,, =+=+=

(C) A G.

628 ===

( )( ) ( )

( )

74640

2

2

289204800032

3

2

1 ,

.

=

+

=

( ) ( ) 82617302791574640509330213 ,,, =+=+= oo

M. S

( )

2651050932

82617

2

2

1

222

1

2

2

,,

=

+

=

+

=

M. N

( )

1781950932

82617

2

82617

22

2

1

222

1

2

2

,,,

=

+

+=

+

+=

O S S

( ) ( ) ( )[ ] 937650933826173

23

3

22

122

2

122

=+=+= ,

411. A 4. 20 . T 2/3

; AISI 8630, WQT 1100 F, =3. U

2000 ?

S:

F AISI 8630, WQT 1100F, 125=

23432

+=

3

16

=

3

2=

20=


73/133


Page 73 of 133

4=

( )

( )

( )59155110610

4

204

4

3

232

23 .. +=+

=

( )

079604

16

3 .==

B .

( ) 5621255050 ... ===

2

122

1

+

=

2

122

562

07960

125

59155110610

3

1

+

+=

.

...

== 000213213 ,

( )( )

6762

00063

2000000213

00063===

,

,

,

412. T 411, 2 .

S:

( ) ( )2244432

+

=

( )

( ) ( )[ ]

( )

( ) ( )[ ] 612212520524204

524

43

232

2244 ....+=

+

=

( )( )

( ) ( )[ ]

09390

524

416164444

..

=

=

=

2

122

1

+

=

2

1

22

562

09390

125

612212520

3

1

+

+=

.

...

==

000177177 ,( )( )

561900063

2000000177

00063===

,

,

,

413. A , , AISI 4130, OQT 1100 F, OD 3 . ID 2

. I 1500 1200 ,

40,000 . = 10 .

T 10 . U ,


74/133


Page 74 of 133

() , () ,

() . () A N

.

S:

F , AISI 4130, WQT 1100F,

114= (T AT 7)

( )

=== 75078

1200

15000006300063,

,,

4

13=

2

12=

( ) ( ) ( )[ ] 9620522534

28404

28402222 ..... =

=

=

8

2

1

+= (T AT 8)

12010 ==

( ) =+= 73241

8

120962000040

2

,.

,

( ) ( )2244432

+

=

( )( )

( ) ( )[ ]( )

( ) ( )[ ] 00022

52253

000104

52253

25373241322244

,..

,

..

.,=

+

=

( )( )( )

( ) ( )[ ]

97817

52253

2537507816164444

,..

.,=

=

=

(A) ( ) 07621978172

00022

2

2

1

222

1

22

,,,

=

+

=

+

=

(B) ( )

07632978172

00022

2

00022

22

2

1

2

22

1

2

2

,,,,

=

+

+=

+

+=

(C)( )

704207621

1145050.

.

..====

554307632

114.

.===

(D)

2

122

1

+

=

82653

114

3.===


75/133


Page 75 of 133

2

122

8265

97817

114

0221

+

=

.

..

992.=

VARING STRESSES COMBINEDDESIGN PROBLEMS

414. T F ( )

424.2 . 141.4 .; = 20 ., = 15 ., 2= 1.21, =

0.1251, = 45; SAE 1040, 10% ,

= 1.5. C 1 S

; .

S:

F SAE 040, 10% W

54=

85=

5741

1

85

54

.==

5741

1

.==

850.=

S R FW 12501 .==

2112 .==

F. AF 12

541.=

271.=


76/133


Page 76 of 133

A 1=

( ) ( )( ) =+=+= 11111

541.=

271.=

F:

2424. =

4141. =

( ) ( ) 4141414124242

1

2

1... ==+=

( ) ( ) 8282414124242

1

2

1... =+==

22 22304

2840 .. =

=

22

22

1

+=+=

( )( ) ( ) 2

22

64428282

202330204141

.

.. +=+=

( )( ) ( ) 2

22

64456562

202330208282

.

.. +=+=

( ) =

( )( )( ) == 150015454141 o. ( )( )( ) == 300015458282 o.

3

32

=

( )

4548062864428283233

2

+=+

= ,.

( )

4546125764456563233

2

+=+

= ,.

3

16

=

( )33

7640150016

==

( )33

28015300016

,==


77/133


Page 77 of 133

+=

333

6842728015

850

2717640

5741

1

,,

.

.

.=

+

=

+=

111168112245461257

850

54145480628

5741

1333

+=

+

+

+=

,,

.

.,

.

2

122

1

+

=

ns

es

n

e

s

s

s

s

N

M , ( ) 00027000545050 ,,.. ===

2

1

2

3

2

3

00027

68427

00054

1111681122

51

1

+

+

=

,

,

,

,

.

