Eclissage

ECLISSAGE nb de boulons sur une file verticale? nb de files? distance entre 2 files? distance entre boulons? Effort Tranchant V? excentricité Vert.? Effort Tranchant H? excentricité Horiz.? Moment appliqué? Moment en kgm= BOULONS Classe? Diamètre?

2 2

Unités kg mm

Io des boulons/S= To vert.boulon= To horiz.= Cisaill. Total=

800.00 2300.00 1250.00 2618 kg

5.5 mm

Le calcul est conduit avec les boulons en simple cisaillement.

200.0 mm 200.0 mm 4200 kg 0.0 mm 0 kg 0.0 mm 1000 kgm 1000 kgm

Vérification Eclisse nb éclisses? 1 épaisseur? 20.0 mm Hauteur? 500.0 mm sf+traction due à H= 1.24 kg/mm2 t= 0.68 kg/mm2 Von Mises= 1.71 kg/mm2 Von Mises non réduit= 1.62 kg/mm2

10.99 16.0 mm

9175 kg 11304 kg

Vérification Ame semelles non prises en compte

épaisseur? Hauteur? sf= t= Von Mises= Von Mises non réduit= contrainte Cf avec UPE 180=

pression diamétrale

RESULTATS Cisaillement= traction=

ea=

8.18 kg/mm2

fe?

pression diamétrale

Avec D+2mm 24 kg/mm2

5.5 mm 400.0 mm 7.31 kg/mm2 2.10 kg/mm2 8.17 kg/mm2 7.58 kg/mm2 6.65 kg/mm2 29.75 kg/mm2 26.44 kg/mm2

pince dans le sens de l'effort

27.00 mm

pince dans le sens de l'effort

27.00 mm

et doit être < à 2,5 d soit

45.00 mm

et doit être < à 2,5 d soit

45.00 mm

7,000 kgm

7,600 kgm

9,000 kg

compession=

8,410 kg

19000

calcul en tenant compte des trous

éclisse Itotale= 208,333,333 à déduire= 7,219,440 Iréduit= Strou= I/V= I/Vnon réduit= moment pour avoir la même contrainte en tranchant pour avoir la même contrainte en effort normal pour avoir la même contrainte en

NON REDUIT sf+traction due à H=

1.20 kg/mm2 t= 0.63 kg/mm2 Von Mises= 1.62 kg/mm2

âme Itotale= à déduire=

201,113,893 Iréduit= 360 Strou= 804.46 I/V= 833.3333333 I/Vnon réduit= éclisse 1036 kgm section pleine= 4526 kg section pleine= 0 kg section pleine=

NON REDUIT sf= t= Von Mises=

29,333,333 1,985,346 27,347,987 99 136.74 146.6666667 âme 1073 kgm 4615 kg 0 kg

6.82 kg/mm2 1.91 kg/mm2 7.58 kg/mm2

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

0.5 2 5 10 17.5 28 42 60 82.5 110 143 182 227.5 280 340 408 484.5 570 665 770 885.5 1012 1150 1300 1462.5 1638 1827 2030 2247.5

1985346 7925346 19805346 39605346 69305346 110885346 166325346 237605346 326705346 435605346 566285346 720725346 900905346 1.109E+09 1.346E+09 1.616E+09 1.919E+09 2.257E+09 2.633E+09 3.049E+09 3.507E+09 4.008E+09 4.554E+09 5.148E+09 5.792E+09 6.486E+09 7.235E+09 8.039E+09 8.9E+09

N=6 0.25 2.25 6.25 17.5

31

2480 9.821E+09

N=8 0.25 2.25 6.25 12.25 42

N=9 1 4 9 16 60

N=10 0.25 2.25 6.25 12.25 20.25 82.5

N=11

C5= 2 C5 PAIR= 1 C5 IMPAIR 0.5

1 4 9 16 25 110

N=12 0.25 2.25 6.25 12.25 20.25 30.25 143

N=13 1 4 9 16 25 36 182

0.5 0.5 0.5

1^2+2^2+3^2..= n(n+1)(2n+1)/6 1^2+3^2+5^2..= n(2n+1)(2n-1)/3

Nb de termes n= 8.0 n= 3.0

Somme 204 35

grugeage

calcul des contraintes Unités kg; mm

g

Tranchant? hauteur totale: ht= largeur semelle:bs= épaisseur semelle:es= épaisseur âme;ea= diam.trou?

b

30,900 kg 550.0 mm 210.0 mm 17.2 mm 11.1 mm 20.0 mm

nb de boulons sur une verticale? écartement entre boulons: e? distance fin de grugeage au profil porteur: g? distance axe vertical boulons au profil porteur: d?

d

hauteur grugeage: b?

6 70.0 mm 250.0 mm 45.0 mm 30.0 mm

ht? b? es (tf)? ea (tw)? ha=

490.0 mm grugeage haut et bas

en fin de grugeage

sf= t=

stotale=

ha=

22.8 kg/mm2

502.8 mm grugeage haut ou bas

en fin de grugeage

sf= t=

stotale=

e

Page 6

au droit des trous

17.39 8.52

10.27 5.54 14.1 kg/mm2

au droit des trous

grugeage

s= ms= cdg= I/base= I/cdg= wel= wel=

550 mm 300 mm 25 mm 12 mm

grugeage haut et bas

9193.08 1530141.29 166.44 52058.70 26590.27 1597.54 752.08

avec 3 trous 7861.08 1436901.29 182.79 50535.78 24271.12 1327.84 719.76

au droit des trous

sf= t=

3.80 11.29

stotale= 19.9 kg/mm2

grugeage haut ou bas

calcul en tenant compte des trous avec grugeage symétrique

Itotale= à déduire= Iréduit= Strou= I/V=

108,825,325 19,080,900 89,744,425 222 366.3037755

au droit des trous

sf= t=

1.85 7.27

C5= 6 PAIR= 3 IMPAIR 2.5

stotale= 12.7 kg/mm2

17.5 17.5 17.5

Page 7

Boulons

EFFORTS

ADMISSIBLES

DANS LES

BOULONS

Unités kg; mm boulons en simple cisaillement boulons Hr 10,9 taper10,99; Hr 8,8 taper 8,88

BOULONS Classe? 6.4 Diamètre? 12

RESULTATS Cisaillement= 1314 traction= 1619

EFFORTS INCLINES Effort de traction Effort decisaillement

BOULONS Classe? 8.8 Diamètre? 12

N? T?

1940 2333.3333 RESULTATS

Classe? Diamètre?

8.8 8

Cisaillement= traction=

1307 1610

Classe? Diamètre?

8.88 20

Cisaillement= traction=

10182 12544

Classe? Diamètre?

8.8 12

Section filetée cisaillée

Classe? Diamètre?

8.8 22

Cisaillement= traction=

10821 13332

Classe? Diamètre?

8.8 12

Section filetée cisaillée

Classe? Diamètre?

8.88 20

Cisaillement= traction=

10182 12544

Classe? Diamètre?

8.8 12

Section filetée cisaillée

Classe? Diamètre?

6.4 10

Cisaillement ou traction=

1508

Classe? Diamètre?

6.4 12

Cisaillement ou traction=

2171

Classe? Diamètre?

8.8 8

Cisaillement ou traction=

2212

Classe? Diamètre?

10.9 16

Cisaillement ou traction=

10777

Classe? Diamètre?

5.6 20

Cisaillement ou traction=

7540

RIVETS

Section filetée cisaillée Section lisse cisaillée

Section lisse cisaillée

Section lisse cisaillée

Section lisse cisaillée

RESULTATS

partie lisse cisaillée

BOULONS Classe? 6.4 Diamètre? 12

RESULTATS Cisaillement= 1763 traction= 1619

Classe? Diamètre?

8.8 8

Cisaillement= traction=

1795 1610

Classe? Diamètre?

8.88 24

Cisaillement= traction=

18801 18074

Classe? Diamètre?

