lifting lug mec fractura

Sample CalculationThickness of Lug (t) =Width of Lug (W) =Radius of Circular Section (R) =

=

=Distance from centre of hole to Welding (h)=

Area of Cross Section =Length of Crack ( a ) =

Temperature (T) =

=

=

Check For Geometry

= 100 - 60/ 2 =

= 100 - 60/ 2 =

= 100 - 60/ 2 =

By Yeild TheoryYeild Strength of Plate = 345Effective width of plate = 200 - 60- 2 x4.5 =Tensile Load capacity = 0.9 x 345 x 131 x 20/1000 =

By Fracture Theory

=

=

Where, d =d = 4.5 / (60/ 2 + 4.5)

= 0.5 x (3 -0.13) [ 1 + 1.243 x (1 -0.13)^3 ]= 2.61

= Load (P) =Area

=63 = 2.61 x 0.00025P x sqrt(3.1416 x 0.0045)

1 Lifting Lug Load Capacity Vs Crack length Calculation

Diameter of Hole ( Dh)

Diameter of Pin ( Dp)

Distance from centre of hole to edge of crack = (Dh / 2 + a) =

Fracture Toughness ( k1c

)

K1c

We =R- Dh/2

We =R- Dh/2

We =R- Dh/2

K1c

Fd . . Sqrt(. a)

Fd 0.5 x (3 - d) [ 1 + 1.243 x (1 - d)3 ]

a / (Dh / 2 + a)

Fd

K1c

Fd . . Sqrt(. a)

Load ( P) = 812 kN

Temp = 30 Degree Celcius

1 31 30 66 0.032

1.5 31.5 30 66 0.048

2 32 30 66 0.063

2.5 32.5 30 66 0.077

3 33 30 66 0.091

3.5 33.5 30 66 0.104

4 34 30 66 0.118

5 35 30 66 0.143

5.8 35.8 30 66 0.162

7 37 30 66 0.1898 38 30 66 0.2119 39 30 66 0.23110 40 30 66 0.25


1 31 15 63 0.032

1.5 31.5 15 63 0.048

2 32 15 63 0.063

2.5 32.5 15 63 0.077

3 33 15 63 0.091

3.5 33.5 15 63 0.104

4 34 15 63 0.118

4.5 34.5 15 63 0.13

6 36 15 63 0.167

7 37 15 63 0.189

8 38 15 63 0.211

9 39 15 63 0.231

10 40 15 63 0.25

Length of Crack ( a ) (mm) (D

h / 2 + a)

Temperature (T) oC

Fracture Toughness ( k

1c) d = a / (D

h / 2 + a)


h / 2 + a)

Temperature (T) oC


1c) d = a / (D

h / 2 + a)

Temp = Zero Degree Celcius

1 31 0 60 0.032

1.5 31.5 0 60 0.048

2 32 0 60 0.063

2.5 32.5 0 60 0.077

3 33 0 60 0.091

3.5 33.5 0 60 0.104

3.7 33.7 0 60 0.11

5 35 0 60 0.143

6 36 0 60 0.167

7 37 0 60 0.189

8 38 0 60 0.211

9 39 0 60 0.231

10 40 0 60 0.25

Temp = -15 Degree Celcius

1 31 -15 57 0.032

1.5 31.5 -15 57 0.048

2 32 -15 57 0.063

2.5 32.5 -15 57 0.077

3 33 -15 57 0.091

3.1 33.1 -15 57 0.094

4 34 -15 57 0.118

5 35 -15 57 0.143

6 36 -15 57 0.167

7 37 -15 57 0.189

8 38 -15 57 0.211

9 39 -15 57 0.231

10 40 -15 57 0.25



h / 2 + a)

Temperature (T) oC


1c) d = a / (D

h / 2 + a)


h / 2 + a)

Temperature (T) oC


1c) d = a / (D

h / 2 + a)