16

9156251 == .

O S.

177313

00054

3,

,===

2

1

2

3

2

3

17731

68427

00054

1111681122

51

1

+

+

=

,

,

,

,

.

551.=

16

91=

8

51=

417. A , SAE 1045, ,

1600 600 . T

40,000. D = 3

. S . U S

.


78/133


Page 78 of 133

S:

F SAE 1045, , 59= , 96=

4850 == .

2291

1

59

48

.===

A 1==

2=

F :

0=

=

( ) ( )

=+=+= 10

2291

1

.

( )( )( )

( )[ ] 3444432554

2

2000403232

,,=

=

==

F :( )

=== 000168

600

16000006300063,

,,

+=

0=

=

( )( )( )

( )[ ] 3444482592

2

200016816

2291

116

2291

1

,,

..=

=

==

M , ( ) 00024000485050 ,,.. ===

2

12

3

2

300024

82592

00048

32554

51

1

+

=

,

,

,

,

.

2952.=

252.= , 542 .==

O S.

713273

00048

3,

,===

2

1

2

3

2

3 71327

82592

00048

32554

51

1

+

=

,

,

,

,

.

202.=

252.= , 542 .==


79/133


Page 79 of 133

S S 4

12= ,

2

14=

418. A

30 15 30 ,

25 15 25 ;

40 ; AISI 2340, OQT 1000 F; = 1.5. D

() ; () .

S:

F AISI 2340, OQT 1000F. ksisy 120= , ksisu 137=

( ) ksiss un 5.681375.05.0 ===

7521

1

120

568

.

.===

A 1==

( ) =+= 52215302

1.

( ) == 5715302

1.

( ) =+= 2015252

1

( ) == 515252

1

( ) ( )232323

5122940452232432

+=+=+=

.

( )333

76573232

===

.

( )333

102201616

===

( )333

52551616

.===

23323

2922076

850

151229

7521

1

+=

+

+=+= ..

333

88525

850

1102

7521

1

=

+

=+=

.

..

() M , ( ) 25345685050 .... ===


80/133


Page 80 of 133

2

1

2

3

2

23

2534

88

568

29220

51

1

+

+

=

...

931.=

2= ,

O S.

55393

568

3.

.===

2

1

2

3

2

23

5539

88

568

29220

51

1

+

+

=

...

inD 909.1=

inD 2=

419. T ,

.

S:

61.=

31.=

23323

2927476

850

6151229

7521

1

+=

+

+=+=

.

.

.

333

97525

850

31102

7521

1

=

+

=+=

.

.

.

.

() M , ( ) 25345685050 .... ===

2

1

2

3

2

23

2534

97

568

29274

51

1

+

+

=

...

042.=

2=

() O S.

55393

568

3.

.===


81/133


Page 81 of 133

2

1

2

3

2

23

5539

97

568

29274

51

1

+

+

=

...

022.= 2=

CHECK PROBLEMS

420. A 2. AISI 1144, , 200 600

. I , = 4.62 = 1.68

. C

.

S:

F AISI 1144, E T, , 83= , 118=

( ) 591185050 === ..

4071

1

83

59

.==

( )( ) == 211012. , ( )( ) == 81610681 ..

( )

==== 2100021

600

2000006300063,

,,

T AT 13

02.= , 61.=

+=

0= , 0=

=

( )( )

842

2

8163202

3233

..

. =

=

==

+=

= ,

0=


82/133


Page 82 of 133

( )

( )

59

2

2116

4071

11633

..

=

=

==

M , ( ) 529595050 ... ===

2

1

221

+

=

2

122

529

59

59

8421

+

=

.

..

26.1=N

O S. ( ) psiss nns 05.3459577.0577.0 ===

2

122

05.34

5.9

59

8.421

+

=N

261.=

421. I (), = 3000 . ; = 16 ., =

12 ., = 7 . T = 2500 .

. T

1. , UNC , AISI C1137, ,

4600 . T 2 . ()

C , ()

( ),

.

S:

F AISI C1137, , 50= , 85=

( ) 542855050 ... ===

82.= (T AT 12)

17651

1

50

542

.

.===

20.=

( )( )1204600 .=


83/133


Page 83 of 133

2300023 == ,

F 1 , UNC26060 .=

N: 51.=

+=

= ,

=

( )25540

514

6060

6060

2

.

..