8.8 22

Cisaillement= traction=

13576 13332

Page 8

effort admissible de cisaillement 0.3 4,140 kg j? 0.45 6,209 kg couple de serrage Classe? 8.88 Pv= 12,544 kg Diamètre? 20 Ms= 45.16 kgm

Boulons

Classe? Diamètre?

8.88 20

Cisaillement= traction=

13056 12544

Page 9

Boulons

Diamètre

kg kg

RESULTATS BON BON BON BON BON BON BON BON

Section 5 6 8 10 12 14 16 18 20 22 24 27 30 33 36 39 42 45 48

14.2 20.1 36.6 58 84.3 115 157 192 245 303 353 459 561 694 817 976 1121.8 1306 1473

Classe 4.6 4.8 5.6 5.8 6.4 6.5 6.6 6.8 8.4 8.6 8.8 8.88 10.9 10.99

missible de cisaillement

couple de serrage acier galvanisé Ms= 35.12 kgm

Page 10

Contrainte fyb 24 28 30 34

24 30 35 41 28 41 55 64 67 90

fub 40 40 50 50 40 50 60 60 40 60 80 80 100 100

0.6 0.5 0.6 0.5 0.6 0.6 0.6 0.5 0.5 0.5 0.6 0.6 0.5 0.5

Boulons

Page 11

Boulons

19.63 28.27 50.27 78.54 113.10 153.94 201.06 254.47 314.16 380.13 452.39 572.56 706.86 855.30 1017.88 1194.59 1385.44 1590.43 1809.56

Page 12

Arbed

Fer en I Traverse UPN 140 Poteaux PRS

219

1

FER en U Traverse IPE 140 Poteaux UPN 120

13

grugeage IPE 550 Eclissage UPE 180 Long-flamt IPE 550

18 239 20

5

TUBE RECT TUBE ROND PRS IPE 80 IPE 100 IPE 120 IPE 140 IPE 160 IPE 180 IPE 200 IPE 220 IPE 240 IPE 270 IPE 300 IPE 330 IPE 360 IPE 400 IPE 450 IPE 500 IPE 550 IPE 600 HEA 100 HEA 120 HEA 140 HEA 160 HEA 180 HEA 200 HEA 220 HEA 240 HEA 260 HEA 280 HEA 300 HEA 320 HEA 340 HEA 360 HEA 400 HEA 450

1

2

3

4

5

6

140 0

60 0

7 0

10 0

10 0

98 0

140 120

73 55

4.7 7

6.9 9

7 9

112.2 82

550 180 550 h

210 75 210 b

11.1 5.5 11.1 a ou Vw

17.2 10.5 17.2 e ou Vf

24 12 24 r

467.6 159 467.6 h1

80 100 120 140 160 180 200 220 240 270 300 330 360 400 450 500 550 600 h 96 114 133 152 171 190 210 230 250 270 290 310 330 350 390 440

46 55 64 73 82 91 100 110 120 135 150 160 170 180 190 200 210 220 b 100 120 140 160 180 200 220 240 260 280 300 300 300 300 300 300

3.8 4.1 4.4 4.7 5.0 5.3 5.6 5.9 6.2 6.6 7.1 7.5 8.0 8.6 9.4 10.2 11.1 12.0 a ou Vw 5.0 5.0 5.5 6.0 6.0 6.5 7.0 7.5 7.5 8.0 8.5 9 9.5 10.0 11.0 11.5

5.2 5.7 6.3 6.9 7.4 8.0 8.5 9.2 9.8 10.2 10.7 11.5 12.7 13.5 14.6 16.0 17.2 19.0 e ou Vf 8.0 8.0 8.5 9.0 9.5 10.0 11.0 12.0 12.5 13.0 14.0 15.5 16.5 17.5 19.0 21.0

5 7 7 7 9 9 12 12 15 15 15 18 18 21 21 21 24 24 r 12 12 12 15 15 18 18 21 24 24 27 27 27 27 27 27

59.6 74.6 93.4 112.2 127.2 146 159 177.6 190.4 219.6 248.6 271 298.6 331 378.8 426 467.6 514 h1 56 74 92 104 122 134 152 164 177 196 208 225 243 261 298 344

Page 13

Arbed

HEA 500 HEA 550 HEA 600 HEA 650 HEA 700 HEA 800 HEA 900 HEA 1000 HEB 100 HEB 120 HEB 140 HEB 160 HEB 180 HEB 200 HEB 220 HEB 240 HEB 260 HEB 280 HEB 300 HEB 320 HEB 340 HEB 360 HEB 400 HEB 450 HEB 500 HEB 550 HEB 600 HEB 650 HEB 700 HEB 800 HEB 900 HEB 1000 HEM 100 HEM 120 HEM 140 HEM 160 HEM 180 HEM 200 HEM 220 HEM 240 HEM 260 HEM 280 HEM 300C HEM 300 HEM 320 HEM 340 HEM 360 HEM 400 HEM 450 HEM 500 HEM 550

490 540 590 640 690 790 890 990 h 100 120 140 160 180 200 220 240 260 280 300 320 340 360 400 450 500 550 600 650 700 800 900 1000 h 120 140 160 180 200 220 240 270 290 310 320 340 359 377 395 432 478 524 572

300 300 300 300 300 300 300 300 b 100 120 140 160 180 200 220 240 260 280 300 300 300 300 300 300 300 300 300 300 300 300 300 300 b 106 126 146 166 186 206 226 248 268 288 305 310 309 309 308 307 307 306 306

12.0 12.5 13.0 13.5 14.5 15.0 16.0 16.5 a ou Vw 6.0 6.5 7.0 8.0 8.5 9.0 9.5 10.0 10.0 10.5 11.0 11.5 12.0 12.5 13.5 14.0 14.5 15.0 15.5 16.0 17.0 17.5 18.5 19.0 a ou Vw 12.0 12.5 13.0 14.0 14.5 15.0 15.5 18.0 18.0 18.5 16.0 21.0 21.0 21.0 21.0 21.0 21.0 21.0 21.0

Page 14

23.0 24.0 25.0 26.0 27.0 28.0 30.0 31.0 e ou Vf 10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0 17.5 18.0 19.0 20.5 21.5 22.5 24.0 26.0 28.0 29.0 30.0 31.0 32.0 33.0 35.0 36.0 e ou Vf 20.0 21.0 22.0 23.0 24.0 25.0 26.0 32.0 32.5 33.0 29.0 39.0 40 40 40 40 40 40 40

27 27 27 27 27 30 30 30 r 12 12 12 15 15 18 18 21 24 24 27 27 27 27 27 27 27 27 27 27 27 30 30 30 r 12 12 12 15 15 18 18 21 24 24 27 27 27 27 27 27 27 27 27

390 438 486 534 582 674 770 868 h1 56 74 92 104 122 134 152 164 177 196 208 225 243 261 298 344 390 438 486 534 582 674 770 868 h1 56 74 92 104 122 134 152 164 177 196 208 208 225 243 261 298 344 390 438

Arbed

HEM 600 HEM 650 HEM 700 HEM 800 HEM 900 HEM 1000 IAO 100 IAO 100R IAO 120 IAO 120R IAO 140 IAO 140R IAO 160 IAO 160R IAO 250 IAO 250R IPN 80 IPN 100 IPN 120 IPN 140 IPN 160 IPN 180 IPN 200 IPN 220 IPN 240 IPN 260 IPN 280 IPN 300 IPN 320 IPN 340 IPN 360 IPN 380 IPN 400 IPN 425 IPN 450 IPN 475 IPN 500 IPN 550 IPN 600 IPE-A 80 IPE-A 100 IPE-A 120 IPE-A 140 IPE-A 160 IPE-A 180 IPE-A 200 IPE-A 220 IPE-A 240 IPE-A 270

620 668 716 814 910 1008 h 100 100 120 120 140 140 160 160 250 250 h 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 425 450 475 500 550 600 h 78 98 117.6 137.4 157 177 197 217 237 267