1 31 -30 54 0.032

1.5 31.5 -30 54 0.048

2 32 -30 54 0.063

2.5 32.5 -30 54 0.077

2.6 32.6 -30 54 0.08

3.5 33.5 -30 54 0.104

4 34 -30 54 0.118

5 35 -30 54 0.143

6 36 -30 54 0.167

7 37 -30 54 0.189

8 38 -30 54 0.211

9 39 -30 54 0.231

10 40 -30 54 0.25


1 31 -45 51 0.032

1.5 31.5 -45 51 0.048

2 32 -45 51 0.063

2.15 32.15 -45 51 0.067

3 33 -45 51 0.091

3.5 33.5 -45 51 0.104

4 34 -45 51 0.118

5 35 -45 51 0.143

6 36 -45 51 0.167

7 37 -45 51 0.189

8 38 -45 51 0.211

9 39 -45 51 0.231

10 40 -45 51 0.25

Length of Crack ( a ) (mm) (Dh / 2 + a)

Temperature (T) oC

Fracture Toughness ( k1c) d = a / (Dh / 2 + a)


Temperature (T) oC


Kawish Shaikh P.Eng. UofC

20 mm > Dh/4 ; Hence OK200 mm100 mm

60 mm

57 mm100 mm > 1.5xDh ; Hence OK

20 x 200 = 40004.5 mm Both side of Hole

35 mm

15

(60 + 0.2 T) Mpa. Sqrt(m) (60 for Steel WT Caterary 4)For -140 < T < 150

63

70 mm > Dh/2 ; Hence OK

70 mm < 5t ; Hence OK

70 mm > 2t ; Hence OK

MPa131 mm

0.9 x 345 x 131 x 20/1000 = 814 kN

= 0.13

0.5 x (3 -0.13) [ 1 + 1.243 x (1 -0.13)^3 ]

P / 4000 = 0.0003 P

2.61 x 0.00025P x sqrt(3.1416 x 0.0045)

mm2

oC

oC

100

m

m

Crack Length (a)

Fracture Theory Yeild Theory

3.157 1492 601 138 857 345

3.059 1257 510 137 851 345

2.97 1121 458 136 845 345

2.89 1031 424 135 838 345

2.812 967 401 134 832 345

2.743 918 383 133 826 345

2.67 882 371 132 820 345

2.546 827 354 130 807 345

2.457 796 344 128.4 797 345

2.337 762 336 126 782 3452.246 741 332 124 770 3452.167 725 330 122 758 3452.096 711 329 120 745 345


3.157 1424 573 138 857 345

3.059 1200 487 137 851 345

2.97 1070 437 136 845 345

2.89 984 405 135 838 345

2.812 923 383 134 832 345

2.743 876 366 133 826 345

2.67 842 354 132 820 345

2.61 812 344 131 814 345

2.434 754 327 128 795 345

2.337 727 321 126 782 345

2.246 708 317 124 770 345

2.167 692 315 122 758 345

2.096 678 314 120 745 345

Fd

Load (P) (kN) - Fracture

TheoryStress in the Net Section

Effective width of Plate (mm)

Load (P) (kN) -Yeild

TheoryYeild Stress (s)