.=

+

=+

=+

33000 ==

522500 .==

()

V, M E = 0, >

( ) ( )( ) +=

( ) ( )( )75203712 .. +=

77. =

( ) ( )( ) =

( ) ( )( )75203712 .. =

70. =

( )( ) 9712554077 ... ==

( )( ) 1802554070 ... ==

972497123 .. =+=+=

182318023 .. =+=+=

( ) ( ) 124182397242

1

2

1... =+=+=

( ) ( ) 90182397242

1

2

1... ===

839

6060

124.

.

.===

51

6060

90.

.

.===


84/133


Page 84 of 133

+=

1

82.= , 850.= , F = 0.80

( )( )( ) 928542800850 .... ==

( )

928

5182

50

8391

.

...+=

061.=

() H:

( ) =

( ) ( )( )73712 =

24.=

( )( ) 07312554024 ... ==

124073123 .. =+=+=

839

6060

124.

.

.===

=

0=

( )

83330839

17651

1..

.=+=+=

S:

0=

( ) 522

1. ==

0=mss

134

6060

52.

.

.===

( )( )

864

850

134010 .

.

..=+=+=

2

122

1

+

=

( ) 25215425050 .... === ,

2122

2521

864

542

83331

+

=

.

.

.

.

211.=


85/133


Page 85 of 133

422. T , (), 0 3 . T

A B . T AISI 1045,

; 1= 2, 2= 2.5, = 15, = 10, = 20 . F ,

. D

. I

I II. W 100% ?

S:

=

( )( ) == 45153

=+ 4521

21=

42

2

41

1

=

( )

( )

( )

( )42

4

1

52

20

2

10

.

=

21 81920 .=

=+ 4581920 22.

kipsinT = 74.242

( ) === 272074248192081920 21 ....

( ) ==== 141027202

1

2

1111 ..

( ) ==== 371274242

1

2

1222 ..

3

16

==

( )

( )

466

2

1410161633

1

111 .

.====


86/133


Page 86 of 133

( )

( )

034

52

3712161633

2

222 .

.

.====

3==+

=

( ) ( )2010 = 2=

32 =+

1=

2=

( )( ) ==== 20102

== 20

=== 102

1

332

==

( )

( ) 7312

2

1032311

.===

( )

( ) 526

52

1032322

..

===

U (1)

466.= , 7312.=

466.= , 7312.=

1150 .=

1501

.=

, 251

02

52

1

2 ..

.===

51.= , 251.= (F AF 12)

( ) 3002150150 1 ... ===

9680

30

0101

1

1

1.

.

. =

+

=

+

=

( ) ( ) 48411151968011 ... =+=+=

( ) ( ) 242111251968011 ... =+=+=

P K

61.= , 31.=

N


87/133


Page 87 of 133

( )( )( ) 912001614841 .... ==

( )( )( ) 312001312421 .... ==

F AISI 1045, , 59= , 96=

4850 == .

2291

1

59

48

.===

850.= , 850.=

( )( ) ( )

( )

( )( )

8443

850850

7312917312

2291

1.

..

...

.=+=+=

( )( ) ( )

( )

( )( )

8816

850850

46631466

2291

1.

..

...

.=+=+=

M , ( ) 24485050 === ..

2

122

1

+

=

2

122

24

8816

48

84431

+

=

..

870.=

O S. ( ) 7274857705770 ... ===

2122

727

8816

48

84431

+

=

.

..

910.=

N 100% , < 100.

423. A , . A .

AB. T 2 0 5 ,

. A = 8

; = 2, 2= 2.5, = 2, = 5, = 0.5, = . T AISI C1040, .

W 1 2.5 ? A 2

.


88/133


Page 88 of 133

S:

AISI C1040, , 48= (F. AF 1), 80=

4050 == .

21

1

48

40

.==

F : 12502250 .. ==

22.=

, 61.=

010.= ()

12502

250.

.==

9260

1250

0101

1

1

1.

.

. =

+

=

+

=

( ) ( ) 1121122926011 ... =+=+=

( ) ( ) 5611161926011 ... =+=+=

A

213 +=

B 2 :

==2

( )( )

( ) ( )( )

044

6

2250

32

2

505

632

2323

22 .

.

.=

=

=

( )

( ) ( )( )

8912250

4

2

5

4

22

2

3 ..

=

=

=

( )( )

( ) ( )( )123

1

23

11 088

6

2250

32

2

5

632

.

.=

=

=


89/133


Page 89 of 133

( )

( ) ( )( )

705

6

2250

16

2

8

616

2323 .

.=

=

=

152088044088891 11213 ..... =+=+=

11 088 . ==

( ) ( ) 0810881520880882

1

2

1111 ..... =+=+=

( ) ( ) 0811520880882

1

2

111 .... =+==

781746 1 .. =

+=

=

0=

( ) 7547521

1..