305 305 304 303 302 302 b 42 51 44 49 47 52 51 56 100 105 b 42 50 58 66 74 82 90 98 106 113 119 125 131 137 143 149 155 163 170 178 185 200 215 b 46 55 64 73 82 91 100 110 120 135

21.0 21.0 21.0 21.0 21.0 21.0 a ou Vw 4.0 13.0 4.5 9.5 4.5 9.5 5.0 10.0 10.0 15.0 a ou Vw 3.9 4.5 5.1 5.7 6.3 6.9 7.5 8.1 8.7 9.4 10.1 10.8 11.5 12.2 13.0 13.7 14.4 15.3 16.2 17.1 18.0 19.0 21.6 a ou Vw 3.3 3.6 3.8 3.8 4.0 4.3 4.5 5.0 5.2 5.5

Page 15

40 40 40 40 40 40 e ou Vf 6.5 6.5 6.8 6.8 7.5 7.5 8.2 8.2 12.5 12.5 e ou Vf 5.9 6.8 7.7 8.6 9.5 10.4 11.3 12.2 13.1 14.1 15.2 16.2 17.3 18.3 19.5 20.5 21.6 23.0 24.3 25.6 27.0 30.0 32.4 e ou Vf 4.2 4.7 5.1 5.6 5.9 6.5 7.0 7.7 8.3 8.7

27 27 27 30 30 30 r 0 0 0 0 0 0 0 0 0 0 r 3.9 4.5 5.1 5.7 6.3 6.9 7.5 8.1 8.7 9.4 10.1 10.8 11.5 12.2 13.0 13.7 14.4 15.3 16.2 17.1 18.0 19.0 21.6 r 5 7 7 7 9 9 12 12 15 15

486 534 582 674 770 868 h1 0 0 0 0 0 0 0 0 0 0 h1 2.3 2.7 3.1 3.4 3.8 4.1 4.5 4.9 5.2 5.6 6.1 6.5 6.9 7.3 7.8 8.2 8.6 9.2 9.7 10.3 10.8 11.9 13 h1 59.6 74.6 93.4 112.2 127.2 146 159 177.6 190.4 219.6

Arbed

IPE-A 300 IPE-A 330 IPE-A 360 IPE-A 400 IPE-A 450 IPE-A 500 IPE-A 550 IPE-A 600 IPE-R 140 IPE-R 160 IPE-R 180 IPE-R 200 IPE-R 220 IPE-R 240 IPE-R 270 IPE-R 300 IPE-R 330 IPE-R 360 IPE-R 400 IPE-R 450 IPE-R 500 IPE-R 550 IPE-R 600 IPE-O 180 IPE-O 200 IPE-O 220 IPE-O 240 IPE-O 270 IPE-O 300 IPE-O 330 IPE-O 360 IPE-O 400 IPE-O 450 IPE-O 500 IPE-O 550 IPE-O 600 HEA-A 100 HEA-A 120 HEA-A 140 HEA-A 160 HEA-A 180 HEA-A 200 HEA-A 220 HEA-A 240 HEA-A 260 HEA-A 280 HEA-A 300 HEA-A 320 HEA-A 340

297 327 357.6 397 447 497 547 597 h 142 162 183 204 225 245 276 306 336 366 407 458 508 560 608 h 182 202 222 242 274 304 334 364 404 456 506 556 610 h 91 109 128 148 167 186 205 224 244 264 283 301 320

150 160 170 180 190 200 237 220 b 72 81 89 98 108 118 133 147 158 168 178 188 198 237 218 b 92 102 112 122 136 152 162 172 182 192 202 212 224 b 100 120 140 160 180 200 220 240 260 280 300 300 300

6.1 6.5 6.6 7.0 7.6 8.4 9.0 9.8 a ou Vw 5.3 5.6 6.4 6.6 6.7 7.5 7.7 8.5 9.2 9.9 10.6 11.3 12.6 14.0 14.0 a ou Vw 6.0 6.2 6.6 7.0 7.5 8.0 8.5 9.2 9.7 11.0 12.0 12.7 15.0 a ou Vw 4.2 4.2 4.3 4.5 5.0 5.5 6.0 6.5 6.5 7.0 7.5 8 8.5

Page 16

9.2 10 11.5 12.0 13.1 14.5 15.7 17.5 e ou Vf 7.8 8.5 9.5 10.5 11.8 12.3 13.1 13.7 14.5 16.0 17.0 18.6 20.0 22.2 23.0 e ou Vf 9.0 9.5 10.2 10.8 12.2 12.7 13.5 14.7 15.5 17.6 19.0 20.2 24.0 e ou Vf 5.5 5.5 6.0 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11 11.5

15 18 18 21 21 21 24 24 r 7 9 9 12 12 15 15 15 18 18 21 21 21 24 24 r 9 12 12 15 15 15 18 18 21 21 21 24 24 r 12 12 12 15 15 18 18 21 24 24 27 27 27

248.6 271 298.6 331 378.8 426 467.6 514 h1 112.4 127 146 159 177.4 190.4 219.8 248.6 271 298 331 378.8 426 467.6 514 h1 146 159 177.6 190.4 219.6 248.6 271 298.6 331 378.8 426 467.6 514 h1 56 74 92 104 122 134 152 164 177 196 208 225 243

Arbed

HEA-A 360 HEA-A 400 HEA-A 450 HEA-A 500 HEA-A 550 HEA-A 600 HEA-A 650 HEA-A 700 HEA-A 800 HEA-A 900 HEA-A 1000

339 378 425 472 522 571 620 670 770 870 970 h

UAP 80 UAP100 UAP 130 UAP 150 UAP 175 UAP 200 UAP 220 UAP 250 UAP 300

300 300 300 300 300 300 300 300 300 300 300 b 80 100 130 150 175 200 220 250 300

h UPN 80 UPN 100 UPN 120 UPN 140 UPN 160 UPN 180 UPN 200 UPN 220 UPN 240 UPN 260 UPN 280 UPN 300 UPN 320 UPN 350 UPN 380 UPN 400

b 80 100 120 140 160 180 200 220 240 260 280 300 320 350 380 400

h UPE 80 UPE 100 UPE 120 UPE 140 UPE 160 UPE 180 UPE 200 UPE 220 UPE 240 UPE 270 UPE 300 UPE 330

45 50 55 65 70 75 80 85 100 45 50 55 60 65 70 75 80 85 90 95 100 100 100 102 110 b

80 100 120 140 160 180 200 220 240 270 300 330

9.0 9.5 10.0 10.5 11.5 12.0 12.5 13.0 14.0 15.0 16.0 a ou Vw

12.0 13.0 13.5 14.0 15.0 15.5 16.0 17.0 18.0 20.0 21.0 e ou Vf

5 5.5 6 7 7.5 8 8 9 9.5 a ou Vw 6 6 7 7 7.5 8 8.5 9 9.5 10 10 10 14 14 13.5 14

8 8.5 9.5 10.25 10.75 11.5 12.5 13.5 16 e ou Vf 8 8.5 9 10 10.5 11 11.5 12.5 13 14 15 16 17.5 16 16 18

8 8.5 9.5 10.25 10.75 11.5 12.5 13.5 16 r 8 8.5 9 10 10.5 11 11.5 12.5 13 14 15 16 17.5 16 16 18

a ou Vw

e ou Vf

r

50 55 60 65 70 75 80 85 90 95 100 105

Page 17

4 4.5 5 5 5.5 5.5 6 6.5 7 7.5 9.5 11

7 7.5 8 9 9.5 10.5 11 12 12.5 13.5 15 16

27 27 27 27 27 27 27 27 30 30 30 r

261 298 344 390 438 486 534 582 674 770 868 h1 48 66 92 109 132 154 170 196 236 h1 46 64 82 98 115 133 151 167 184 200 216 232 246 282 313 324 h1

