aa-sm-004 bolt group - 1 -2d bolt group.xls

8/11/2019 AA-SM-004 Bolt Group - 1 -2D Bolt Group.xls

1/17

Doc: AA-SM-004

Revision: A

Page: 1

C.1.0.0 BOLT GROUP UNDER ECCENTRIC LOAD

Reference: Michael Niu - Airframe Stress Analysis & Sizing, Chapter 9.0

Px= 0N Applied Load in x-direction

Py= -10,000N Applied Load in y-direction

Txy= 12,000Nmm Applied Moment

xp= 0.3mm X-coordinate of the Applied Load

yp= 0.0mm Y-coordinate of the Applied Load

xc= 2.6 mm X-coordinate of the centroid

yc= 2.4 mm Y-coordinate of the centroid

Tc= -10,641 Nmm Moment About the Centroid

Bolt No. 1 2 3 4 5 6 S

x 1.00 -1.00 -1.00 1.00 0.00 10.00

y 1.00 1.00 -1.00 5.00 5.00 2.00

Bolt Dia. 0.38 0.25 0.25 0.38 0.25 0.38

Area, A 0.11 0.05 0.05 0.11 0.05 0.11 0.48

Ax 0 0 0 0 0 1 1.2

Ay 0 0 0 1 0 0 1.1

xb -1.6 -3.6 -3.6 -1.6 -2.6 7.4

yb -1.4 -1.4 -3.4 2.6 2.6 -0.4

Ar2

0.474 0.714 1.177 1.041 0.665 6.121 10.193

Axb

-0.2 -0.2 -0.2 -0.2 -0.1 0.8

Ayb -0.2 -0.1 -0.2 0.3 0.1 0.0

Sx 0 0 0 0 0 0 0

Sy -2,308 -1,026 -1,026 -2,308 -1,026 -2,308 -10,000

Sx 157 70 172 -305 -135 41 0

sy -180 -183 -183 -180 -131 857 0

Fx 157 70 172 -305 -135 41 0

Fy -2,488 -1,208 -1,208 -2,488 -1,157 -1,450 -10,000

F 2,493 1,210 1,220 2,507 1,165 1,451

Table 1 Bolt Group Loads

Check for balance by taking sum of forces and moments about centroid:

SFx = 0 N OK

SFy = -10,000 N OK

SM = -10641 Nmm OK

Prepared by: R. Abbott Date: Jan 2008 Checked by:___________________Date:__________

Standard Stress Methods

Bolt Group Analysis


2/17

Doc: AA-SM-004

Revision: A

Page: 2

C.2.0.0 DIAGRAM AND EQUATIONS

Equations used for the Bolt Group Method:

A = p D2

/4 Bolt Cross-Sectional Area

xb= x - xc x - Distance to Centroid

yb= y - yc y - Distance to Centroid

Location of the Centroid

Force Component Due to Shear Load

Force Component Due to Moment

Moment About Centroid

Sum of the Forces Due

to Shear and Moment

Fig. 1 Diagram for the Bolt Group Method



Bolt Group Analysis


3/17

Doc: AA-SM-00

Revision:

Page:

D.1.0.0 BOLT GROUP UNDER ECCENTRIC LOAD

Px= 0 N Applied Load in x-direction Reference:

Py= -10,000 N Applied Load in y-direction Michael Niu - Airframe Stress Analysis & Sizing,