.==

52.=

O S T

( )

082340577057703

... ====

2

122

1

+

=

2

1

22

1

0823

754

40

781746

52

1

+

=

.

...

.

321 .=

POWER SCREWS

424. D , ,

5 . T 18 . T AISI C1035,

, 3.3 .


90/133


Page 90 of 133

S:

AISI C1035, , 55=

616

33

55.

.===

( )( ) 1025 == 2

60340616

10

.

.===

22

603404

.==

8760.=

1 , 0001.=

18=

362 ==

( ) 125000018

1

8

1.. ===

402881250

36>==

.

T:

( )104

55

0003022 21

22

1

2

=

=

=

,

U , E 104>

2

2

=

( )2

62

3633

103000010

.,

=

14444064

4

.==

311.=

1 , 4001.=


91/133


Page 91 of 133

425. () F ,

1800 ? () C . L

. D

. () W

? I 150

. , ?

S:

()

T/ = 2.5

401.=

4052

1.

.==

1=

( ) 57514017512

1... =+=

( )o

6245751

4001 ..

. =

=

15.0=f

150. == o538.=

( )

( )

+

=

( )

( )401751

624538000101800

..

..,

+=

3016.=

3216243016 ... === o

51.=


92/133


Page 92 of 133

() A ASTM 20. 32= , 20= , 5=

465

32.==

4520 ==

=

( )51

1046

..

=

330.=

33041 .. >=

4

3

1=

U .

M: M, .

() 8

7= (B )

( ) ( )( )

( )

=+=+= 8416245382

575110

2...

.

=

150150 .==

150841 .. =

312.=

426. A , 1 . , 6000 . T

AISI C1022, ,

0.15. T 15 . () C

= ,

. () I ,

. W

? () W 20.

? () F

500 . () W

?


93/133


Page 93 of 133

S:

F T AT 7,

AISI C1022, , = 52

= 6000 = 6

F 1 , = 1.0 , T/. = 3.5

= 0.15

()

W = = 15

( ) 1250018

1

8

1.. ===

1201250

15==

.

T AISI C1020;

( )

10752

0003022 21

22

1

2

=

=

=

,

U , E 107>

( )2

2

==

( )2

2

==

E

2

4

==

( )

( ) 647

01

642

..

==

D

( )2

2

=


94/133


Page 94 of 133

( )

( )2

2

120

00030647

,.

=

692.=

() W = 2= 30

240125030 ==.

T AISI C1020;

( )107

52

0003022 21

22

1

2

=

=

=

,

U , E 107>

( )2

2

==

( )2

2

==

E

2

4

==

( )

( ) 647

01

642

..

==

D

( )2

2

=

( )

( )2

2

240

00030647

,.

=

6730.=

() F 20. =

( )+= 2

2857053

1.

.===

( ) 125100125121 ... =+=

( )o

6241251

2857011 ..

. ===

150. == o538.=

6000=


95/133


Page 95 of 133

( )+== 2

( ) ( )

( )6245382

1251600020 ..

.+=

4339.=

()

L= = 500 , = 6000 , = 1.25 , = 1.00 .

= , = .

( )

22

4

=

( )

( ) ( )[ ] 22 00125160004

500..

=

27=

T

( )( ) 772857027 .. ===

() T .

( )= 2

( )( )( )624538

2

12516000..

.=

.. = 7230

427. A , 2 . , 24,000 .

. T 16 .

AISI C1040, . () W

? I ? () W = 0.15? () W ? () W

?

S:

F 2 . , = 2 , = 1.612 , T/. = 2.25 T 8.1

W = 24,000 = 24 , = 16

()

F , = = 16 .

F AISI C1040, , F AF1, = 47.5

T,

( ) 2015061218

1

8

1.. ===

( )112

547

0003022 21

22

1

2

=

=

=

.

,

T

11247920150

16


96/133


Page 96 of 133

( )

=

2

2

41

( )

=

2

2

2

4

1

4

( )

( ) ( )

( )

=

000304

47954716121

244

2

22

,

...

7415.=

037415

547.

.

.===

()

T

( )+= 2

44450252

1.

.===

( ) 806161210022

1... =+=

( )o484

8061

4445011.

.

. ===

150. == o

538.= 00024,=

( )+= 2

( )( )484538

2

806100024..

.,+=

= 5008

()

T .

( )=

2

( )( )484538

2

806100024..

.,=

. =1535

428. () A 2., 20 . A

0.10 0.15.


97/133


Page 97 of 133

W ? W ? W

? () T ()

. () T () .

S:

T 8.1, 2 . , = 2 , = 1.612 , T/ = 2.25

() S? A T .