10 10 12 12 12 12 13 13 15 15 15 18

66 85 104 122 141 159 178 196 215 243 270 298

Arbed

UPE 360 UPE400 PRS

360 400

110 115

Page 18

12 13.5

17 18

18 18

326 364

Arbed

7

8

9

10

11

12

13

14

16.014 0

20.4 0

605 0

86.428571 0

103 0

5.4458115 0

62.7 0

14.752941 0

12.894425 13.345

16.42602 17

541.22404 77.317721 364 60.666667

88.34438 72.6

5.7401385 44.917811 12.30625 4.6272848 43.2 11.076923

105.51658 134.41603 67116.517 2440.6006 2787.0056 22.345454 2667.5837 254.05559 19.7 25.1 1353 150.4 173 7.34 143.7 28.56 105.51658 134.41603 67116.517 2440.6006 2787.0056 22.345454 2667.5837 254.05559 Pp Iy Wels,y Wpl,y iy Iz Wels,z A

6.0 8.1 10.4 12.9 15.8 18.8 22.4 26.2 30.7 36.1 42.2 49.1 57.1 66.3 77.6 90.7 105.5 122.4 Pp 16.7 19.9 24.7 30.4 35.5 42.3 50.5 60.3 68.2 76.4 88.3 97.6 104.8 112.1 124.8 139.8

7.6 10.3 13.2 16.4 20.1 23.9 28.5 33.4 39.1 45.9 53.8 62.6 72.7 84.5 98.8 115.5 134.4 156.0 A 21.2 25.3 31.4 38.8 45.3 53.8 64.3 76.8 86.8 97.3 112.5 124.4 133.5 142.8 159.0 178.0

80 171 318 541 869 1317 1943 2772 3892 5790 8356 11767 16266 23128 33743 48199 67117 92083 Iy 349 606 1033 1673 2510 3692 5410 7763 10455 13673 18263 22929 27693 33090 45069 63722

20.0 34.2 53.0 77.3 108.7 146.3 194.3 252.0 324.3 428.9 557.1 713.1 903.6 1156.4 1499.7 1927.9 2440.6 3069.4 Wels,y 72.8 106.3 155.4 220.1 293.6 388.6 515.2 675.1 836.4 1012.8 1259.6 1479.3 1678.4 1890.8 2311.3 2896.4

23.2 39.4 60.7 88.3 123.9 166.4 220.6 285.4 366.6 484.0 628.4 804.3 1019.1 1307.1 1701.8 2194.1 2787.0 3512.4 Wpl,y 83.0 119.5 173.5 245.1 324.9 429.5 568.5 744.6 919.8 1112.2 1383.3 1628.1 1850.5 2088.5 2561.8 3215.9

Page 19

3.24 4.07 4.90 5.74 6.58 7.42 8.26 9.11 9.97 11.23 12.46 13.71 14.95 16.55 18.48 20.43 22.35 24.30 iy 4.06 4.89 5.73 6.57 7.45 8.28 9.17 10.05 10.97 11.86 12.74 13.58 14.40 15.22 16.84 18.92

8.5 15.9 27.7 44.9 68.3 100.9 142.4 204.9 283.6 419.9 603.8 788.1 1043.5 1317.8 1675.9 2141.7 2667.6 3387.3 Iz 133.8 230.9 389.3 615.6 924.6 1335.5 1954.6 2768.8 3667.6 4762.6 6309.6 6985.2 7436.0 7886.8 8563.8 9465.3

3.7 5.8 8.6 12.3 16.7 22.2 28.5 37.3 47.3 62.2 80.5 98.5 122.8 146.4 176.4 214.2 254.1 307.9 Wels,z 26.8 38.5 55.6 76.9 102.7 133.6 177.7 230.7 282.1 340.2 420.6 465.7 495.7 525.8 570.9 631.0

Arbed

155.1 166.2 177.8 189.7 204.5 224.4 251.6 272.3 Pp 20.4 26.7 33.7 42.6 51.2 61.3 71.5 83.2 93.0 103.1 117.0 126.7 134.2 141.8 155.3 171.1 187.3 199.4 211.9 224.8 240.5 262.3 291.5 314.0 Pp 41.8 52.1 63.2 76.2 88.9 103.1 117.3 156.7 172.4 188.5 176.7 237.9 245.0 247.9 250.3 255.7 263.3 270.3 278.2

197.5 211.8 226.5 241.6 260.5 285.8 320.5 346.8 A 26.0 34.0 43.0 54.3 65.3 78.1 91.0 106.0 118.4 131.4 149.1 161.3 170.9 180.6 197.8 218.0 238.6 254.1 270.0 286.3 306.4 334.2 371.3 400.0 A 53.2 66.4 80.6 97.1 113.3 131.3 149.4 199.6 219.6 240.2 225.1 303.1 312.0 315.8 318.8 325.8 335.4 344.3 354.4

86975 111932 141208 175178 215301 303443 422075 553846 Iy 450 864 1509 2492 3831 5696 8091 11259 14919 19270 25166 30824 36656 43193 57681 79888 107176 136691 171041 210616 256888 359084 494065 644748 Iy 1143 2018 3291 5098 7483 10642 14605 24290 31307 39547 40951 59201 68135 76372 84867 104119 131484 161929 197984

3550.0 4145.6 4786.7 5474.3 6240.6 7682.1 9484.8 11188.8 Wels,y 89.9 144.1 215.6 311.5 425.7 569.6 735.5 938.3 1147.6 1376.4 1677.7 1926.5 2156.3 2399.6 2884.0 3550.6 4287.0 4970.6 5701.4 6480.5 7339.7 8977.1 10979.2 12895.0 Wels,y 190.4 288.2 411.4 566.5 748.3 967.4 1217.1 1799.2 2159.1 2551.4 2559.4 3482.4 3795.8 4051.5 4297.1 4820.3 5501.4 6180.5 6922.5

3948.9 4621.8 5350.4 6136.3 7031.8 8699.5 10811.0 12824.4 Wpl,y 104.2 165.2 245.4 354.0 481.4 642.5 827.0 1053.1 1282.9 1534.4 1868.7 2149.2 2408.1 2683.0 3231.7 3982.4 4814.6 5590.6 6425.1 7319.9 8327.1 10228.7 12584.1 14855.1 Wpl,y 235.8 350.6 493.8 674.6 883.4 1135.1 1419.4 2116.9 2523.6 2965.6 2926.7 4077.7 4435.0 4717.6 4989.3 5570.6 6331.0 7094.3 7932.7

Page 20

20.98 22.99 24.97 26.93 28.75 32.58 36.29 39.96 iy 4.16 5.04 5.93 6.78 7.66 8.54 9.43 10.31 11.22 12.11 12.99 13.82 14.65 15.46 17.08 19.14 21.19 23.20 25.17 27.12 28.96 32.78 36.48 40.15 iy 4.63 5.51 6.39 7.25 8.13 9.00 9.89 11.03 11.94 12.83 13.49 13.98 14.78 15.55 16.32 17.88 19.80 21.69 23.64

10367.1 10819.0 11271.3 11723.9 12178.8 12638.7 13547.5 14004.5 Iz 167.3 317.5 549.7 889.2 1362.8 2003.4 2843.3 3922.7 5134.5 6594.5 8562.8 9238.8 9689.9 10141.2 10819.0 11721.3 12623.9 13076.9 13530.2 13984.0 14440.9 14903.7 15815.9 16275.8 Iz 399.2 702.8 1144.3 1758.8 2580.1 3651.2 5012.0 8152.6 10448.6 13162.8 13736.3 19403.1 19709.3 19710.7 19521.8 19335.5 19339.0 19154.7 19158.4

691.1 721.3 751.4 781.6 811.9 842.6 903.2 933.6 Wels,z 33.5 52.9 78.5 111.2 151.4 200.3 258.5 326.9 395.0 471.0 570.9 615.9 646.0 676.1 721.3 781.4 841.6 871.8 902.0 932.3 962.7 993.6 1054.4 1085.1 Wels,z 75.3 111.6 156.8 211.9 277.4 354.5 443.5 657.5 779.7 914.1 900.7 1251.8 1275.7 1275.8 1267.6 1259.6 1259.9 1251.9 1252.2

