Orejas de Izaje1

7/27/2019 Orejas de Izaje1

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10/5/2013, 3:03

Equipo:

5,000 Carga (Kg)

3.6 Nd (2-2.1 o 2-2.2)

4 Numero de orejas

A36 Material (A36 o A572)

55 Dh [mm] Diametro de agujero

50 be [mm] Ancho de oreja

20 t [mm] Espesor de oreja

77 R [mm] Radio exterior

6 Soldadura Filete [in] Altura de pierna

E71T-1 E7018/E71T-1 Material de aporte

Y Y(si) o N(no) Terminacion redondeada

40 Dp [mm] Diametro de grillete

50 a [mm] Altura de oreja

115 H [mm] Material base a eje

Cumple Esfuerzo de Traccion

Cumple Resistencia al corte a travs del agujero

Cumple Esfuerzo cortante en Soldadura

Cumple Garganta de Filete mnima 3-3.4.3

Nd factor de Diseo (para. 3-1.3)

2.00 para los estados lmite de fluencia o pandeo,

2.40 para los estados lmite de fractura y para el diseo de conexin.


3.60 para los estados lmite de fractura y para el diseo de conexin. Elaborado por: Luis Enrique Aguilar Montoya

Inspector QA/QC FLSmidth

Memoria de Calculo de Oreja de Izaje: segn ASME BTH-1

Categora de Diseo A: cuando la magnitud y la variacin de las cargas aplicadas son predecibles, donde la carga y condiciones ambientales se definen con precisin o no grave.2-2.1

Categora de Diseo B: cuando la magnitud y la variacin de las cargas aplicadas no son predecibles, las condiciones de carga y del medio ambiente son graves, o no se define con

precisin.2-2.2

Atril de Armado de contraejes Fuller

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10/5/2013, 3:03 PM

1 Oreja con conexin para grillete: ASME BTH-1

2 Descripcion: Atril de Armado de contraejes Fuller

3 11,023 W [lb] Peso de la carga

4 3.6 Nd Design factor

5 Material:

6 A36 Material Material A36 A572 A516 E7018/E71T-1

7 36,000 Fy [psi] Limite elastico Fy [psi] 36,000 50,000 16,000 58,000

8 58,000 Fu [psi] Resistencia a la traccion Fu [psi] 58,000 65,000 30,000 70,000

9 29,000,000 E [psi] Modulo de Elesticidad E [psi] 29,000,000 29,000,000 9,800,000

10 Dimensiones:

11 2.17 Dh [in] Diametro de agujero12 6.10 w [in] Ancho de oreja

13 0.79 t [in] Espesor de oreja

14 3.03 R [in] Radio Exterior de oreja

15 0.24 Leg [in] Altura de filete de soldadura

16 Esfuerzo de Traccion:

17 Ft [psi] = Fy/Nd Esfuerzo de traccion admisible (eq 3-1) psi 10,000

18 A [in^2] = t*(w-Dh) Area en tension in^2 3.10

19 St [psi] = W/A Esfuerzo de traccion psi 3,556

20 CheckSt = St < Ft Cumple

21 Resistencia al Corte a travez del agujero:

22 Av [in 2] = 2*(R-(Dh/2)*cos(radians(45)))*t

23 Area total de dos planos de corte (eq 3-50) in^2 3.568

24 Pv [lb] = 0.7*Fu/(1.2*Nd)*Av Doble plano de resistencia al corte (eq 3-49)

25 lb 33,53626 CheckPv = W < Pv Cumple

27 Esfuerzo Cortante en la Soldadura:

28 Exx [psi] = Fu si Fu


3/69

Lifting Lug Design Per ASME BTH-1-2005

References:

1. ASME. (2006). "Design of below-the-hook lifting devices, BTH-1-2005", New York.

2. Duerr, D. (2008). ASME BTH-1 Pinned Connection Design Provisions. Practice Periodical on Struct

3. Duerr, D. (2006). Pinned connection strength and behavior. J. Struct. Eng., 132(2), 182-194.

Input:

