11/12/2013, 6:32 PM
Memoria de Calculo de Orejas de Izaje de Tanques: según DIN 28086 Equipo:
Orejas de izaje de trunnion OT2013-2644 Oreja DIN 28086 - 3 - 17100 - 17100
Tamaño Oreja Figura Material L Material V Material B F (Kg)
g
R (mm) Se (mm) c1 (mm) c2 (mm)
2 4 A-36 A-36 A-36 4000 1.6 45 60 3600 20 1 1
Tabla 1: de 1 a 5 Figura Seleccionada de 2 a 5 Material base de orejas Material base de placa de refuerzo Material base del tanque Carga Factor de Seguridad Angulo de la eslinga hacia la vertical Angulo entre eslinga y el eje vertical de la oreja Radio exterior del tanque cercano a los puntos de carga Espesor actual de el casco Reduccion en caso el espesor de casco menor que el diseñado Reduccion por uso
Table 0: Seleccon de Materiales Base Ku (N/mm2) Material Numero A-572 Gr.36 235 10037 265 A-36 275 17100 A-572 Gr.50 295 10050
DIN St 37-2 St 44-2 St 50-2
EN
10025
ksi 33000
10025
36000 50000
Tabla 1: Dimensiones de Oreja Tamaño 1 2 3 4 b (mm) 90 110 160 200 d (mm) 38 38 50 62 h (mm) 55 60 75 95 l (mm) 170 220 320 390 r1 (mm) 55 71 105 130 r2 (mm) 20 30 40 50 s1 (mm) 10 15 15 20 s2 (mm) A ser calculado como se especifica en subclase 5.4
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5 240 74 115 470 155 60 25
Elaborado por: Luis Enrique Aguilar Montoya Inspector QA/QC FLSmidth
11/12/2013, 6:32 PM Tabla 2: Cantidades, simbolos y unidades Simbolo Valor Cantidad n 2 Numero de orejas uniformemente cargadas a1 (mm) #NAME? Espesor de garganta entre la oreja y la placa de refuerzo a2 (mm) #NAME? Espesor de garganta entre el casco y la placa de refuerzo S1 (mm) 15 Espesor de la oreja S2 (mm) #NAME? Espesor de la plancha de refuerzo So (mm) #NAME? Espesor del casco con reducciones (So=Se-C1-C2) KV u (N/mm2) 275 Parametro de esfuerzo de placa de refuerzo KB u (N/mm2) 275 Parametro de esfuerzo de tanque A 76 Valor intermedio f #NAME? Factor de correccion de carga U #NAME? Valor intermedio W 1 Factor de incremento de carga Tabla 3: Maxima carga de trabajo segura de grilletes, F, de acuerdo con DIN 82016 o DIN 82101 tamaño de oreja 1 2 3 4 5 tamaño de grillete 5 5 10 16 25 FS, en N 50000 50000 100000 160000 250000 Tabla 4: Maxima carga segura de trabajo, FG para diferentes orden de las orejas Tamaño nominal de orejas Angulo Maxima carga segura de trabajo, en N, a 20°C con KL =240N/mm2 1 2 3 4 5 fig. 2 19000 77000 131000 218000 332000 fig. 3 38000 154000 262000 436000 664000 0 to 15 ° 36000 149000 254000 422000 642000 Over 15 ° up to 30 ° 33000 133000 227000 379000 576000 Over 30 ° up to 45 ° 27000 108000 185000 310000 470000 Over 45 up to 60 ° 19000 77000 131000 218000 332000 0 to 15 ° 55000 223000 380000 633000 962000 Over 15 ° up to 30 ° 50000 199000 341000 567000 863000 Over 30 up to 45 ° 40000 163000 278000 464000 704000 Over 45 up to 60 ° 29000 115000 197000 328000 499000 Orden de las orejas cf. Figura Cant.Orejas Oreja Simple (cf. figura 2) 2 1 Dos orejas con las cabezas cruzadas (cf. figura 3) 3 2 Dos orejas sin cabezas cruzadas (cf. figura 4) 4 2 Tres orejas (cf. figura 5) 5 3