Arbed

285.5 293.4 300.7 317.3 332.5 348.7 Pp 7.0 14.1 8.5 13.2 9.9 15.4 12.2 18.5 37.3 47.1 Pp 6.1 8.5 11.4 14.6 18.3 22.3 26.8 31.7 36.9 42.7 48.9 55.3 62.2 69.4 77.7 85.7 94.3 106.0 117.7 130.4 143.6 169.7 203.3 Pp 5.0 6.9 8.7 10.5 12.7 15.4 18.4 22.2 26.2 30.7

363.7 373.7 383.0 404.3 423.6 444.2 A 8.9 17.9 10.8 16.8 12.7 19.7 15.5 23.5 47.5 60.0 A 7.7 10.9 14.5 18.6 23.3 28.4 34.1 40.3 47.0 54.4 62.3 70.4 79.3 88.4 99.0 109.1 120.1 135.0 149.9 166.1 183.0 216.2 258.9 A 6.4 8.8 11.0 13.4 16.2 19.6 23.5 28.3 33.3 39.1

237448 281668 329278 442598 570434 722299 Iy 141 216 237 309 383 497 606 776 4478 5129 Iy 80 175 337 589 961 1485 2198 3141 4359 5896 7789 10061 12845 16110 20126 24654 29993 37963 47078 57998 70578 101634 142694 Iy 64 141 257 435 689 1063 1591 2317 3290 4917

7659.6 8433.2 9197.7 10874.6 12537.0 14331.3 Wels,y 28.3 43.3 39.5 51.5 54.7 71.0 75.7 97.0 358.2 410.3 Wels,y 20.0 35.0 56.1 84.1 120.1 165.0 219.8 285.6 363.2 453.6 556.3 670.8 802.8 947.7 1118.1 1297.6 1499.6 1786.5 2092.4 2442.0 2823.1 3695.8 4756.5 Wels,y 16.5 28.8 43.8 63.3 87.8 120.1 161.6 213.5 277.7 368.3

8772.1 9657.0 10539.0 12487.7 14441.8 16567.9 Wpl,y 33.1 55.6 46.6 64.6 64.3 88.8 89.3 121.3 423.4 501.6 Wpl,y 23.3 40.8 65.2 97.7 139.5 191.5 255.1 331.3 421.3 526.7 647.0 781.2 936.1 1106.3 1307.2 1518.5 1756.4 2093.9 2455.5 2867.9 3318.7 4335.1 5605.9 Wpl,y 19.0 33.0 49.9 71.6 99.1 135.3 181.7 240.2 311.6 412.5

Page 21

25.55 27.45 29.32 33.09 36.70 40.32 iy 3.98 3.47 4.69 4.29 5.50 5.03 6.24 5.74 9.71 9.25 iy 3.21 4.02 4.82 5.62 6.42 7.22 8.03 8.83 9.63 10.41 11.18 11.95 12.73 13.50 14.26 15.03 15.80 16.77 17.72 18.69 19.64 21.68 23.48 iy 3.18 4.01 4.83 5.70 6.53 7.37 8.23 9.05 9.94 11.21

18975.5 18979.2 18797.4 18627.4 18451.8 18459.3 Iz 8.1 16.0 9.7 14.1 13.1 18.5 18.3 25.2 210.2 247.5 Iz 7.3 14.3 25.2 41.4 64.5 96.1 138.1 192.4 261.5 341.1 429.5 530.8 652.7 789.9 957.6 1139.2 1351.5 1674.1 2007.3 2428.1 2875.9 4034.3 5422.1 Iz 6.9 13.1 22.4 36.4 54.4 81.9 117.2 171.4 240.1 358.0

1244.3 1244.5 1236.7 1229.5 1222.0 1222.5 Wels,z 3.8 6.3 4.4 5.8 5.6 7.1 7.2 9.0 42.0 47.1 Wels,z 3.5 5.7 8.7 12.6 17.4 23.4 30.7 39.3 49.3 60.4 72.2 84.9 99.6 115.3 133.9 152.9 174.4 205.4 236.2 272.8 310.9 403.4 504.4 Wels,z 3.0 4.8 7.0 10.0 13.3 18.0 23.4 31.2 40.0 53.0

Arbed

36.5 43.0 50.2 57.4 67.2 79.4 98.7 107.6 Pp 14.4 17.7 22.1 26.6 31.6 37.3 44.0 51.7 60.3 70.3 81.5 95.2 111.4 143.1 144.4 Pp 21.3 25.1 29.4 34.3 42.3 49.3 57.0 66.0 75.7 92.4 107.3 122.5 154.5 Pp 12.2 14.6 18.1 23.8 28.7 34.6 40.4 47.4 54.1 61.2 69.8 74.2 78.9

46.5 54.7 64.0 73.1 85.5 101.1 125.8 137.0 A 18.4 22.6 28.1 33.9 40.2 47.5 56.0 65.9 76.8 89.6 103.8 121.3 142.0 182.4 183.9 A 27.1 32.0 37.4 43.7 53.8 62.8 72.6 84.1 96.4 117.7 136.7 156.1 196.8 A 15.6 18.6 23.0 30.4 36.5 44.1 51.5 60.4 69.0 78.0 88.9 94.6 100.5

7173 10231 14515 20293 29759 42933 65964 82919 Iy 611 989 1554 2363 3474 4823 7312 10498 14688 20288 28863 42396 59933 95274 110306 Iy 1505 2211 3134 4369 6947 9994 13910 19047 26747 40923 57777 79157 118302 Iy 237 413 719 1283 1967 2944 4170 5835 7981 10558 13804 16447 19552

483.1 625.7 811.8 1022.3 1331.5 1727.7 2411.8 2777.9 Wels,y 86.1 122.1 169.8 231.7 308.8 393.7 529.8 686.2 874.3 1108.7 1418.3 1851.4 2359.6 3402.6 3628.5 Wels,y 165.4 218.9 282.3 361.1 507.1 657.5 833.0 1046.6 1324.1 1794.9 2283.7 2847.4 3878.8 Wels,y 52.0 75.8 112.4 173.4 235.6 316.6 406.9 521.0 654.1 799.8 975.6 1092.8 1222.0

541.8 701.9 906.8 1143.9 1494.3 1946.0 2699.9 3141.2 Wpl,y 99.1 140.0 195.3 265.3 351.8 449.5 601.6 779.9 994.9 1262.2 1617.7 2114.6 2709.2 3884.8 4174.9 Wpl,y 189.1 249.4 321.1 410.3 574.6 743.8 942.8 1186.1 1502.2 2046.3 2613.0 3263.4 4471.0 Wpl,y 58.4 84.1 123.8 190.4 258.2 347.1 445.5 570.6 714.5 873.1 1065.3 1196.2 1340.9

Page 22

12.42 13.67 15.06 16.66 18.65 20.61 22.90 24.60 iy 5.77 6.62 7.44 8.35 9.29 10.08 11.43 12.62 13.83 15.05 16.67 18.70 20.55 22.86 24.49 iy 7.45 8.32 9.16 10.00 11.36 12.61 13.84 15.05 16.66 18.65 20.56 22.52 24.52 iy 3.89 4.72 5.59 6.50 7.34 8.17 9.00 9.83 10.76 11.63 12.46 13.19 13.95

519.0 685.2 944.3 1170.6 1502.4 1939.2 3492.3 3116.3 Iz 48.8 75.7 112.2 165.7 248.8 338.7 515.8 728.0 957.6 1269.7 1606.0 2069.5 2600.4 4945.8 3992.8 Iz 117.3 168.9 239.8 328.5 513.5 745.7 960.4 1251.2 1564.2 2085.4 2621.7 3224.4 4520.8 Iz 92.1 158.8 274.8 478.7 730.0 1068.5 1510.5 2077.0 2788.0 3664.2 4733.5 4959.1 5184.7