Fd







3.157 1356 546 138 857 345

3.059 1143 463 137 851 345

2.97 1019 416 136 845 345

2.89 937 386 135 838 345

2.812 879 364 134 832 345

2.743 834 349 133 826 345

2.711 821 344 132.6 823 345

2.546 752 321 130 807 345

2.434 718 312 128 795 345

2.337 693 305 126 782 345

2.246 674 302 124 770 345

2.167 659 300 122 758 345

2.096 646 299 120 745 345


3.157 1289 519 138 857 345

3.059 1086 440 137 851 345

2.97 968 396 136 845 345

2.89 890 366 135 838 345

2.812 835 346 134 832 345

2.796 826 343 133.8 831 345

2.67 762 321 132 820 345

2.546 715 305 130 807 345

2.434 682 296 128 795 345

2.337 658 290 126 782 345

2.246 640 287 124 770 345

2.167 626 285 122 758 345

2.096 614 284 120 745 345


Fd






Fd






3.157 1221 491 138 857 345

3.059 1029 417 137 851 345

2.97 918 375 136 845 345

2.89 843 347 135 838 345

2.873 832 343 134.8 837 345

2.743 751 314 133 826 345

2.67 722 304 132 820 345

2.546 677 289 130 807 345

2.434 646 281 128 795 345

2.337 623 275 126 782 345

2.246 607 272 124 770 345

2.167 593 270 122 758 345

2.096 581 269 120 745 345


3.157 1153 464 138 857 345

3.059 971 394 137 851 345

2.97 867 354 136 845 345

2.947 842 345 135.7 843 345

2.812 747 310 134 832 345

2.743 709 296 133 826 345

2.67 682 287 132 820 345

2.546 639 273 130 807 345

2.434 610 265 128 795 345

2.337 589 260 126 782 345

2.246 573 257 124 770 345

2.167 560 255 122 758 345

2.096 549 254 120 745 345

Fd






Fd







Crack Lenth (a) Vs Tensile Load (P)

LOAD (P)

100

m

m

200 mm

100

mm

60 mm Dia. hole

Crack Length (a)

Net Section will Yeild before Fracture








Net Section will Fracture

Net Section will FractureNet Section will FractureNet Section will FractureNet Section will Fracture














0 2 4 6 8 10 120

200

400

600

800

1000

1200

1400

1600Crack Length (a) VS Lug Capacity (kN) for 30 oC

Load (P) (kN) - Fracture Theory

Load (P) (kN) -Yeild Theory

a (mm)Load

(kN

)

0 2 4 6 8 10 120

200

400

600

800

1000

1200

1400




a (mm)

Load

(kN

)



























0 2 4 6 8 10 120

200

400

600

800

1000

1200

1400




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

200

400

600

800

1000

1200

1400Crack Length (a) VS Lug Capacity (kN) for -15 oC



a (mm)

Load

(kN

)

0 2 4 6 8 10 120

200

400

600

800

1000

1200




a (mm)

Load

(kN

)



























0 2 4 6 8 10 120

200

400

600

800

1000

1200




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

200

400

600

800

1000

1200




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

200

400

600

800

1000

1200

1400




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

200

400

600

800

1000

1200

1400

1600

Crack Length (a) VS Lug Capacity (kN)







a (mm)

Load

(kN

)

0 2 4 6 8 10 120

200

400

600

800

1000

1200

1400




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

200

400

600

800

1000

1200

1400

1600








a (mm)

Load

(kN

)

0 2 4 6 8 10 120

200

400

600

800

1000

1200

1400




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

200

400

600

800

1000

1200




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

200

400

600

800

1000

1200




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

200

400

600

800

1000

1200




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

200

400

600

800

1000

1200




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

200

400

600

800

1000

1200

1400

1600








a (mm)

Load

(kN

)

Sample CalculationThickness of Lug (t) =Width of Lug (W) =Radius of Circular Section (R) =

=

=Distance from centre of hole to Welding (h)=

Area of Cross Section =Length of Crack ( a ) =

Temperature (T) =

=

=

Check For Geometry

= 100 - 60/ 2 =

= 100 - 60/ 2 =

= 100 - 60/ 2 =

By Yeild TheoryYeild Strength of Plate = 345Effective width of plate = 200 - 60- 2 x4.5 =Tensile Load capacity = 0.9 x 345 x 131 x 20/1000 =

By Fracture Theory

=

=

Where, d =d = 4.5 / (60/ 2 + 4.5)

= 0.5 x (3 -0.13) [ 1 + 1.243 x (1 -0.13)^3 ]= 2.61

= Load (P) =Area

=43 = 2.61 x 0.00025P x sqrt(3.1416 x 0.0045)

1 Lifting Lug Load Capacity Vs Crack length Calculation

Diameter of Hole ( Dh)

Diameter of Pin ( Dp)

Distance from centre of hole to edge of crack = (Dh / 2 + a) =

Fracture Toughness ( k1c

)

K1c

We =R- Dh/2

We =R- Dh/2

We =R- Dh/2

K1c

Fd . . Sqrt(. a)

Fd 0.5 x (3 - d) [ 1 + 1.243 x (1 - d)3 ]

a / (Dh / 2 + a)