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11/12/2013, 6:32 PM 1 Calculos 2 5.2 Maxima carga de trabajo segura de grilletes 3 (1) FSe = FLe = FGe/(n*cos ) 4
5 6 7
N N
FGe
Carga efectiva Tamaño de grillete FS Maxima carga segura de trabajo (2) FSe<= FS table 3
N
28284 40000 5 50000 Cumple
8 5.3 Maxima carga de trabajo segura de orejas (3) FG u = FG*KL u /240 9 10
11
(4) FLe= FSe FG u
N
12 (5) FGe<= FG u tabla 4 13 5.4 Espesor de plancha de refuerzo y espesores de garganta de soldaduras 14 Tabla 5: Factor de incremento de carga <=60° >60° 15 1 2 16 W
17 18 19
20 21 22
23 24 25
26
W (6) S2= 0.5*(FLe*W* g /KV u )^(1/2) Se<= S2<=1.5*Se Espesor de garganta de soldadura a1 S1 S2 (7) a1 >= 0.7*S1min a1 Espesor de garganta de soldadura a2 (8) a2 >= 0.7*S2min a2
27 28 5.5 Capacidad de carga del tanque 29 Tabla 6: Valor Intermedio A 1 30 Tamano de oreja A 59 31 A 32 33 34
35 36
2 76
3 113
4 139
77000 Cumple
mm mm
1 6.4 #NAME?
mm mm mm mm
15.0 #NAME? #NAME? #NAME?
mm mm
#NAME? #NAME?
5 167
(9) U= A/((R*So)^(1/2)) f (10) FB= f*So^2*KB u / g (11) FLe<= FB/W
N
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76 #NAME? #NAME? #NAME? #NAME?
11/12/2013, 6:32 PM
U - factor de correccion de carga 100.00
f
10.00
1.00 0.00
0.20
0.40
0.60
0.80
1.00
U
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1.20
1.40
1.60
1.80
2.00
0.3 0.4 0.4 0.5 0.5 0.6 0.6 0.7 0.7 0.8 0.8 0.9 0.9 1.0 1.0 1.1 1.1 1.2 1.2 1.3 1.3 1.4 1.4 1.5 1.5 1.6 1.6 1.7 1.7 1.8
11/12/2013, 6:32 PM
Memoria de Calculo de Oreja de Izaje: según ASME BTH-1 Equipo:
Atril de Armado de contraejes Fuller
6,000 3.6 2
Carga (Kg) Nd (2-2.1 o 2-2.2) Numero de orejas
A36 50 50 20 75 8 E71T-1 Y 40 50 115
Material (A36 o A572) Dh [mm] be [mm] t [mm] R [mm] Soldadura Filete [in] E7018/E71T-1 Y(si) o N(no) Dp [mm] a [mm] H [mm]
Cumple Cumple Cumple Cumple
Esfuerzo de Traccion Resistencia al corte a través del agujero Esfuerzo cortante en Soldadura Garganta de Filete mínima 3-3.4.3
Diametro de agujero Ancho de oreja Espesor de oreja Radio exterior Altura de pierna Material de aporte Terminacion redondeada Diametro de grillete Altura de oreja Material base a eje
Nd factor de Diseño (para. 3-1.3) 2-2.1 Categoría de Diseño A: cuando la magnitud y la variación de las cargas aplicadas son predecibles, donde la carga y condiciones ambientales se definen con precisión o no grave. 2.00 para los estados límite de fluencia o pandeo, 2.40 para los estados límite de fractura y para el diseño de conexión.
2-2.2 Categoría de Diseño B: cuando la magnitud y la variación de las cargas aplicadas no son predecibles, las condiciones de carga y del medio ambiente son graves, o no se define con precisión.
3.00 para los estados límite de fluencia o pandeo, 3.60 para los estados límite de fractura y para el diseño de conexión.