Nd = 3.00 For most liftin

t = 0.25 inches Lug Plate Thickness

a = 2 inches

Dp = 1.5 inches

be = 3 inches

Dh = 2 inches

Curved Edge? Y Y or N Material For most lugs

Fy = 36 ksi Material Yield Stress Fy = 36 ksi for

Fu = 58 ksi Material Ultimate Stress Fu = 58 ksi for

Output:

beff1 = 1.00 inches ASME Equatio


beff = 1.00 inches

r = 3 inches

R = 3 inches

Z' = 0.08 inches ASME EquatioAv = 1.10 sq. inches ASME Equatio

Pt = 8.06 kips ASME Equatio

Pb = 13.55 kips ASME Equatio

Pv = 12.45 kips ASME Equatio

Pp = 5.63 kips ASME Equatio

Pin Diameter Effect: Note: ASME

It does not tel

Dh/Dp = 1.33

Check All? Y Y or N. Check even when Dh/Dp


4/69

Pb = 11.08 kips

Pv = 12.10 kips

Pp = 5.63 kips If the connecti

Max. P = 5.63 kips

Dimensional Rules of Thumb:

Edge Distance = a+Dh/2

Grip = Length of shackle pin available for bearing against lug.

= Clear distance between shackle legs.

For Dp < 2":

Edge Distance = 1.5 * Dp

Dh = Dp + 1/8"

For Dp >= 2":

Edge Distance = 1.75 * Dp

Dh = Dp + 1/4"

For all Dp, t = Grip/3. Add cheek plates as required to get desired Pp.

Best practice is to add sufficient cheek plates to insure bearing over 80% of the grip.

These are only rules of thumb. Deviation from them is allowed.


5/69

ral Design and Construction, Vol. 13, No. 2, 53-58.

g devices used in construction Nd = 3.00. See Section 3-1.3 of the ASME code for more information.

this is Y, but N is left as an option.

ASTM A36. Fy = 50 ksi for ASTM A572, Grade 50.

ASTM A36. Fu = 65 ksi for ASTM A572, Grade 50.

n (3-46).

n (3-47).

n (C3-2).n (3-50) modified per Commentary.

n (3-45).

n (3-48).

n (3-49).

n (3-51)*Dp*t. If the connection is subject to rotating cyclic loading, this value shall be divided by 2!.

TH-1-2005 requires Dh/Dp


6/69

on is subject to rotating cyclic loading, this value shall be divided by 2!.


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In certain circumstances a value of 2.00 can be justified.

rance shall be taken into account".

ble to the user.


8/69

1 Lug with Pinned Connection: ASME BTH-1

2 Top Lug Description

3 65,000 W [lb] Weight of the load

4 3 Nd Design factor

5 Material:

6 SA-36 Material7 36,000 Fy [psi] Yield strength

8 58,000 Fu [psi] Tensile strength

9 29,000,000 E [psi] Modulus of elasticity

10 Dimensions:

11 3 Dh [in] Hole diameter

12 10 w [in] Width of lug

13 1 t [in] Thickness of lug

14 5 R [in] Outer radius

15 0.625 Leg [in] Weld leg height

16 Tensile Stress:

17 Ft [psi] = Fy/Nd Allowable tensile stress (eq 3-1)18 A [in^2] = t*(w-Dh) Area in tension

19 St [psi] = W/A Tensile stress

20 CheckSt = St < Ft

21 Shear Strength Through Pinhole:

22 Av [in^2] = 2*(R-(Dh/2)*cos(radians(45)))*t

23 Total area of two shear planes (eq 3-50)

24 Pv [lb] = 0.7*Fu/(1.2*Nd)*Av Double plane shear strength (eq 3-49)

25

26 CheckPv = W < Pv

27 Shear Stress in Weld:28 Exx [psi] = Fu Tensile strength of weld filler metal

29 Fv [psi] = 0.6*Exx/(1.2*Nd) Allowable weld shear stress (eq 3-53)

30 Aw [in^2] = (2*w+2*t) * (0.707*Leg) Area of the weld

31 Fw [lb] = Fv*Aw Allowable weld load

32 CheckFw = W < Fw

33 Minimum Weld Throat: 3-3.4.3

34 throat_3-3 [in] = IF(K14


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36000/3 = 12,0001*(10-3) = 7

