lifting lug mec fractura
DESCRIPTION
Diseño de orejas de izaje por mecanica de la fracturaTRANSCRIPT
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
Temp = 15 Degree Celcius
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)
Length of Crack ( a ) (mm) (D
h / 2 + a)
Temperature (T) oC
Fracture Toughness ( k
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
Temp = -30 Degree Celcius
Length of Crack ( a ) (mm) (D
h / 2 + a)
Temperature (T) oC
Fracture Toughness ( k
1c) d = a / (D
h / 2 + a)
Length of Crack ( a ) (mm) (D
h / 2 + a)
Temperature (T) oC
Fracture Toughness ( k
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
Temp = -45 Degree Celcius
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)
Length of Crack ( a ) (mm) (Dh / 2 + a)
Temperature (T) oC
Fracture Toughness ( k1c) d = a / (Dh / 2 + a)
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
Fracture Theory Yeild Theory
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
Load (P) (kN) - Fracture
TheoryStress in the Net Section
Effective width of Plate (mm)
Load (P) (kN) -Yeild
TheoryYeild Stress (s)
Fracture Theory Yeild Theory
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
Fracture Theory Yeild Theory
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
Fracture Theory Yeild Theory
Fd
Load (P) (kN) - Fracture
TheoryStress in the Net Section
Effective width of Plate (mm)
Load (P) (kN) -Yeild
TheoryYeild Stress (s)
Fd
Load (P) (kN) - Fracture
TheoryStress in the Net Section
Effective width of Plate (mm)
Load (P) (kN) -Yeild
TheoryYeild Stress (s)
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
Fracture Theory Yeild Theory
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
Load (P) (kN) - Fracture
TheoryStress in the Net Section
Effective width of Plate (mm)
Load (P) (kN) -Yeild
TheoryYeild Stress (s)
Fd
Load (P) (kN) - Fracture
TheoryStress in the Net Section
Effective width of Plate (mm)
Load (P) (kN) -Yeild
TheoryYeild Stress (s)
Kawish Shaikh P.Eng. UofC
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 Yeild before Fracture
Net Section will Yeild before Fracture
Net Section will Yeild before Fracture
Net Section will Yeild before Fracture
Net Section will Yeild before Fracture
Net Section will Yeild before Fracture
Net Section will Yeild before Fracture
Net Section will Fracture
Net Section will FractureNet Section will FractureNet Section will FractureNet Section will Fracture
Net Section will Yeild before Fracture
Net Section will Yeild before Fracture
Net Section will Yeild before Fracture
Net Section will Yeild before Fracture
Net Section will Yeild before Fracture
Net Section will Yeild before Fracture
Net Section will Yeild before Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net 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
1600Crack Length (a) VS Lug Capacity (kN) for 15 oC
Load (P) (kN) - Fracture Theory
Load (P) (kN) -Yeild Theory
a (mm)
Load
(kN
)
Net Section will Yeild before Fracture
Net Section will Yeild before Fracture
Net Section will Yeild before Fracture
Net Section will Yeild before Fracture
Net Section will Yeild before Fracture
Net Section will Yeild before Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Yeild before Fracture
Net Section will Yeild before Fracture
Net Section will Yeild before Fracture
Net Section will Yeild before Fracture
Net Section will Yeild before Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net 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 0 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
1400Crack Length (a) VS Lug Capacity (kN) for -15 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
1400Crack Length (a) VS Lug Capacity (kN) for -30 oC
Load (P) (kN) - Fracture Theory
Load (P) (kN) -Yeild Theory
a (mm)
Load
(kN
)
Net Section will Yeild before Fracture
Net Section will Yeild before Fracture
Net Section will Yeild before Fracture
Net Section will Yeild before Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Yeild before Fracture
Net Section will Yeild before Fracture
Net Section will Yeild before Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
0 2 4 6 8 10 120
200
400
600
800
1000
1200
1400Crack 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