69.2 85.6 111.1 130.1 158.1 193.9 294.7 283.3 Wels,z 13.5 18.7 25.2 33.8 46.1 57.4 77.6 99.0 121.2 151.2 180.4 220.2 262.7 417.4 366.3 Wels,z 25.5 33.1 42.8 53.9 75.5 98.1 118.6 145.5 171.9 217.2 259.6 304.2 403.6 Wels,z 18.4 26.5 39.3 59.8 81.1 106.8 137.3 173.1 214.5 261.7 315.6 330.6 345.6

Arbed

83.7 92.4 99.7 107.4 120.0 128.8 138.0 149.9 171.5 198.0 221.5 Pp 8.4 10.5 13.7 17.9 21.2 25.1 28.5 34.4 46.0 Pp 8.6 10.6 13.3 16.0 18.8 22.0 25.3 29.4 33.2 37.9 41.8 46.2 59.5 60.7 63.1 71.8

106.6 117.7 127.1 136.9 152.8 164.1 175.8 190.9 218.5 252.2 282.2 A 10.67 13.38 17.50 22.84 27.06 31.98 36.27 43.80 58.56 A 11.00 13.50 17.00

Pp

A 7.9 9.82 12.1 14.5 17 19.7 22.8 26.6 30.2 35.2 44.4 53.2

20.4 24.00 28.00 32.20 37.40 42.30 48.30 53.30 58.80 75.80

77.3 80.40

91.5

10.1 12.5 15.4 18.4 21.7 25.1 29 33.9 38.5 44.8 56.6 67.8

23037 31252 41888 54643 72871 91872 113944 142721 208882 301145 406451 Iy 107 209.5 459.6 796.1 1270 1946 2710 4137 8171 Iy 106 206 364 605 925 1350 1910 2690 3600 4820 6280 8030 10870 12840 15760 20350

1359.1 1653.6 1971.2 2315.4 2792.0 3217.9 3675.6 4260.3 5425.5 6922.9 8380.4 Wels,y 26.8 41.9 70.7 106.1 145.1 194.6 246.4 331.0 544.7 Wels,y 26.5 41.2 60.7 86.4 115.6 150.0 191.0 244.5 300.0 370.8 448.6 535.3 679.4 733.7 829.5 1017.5

1495.2 1824.1 2183.3 2576.2 3127.6 3623.1 4159.9 4840.1 6224.8 7998.8 9776.7 Wpl,y 31.87 49.59 83.51 125.3 171.5 230.1 289.9 391.8 693.3 Wpl,y 31.8 49 72.6 103 138 179 228 292 358 442 532 632 826 918 1014 1240

14.70 16.30 18.16 19.98 21.84 23.66 25.46 27.34 30.92 34.55 37.95 iy 3.17 3.96 5.13 5.90 6.85 7.80 8.64 9.72 11.81 iy 3.10 3.91 4.63 5.45 6.21 6.94 7.70 8.48 9.23 9.99 10.85 11.69 11.98 12.89 14.00 14.91

Iy 107.2 206.9 363.5 599.5 911.1 1353 1909 2682 3599 5255 7823 11010

Wels,y 26.8 41.4 60.6 85.6 113.9 150.4 190.9 243.9 299.9 389.2 521.5 667.1

Wpl,y 31.23 48.01 70.33 98.84 131.6 173 220.1 281.5 346.9 451.1 613.4 791.9

iy

Page 23

3.26 4.07 4.86 5.71 6.48 7.34 8.11 8.9 9.67 10.83 11.76 12.74

5410.5 5861.4 6087.5 6313.9 6766.5 6993.4 7220.6 7673.1 8133.7 9041.4 9500.8 Iz 21.33 32.83 51.34 93.26 126.4 169.7 222.3 295.4 562.1 Iz 19.4 29.3 43.2 62.7 85.3 114 148 197 248 317 399 495 597 570 615 846

360.7 390.8 405.8 420.9 451.1 466.2 481.4 511.5 542.2 602.8 633.4 Wels,z 7.38 9.95 13.76 20.96 25.90 32.14 39.70 48.83 79.84 Wels,z 6.36 8.49 11.08 14.75 18.30 22.44 26.96 33.62 39.55 47.74 57.25 67.81 80.68 75.00 78.64 101.32

Iz 25.41 38.21 55.4 78.7 106.8 143.7 187.3 246.4 310.9 401 537.7 681.5

Wels,z 7.98 10.63 13.79 18.19 22.58 28.56 34.43 42.51 50.08 60.69 75.58 89.66

Arbed

61.2 72.2

77.9 91.9

14830 20980

823.6 1049

982.3 1263

Page 24

13.79 15.11

843.7 1045

105.1 122.6

Arbed

15

16

17

18

19

20

28.3 0

1.7531484 0

5.68 0

1.8 0

1.75 0

3.37 0

19.246602 1.6536482 2.4571145 1981.3561 21.2 1.5941068 4.15 0.9

0 1.6

0 3.03

400.53655 4.4548543 123.80113 1884098.1 52.3 2.39 6.99 6.81 400.53655 4.4548543 123.80113 1884098.1 Wpl,z iz Iw IV

0 2.47 0

0 5.19 0

5.8 9.1 13.6 19.2 26.1 34.6 44.6 58.1 73.9 97.0 125.2 153.7 191.1 229.0 276.4 335.9 400.5 485.6 Wpl,z 41.1 58.9 84.8 117.6 156.5 203.8 270.6 351.7 430.2 518.1 641.2 709.7 755.9 802.3 872.9 965.5

1.05 1.24 1.45 1.65 1.84 2.05 2.24 2.48 2.69 3.02 3.35 3.55 3.79 3.95 4.12 4.31 4.45 4.66 iz 2.51 3.02 3.52 3.98 4.52 4.98 5.51 6.00 6.50 7.00 7.49 7.49 7.46 7.43 7.34 7.29

0.70 1.21 1.74 2.46 3.62 4.81 7.02 9.11 12.95 16.02 20.21 28.28 37.49 51.33 67.18 89.66 123.80 166.12 IV 5.26 6.02 8.16 12.25 14.86 21.09 28.58 41.74 52.62 62.37 85.57 108.43 127.71 149.41 189.76 244.61

118 351 890 1981 3959 7431 12988 22672 37391 70578 125934 199097 313580 490048 791005 1249365 1884098 2845527 Iw 2581 6472 15064 31410 60211 108000 193266 328486 516352 785367 1199772 1512359 1824364 2176576 2942076 4147629

Page 25

Arbed

1058.5 1106.9 1155.7 1204.8 1256.7 1312.3 1414.5 1469.7 Wpl,z 51.4 81.0 119.8 170.0 231.0 305.8 393.9 498.4 602.2 717.6 870.1 939.1 985.7 1032.5 1104.0 1197.7 1291.6 1341.1 1391.1 1441.4 1495.0 1553.1 1658.3 1716.3 Wpl,z 116.3 171.6 240.5 325.5 425.2 543.2 678.6 1005.9 1192.5 1396.7 1374.4 1913.2 1950.7 1952.7 1942.4 1934.1 1939.2 1932.0 1937.3

7.24 7.15 7.05 6.97 6.84 6.65 6.50 6.35 iz 2.53 3.06 3.58 4.05 4.57 5.07 5.59 6.08 6.58 7.09 7.58 7.57 7.53 7.49 7.40 7.33 7.27 7.17 7.08 6.99 6.87 6.68 6.53 6.38 iz 2.74 3.25 3.77 4.26 4.77 5.27 5.79 6.39 6.90 7.40 7.81 8.00 7.95 7.90 7.83 7.70 7.59 7.46 7.35