65000/7 = 9,286

9286 < 12000 = Acceptable

2*(5-(3/2)*COS(RADIANS(45)))*1 = 7.879

0.7*58000/(1.2*3)*7.879 = 88,854

65000 < 88854 = Acceptable

58000 = 58,000

0.6*58000/(1.2*3) = 9,667

(2*10+2*1) * (0.707*0.625) = 9.721

9667*9.721 = 93,972

65000 < 93972 = Acceptable

.25,0.125,IF(K14


10/69

Diseo Oreja de Izaje segun ASME BTH-1-2005

Entrada:

Nd = 3.00 Factor de Diseo

t = 10 mm Espesor de la oreja de izajea = 50 mm

Dp = 40 mm

be = 75 mm

Dh = 50 mm

Curved Edge? Y Y or N Material

Fy = 36 ksi Material Yield Stress

Fu = 58 ksi Material Ultimate Stress

Max. P = 4218.42 Kg

IF(B8="Y",B17-SQRT(B17^2-B7^2/8),IF(B8 = "N", 0,"Error!"))

Input:

Nd = 3.00 For most liftin

t = 0.39 inches Lug Plate Thickness

a = 1.97 inches

Dp = 1.57 inches

be = 2.95 inches

Dh = 1.97 inches

Curved Edge? Y Y or N Material For most lugs

Fy = 36 ksi Material Yield Stress Fy = 36 ksi for

Fu = 58 ksi Material Ultimate Stress Fu = 58 ksi for

Output:



beff = 1.57 inches

r = 2.95275591 inches

R = 2.95275591 inches


11/69

Z' = 0.08 inches ASME Equatio

Av = 1.71 sq. inches ASME Equatio

Pt = 19.98 kips ASME Equatio

Pb = 21.00 kips ASME Equatio

Pv = 19.30 kips ASME Equatio

Pp = 9.30 kips ASME Equatio

Pin Diameter Effect: Note: ASME

It does not tel

Dh/Dp = 1.25

Check All? Y Y or N. Check even when Dh/Dp


12/69

g devices used in construction Nd = 3.00. See Section 3-1.3 of the ASME code for more information.

this is Y, but N is left as an option.

ASTM A36. Fy = 50 ksi for ASTM A572, Grade 50.

ASTM A36. Fu = 65 ksi for ASTM A572, Grade 50.

n (3-46).

n (3-47).


13/69

n (C3-2).

n (3-50) modified per Commentary.

n (3-45).

n (3-48).

n (3-49).

n (3-51)*Dp*t. If the connection is subject to rotating cyclic loading, this value shall be divided by 2!.

TH-1-2005 requires Dh/Dp


14/69

In certain circumstances a value of 2.00 can be justified.


15/69

rance shall be taken into account".

ble to the user.