Fd

K1c

Fd . . Sqrt(. a)

Load ( P) = 554 kN


1 31 30 46 0.032

1.5 31.5 30 46 0.048

2 32 30 46 0.063

2.5 32.5 30 46 0.077

3 33 30 46 0.091

3.5 33.5 30 46 0.104

4 34 30 46 0.118

5 35 30 46 0.143

5.8 35.8 30 46 0.162

7 37 30 46 0.1898 38 30 46 0.2119 39 30 46 0.23110 40 30 46 0.25


1 31 15 43 0.032

1.5 31.5 15 43 0.048

2 32 15 43 0.063

2.5 32.5 15 43 0.077

3 33 15 43 0.091

3.5 33.5 15 43 0.104

4 34 15 43 0.118

4.5 34.5 15 43 0.13

6 36 15 43 0.167

7 37 15 43 0.189

8 38 15 43 0.211

9 39 15 43 0.231

10 40 15 43 0.25


h / 2 + a)

Temperature (T) oC


1c) d = a / (D

h / 2 + a)


h / 2 + a)

Temperature (T) oC


1c) d = a / (D

h / 2 + a)


1 31 0 40 0.032

1.5 31.5 0 40 0.048

2 32 0 40 0.063

2.5 32.5 0 40 0.077

3 33 0 40 0.091

3.5 33.5 0 40 0.104

3.7 33.7 0 40 0.11

5 35 0 40 0.143

6 36 0 40 0.167

7 37 0 40 0.189

8 38 0 40 0.211

9 39 0 40 0.231

10 40 0 40 0.25


1 31 -15 37 0.032

1.5 31.5 -15 37 0.048

2 32 -15 37 0.063

2.5 32.5 -15 37 0.077

3 33 -15 37 0.091

3.1 33.1 -15 37 0.094

4 34 -15 37 0.118

5 35 -15 37 0.143

6 36 -15 37 0.167

7 37 -15 37 0.189

8 38 -15 37 0.211

9 39 -15 37 0.231

10 40 -15 37 0.25



h / 2 + a)

Temperature (T) oC


1c) d = a / (D

h / 2 + a)


h / 2 + a)

Temperature (T) oC


1c) d = a / (D

h / 2 + a)

1 31 -30 34 0.032

1.5 31.5 -30 34 0.048

2 32 -30 34 0.063

2.5 32.5 -30 34 0.077

2.6 32.6 -30 34 0.08

3.5 33.5 -30 34 0.104

4 34 -30 34 0.118

5 35 -30 34 0.143

6 36 -30 34 0.167

7 37 -30 34 0.189

8 38 -30 34 0.211

9 39 -30 34 0.231

10 40 -30 34 0.25


1 31 -45 31 0.032

1.5 31.5 -45 31 0.048

2 32 -45 31 0.063

2.15 32.15 -45 31 0.067

3 33 -45 31 0.091

3.5 33.5 -45 31 0.104

4 34 -45 31 0.118

5 35 -45 31 0.143

6 36 -45 31 0.167

7 37 -45 31 0.189

8 38 -45 31 0.211

9 39 -45 31 0.231

10 40 -45 31 0.25


Temperature (T) oC



Temperature (T) oC



20 mm > Dh/4 ; Hence OK200 mm100 mm

60 mm

57 mm100 mm > 1.5xDh ; Hence OK

20 x 200 = 40004.5 mm Both side of Hole

35 mm

15

(40 + 0.2 T) Mpa. Sqrt(m) (40 for Steel W 350)For -140 < T < 150

43

70 mm > Dh/2 ; Hence OK

70 mm < 5t ; Hence OK

70 mm > 2t ; Hence OK

MPa131 mm

0.9 x 345 x 131 x 20/1000 = 814 kN

= 0.13

0.5 x (3 -0.13) [ 1 + 1.243 x (1 -0.13)^3 ]

P / 4000 = 0.0003 P

2.61 x 0.00025P x sqrt(3.1416 x 0.0045)

mm2

oC

oC

100

m

m

Crack Length (a)