Txy= 12,000 Nmm Applied Moment Chapter 9.0

xp= 0.3 mm X-coordinate of the Applied Load

yp= 0.0 mm Y-coordinate of the Applied Load

xc= 0.3 mm X-coordinate of the centroid

yc= 0.2 mm Y-coordinate of the centroid

Tc= 12,059 Nmm Moment About the Centroid

Bolt No. 1 2 3 4 5 6 7 8 S

x 1.00 -1.00 -1.00 1.00 0.00 0.00

y 1.00 1.00 -1.00 -1.00 0.00 2.00

Bolt Dia. 0.38 0.25 0.25 0.38 0.25 0.25

Area, A 0.11 0.05 0.05 0.11 0.05 0.05 0.00 0.00 0.42

Ax 0 0 0 0 0 0 0 0 0.1

Ay 0 0 0 0 0 0 0 0 0.1

xb 0.7 -1.3 -1.3 0.7 -0.3 -0.3 -0.3 -0.3

yb 0.8 0.8 -1.2 -1.2 -0.2 1.8 -0.2 -0.2Ar

20 0 0 0 0 0 0 0 1

Axb 0.1 -0.1 -0.1 0.1 0.0 0.0 0.0 0.0

Ayb 0.1 0.0 -0.1 -0.1 0.0 0.1 0.0 0.0

Sx 0 0 0 0 0 0 0 0 0

Sy -2,647 -1,176 -1,176 -2,647 -1,176 -1,176 0 0 -10,000

Sx 1,314 584 -943 -2,122 -180 1,347 0 0 0

sy -1,213 988 988 -1,213 225 225 0 0 0

Fx 1,314 584 -943 -2,122 -180 1,347 0 0 0

Fy -3,860 -188 -188 -3,860 -952 -952 0 0 -10,000

F 4,077 614 962 4,405 969 1,650 0 0



Bolt Group Analysis


4/17

Doc: AA-SM

Revisi

Pa

D.2.0.0 DIAGRAM AND EQUATIONS

Equations used in Bolt Group Calculation:

Check for balance by taking sum of forces and moments about centroid:

SFx = 0 N OKSFy = -10,000 N OK

SM = 12,059 Nmm OK



Bolt Group Analysis


5/17

References:

[1] AN3 Thru AN20 Bolt - Machine, Aircraft Military Specification Sheet

[2] NAS498 Fasteners, Alloy Steel, Externally Threaded, 95 KSI Fsu, 450 F

[3] E.F. Bruhn - Analysis & Design of Flight Vehicle Structures

AN Steel BoltsFtu = 125 ksi

Fsu = 75 ksi

Fb = 180 ksi

Decimal Ult. Tensile Yield Tensile Double Shear Single Shear

Size Dia. Dia Strength Strength Strength Strength

[in] [in] [lbs] [lbs] [lbs] [lbs]

AN3 0.19 0.190 2,210 1,690 4,250 2,125

AN4 1/4 0.250 4,080 3,130 7,360 3,680

AN5 5/16 0.313 6,500 4,980 11,500 5,750

AN6 3/8 0.375 10,100 7,740 16,560 8,280

AN7 7/16 0.438 13,600 10,430 22,500 11,250

AN8 1/2 0.500 18,500 14,190 29,400 14,700AN9 9/16 0.563 23,600 18,100 37,400 18,700

AN10 5/8 0.625 30,100 23,080 46,000 23,000

AN12 3/4 0.750 44,000 33,730 66,300 33,150

AN14 7/8 0.875 60,000 46,000 90,100 45,050

AN17 1.00 1.000 80,700 61,870 117,800 58,900

AN18 1 1/8 1.125 101,800 78,050 147,500 73,750

AN20 1 1/4 1.250 130,200 99,820 182,100 91,050

[1] [3] [1] [1] [3] [1] [3]

High Strength Steel Bolts

Ftu = 160 ksiFsu = 95 ksi

Fb = 230 ksi




#4 0.112 0.112 1880 940

#6 0.138 0.138 2850 1420

#8 0.164 0.164 4010 2000

#10 0.19 0.190 5,380 2,700

1/4 0.250 6,190 9,300 4,660

5/16 0.313 9,820 14,600 7,290

3/8 0.375 15,200 21,000 10,500

7/16 0.438 20,600 28,600 14,300

1/2 0.500 27,400 37,300 18,600

9/16 0.563 34,800 47,200 23,600

5/8 0.625 43,600 58,300 29,100

3/4 0.750 63,200 83,900 42,000

7/8 0.875 86,100 114,000 57,100

1.00 1.000 114,000 149,000 74,600

1 1/8 1.125 144,000 189,000 94,400


6/17

1 1/4 1.250 180,000 233,000 116,600

1 1/2 1.500 336,000 167,900

[3] [2] [2]

AN 2024 Aluminum Alloy Bolts

Ftu = 62 ksiFsu = 35 ksi

Fb = 72 ksi




AN3 0.19 0.190 1,100 710 1,980 990

AN4 1/4 0.250 2,030 1,310 3,430 1,715

AN5 5/16 0.313 3,220 2,080 5,370 2,685

AN6 3/8 0.375 5,020 3,240 7,740 3,870

AN7 7/16 0.438 6,750 4,350 10,500 5,250

AN8 1/2 0.500 9,180 5,920 13,700 6,850

AN9 9/16 0.563 11,700 7,550 17,400 8,700AN10 5/8 0.625 14,900 9,610 21,500 10,750

AN12 3/4 0.750 21,800 14,100 31,000 15,500

AN14 7/8 0.875 29,800 19,200 42,100 21,050

AN17 1.00 1.000 40,000 25,800 55,000 27,500

AN18 1 1/8 1.125 50,500 32,600 69,000 34,500

AN20 1 1/4 1.250 64,400 41,500 85,000 42,500

[1] [1] [1] [1]