16/69

1 Lug with Pinned Connection: ASME BTH-1

2 Top Lug Description

3 20,000 W [lb] Weight of the load

4 3 Nd Design factor

5 Material:

6 SA-36 Material7 36,000 Fy [psi] Yield strength

8 58,000 Fu [psi] Tensile strength

9 29,000,000 E [psi] Modulus of elasticity

10 Dimensions:

11 3 Dh [in] Hole diameter

12 10 w [in] Width of lug

13 0.5 t [in] Thickness of lug

14 5 R [in] Outer radius

15 0.5 Leg [in] Weld leg height

16 Tensile Stress:

17 Ft [psi] = Fy/Nd Allowable tensile stress (eq 3-1)

18 A [in^2] = t*(w-Dh) Area in tension

19 St [psi] = W/A Tensile stress

20 CheckSt = St < Ft

21 Shear Strength Through Pinhole:

22 Av [in^2] = 2*(R-(Dh/2)*cos(radians(45)))*t

23 Total area of two shear planes (eq 3-50)

24 Pv [lb] = 0.7*Fu/(1.2*Nd)*Av Double plane shear strength (eq 3-49)

25

26 CheckPv = W < Pv

27 Shear Stress in Weld:28 Exx [psi] = Fu Tensile strength of weld filler metal

29 Fv [psi] = 0.6*Exx/(1.2*Nd) Allowable weld shear stress (eq 3-53)

30 Aw [in^2] = (2*w+2*t) * (0.707*Leg) Area of the weld

31 Fw [lb] = Fv*Aw Allowable weld load

32 CheckFw = W < Fw

33 Minimum Weld Throat: 3-3.4.3

34 throat_3-3 [in] = IF(K14


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12,000

3.5

5,714

Cumple

3.939

44,427

Cumple

58,000

9,667

7.424

71,761

Cumple

0.188

Cumple


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10/5/2013, 3:03

Equipo:

5,000 Carga (Kg)

3.6 Nd (2-2.1 o 2-2.2)

4 Numero de orejas
























2-2.1 Categora de Diseo A: cuando la magnitud y la variacin de las cargas aplicadas son predecibles, donde la carga y condiciones ambientales se definen con precisin o no grave.

2-2.2 Categora de Diseo B: cuando la magnitud y la variacin de las cargas aplicadas no son predecibles, las condiciones de carga y del medio ambiente son graves, o no se define conprecisin.

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5 Material:





10 Dimensiones:


















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10/5/2013, 3:03

Equipo:

5,000 Carga (Kg)

3.6 Nd (2-2.1 o 2-2.2)

4 Numero de orejas
























2-2.1 Categora de Diseo A: cuando la magnitud y la variacin de las cargas aplicadas son predecibles, donde la carga y condiciones ambientales se definen con precisin o no grave.

2-2.2 Categora de Diseo B: cuando la magnitud y la variacin de las cargas aplicadas no son predecibles, las condiciones de carga y del medio ambiente son graves, o no se define conprecisin.

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5 Material:





10 Dimensiones:


















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1Lif t ing Lug Lo ad Capacity Vs Crack length Calculat ionSample Calculation

Thickness of Lug (t) = 20 mm

Width of Lug (W) = 200 mm

Radius of Circular Section (R) = 100 mm

Diameter of Hole ( D h) = 60 mmDiameter of Pin ( Dp) = 57 mm

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

Area of Cross Section = 20 x 200 = 4000

Length of Crack ( a ) = 4.5 mm

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

Temperature (T) = 15 oC

Fracture Toughness ( k1c) = (60 + 0.2 T) Mpa. Sqrt(

For -140 < T < 150

K1c = 63

oC

Check For Geometry

We =R- D h/2 = 100 - 60/ 2 = 70 mm

We =R- D h/2 = 100 - 60/ 2 = 70 mm

We =R- D h/2 = 100 - 60/ 2 = 70 mm

By Yeild Theory

Yeild Strength of Plate = 345 MPa

Effective width of plate = 200 - 60- 2 x4.5 = 131

Tensile Load capacity = 0.9 x 345 x 131 x 20/1000 =

By Fracture Theory

K1c = Fd . s. Sqrt( p. a)

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

Where, d = a / (D h/ 2 + a)

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

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

= 2.61

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

Area

K1c = Fd . s . Sqrt( p . a)

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

Load ( P) = 812kN


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Temp = 30 Degree Celcius

Length of

Crack ( a )

(mm) (D h / 2 + a)

Temperatu

re (T) o C

Fracture

Toughness (

k1c) d = a / (D h/ 2 + a) Fd

Load (P)