310.27 352.64 399.03 449.66 515.48 598.88 739.16 825.02 IV 9.29 13.90 20.13 31.37 42.32 59.51 76.84 103.07 124.26 144.25 185.77 225.90 258.13 293.49 357.00 441.92 540.10 602.16 669.18 741.40 833.45 949.12 1141.11 1258.36 IV 68.55 92.05 120.46 163.08 204.00 260.38 316.35 630.04 721.50 809.94 600.33 1412.20 1505.38 1510.94 1512.23 1519.38 1533.58 1543.52 1558.33

5643053 7188912 8978203 11027133 13351908 18290286 24961500 32073875 Iw 3375 9410 22479 47943 93746 171125 295418 486946 753651 1130155 1687791 2068712 2453634 2883252 3817152 5258448 7017696 8855763 10965375 13362740 16064064 21840229 29461359 37636488 Iw 9925 24786 54329 108054 199326 346258 572684 1151987 1728347 2520227 2903169 4386028 5003865 5584496 6137021 7410304 9251499 11186745 13515630

Page 26

Arbed

1930.4 1935.7 1928.8 1930.4 1928.9 1939.7 Wpl,z 6.1 12.1 7.1 10.6 8.9 13.0 11.6 16.4 68.1 81.6 Wpl,z 5.5 9.0 13.7 19.8 27.6 37.1 48.5 62.1 78.1 95.7 114.6 135.1 158.8 184.2 214.3 245.1 279.8 329.9 380.1 439.6 501.8 648.5 817.5 Wpl,z 4.7 7.5 11.0 15.5 20.7 28.0 36.5 48.5 62.4 82.3

7.22 7.13 7.01 6.79 6.60 6.45 iz 0.95 0.94 0.95 0.92 1.02 0.97 1.08 1.03 2.10 2.03 iz 0.97 1.15 1.32 1.49 1.66 1.84 2.01 2.18 2.36 2.50 2.63 2.75 2.87 2.99 3.11 3.23 3.35 3.52 3.66 3.82 3.96 4.32 4.58 iz 1.04 1.22 1.42 1.65 1.83 2.05 2.23 2.46 2.68 3.02

1568.89 1583.70 1594.25 1650.96 1676.33 1706.58 IV 0.93 8.94 1.22 4.42 1.65 5.37 2.40 7.24 20.56 40.97 IV 0.80 1.47 2.49 3.97 6.03 8.79 12.40 17.03 22.85 30.63 40.55 52.06 66.61 83.12 105.52 128.62 156.70 199.16 246.82 303.67 371.08 521.66 753.61 IV 0.42 0.78 1.05 1.37 1.97 2.71 4.13 5.72 8.40 10.35

15907585 18649516 21397493 27775287 34746261 43015036 Iw 175 314 309 427 570 771 1044 1383 29378 34009 Iw 100 308 789 1779 3633 6873 12222 20659 33469 51258 74836 106184 148482 202910 275465 365173 479888 670705 901465 1214940 1593639 2704000 4322489 Iw 93 284 705 1577 3095 5933 10529 18707 31257 59506

Page 27

Arbed

107.3 133.3 171.9 202.1 245.7 301.6 456.2 442.1 Wpl,z 21.3 29.4 39.7 53.2 71.8 90.1 121.0 154.5 189.9 236.5 283.6 346.0 414.8 654.9 580.2 Wpl,z 39.9 51.9 66.9 84.4 117.7 152.6 185.0 226.9 269.1 341.0 408.5 480.5 640.1 Wpl,z 28.4 40.6 59.9 91.4 123.6 163.2 209.3 264.4 327.7 399.4 482.3 505.7 529.3

3.34 3.54 3.84 4.00 4.19 4.38 5.27 4.77 iz 1.63 1.83 2.00 2.21 2.49 2.67 3.03 3.32 3.53 3.76 3.93 4.13 4.28 5.21 4.66 iz 2.08 2.30 2.53 2.74 3.09 3.45 3.64 3.86 4.03 4.21 4.38 4.55 4.79 iz 2.43 2.93 3.45 3.97 4.47 4.92 5.42 5.87 6.36 6.85 7.30 7.24 7.18

13.50 19.67 26.62 34.96 45.87 63.03 93.87 119.23 IV 3.44 5.15 7.81 11.77 16.30 22.76 28.95 37.22 50.99 69.07 92.82 122.86 163.86 263.84 271.65 IV 6.78 9.49 12.32 17.27 25.01 31.18 42.35 55.99 73.44 109.51 144.05 188.33 319.40 IV 2.53 2.80 3.56 6.36 8.37 12.76 16.01 23.11 30.49 36.42 49.63 56.19 63.43

107160 171501 281992 432224 704856 1125230 2458177 2607364 Iw 2185 4435 8400 15418 28152 45597 88756 154924 246314 387233 607613 994249 1540473 3561462 3397800 Iw 8740 15566 26785 43678 87640 157690 245654 380267 587647 997576 1547585 2302253 3859573 Iw 1675 4242 10210 23751 46365 84491 145613 239630 382576 590106 877152 1040738 1231291

Page 28

Arbed

553.0 599.7 624.4 649.3 698.6 724.5 750.7 799.7 856.6 957.7 1015.7 Wpl,z 13.64 18.47 25.55 38.78 47.47 58.29 72.56 87.64 145.8 Wpl,z 12.1 16.2 21.2 28.3 35.2 42.9 51.8 64.1 75.7 91.6 109 130 152 143 148 190 Wpl,z 14.28 19.34 25.28 33.22 41.49 52.3 63.28 78.25 92.18 111.6 136.6 156.2

7.12 7.06 6.92 6.79 6.65 6.53 6.41 6.34 6.10 5.99 5.80 iz 1.41 1.57 1.71 2.02 2.16 2.30 2.48 2.60 3.10 iz 1.33 1.47 1.59 1.75 1.89 2.02 2.14 2.30 2.42 2.56 2.74 2.90 2.81 2.72 2.77 3.04 iz

71.39 1443542 85.14 1948416 96.11 2571734 108.28 3303783 134.36 4337702 150.54 5380868 168.34 6566688 196.04 8155072 258.06 11451456 336.39 16256250 405.18 21276699 Iw IV 1.9 0.18 2.65 0.45 4.15 1.22 6.51 2.99 8.43 5.62 11.24 9.98 14.4 15.82 20.38 27.43 36.3 75.04 Iw IV 2.16 0.17 2.81 0.41 4.15 0.9 5.68 1.8 7.39 3.26 9.55 5.57 11.9 9.07 16 14.6 19.7 22.1 25.5 33.3 31 48.5 37.4 69.1 66.7 96.1 61.2 114 59.1 146 81.6 221 IV

1.59 1.75 1.9 2.07 2.22 2.39 2.54 2.7 2.84 2.99 3.08 3.17

1.47 2.01 2.9 4.05 5.2 6.99 8.89 12.05 15.14 19.91 31.52 45.18

Iw 0.22 0.53 1.12 2.2 3.96 6.81 11 17.61 26.42 43.55 72.66 111.3

Ys 1.61 1.7 1.77 2.05 2.12 2.22 2.4 2.45 2.96 Ys 1.45 1.55 1.6 1.75 1.84 1.92 2.01 2.14 2.23 2.36 2.53 2.7 2.6 2.4 2.38 2.65

Ym 3.17 3.38 3.56 4.1 4.32 4.53 4.94 5.04 6.17 Ym 2.67 2.93 3.03 3.37 3.56 3.75 3.94 4.2 4.39 4.66 5.02 5.41 4.82 4.45 4.58 5.11

Ys 1.82 1.91 1.98 2.17 2.27 2.47 2.56 2.7 2.79 2.89 2.89 2.9

Ym 3.71 3.93 4.12 4.54 4.76 5.19 5.41 5.7 5.91 6.14 6.03 6

Page 29

Arbed

177.8 191.4

3.29 3.37

58.49 79.14

166.4 259

2.97 2.98

Page 30

6.12 6.06

Eclisses en traction kg mm ht? b? es (tf)? ea (tw)?

