lifting lug

Sample CalculationThickness of Lug (t) = 20 mmWidth of Lug (W) = 200 mmRadius of Circular Section (R) = 100 mm

= 60 mm

= 57 mmDistance from centre of hole to Welding (h)= 100 mm

Area of Cross Section = 20 x 200 = 4000Length of Crack ( a ) = 4.5 mm

Temperature (T) = 15

= (60 + 0.2 T) Mpa. Sqrt(m)For -140 < T < 150

= 63

Check For Geometry

= 100 - 60/ 2 = 70 mm

= 100 - 60/ 2 = 70 mm

= 100 - 60/ 2 = 70 mm

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

By Fracture Theory

=

=

Where, d =d = 4.5 / (60/ 2 + 4.5) = 0.13

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

s = Load (P) = P / 4000 = 0.0003Area

=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) =oC

Fracture Toughness ( k1c)

K1c oC

We =R- Dh/2

We =R- Dh/2

We =R- Dh/2

K1c Fd . s. Sqrt( p. a)

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

a / (Dh / 2 + a)

Fd


Load ( P) = 812 kN

Temp = 30 Degree Celcius Fracture Theory

1 31 30 66 0.032 3.157 1492

1.5 31.5 30 66 0.048 3.059 1257

2 32 30 66 0.063 2.97 1121

2.5 32.5 30 66 0.077 2.89 1031

3 33 30 66 0.091 2.812 967

3.5 33.5 30 66 0.104 2.743 918

4 34 30 66 0.118 2.67 882

5 35 30 66 0.143 2.546 827

5.8 35.8 30 66 0.162 2.457 7967 37 30 66 0.189 2.337 7628 38 30 66 0.211 2.246 7419 39 30 66 0.231 2.167 725

10 40 30 66 0.25 2.096 711


1 31 15 63 0.032 3.157 1424

1.5 31.5 15 63 0.048 3.059 1200

2 32 15 63 0.063 2.97 1070

2.5 32.5 15 63 0.077 2.89 984

3 33 15 63 0.091 2.812 923

3.5 33.5 15 63 0.104 2.743 876

4 34 15 63 0.118 2.67 842

4.5 34.5 15 63 0.13 2.61 8126 36 15 63 0.167 2.434 7547 37 15 63 0.189 2.337 7278 38 15 63 0.211 2.246 7089 39 15 63 0.231 2.167 692

10 40 15 63 0.25 2.096 678

Length of Crack ( a )

(mm) (Dh / 2 + a)Temperature (T) oC

Fracture Toughness

( k1c) d = a / (Dh / 2 + a) Fd

Load (P) (kN) -

Fracture Theory



Fracture Toughness

( k1c) d = a / (Dh / 2 + a) Fd

Load (P) (kN) -

Fracture Theory

Temp = Zero Degree Celcius Fracture Theory

1 31 0 60 0.032 3.157 1356

1.5 31.5 0 60 0.048 3.059 1143

2 32 0 60 0.063 2.97 1019

2.5 32.5 0 60 0.077 2.89 937

3 33 0 60 0.091 2.812 879

3.5 33.5 0 60 0.104 2.743 834

3.7 33.7 0 60 0.11 2.711 8215 35 0 60 0.143 2.546 7526 36 0 60 0.167 2.434 7187 37 0 60 0.189 2.337 6938 38 0 60 0.211 2.246 6749 39 0 60 0.231 2.167 659

10 40 0 60 0.25 2.096 646

Temp = -15 Degree Celcius Fracture Theory

1 31 -15 57 0.032 3.157 1289

1.5 31.5 -15 57 0.048 3.059 1086

2 32 -15 57 0.063 2.97 968

2.5 32.5 -15 57 0.077 2.89 890

3 33 -15 57 0.091 2.812 835

3.1 33.1 -15 57 0.094 2.796 8264 34 -15 57 0.118 2.67 7625 35 -15 57 0.143 2.546 7156 36 -15 57 0.167 2.434 6827 37 -15 57 0.189 2.337 6588 38 -15 57 0.211 2.246 6409 39 -15 57 0.231 2.167 626

10 40 -15 57 0.25 2.096 614




Fracture Toughness

( k1c) d = a / (Dh / 2 + a) Fd

Load (P) (kN) -

Fracture Theory



Fracture Toughness

( k1c) d = a / (Dh / 2 + a) Fd

Load (P) (kN) -

Fracture Theory

1 31 -30 54 0.032 3.157 1221

1.5 31.5 -30 54 0.048 3.059 1029

2 32 -30 54 0.063 2.97 918

2.5 32.5 -30 54 0.077 2.89 843

2.6 32.6 -30 54 0.08 2.873 8323.5 33.5 -30 54 0.104 2.743 7514 34 -30 54 0.118 2.67 7225 35 -30 54 0.143 2.546 6776 36 -30 54 0.167 2.434 6467 37 -30 54 0.189 2.337 6238 38 -30 54 0.211 2.246 6079 39 -30 54 0.231 2.167 593