(kN) -

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 2.457 796

7 37 30 66 0.189 2.337 7628 38 30 66 0.211 2.246 741

9 39 30 66 0.231 2.167 725

10 40 30 66 0.25 2.096 711


Length of

Crack ( a )

(mm)(D h / 2 + a)

Temperatu

re (T)oC

Fracture

Toughness (

k1c) d = a / (D h/ 2 + a) Fd

Load (P)

(kN) -

Fracture

Theory

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 2.61 812

6 36 15 63 0.167 2.434 754

7 37 15 63 0.189 2.337 727

8 38 15 63 0.211 2.246 708

9 39 15 63 0.231 2.167 692

10 40 15 63 0.25 2.096 678

Temp = Zero Degree Celcius

Fracture

Fracture

Fracture


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Length of

Crack ( a )

(mm) (D h / 2 + a)

Temperatu

re (T)oC

Fracture

Toughness (

k1c) d = a / (D h/ 2 + a) Fd

Load (P)

(kN) -

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 2.711 821

5 35 0 60 0.143 2.546 752

6 36 0 60 0.167 2.434 718

7 37 0 60 0.189 2.337 693

8 38 0 60 0.211 2.246 674

9 39 0 60 0.231 2.167 659

10 40 0 60 0.25 2.096 646

Temp = -15 Degree Celcius

Length of

Crack ( a )

(mm) (D h / 2 + a)

Temperatu

re (T)oC

Fracture

Toughness (

k1c) d = a / (D h/ 2 + a) Fd

Load (P)

(kN) -

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 2.796 826

4 34 -15 57 0.118 2.67 762

5 35 -15 57 0.143 2.546 715

6 36 -15 57 0.167 2.434 682

7 37 -15 57 0.189 2.337 658

8 38 -15 57 0.211 2.246 640

9 39 -15 57 0.231 2.167 626

10 40 -15 57 0.25 2.096 614


Length of

Crack ( a )

(mm) (D h / 2 + a)

Temperatu

re (T)oC

Fracture

Toughness (

k1c) d = a / (D h/ 2 + a) Fd

Load (P)

(kN) -

Fracture

Theory

Fracture

Fracture


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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 2.873 832

3.5 33.5 -30 54 0.104 2.743 751

4 34 -30 54 0.118 2.67 7225 35 -30 54 0.143 2.546 677

6 36 -30 54 0.167 2.434 646

7 37 -30 54 0.189 2.337 623

8 38 -30 54 0.211 2.246 607

9 39 -30 54 0.231 2.167 593

10 40 -30 54 0.25 2.096 581


Length of

Crack ( a )

(mm) (D h / 2 + a)

Temperatu

re (T)oC

Fracture

Toughness (

k1c) d = a / (D h/ 2 + a) Fd

Load (P)

(kN) -

Fracture

Theory

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 2.947 842

3 33 -45 51 0.091 2.812 747

3.5 33.5 -45 51 0.104 2.743 709

4 34 -45 51 0.118 2.67 6825 35 -45 51 0.143 2.546 639

6 36 -45 51 0.167 2.434 610

7 37 -45 51 0.189 2.337 589

8 38 -45 51 0.211 2.246 573

9 39 -45 51 0.231 2.167 560

10 40 -45 51 0.25 2.096 549

Fracture


38/69

Kawish Shaikh P.Eng. UofC

> Dh/4 ; Hence OK

> 1.5xDh ; Hence OK

mm2

Both side of Hole

35 mm

) (60 for Steel WT Caterary 4)

> Dh/2 ; Hence OK

< 5t ; Hence OK

> 2t ; Hence OK

mm

814kN

P

Crack Lenth (a) Vs Tensile Load (P)

LOAD (P)

100

mm

200mm

100

mm

60 mmDia. hole

Crack Length(a)


39/69

Yeild

Theory

Stress in

the Net

Section

Effective

width of

Plate (mm)

Load (P)