###### ###### 25 mm 15 mm

PROFILE Aire profil= larg.semelle=

13442 mm2

Fadmsem=

210.0 mm

Fadmeclis=

épais.semelle=

17.2 mm

épaisseur âme=

11.1 mm

Fdiamsem=

24.00 kg/mm2

Fdiameclis=

fe acier?

Fadmboulons=

Fsemelles=

ECLISSES

AME

SEMELLE

2

2

120.0 mm

170.0 mm

épaisseur?

10.0 mm

10.0 mm

diamètre trous?

18.0 mm

18.0 mm

nb trous sur 1 file vert?

2

2

nb files vert?

3

4

10.99

10.99

nombre d'éclisses? hauteur?

BOULONS classe? diamètre? Cisaillement simple=

16.0 mm

16.0 mm

11304 kg

11304 kg

143,654 kg 128,640 kg 361,728 kg 317,030 kg 368,640 kg 128,640 kg

139,632 kg 40,320 kg Fadmboulon= 135,648 kg Fdiamâme= 76,723 kg Fdiameclis= 138,240 kg Fâme= 40,320 kg Fadmâme=

Fadmeclis=

Fadmissible=

168,960 kg

Fadmissible + après redistribution = 168,960 kg

Fsemdispo = Feclisses-âme+

15,014 kg 40,320 kg

Féclisse-âme+ qui peut être redistribué

0 kg

dans semelle Max qui peut être distribué

0 kg

F âme dispo=

99,312 kg 128,640 kg

Feclis.semelle + Feclis.semelle qui peut être redistribué

0 kg

dans âme Max qui peut être distribué

0 kg

tw

20 mm

Mx

hw

500 mm

Vy

tf

0.0001 mm

My

bf

20 mm

Vx

Sollicitation au centre de gravité 1035.9 daN.m TORSION Tv 4525.86 daN daN.m Tw daN.m daN.m daN

N Tv moment de torsion de St Venant

Avec :

B

daN.m

0 daN Tv = GIt.(dq/dz) Tw = -EIw.(d q/dz ) B = integrale de Tw 3

Tw moment de torsion non uniforme B Bimoment

3

Semelle

yc

Caractéristiques dans le repére principal d'inertie 4 Iy Ix 250.00 mm 33.3 cm iy ix 0.00 mm 0.58 cm

A

10,000 mm²

yg

P S/V It Iw bx

1040.0002 mm -1 104 m

vy Iy/vy

10.00 mm 3 33.3 cm

vx,2

4 480,131.65 cm cm6

Tpl,z

Ix/vx,2 W pl,y

3 98.67 cm

vx,1 Ix/vx,1

Apl,y

3

50.0 cm 2 100.0 cm

Classe de la section pour S235 et S355 Semelle Âme Compression simple 4 4 4 Flexion simple xx - y>0 comp. 4 4 3 Flexion simple xx - y>0 tend. Flexion composée 0 0 0

W pl,x Apl,x

20,833 cm

4

14.43 cm 250.00 mm 3 833.3 cm 250.00 mm 3 833.3 cm 3

1250.0 cm 2 0.0 cm

4 3

Totale 4 4 4 4

0

0

0

Calcul Moment critique EC3 Annexe F C1? 1.132 C2? 0.459 C3? 0.525 k? 1 Portée L? 7.2 m fe? 24.0 kg/mm2 Za=yg? 68.6 mm

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Mcr= Kd= Mul=

257710.1 kgm 0.993 29798.8 kgm

6/7/2014

700

600

500

400

300

200

100

0 -15

x (mm) -10.0 -9.0 -8.0 -7.0 -6.0

-10

-5

0

5

10

Points caractéristiques Semelle Contrainte en daN/mm² y (mm) 0.00 500.0 0.01 475.0 0.01 450.0 0.02 425.0 0.02 400.0

15

Ame Contrainte en daN/mm² 0.00 0.13 0.24 0.35 0.43

-5.0

0.03

375.0

0.51

-4.0 -3.0

0.03 0.04

350.0 325.0

0.57 0.62

-2.0

0.04

300.0

0.65

-1.0

0.05

275.0

0.67

0.0

0.05

250.0

0.68

1.0

0.05

225.0

0.67

2.0

0.04

200.0

0.65

3.0

0.04

175.0

0.62

4.0 5.0 6.0 7.0 8.0 9.0 10.0

0.03 0.03 0.02 0.02 0.01 0.01 0.00

150.0 125.0 100.0 75.0 50.0 25.0 0.0

0.57 0.51 0.43 0.35 0.24 0.13 0.00

Maximum

Maximum

charges dirigées vers C Semelle tendue charges s'éloignant de CSemelle comprimée 2 2

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6/7/2014

tw

5.5 mm

Mx

hw

400 mm

Vy

tf

0.00001 mm

My

bf

5.5 mm

Vx

Sollicitation au centre de gravité 1072.6 daN.m TORSION Tv 4615.38 daN daN.m Tw daN.m daN.m daN

N Tv moment de torsion de St Venant

Avec :

B

daN.m

0 daN Tv = GIt.(dq/dz) Tw = -EIw.(d q/dz ) B = integrale de Tw 3

Tw moment de torsion non uniforme B Bimoment

3

Semelle

Caractéristiques dans le repére principal d'inertie 4 Iy Ix 200.00 mm 0.6 cm iy ix 0.00 mm 0.16 cm

yg yc A P S/V It

2,200 mm² 811.00002 mm -1 369 m

Iw bx Tpl,z

vy

2.75 mm 3 2.0 cm

Iy/vy

vx,2

4 7,551.47 cm cm6

Ix/vx,2 3

3.0 cm 2 22.0 cm

W pl,y 3 6.02 cm

vx,1 Ix/vx,1

Apl,y

Classe de la section pour S235 et S355 Semelle Âme Compression simple 4 4 4 Flexion simple xx - y>0 comp. 4 4 3 Flexion simple xx - y>0 tend. Flexion composée 0 0 0

2,933 cm 11.55 cm

200.00 mm 3 146.7 cm 200.00 mm 3 146.7 cm 3

Apl,x

220.0 cm 2 0.0 cm

4 3

Totale 4 4 4 4

0

0

W pl,x

Calcul Moment critique EC3 Annexe F C1? 1.132 C2? 0.459 C3? 0.525 k? 1 Portée L? 7.2 m fe? 24.0 kg/mm2 Za=yg? 68.6 mm

SOCOTEC - Service Charpente

Zg= Zj= >0 si la charge est Page 36

4

0

Pour le cisaillement les valeurs so de la poutre

####### #######

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Mcr= Kd= Mul=

4167.8 kgm 0.620 3271.4 kgm

6/7/2014

600

500

400

300

200

100

0 -4

x (mm) -2.8 -2.5 -2.2 -1.9 -1.7

-3

-2

-1

0

1

2

Points caractéristiques Semelle Contrainte en daN/mm² y (mm) 0.00 400.0 0.01 380.0 0.02 360.0 0.03 340.0 0.03 320.0

3

4

Ame Contrainte en daN/mm² 0.00 0.40 0.76 1.07 1.34

-1.4

0.04

300.0

1.57

-1.1 -0.8

0.05 0.06

280.0 260.0

1.76 1.91

-0.6

0.07

240.0

2.01

-0.3

0.08

220.0

2.08

0.0

0.09

200.0

2.10

0.3

0.08

180.0

2.08

0.6

0.07

160.0

2.01

0.8

0.06

140.0

1.91

1.1 1.4 1.7 1.9 2.2 2.5 2.8

0.05 0.04 0.03 0.03 0.02 0.01 0.00

120.0 100.0 80.0 60.0 40.0 20.0 0.0

1.76 1.57 1.34 1.07 0.76 0.40 0.00

Maximum

Maximum

Pour le cisaillement les valeurs sont divisées par 1.5 pour tenir compte des semelles de la poutre charges dirigées vers C Semelle tendue charges s'éloignant de CSemelle comprimée 2 2

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