7/17

Plasticity

Corrected

Ult. Bending Ult. Bending Shank Moment Ult. Bending NAS 6208

Moment Moment Area of Inertia Moment

[in-lbs] [in-lbs] [in4] [in

4] [in-lbs] Procureme

121 138 0.0284 6.397E-05 121 D =

276 314 0.0491 1.917E-04 276 FTU=

539 614 0.0767 4.681E-04 539 FSU=

932 1,061 0.1104 9.707E-04 932

1,480 1,685 0.1503 1.798E-03 1480 Allowable i

2,210 2,516 0.1963 3.068E-03 2209 Chapter 6.3,140 3,582 0.2485 4.914E-03 3145

4,320 4,914 0.3068 7.490E-03 4314 Shape fact

7,450 8,491 0.4418 1.553E-02 7455 k =

11,850 13,483 0.6013 2.877E-02 11838

17,670 20,126 0.7854 4.909E-02 17671 Moment ar

25,161 28,656 0.9940 7.863E-02 25161 c = D/2 =

34,515 39,308 1.2272 1.198E-01 34515

[3] Moment of

I = pr4/4 =

I/c =

Plasticity Apparent S

Corrected Mc/I =

Ult. Bending Ult. Bending Shank Moment Ult. Bending =


[in-lbs] [in-lbs] [in ] [in ] [in-lbs] MALL=

37 0.0099 7.724E-06 32

70 0.0150 1.780E-05 59

117 0.0211 3.551E-05 100

182 0.0284 6.397E-05 155

414 0.0491 1.917E-04 353

809 0.0767 4.681E-04 689

1,398 0.1104 9.707E-04 1191

2,220 0.1503 1.798E-03 1891

3,313 0.1963 3.068E-03 2823

4,718 0.2485 4.914E-03 4019

6,471 0.3068 7.490E-03 5513

11,183 0.4418 1.553E-02 9526

17,758 0.6013 2.877E-02 15127

26,507 0.7854 4.909E-02 22580

37,742 0.9940 7.863E-02 32150


8/17

51,772 1.2272 1.198E-01 44102

89,462 1.7671 2.485E-01 76208

Plasticity

Corrected

Ult. Bending Ult. Bending Shank Moment Ult. Bending


[in-lbs] [in-lbs] [in4] [in4] [in-lbs]

46 0.0284 6.397E-05 48

110 0.0491 1.917E-04 110

216 0.0767 4.681E-04 216

373 0.1104 9.707E-04 373

592 0.1503 1.798E-03 592

884 0.1963 3.068E-03 884

1,260 0.2485 4.914E-03 12581,730 0.3068 7.490E-03 1726

2,980 0.4418 1.553E-02 2982

4,740 0.6013 2.877E-02 4735

7,070 0.7854 4.909E-02 7069

10,064 0.9940 7.863E-02 10064

13,806 1.2272 1.198E-01 13806

[3]


9/17

OLT MECHANICAL PROPERTIES

nt Specifica NAS4002

0.25 in 6.35 mm

125,000 psi 862 MPa

75,000 psi 517 MPa

calculated using method in Niu,

"Plastic Bending", Ref. [4].

r from fig. 6.4.2 in Ref. [4]:

1.7

:

3.175 mm

Inertia:

79.81 mm4

25.14 mm3

tress from fig. 6.4.6 in Ref. [4]:

270 ksi

1861.58 MPa

414 in-lbs 4.68E+04 Nmm

160

160

1.7

270

205


10/17


11/17


12/17

References:

[1] AN3 Thru AN20 Bolt - Machine, Aircraft Military Specification Sheet

[2] NAS498 Fasteners, Alloy Steel, Externally Threaded, 95 KSI Fsu, 450 F

[3] E.F. Bruhn - Analysis & Design of Flight Vehicle Structures

AN Steel BoltsFtu = 862 MPa

Fsu = 517 MPa

Fb = 1241 MPa

Ult. Tensile Yield Tensile Double Shear Single Shear


[in] [mm] [N] [N] [N] [N]