(kN) - Yeild

Theory

Yeild Stress

(s)

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 Fracture

330 122 758 345 Net Section will Fracture


Yeild

Theory

Stress in

the Net

Section

Effective

width of

Plate (mm)

Load (P)

(kN) - Yeild

Theory

Yeild Stress

(s)














Yeild

Theory

Theory

Theory

Theory


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Stress in

the Net

Section

Effective

width of

Plate (mm)

Load (P)

(kN) - Yeild

Theory

Yeild Stress

(s)














Yeild

Theory

Stress in

the Net

Section

Effective

width of

Plate (mm)

Load (P)

(kN) - Yeild

Theory

Yeild Stress

(s)














Yeild

Theory

Stress in

the Net

Section

Effective

width of

Plate (mm)

Load (P)

(kN) - Yeild

Theory

Yeild Stress

(s)

Theory

Theory


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Yeild

Theory

Stress in

the Net

Section

Effective

width of

Plate (mm)

Load (P)

(kN) - Yeild

Theory

Yeild Stress

(s)













Theory


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0

200

400

600

800

1000

1200

1400

1600

0 5 10 15

Load

(kN)

a (mm)

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

Load (P) (kN)

Load (P) (kN)

0

200

400

600

800

1000

1200

1400

1600

0 5 10 15

Load

(kN)

a (mm)


Load (P) (k

Load (P) (k


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0

200

400

600

800

1000

1200

1400

1600

0 5 10 15

Load

(kN)

a (mm)


Load (P) (k

Load (P) (k

0

200

400

600

800

1000

1200

1400

0 5 10 15

Load

(kN)

a (mm)

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

Load (P) (k

Load (P) (k

1400



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- Fracture Theory

-Yeild Theory

0

200

400

600

800

1000

1200

1400

1600

0 2 4 6 8 10

Load

(kN)

a (mm)

Crack Length (a) VS Lug Capacity (k

) - Fracture Theory

) -Yeild Theory


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) - Fracture Theory

) -Yeild Theory

) - Fracture Theory

) -Yeild Theory


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) - Fracture Theory

) -Yeild Theory

) - Fracture Theory

) -Yeild Theory


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12

N)






Load (P) (kN) -Yeild Theory


52/69

1Lif t ing Lug Lo ad Capacity Vs Crack length Calculat ionSample Calculation

Thickness of Lug (t) = 20 mm

Width of Lug (W) = 200 mm

Radius of Circular Section (R) = 100 mm

Diameter of Hole ( D h) = 60 mmDiameter of Pin ( Dp) = 57 mm

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

Area of Cross Section = 20 x 200 = 4000

Length of Crack ( a ) = 4.5 mm

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

Temperature (T) = 15 oC

Fracture Toughness ( k1c) = (40 + 0.2 T) Mpa. Sqrt(

For -140 < T < 150

K1c = 43

oC

Check For Geometry

We =R- D h/2 = 100 - 60/ 2 = 70 mm

We =R- D h/2 = 100 - 60/ 2 = 70 mm

We =R- D h/2 = 100 - 60/ 2 = 70 mm

By Yeild Theory

Yeild Strength of Plate = 345 MPa

Effective width of plate = 200 - 60- 2 x4.5 = 131

Tensile Load capacity = 0.9 x 345 x 131 x 20/1000 =

By Fracture Theory

K1c = Fd . s. Sqrt( p. a)

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

Where, d = a / (D h/ 2 + a)

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

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

= 2.61

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

Area

K1c = Fd . s . Sqrt( p . a)

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

Load ( P) = 554kN


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Length of

Crack ( a )

(mm) (D h / 2 + a)

Temperatu

re (T) o C

Fracture

Toughness (

k1c) d = a / (D h/ 2 + a) Fd

Load (P)