1400Crack Length (a) VS Lug Capacity (kN) for -45 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
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
1600
Crack Length (a) VS Lug Capacity (kN)
Temp = 30 Degree Celcius
Temp = 15 Degree Celcius
Temp = Zero Degree Celcius
Temp = -15 Degree Celcius
Temp = -45 Degree Celcius
Load (P) (kN) -Yeild Theory
a (mm)
Load
(kN
)
0 2 4 6 8 10 120
200
400
600
800
1000
1200
1400
1600Crack Length (a) VS Lug Capacity (kN) for 15 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
1600
Crack Length (a) VS Lug Capacity (kN)
Temp = 30 Degree Celcius
Temp = 15 Degree Celcius
Temp = Zero Degree Celcius
Temp = -15 Degree Celcius
Temp = -45 Degree Celcius
Load (P) (kN) -Yeild Theory
a (mm)
Load
(kN
)
0 2 4 6 8 10 120
200
400
600
800
1000
1200
1400
1600Crack Length (a) VS Lug Capacity (kN) for 0 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
1400Crack Length (a) VS Lug Capacity (kN) for -15 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
1400Crack 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
1400Crack 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
1400Crack Length (a) VS Lug Capacity (kN) for -45 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
1600
Crack Length (a) VS Lug Capacity (kN)
Temp = 30 Degree Celcius
Temp = 15 Degree Celcius
Temp = Zero Degree Celcius
Temp = -15 Degree Celcius
Temp = -45 Degree Celcius
Load (P) (kN) -Yeild Theory
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)
Temp = 30 Degree Celcius
Temp = 15 Degree Celcius
Temp = Zero Degree Celcius
Temp = -15 Degree Celcius
Temp = -45 Degree Celcius
Load (P) (kN) -Yeild Theory
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)
Temp = 30 Degree Celcius
Temp = 15 Degree Celcius
Temp = Zero Degree Celcius
Temp = -15 Degree Celcius
Temp = -45 Degree Celcius
Load (P) (kN) -Yeild Theory
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)
Temp = 30 Degree Celcius
Temp = 15 Degree Celcius
Temp = Zero Degree Celcius
Temp = -15 Degree Celcius
Temp = -45 Degree Celcius
Load (P) (kN) -Yeild Theory
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
Temp = 30 Degree Celcius
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
Temp = 15 Degree Celcius
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
Length of Crack ( a ) (mm) (D
h / 2 + a)
Temperature (T) oC
Fracture Toughness ( k
1c) d = a / (D
h / 2 + a)
Length of Crack ( a ) (mm) (D
h / 2 + a)
Temperature (T) oC
Fracture Toughness ( k
1c) d = a / (D
h / 2 + a)
Temp = Zero Degree Celcius
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
Temp = -15 Degree Celcius
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
Temp = -30 Degree Celcius
Length of Crack ( a ) (mm) (D
h / 2 + a)
Temperature (T) oC
Fracture Toughness ( k
1c) d = a / (D
h / 2 + a)
Length of Crack ( a ) (mm) (D
h / 2 + a)
Temperature (T) oC
Fracture Toughness ( k
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
Temp = -45 Degree Celcius
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
Length of Crack ( a ) (mm) (Dh / 2 + a)
Temperature (T) oC
Fracture Toughness ( k1c) d = a / (Dh / 2 + a)
Length of Crack ( a ) (mm) (Dh / 2 + a)
Temperature (T) oC
Fracture Toughness ( k1c) d = a / (Dh / 2 + a)
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
(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)
Fracture Theory Yeild Theory
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
Fracture Theory Yeild Theory
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
Load (P) (kN) - Fracture
TheoryStress in the Net Section
Effective width of Plate (mm)
Load (P) (kN) -Yeild
TheoryYeild Stress (s)
Fd
Load (P) (kN) - Fracture
TheoryStress in the Net Section
Effective width of Plate (mm)
Load (P) (kN) -Yeild
TheoryYeild Stress (s)
Fracture Theory Yeild Theory
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
Fracture Theory Yeild Theory
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
Fracture Theory Yeild Theory
Fd
Load (P) (kN) - Fracture
TheoryStress in the Net Section
Effective width of Plate (mm)
Load (P) (kN) -Yeild
TheoryYeild Stress (s)
Fd
Load (P) (kN) - Fracture
TheoryStress in the Net Section
Effective width of Plate (mm)
Load (P) (kN) -Yeild
TheoryYeild Stress (s)