AN3 0.19 4.83 9,831 7,517 18,905 9,452

AN4 1/4 6.35 18,149 13,923 32,739 16,369

AN5 5/16 7.94 28,913 22,152 51,155 25,577

AN6 3/8 9.53 44,927 34,429 73,663 36,831

AN7 7/16 11.11 60,496 46,395 100,085 50,042

AN8 1/2 12.70 82,292 63,120 130,778 65,389AN9 9/16 14.29 104,978 80,513 166,364 83,182

AN10 5/8 15.88 133,891 102,665 204,618 102,309

AN12 3/4 19.05 195,722 150,039 294,917 147,459

AN14 7/8 22.23 266,893 204,618 400,785 200,392

AN17 1.00 25.40 358,972 275,211 524,001 262,000

AN18 1 1/8 28.58 452,829 347,184 656,113 328,056

AN20 1 1/4 31.75 579,159 444,022 810,021 405,011

[1] [3] [1] [1] [3] [1] [3]

High Strength Steel Bolts

Ftu = 1103 MPa

Fsu = 655 MPa

Fb = MPa

Ult. Tensile Yield Tensile Double Shear Single Shear


[in] [mm] [N] [N] [N] [N]

#4 0.112 2.84 8,363 4,181

#6 0.138 3.51 12,677 6,316

#8 0.164 4.17 17,837 8,896

#10 0.19 4.83 23,931 12,010

1/4 6.35 27,534 41,368 20,729

5/16 7.94 43,682 64,944 32,428

3/8 9.53 67,613 93,413 46,706

7/16 11.11 91,633 127,219 63,6101/2 12.70 121,881 165,919 82,737

9/16 14.29 154,798 209,956 104,978

5/8 15.88 193,942 259,331 129,443

3/4 19.05 281,128 373,206 186,825

7/8 22.23 382,992 507,097 253,993

1.00 25.40 507,097 662,785 331,837

1 1/8 28.58 640,544 840,714 419,912

1 1/4 31.75 800,680 1,036,436 518,663


13/17

1 1/2 38.10 1,494,603 746,856

[3] [2] [2]

AN 2024 Aluminum Alloy Bolts

Ftu = 427 MPa

Fsu = 241 MPaFb = 496 MPa



[in] [mm] [N] [N] [N] [N]

AN3 0.19 4.83 4,893 3,158 8,807 4,404

AN4 1/4 6.35 9,030 5,827 15,257 7,629

AN5 5/16 7.94 14,323 9,252 23,887 11,943

AN6 3/8 9.53 22,330 14,412 34,429 17,215

AN7 7/16 11.11 30,025 19,350 46,706 23,353

AN8 1/2 12.70 40,835 26,333 60,941 30,470

AN9 9/16 14.29 52,044 33,584 77,399 38,700

AN10 5/8 15.88 66,279 42,747 95,637 47,818AN12 3/4 19.05 96,971 62,720 137,895 68,947

AN14 7/8 22.23 132,557 85,406 187,270 93,635

AN17 1.00 25.40 177,929 114,764 244,652 122,326

AN18 1 1/8 28.58 224,635 145,012 306,927 153,464

AN20 1 1/4 31.75 286,465 184,601 378,099 189,049

[1] [1] [1] [1]


14/17

Conversions in-lb = 112.9849 Nmm

lbs = 4.448222 N

Plasticity

Corrected

Ult. Bending Ult. Bending

Moment Moment

[Nmm] [Nmm]

13,671 15,592

31,184 35,477

60,899 69,373

105,302 119,877

167,218 190,379

249,697 284,270354,772 404,712

488,095 555,208

841,737 959,354

1,338,870 1,523,375

1,996,442 2,273,933

2,842,812 3,237,694

3,899,672 4,441,209

[3]

Plasticity

Corrected


Moment Moment

[Nmm] [Nmm]

4,180

7,909

13,219

20,563

46,776

91,405

157,953

250,826374,319

533,063

731,125

1,263,510

2,006,385

2,994,889

4,264,274

5,849,452


15/17

10,107,851

PlasticityCorrected


Moment Moment

[Nmm] [Nmm]

5,197

12,428

24,405

42,143

66,887

99,879

142,361

195,464336,695

535,548

798,803

1,137,080

1,559,869

[3]


16/17

Fastener Fastener

Fastener Dia. Area

No. x y D A Ax Ay xb yb r Ar AxbA -276.000 38.000 0.125 0.0123 -3.3870 0.4663 ####### 38.0000 ####### 712.8470 -2.9207