(kN) -

Fracture

Theory

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 2.97 782

2.5 32.5 30 46 0.077 2.89 718

3 33 30 46 0.091 2.812 674

3.5 33.5 30 46 0.104 2.743 640

4 34 30 46 0.118 2.67 615

5 35 30 46 0.143 2.546 577

5.8 35.8 30 46 0.162 2.457 555

7 37 30 46 0.189 2.337 5318 38 30 46 0.211 2.246 517

9 39 30 46 0.231 2.167 505

10 40 30 46 0.25 2.096 495


Length of

Crack ( a )

(mm)(D h / 2 + a)

Temperatu

re (T)oC

Fracture

Toughness (

k1c) d = a / (D h/ 2 + a) Fd

Load (P)

(kN) -

Fracture

Theory

1 31 15 43 0.032 3.157 972

1.5 31.5 15 43 0.048 3.059 819

2 32 15 43 0.063 2.97 731

2.5 32.5 15 43 0.077 2.89 672

3 33 15 43 0.091 2.812 630

3.5 33.5 15 43 0.104 2.743 598

4 34 15 43 0.118 2.67 575

4.5 34.5 15 43 0.13 2.61 554

6 36 15 43 0.167 2.434 515

7 37 15 43 0.189 2.337 496

8 38 15 43 0.211 2.246 483

9 39 15 43 0.231 2.167 472

10 40 15 43 0.25 2.096 463


Fracture

Fracture

Fracture


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Length of

Crack ( a )

(mm) (D h / 2 + a)

Temperatu

re (T)oC

Fracture

Toughness (

k1c) d = a / (D h/ 2 + a) Fd

Load (P)

(kN) -

Fracture

Theory

1 31 0 40 0.032 3.157 904

1.5 31.5 0 40 0.048 3.059 762

2 32 0 40 0.063 2.97 680

2.5 32.5 0 40 0.077 2.89 625

3 33 0 40 0.091 2.812 586

3.5 33.5 0 40 0.104 2.743 556

3.7 33.7 0 40 0.11 2.711 547

5 35 0 40 0.143 2.546 501

6 36 0 40 0.167 2.434 479

7 37 0 40 0.189 2.337 462

8 38 0 40 0.211 2.246 449

9 39 0 40 0.231 2.167 439

10 40 0 40 0.25 2.096 431


Length of

Crack ( a )

(mm) (D h / 2 + a)

Temperatu

re (T)oC

Fracture

Toughness (

k1c) d = a / (D h/ 2 + a) Fd

Load (P)

(kN) -

Fracture

Theory

1 31 -15 37 0.032 3.157 836

1.5 31.5 -15 37 0.048 3.059 705

2 32 -15 37 0.063 2.97 629

2.5 32.5 -15 37 0.077 2.89 578

3 33 -15 37 0.091 2.812 542

3.1 33.1 -15 37 0.094 2.796 536

4 34 -15 37 0.118 2.67 494

5 35 -15 37 0.143 2.546 464

6 36 -15 37 0.167 2.434 443

7 37 -15 37 0.189 2.337 427

8 38 -15 37 0.211 2.246 416

9 39 -15 37 0.231 2.167 406

10 40 -15 37 0.25 2.096 398


Length of

Crack ( a )

(mm) (D h / 2 + a)

Temperatu

re (T)oC

Fracture

Toughness (

k1c) d = a / (D h/ 2 + a) Fd

Load (P)

(kN) -

Fracture

Theory

Fracture

Fracture


55/69

1 31 -30 34 0.032 3.157 769

1.5 31.5 -30 34 0.048 3.059 648

2 32 -30 34 0.063 2.97 578

2.5 32.5 -30 34 0.077 2.89 531

2.6 32.6 -30 34 0.08 2.873 524

3.5 33.5 -30 34 0.104 2.743 473

4 34 -30 34 0.118 2.67 4545 35 -30 34 0.143 2.546 426

6 36 -30 34 0.167 2.434 407

7 37 -30 34 0.189 2.337 392

8 38 -30 34 0.211 2.246 382

9 39 -30 34 0.231 2.167 373

10 40 -30 34 0.25 2.096 366


Length of

Crack ( a )