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
Fracture Theory Yeild Theory
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
Load (P) (kN) - Fracture
TheoryStress in the Net Section
Effective width of Plate (mm)
Load (P) (kN) -Yeild
TheoryYeild Stress (s)
Fd
Load (P) (kN) - Fracture
TheoryStress in the Net Section
Effective width of Plate (mm)
Load (P) (kN) -Yeild
TheoryYeild Stress (s)
Kawish Shaikh P.Eng. UofC
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 Yeild before Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will FractureNet Section will FractureNet Section will FractureNet Section will Fracture
Net Section will Yeild before Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
0 2 4 6 8 10 120
200
400
600
800
1000
1200Crack 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
1200Crack Length (a) VS Lug Capacity (kN) for 15 oC
Load (P) (kN) - Fracture Theory
Load (P) (kN) -Yeild Theory
a (mm)
Load
(kN
)
Net Section will Yeild before Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
0 2 4 6 8 10 120
100
200
300
400
500
600
700
800
900
1000Crack Length (a) VS Lug Capacity (kN) for 0 oC
Load (P) (kN) - Fracture Theory
Load (P) (kN) -Yeild Theory
a (mm)
Load
(kN
)
0 2 4 6 8 10 120
100
200
300
400
500
600
700
800
900Crack Length (a) VS Lug Capacity (kN) for -15 oC
Load (P) (kN) - Fracture Theory
Load (P) (kN) -Yeild Theory
a (mm)
Load
(kN
)
0 2 4 6 8 10 120
100
200
300
400
500
600
700
800
900Crack Length (a) VS Lug Capacity (kN) for -30 oC
Load (P) (kN) - Fracture Theory
Load (P) (kN) -Yeild Theory
a (mm)
Load
(kN
)
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
Net Section will Fracture
0 2 4 6 8 10 120
100
200
300
400
500
600
700
800
900Crack 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
100
200
300
400
500
600
700
800
900Crack Length (a) VS Lug Capacity (kN) for -45 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
1200Crack 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
Crack Length (a) VS Lug Capacity (kN)
Temp = 30 Degree Celcius
Temp = 15 Degree Celcius
Temp = Zero Degree Celcius
Temp = -15 Degree Celcius
Temp = -45 Degree Celcius
Load (P) (kN) -Yeild Theory
a (mm)
Load
(kN
)
0 2 4 6 8 10 120
200
400
600
800
1000
1200Crack Length (a) VS Lug Capacity (kN) for 15 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
Crack Length (a) VS Lug Capacity (kN)
Temp = 30 Degree Celcius
Temp = 15 Degree Celcius
Temp = Zero Degree Celcius
Temp = -15 Degree Celcius
Temp = -45 Degree Celcius
Load (P) (kN) -Yeild Theory
a (mm)
Load
(kN
)
0 2 4 6 8 10 120
100
200
300
400
500
600
700
800
900
1000Crack Length (a) VS Lug Capacity (kN) for 0 oC
Load (P) (kN) - Fracture Theory
Load (P) (kN) -Yeild Theory
a (mm)
Load
(kN
)
0 2 4 6 8 10 120
100
200
300
400
500
600
700
800
900Crack Length (a) VS Lug Capacity (kN) for -15 oC
Load (P) (kN) - Fracture Theory
Load (P) (kN) -Yeild Theory
a (mm)
Load
(kN
)
0 2 4 6 8 10 120
100
200
300
400
500
600
700
800
900Crack 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
100
200
300
400
500
600
700
800
900Crack 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
100
200
300
400
500
600
700
800
900Crack Length (a) VS Lug Capacity (kN) for -45 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
Crack Length (a) VS Lug Capacity (kN)
Temp = 30 Degree Celcius
Temp = 15 Degree Celcius
Temp = Zero Degree Celcius
Temp = -15 Degree Celcius
Temp = -45 Degree Celcius
Load (P) (kN) -Yeild Theory
a (mm)
Load
(kN
)
0 2 4 6 8 10 120
200
400
600
800
1000
1200
Crack Length (a) VS Lug Capacity (kN)
Temp = 30 Degree Celcius
Temp = 15 Degree Celcius
Temp = Zero Degree Celcius
Temp = -15 Degree Celcius
Temp = -45 Degree Celcius
Load (P) (kN) -Yeild Theory
a (mm)
Load
(kN
)
0 2 4 6 8 10 120
200
400
600
800
1000
1200
Crack Length (a) VS Lug Capacity (kN)
Temp = 30 Degree Celcius
Temp = 15 Degree Celcius
Temp = Zero Degree Celcius
Temp = -15 Degree Celcius
Temp = -45 Degree Celcius
Load (P) (kN) -Yeild Theory
a (mm)
Load
(kN
)
0 2 4 6 8 10 120
200
400
600
800
1000
1200
Crack Length (a) VS Lug Capacity (kN)
Temp = 30 Degree Celcius
Temp = 15 Degree Celcius
Temp = Zero Degree Celcius
Temp = -15 Degree Celcius
Temp = -45 Degree Celcius
Load (P) (kN) -Yeild Theory
a (mm)
Load
(kN
)