3.157 1040 419 138 857 345

3.059 876 355 137 851 345

2.97 782 319 136 845 345

2.89 718 296 135 838 345

2.812 674 279 134 832 345

2.743 640 267 133 826 345

2.67 615 259 132 820 345

2.546 577 246 130 807 345

2.457 555 240 128.4 797 345

2.337 531 234 126 782 3452.246 517 232 124 770 3452.167 505 230 122 758 3452.096 495 229 120 745 345


3.157 972 391 138 857 345

3.059 819 332 137 851 345

2.97 731 298 136 845 345

2.89 672 276 135 838 345

2.812 630 261 134 832 345

2.743 598 250 133 826 345

2.67 575 242 132 820 345

2.61 554 235 131 814 345

2.434 515 223 128 795 345

2.337 496 219 126 782 345

2.246 483 216 124 770 345

2.167 472 215 122 758 345

2.096 463 214 120 745 345

Fd






Fd







3.157 904 364 138 857 345

3.059 762 309 137 851 345

2.97 680 278 136 845 345

2.89 625 257 135 838 345

2.812 586 243 134 832 345

2.743 556 232 133 826 345

2.711 547 229 132.6 823 345

2.546 501 214 130 807 345

2.434 479 208 128 795 345

2.337 462 204 126 782 345

2.246 449 201 124 770 345

2.167 439 200 122 758 345

2.096 431 199 120 745 345


3.157 836 337 138 857 345

3.059 705 286 137 851 345

2.97 629 257 136 845 345

2.89 578 238 135 838 345

2.812 542 225 134 832 345

2.796 536 223 133.8 831 345

2.67 494 208 132 820 345

2.546 464 198 130 807 345

2.434 443 192 128 795 345

2.337 427 188 126 782 345

2.246 416 186 124 770 345

2.167 406 185 122 758 345

2.096 398 184 120 745 345


Fd






Fd






3.157 769 309 138 857 345

3.059 648 263 137 851 345

2.97 578 236 136 845 345

2.89 531 219 135 838 345

2.873 524 216 134.8 837 345

2.743 473 198 133 826 345

2.67 454 191 132 820 345

2.546 426 182 130 807 345

2.434 407 177 128 795 345

2.337 392 173 126 782 345

2.246 382 171 124 770 345

2.167 373 170 122 758 345

2.096 366 169 120 745 345


3.157 701 282 138 857 345

3.059 591 239 137 851 345

2.97 527 215 136 845 345

2.947 512 210 135.7 843 345

2.812 454 188 134 832 345

2.743 431 180 133 826 345

2.67 414 174 132 820 345

2.546 389 166 130 807 345

2.434 371 161 128 795 345

2.337 358 158 126 782 345

2.246 348 156 124 770 345

2.167 340 155 122 758 345

2.096 334 155 120 745 345

Fd






Fd







Crack Lenth (a) Vs Tensile Load (P)

LOAD (P)

100

m

m

200 mm

100

mm

60 mm Dia. hole

Crack Length (a)










Net Section will FractureNet Section will FractureNet Section will FractureNet Section will Fracture














0 2 4 6 8 10 120

200

400

600

800

1000




a (mm)Load

(kN

)

0 2 4 6 8 10 120

200

400

600

800

1000




a (mm)

Load

(kN

)



























0 2 4 6 8 10 120

100

200

300

400

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700

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900




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

100

200

300

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800




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

100

200

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800




a (mm)

Load

(kN

)



























0 2 4 6 8 10 120

100

200

300

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500

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800




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

100

200

300

400

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600

700

800




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

200

400

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1000




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

200

400

600

800

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1200








a (mm)

Load

(kN

)

0 2 4 6 8 10 120

200

400

600

800

1000




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

200

400

600

800

1000

1200








a (mm)

Load

(kN

)

0 2 4 6 8 10 120

100

200

300

400

500

600

700

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900




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

100

200

300

400

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800




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

100

200

300

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600

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800




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

100

200

300

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800




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

100

200

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800




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

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a (mm)

Load

(kN

)

lifting lug mec fractura

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