(mm) (D h / 2 + a)

Temperatu

re (T)oC

Fracture

Toughness (

k1c) d = a / (D h/ 2 + a) Fd

Load (P)

(kN) -

Fracture

Theory

1 31 -45 31 0.032 3.157 701

1.5 31.5 -45 31 0.048 3.059 591

2 32 -45 31 0.063 2.97 527

2.15 32.15 -45 31 0.067 2.947 512

3 33 -45 31 0.091 2.812 454

3.5 33.5 -45 31 0.104 2.743 431

4 34 -45 31 0.118 2.67 4145 35 -45 31 0.143 2.546 389

6 36 -45 31 0.167 2.434 371

7 37 -45 31 0.189 2.337 358

8 38 -45 31 0.211 2.246 348

9 39 -45 31 0.231 2.167 340

10 40 -45 31 0.25 2.096 334

Fracture


56/69

Kawish Shaikh P.Eng. UofC

> Dh/4 ; Hence OK

> 1.5xDh ; Hence OK

mm2

Both side of Hole

35 mm

) (40 for Steel W 350)

> Dh/2 ; Hence OK

< 5t ; Hence OK

> 2t ; Hence OK

mm

814kN

P

Crack Lenth (a) Vs Tensile Load (P)

LOAD (P)

100

mm

200mm

100

mm

60 mmDia. hole

Crack Length(a)


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Yeild

Theory

Stress in

the Net

Section

Effective

width of

Plate (mm)

Load (P)

(kN) - Yeild

Theory

Yeild Stress

(s)













Yeild

Theory

Stress in

the Net

Section

Effective

width of

Plate (mm)

Load (P)

(kN) - Yeild

Theory

Yeild Stress

(s)














Yeild

Theory

Theory

Theory

Theory


58/69

Stress in

the Net

Section

Effective

width of

Plate (mm)

Load (P)

(kN) - Yeild

Theory

Yeild Stress

(s)














Yeild

Theory

Stress in

the Net

Section

Effective

width of

Plate (mm)

Load (P)

(kN) - Yeild

Theory

Yeild Stress

(s)














Yeild

Theory

Stress in

the Net

Section

Effective

width of

Plate (mm)

Load (P)

(kN) - Yeild

Theory

Yeild Stress

(s)

Theory

Theory


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Yeild

Theory

Stress in

the Net

Section

Effective

width of

Plate (mm)

Load (P)

(kN) - Yeild

Theory

Yeild Stress

(s)













Theory


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0

200

400

600

800

1000

1200

0 5 10 15

Load

(kN)

a (mm)


Load (P) (kN)

Load (P) (kN)

0

200

400

600

800

1000

1200

0 5 10 15

Load

(kN)

a (mm)


Load (P) (k

Load (P) (k


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0

100

200

300

400

500

600

700

800

900

1000

0 5 10 15

Load

(kN)

a (mm)


Load (P) (k

Load (P) (k

0

100

200

300

400

500

600

700

800

900

0 5 10 15

Load

(kN)

a (mm)


Load (P) (k

Load (P) (k

800

900



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0

100

200

300

400

500

600

700

0 5 10 15

Load

(kN)

a (mm)

Load (P) (k

Load (P) (k

0

100

200

300

400

500

600

700

800

900

0 5 10 15

Load

(kN)

a (mm)


Load (P) (k

Load (P) (k


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- Fracture Theory

-Yeild Theory

0

200

400

600

800

1000

1200

0 2 4 6 8 10

Load

(kN)

a (mm)

Crack Length (a) VS Lug Capacity (k

) - Fracture Theory

) -Yeild Theory


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) - Fracture Theory

) -Yeild Theory

) - Fracture Theory

) -Yeild Theory


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) - Fracture Theory

) -Yeild Theory

) - Fracture Theory

) -Yeild Theory


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N)





Orejas de Izaje1

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