10 40 -30 54 0.25 2.096 581


1 31 -45 51 0.032 3.157 1153

1.5 31.5 -45 51 0.048 3.059 971

2 32 -45 51 0.063 2.97 867

2.15 32.15 -45 51 0.067 2.947 8423 33 -45 51 0.091 2.812 747

3.5 33.5 -45 51 0.104 2.743 7094 34 -45 51 0.118 2.67 6825 35 -45 51 0.143 2.546 6396 36 -45 51 0.167 2.434 6107 37 -45 51 0.189 2.337 5898 38 -45 51 0.211 2.246 5739 39 -45 51 0.231 2.167 560

10 40 -45 51 0.25 2.096 549



Fracture Toughness

( k1c) d = a / (Dh / 2 + a) Fd

Load (P) (kN) -

Fracture Theory



Fracture Toughness

( k1c) d = a / (Dh / 2 + a) Fd

Load (P) (kN) -

Fracture Theory

Kawish Shaikh P.Eng. UofC

> Dh/4 ; Hence OK

> 1.5xDh ; Hence OK

Both side of Hole

35 mm

Mpa. Sqrt(m) (60 for Steel WT Caterary 4)

> Dh/2 ; Hence OK

< 5t ; Hence OK

> 2t ; Hence OK

mm814 kN

P

Crack Lenth (a) Vs Tensile Load (P)

mm2

LOAD (P)

100

mm

200 mm

100

mm

60 mm Dia. hole

Crack Length (a)

Fracture Theory

601 138 857 345 Net Section will Yeild before Fracture








344 128.4 797 345 Net Section will Fracture

336 126 782 345 Net Section will Fracture332 124 770 345 Net Section will Fracture330 122 758 345 Net Section will Fracture329 120 745 345 Net Section will Fracture

Fracture Theory








344 131 814 345 Net Section will Fracture






Yeild Theory

Stress in the Net Section

Effective width of

Plate (mm)

Load (P) (kN) -Yeild

TheoryYeild Stress (s)

Yeild Theory


Effective width of

Plate (mm)



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

)

Fracture Theory














Fracture Theory














Fracture Theory

Yeild Theory


Effective width of

Plate (mm)



Yeild Theory


Effective width of

Plate (mm)



Yeild Theory

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

)














Fracture Theory















Effective width of

Plate (mm)



Yeild Theory


Effective width of

Plate (mm)



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

1600Crack Length (a) VS Lug Capacity (kN)

Temp = 30 Degree Celcius


Temp = Zero Degree Celcius

Temp = -15 Degree Celcius


Load (P) (kN) -Yeild Theorya (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








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








Load

(kN

)

Sample CalculationThickness of Lug (t) = 20 mmWidth of Lug (W) = 200 mmRadius of Circular Section (R) = 100 mm

= 60 mm

= 57 mmDistance from centre of hole to Welding (h)= 100 mm

Area of Cross Section = 20 x 200 = 4000Length of Crack ( a ) = 4.5 mm

Temperature (T) = 15

= (40 + 0.2 T) Mpa. Sqrt(m)For -140 < T < 150

= 43

Check For Geometry

= 100 - 60/ 2 = 70 mm

= 100 - 60/ 2 = 70 mm

= 100 - 60/ 2 = 70 mm

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

By Fracture Theory

=

=

Where, d =d = 4.5 / (60/ 2 + 4.5) = 0.13

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

s = Load (P) = P / 4000 = 0.0003Area

=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) =oC

Fracture Toughness ( k1c)

K1c oC

We =R- Dh/2

We =R- Dh/2

We =R- Dh/2


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

a / (Dh / 2 + a)

Fd


Load ( P) = 554 kN


1 31 30 46 0.032 3.157 1040

1.5 31.5 30 46 0.048 3.059 876

2 32 30 46 0.063 2.97 7822.5 32.5 30 46 0.077 2.89 7183 33 30 46 0.091 2.812 674

3.5 33.5 30 46 0.104 2.743 6404 34 30 46 0.118 2.67 6155 35 30 46 0.143 2.546 577

5.8 35.8 30 46 0.162 2.457 5557 37 30 46 0.189 2.337 5318 38 30 46 0.211 2.246 5179 39 30 46 0.231 2.167 505

10 40 30 46 0.25 2.096 495


1 31 15 43 0.032 3.157 972

1.5 31.5 15 43 0.048 3.059 8192 32 15 43 0.063 2.97 731

2.5 32.5 15 43 0.077 2.89 6723 33 15 43 0.091 2.812 630

3.5 33.5 15 43 0.104 2.743 5984 34 15 43 0.118 2.67 575

4.5 34.5 15 43 0.13 2.61 5546 36 15 43 0.167 2.434 5157 37 15 43 0.189 2.337 4968 38 15 43 0.211 2.246 4839 39 15 43 0.231 2.167 472