( ) 806161210022

1... =+=

44450252

1.

.===

( )o484

8061

4445011.

.

. ===

I= 0.10

100. == o715.=

I = 0.15

150. == o538.=

S , .

( )+= 2

20=

( )+= 2

( )( )484538

2

806120..

.+=

= 1734.T .

( )= 2

( )( )484538

2

806120..

.=

.. = 2791

() S? A T .

88890252

22 .

.===

( )o9048

8061

8889011 ..

. ===

I= 0.10

100. == o715.=

I= 0.15


98/133


Page 98 of 133

150. == o538.=

S , .

( )+= 2

20=

( )+= 2

( )( )9048538

2

806120..

.+=

= 6715.

T = 0

()

S? A T .

33331252

33 .

.===

( )o22413

8061

3333111.

.

. ===

I= 0.10

100. == o715.=

I= 0.15

150. == o538.=

S , .

( )+= 2

20=

( )+= 2

( )( )22413538

2

806120..

.+=

= 2077.

T = 0

429. T 8.23, . A

50%.

S:

( )

+

+=

F ,> , + > 2T,


99/133


Page 99 of 133

2


100/133


Page 100 of 133

4

2

=

64

4 =

2

=

=

( )

64

2442

+=

U T T AT 18:

( )

115522===

.

( ) ( )( )32

352325243813

... +=

B D = 1.92

09086921

11.

.==

T AT 18: = 1.152

( )

( )

( )( )( )

( ) 38133013

921

352152132

921

52432

...

..

.

.=+=

U D = 2 .

() R .

431. T , 3; .

S:

() T AT3. W 2014 T6

810518 = @

60=

A 106

32

324

+=


101/133


Page 101 of 133

090610

.

=

090

8

6

105

1018

.

=

4931.=

W .

( ) 77264931850850 .... ===

3813

2

7726.

.===

E:

+=

( ) 233 ===

( ) 433

25212

3

12

.===

51502

.. ===

=

( )( )42

252

51

3

.

.+=

U T T AT 18:

( )

3

11115522==== .

( )( )32

51

352

3

523813

.

... +=

B = 0.787

( )664

78703

11.

.==

T AT 18: = 1.1736

( )

( )( )( )

( ) 3813

787051

35217361

78703

5232

...

..

.

.=+=

U = 7/8 . = 3 = 2 5/8

()

R .

432. A = 2500 .

;

1 . () D

32513

.+=


102/133


Page 102 of 133

= 2 S , AISI 4130,

WQT 1100 F. () C .

S:

()

F AISI 4130, WQT 1100 F, T AT 7

= 114 , = 127 , = /2

( )2850850 .. === S :

+=

1

2

==

01.=

( )2850

2

2

1

.

+=

+=

850

1

2

11

.

( ) ( )

+=

127850

1

1142

1

2

1

.

6336.=

F

+=

51.=

( ) 2224

==

522500 .==

( ) +=

( )

464

2 44

==


103/133


Page 103 of 133

T AT 18,

+=

+=

+=

51.

S:

( )( )45152526336 42

++= ....

( )32

5110526336

++=

...

B : = 0.633

3736330

633051.

.

..=

+=

, 2931.=

( )

( )( )

( )32 6330

633051293110

6330

526336

.

...

.

..

++==

60366336 .. =

U = 11/16 = 0.6875

D = 2 = 1.375 = 1 3/8

() S .

= = 114

+=

( )( )

4

51114

42

++=

.

( )( )32

51114

++=

.

18368750

6875051 ..

.. =+= , 3121.=

( )

( )( )

( )32 68750

68750513121

68750114

.

...

.

++=

7132.=

433. T 432, 100,000

.


104/133


Page 104 of 133

S:

()

F AISI 4130, WQT 1100 F, T AT 7

= 114 , = 127 , = /2

A 100,000

( ) ( )

51690000100

102850

102850

0850608506

.,

..

..

=

=

=

S :

+=

1

2

==

01.=

51690

2

2

1

.+=

+=

033811

211

.

( ) ( )

+=

12703381

1

1142

1

2

1

.

6641.=

F

+=

51.=

( ) 2224

==

522500 .==

( ) +=

( )

464

2 44

==

T AT 18,

+=

+=

+=

51.

S:

( )( )

4

5152526641 42

+

+=

....

( )32

5110526641

++=

...

B : = 0.601

536010

601051.

.

..=

+=

, 281.=


105/133


Page 105 of 133

( )

( )( )

( )32 6010

60105128110

6010

526641

.

...

.

..

++==

6441

Section 6 - Combined Stresses.pdf

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Transcript of Section 6 - Combined Stresses.pdf