B -276.000 -38.000 0.125 0.0123 -3.3870 -0.4663 ####### -38.0000 ####### 712.8470 -2.9207

C 200.000 121.000 0.125 0.0123 2.4544 1.4849 238.0000 121.0000 ####### 874.7985 2.9207

D 200.000 -121.000 0.125 0.0123 2.4544 -1.4849 238.0000 ####### ####### 874.7985 2.9207

E 0.0000 0.0000 0.0000 38.0000 0.0000 ####### 0.0000 0.0000

F 0.0000 0.0000 0.0000 38.0000 0.0000 ####### 0.0000 0.0000

G 0.0000 0.0000 0.0000 38.0000 0.0000 ####### 0.0000 0.0000

H 0.0000 0.0000 0.0000 38.0000 0.0000 ####### 0.0000 0.0000

I 0.0000 0.0000 0.0000 38.0000 0.0000 ####### 0.0000 0.0000

K 0.0000 0.0000 0.0000 38.0000 0.0000 ####### 0.0000 0.0000

L 0.0000 0.0000 0.0000 38.0000 0.0000 ####### 0.0000 0.0000

M 0.0000 0.0000 0.0000 38.0000 0.0000 ####### 0.0000 0.0000

N 0.0000 0.0000 0.0000 38.0000 0.0000 ####### 0.0000 0.0000

O 0.0000 0.0000 0.0000 38.0000 0.0000 ####### 0.0000 0.0000

P 0.0000 0.0000 0.0000 38.0000 0.0000 ####### 0.0000 0.0000

Q 0.0000 0.0000 0.0000 38.0000 0.0000 ####### 0.0000 0.0000

R 0.0000 0.0000 0.0000 38.0000 0.0000 ####### 0.0000 0.0000

S 0.0000 0.0000 0.0000 38.0000 0.0000 ####### 0.0000 0.0000

T 0.0000 0.0000 0.0000 38.0000 0.0000 ####### 0.0000 0.0000

U 0.0000 0.0000 0.0000 38.0000 0.0000 ####### 0.0000 0.0000

V 0.0000 0.0000 0.0000 38.0000 0.0000 ####### 0.0000 0.0000

W 0.0000 0.0000 0.0000 38.0000 0.0000 ####### 0.0000 0.0000

X 0.0000 0.0000 0.0000 38.0000 0.0000 ####### 0.0000 0.0000

Y 0.0000 0.0000 0.0000 38.0000 0.0000 ####### 0.0000 0.0000

Z 0.0000 0.0000 0.0000 38.0000 0.0000 ####### 0.0000 0.0000

0.0491 -1.86532 0 #######

Input Data:

xp= 0.000 Applied xc= -38.000 Centroid +ve Torqu

yp= 0.000 Coordinates yc= 0.000 Coordinates

Px= 190 Applied Load Tc= 127,780

Py= 190 Components (lbs.)Txy= 135,000 Applied Torque at load application point

Coordinates


17/17

Ayb Sx Sy Sx sy Fx Fy F

0.4663 48 48 19 118 66 165 178

-0.4663 48 48 -19 118 29 165 168

1.4849 48 48 60 -118 107 -70 128

-1.4849 48 48 -60 -118 -12 -70 71

0.0000 0 0 0 0 0 0 0

0.0000 0 0 0 0 0 0 0

0.0000 0 0 0 0 0 0 0

0.0000 0 0 0 0 0 0 0

0.0000 0 0 0 0 0 0 0

0.0000 0 0 0 0 0 0 0

0.0000 0 0 0 0 0 0 0

0.0000 0 0 0 0 0 0 0

0.0000 0 0 0 0 0 0 0

0.0000 0 0 0 0 0 0 0

0.0000 0 0 0 0 0 0 0

0.0000 0 0 0 0 0 0 0

0.0000 0 0 0 0 0 0 0

0.0000 0 0 0 0 0 0 0

0.0000 0 0 0 0 0 0 0

0.0000 0 0 0 0 0 0 0

0.0000 0 0 0 0 0 0 0

0.0000 0 0 0 0 0 0 0

0.0000 0 0 0 0 0 0 0

0.0000 0 0 0 0 0 0 0

0.0000 0 0 0 0 0 0 0

190 190 0 0 190 190

Note: Bearing Loads on plate/lug

will have an opposite sign

Shear due to

applied load

Shear due to

torque

Loads Transferred

to Fastener

aa-sm-004 bolt group - 1 -2d bolt group.xls

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