10 40 15 43 0.25 2.096 463



Fracture Toughness

( k1c) d = a / (Dh / 2 + a) Fd

Load (P) (kN) -

Fracture Theory



Fracture Toughness

( k1c) d = a / (Dh / 2 + a) Fd

Load (P) (kN) -

Fracture Theory

Temp = Zero Degree Celcius Fracture Theory

1 31 0 40 0.032 3.157 904

1.5 31.5 0 40 0.048 3.059 7622 32 0 40 0.063 2.97 680

2.5 32.5 0 40 0.077 2.89 6253 33 0 40 0.091 2.812 586

3.5 33.5 0 40 0.104 2.743 5563.7 33.7 0 40 0.11 2.711 5475 35 0 40 0.143 2.546 5016 36 0 40 0.167 2.434 4797 37 0 40 0.189 2.337 4628 38 0 40 0.211 2.246 4499 39 0 40 0.231 2.167 439

10 40 0 40 0.25 2.096 431


1 31 -15 37 0.032 3.157 8361.5 31.5 -15 37 0.048 3.059 7052 32 -15 37 0.063 2.97 629

2.5 32.5 -15 37 0.077 2.89 5783 33 -15 37 0.091 2.812 542

3.1 33.1 -15 37 0.094 2.796 5364 34 -15 37 0.118 2.67 4945 35 -15 37 0.143 2.546 4646 36 -15 37 0.167 2.434 4437 37 -15 37 0.189 2.337 4278 38 -15 37 0.211 2.246 4169 39 -15 37 0.231 2.167 406

10 40 -15 37 0.25 2.096 398




Fracture Toughness

( k1c) d = a / (Dh / 2 + a) Fd

Load (P) (kN) -

Fracture Theory



Fracture Toughness

( k1c) d = a / (Dh / 2 + a) Fd

Load (P) (kN) -

Fracture Theory

1 31 -30 34 0.032 3.157 7691.5 31.5 -30 34 0.048 3.059 6482 32 -30 34 0.063 2.97 578

2.5 32.5 -30 34 0.077 2.89 5312.6 32.6 -30 34 0.08 2.873 5243.5 33.5 -30 34 0.104 2.743 4734 34 -30 34 0.118 2.67 4545 35 -30 34 0.143 2.546 4266 36 -30 34 0.167 2.434 4077 37 -30 34 0.189 2.337 3928 38 -30 34 0.211 2.246 3829 39 -30 34 0.231 2.167 373

10 40 -30 34 0.25 2.096 366


1 31 -45 31 0.032 3.157 7011.5 31.5 -45 31 0.048 3.059 5912 32 -45 31 0.063 2.97 527

2.15 32.15 -45 31 0.067 2.947 5123 33 -45 31 0.091 2.812 454

3.5 33.5 -45 31 0.104 2.743 4314 34 -45 31 0.118 2.67 4145 35 -45 31 0.143 2.546 3896 36 -45 31 0.167 2.434 3717 37 -45 31 0.189 2.337 3588 38 -45 31 0.211 2.246 3489 39 -45 31 0.231 2.167 340

10 40 -45 31 0.25 2.096 334



Fracture Toughness

( k1c) d = a / (Dh / 2 + a) Fd

Load (P) (kN) -

Fracture Theory



Fracture Toughness

( k1c) d = a / (Dh / 2 + a) Fd

Load (P) (kN) -

Fracture Theory

Kawish Shaikh P.Eng. UofC

> Dh/4 ; Hence OK

> 1.5xDh ; Hence OK

Both side of Hole

35 mm

Mpa. Sqrt(m) (40 for Steel W 350)

> Dh/2 ; Hence OK

< 5t ; Hence OK

> 2t ; Hence OK

mm814 kN

P

Crack Lenth (a) Vs Tensile Load (P)

mm2

LOAD (P)

100

mm

200 mm

100

mm

60 mm Dia. hole

Crack Length (a)

Fracture Theory










234 126 782 345 Net Section will Fracture232 124 770 345 Net Section will Fracture230 122 758 345 Net Section will Fracture229 120 745 345 Net Section will Fracture

Fracture Theory














Yeild Theory


Effective width of

Plate (mm)



Yeild Theory


Effective width of

Plate (mm)



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

)

Fracture Theory














Fracture Theory














Fracture Theory

Yeild Theory


Effective width of

Plate (mm)



Yeild Theory


Effective width of

Plate (mm)



Yeild Theory

0 2 4 6 8 10 120

100

200

300

400

500

600

700

800

900




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

100

200

300

400

500

600

700

800




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

100

200

300

400

500

600

700

800




a (mm)

Load

(kN

)














Fracture Theory















Effective width of

Plate (mm)



Yeild Theory


Effective width of

Plate (mm)



0 2 4 6 8 10 120

100

200

300

400

500

600

700

800




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

100

200

300

400

500

600

700

800




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








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








Load

(kN

)

0 2 4 6 8 10 120

100

200

300

400

500

600

700

800

900




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

100

200

300

400

500

600

700

800




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

100

200

300

400

500

600

700

800




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

100

200

300

400

500

600

700

800




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

100

200

300

400

500

600

700

800




a (mm)

Load

(kN

)

0 2 4 6 8 10 120

200

400

600

800

1000








Load

(kN

)

lifting lug

Documents