5 de 48
Elaborado por: Luis Enrique Aguilar Montoya Inspector QA/QC FLSmidth
11/12/2013, 6:32 PM 1 2 3 4 5 6 7 8 9
Oreja con conexión para grillete: ASME BTH-1 Descripcion: Atril de Armado de contraejes Fuller 13,228 W [lb] 3.6 Nd
Peso de la carga Design factor
Material: A36 36,000 58,000 29,000,000
Material Fy [psi] Fu [psi] E [psi]
Limite elastico Resistencia a la traccion Modulo de Elesticidad
Dh [in] w [in] t [in] R [in] Leg [in]
Diametro de agujero Ancho de oreja Espesor de oreja Radio Exterior de oreja Altura de filete de soldadura
10 11 12 13 14 15
Dimensiones:
16 17 18 19 20
Esfuerzo de Traccion:
21 22 23 24 25 26
Resistencia al Corte a travez del agujero:
27 28 29 30 31 32
Esfuerzo Cortante en la Soldadura:
1.97 5.91 0.79 2.95 0.31 Ft [psi] = A [in^2] = St [psi] = CheckSt =
Fy/Nd t*(w-Dh) W/A St < Ft
Material Fy [psi] Fu [psi] E [psi]
A36 36,000 58,000
A572 50,000 65,000
A516 16,000 30,000
29,000,000
29,000,000
9,800,000
Esfuerzo de traccion admisible (eq 3-1) Area en tension Esfuerzo de traccion
Av [in^2] = 2*(R-(Dh/2)*cos(radians(45)))*t Area total de dos planos de corte (eq 3-50) Pv [lb] = 0.7*Fu/(1.2*Nd)*Av Doble plano de resistencia al corte (eq 3-49)
E7018/E71T-1
58,000 70,000
psi in^2 psi
10,000 3.10 4,267 Cumple
in^2
3.554
lb
33,401 Cumple
psi psi in^2 lb
58,000 8,056 2.981 24,011 Cumple
in
0.188 Cumple
CheckPv = W < Pv Exx [psi] = Fv [psi] = Aw [in^2] = Fw [lb] = CheckFw =
Fu si Fu
Resistencia a la tracción de la soldadura del metal de aporte Esfuerzo cortante de soldadura admisible(eq 3-53) Área de la soldadura Carga de soldadura admisible
33 Garganta de Soldadura minima: 3-3.4.3 34 garganta_3-3 [in] = IF(K14<=0.25,0.125,IF(K14<=0.5,0.188,(IF(K14<=0.75,0.25,(IF(K14<1.5,0.313)))))) 35 36 check_garganta = Pierna filete*0.707 >=garganta_3-3
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11/12/2013, 6:32 PM
Memoria de Calculo de Oreja de Izaje: según ASME BTH-1 Equipo:
Atril de Armado de contraejes Fuller
5,000 3.6 4
Carga (Kg) Nd (2-2.1 o 2-2.2) Numero de orejas
A36 55 50 20 77 6 E71T-1 Y 40 50 115
Material (A36 o A572) Dh [mm] be [mm] t [mm] R [mm] Soldadura Filete [in] E7018/E71T-1 Y(si) o N(no) Dp [mm] a [mm] H [mm]
Cumple Cumple Cumple Cumple
Esfuerzo de Traccion Resistencia al corte a través del agujero Esfuerzo cortante en Soldadura Garganta de Filete mínima 3-3.4.3
Diametro de agujero Ancho de oreja Espesor de oreja Radio exterior Altura de pierna Material de aporte Terminacion redondeada Diametro de grillete Altura de oreja Material base a eje
Nd factor de Diseño (para. 3-1.3) 2-2.1 Categoría de Diseño A: cuando la magnitud y la variación de las cargas aplicadas son predecibles, donde la carga y condiciones ambientales se definen con precisión o no grave. 2.00 para los estados límite de fluencia o pandeo, 2.40 para los estados límite de fractura y para el diseño de conexión.
2-2.2 Categoría de Diseño B: cuando la magnitud y la variación de las cargas aplicadas no son predecibles, las condiciones de carga y del medio ambiente son graves, o no se define con precisión.
3.00 para los estados límite de fluencia o pandeo, 3.60 para los estados límite de fractura y para el diseño de conexión.
7 de 48
Elaborado por: Luis Enrique Aguilar Montoya Inspector QA/QC FLSmidth
11/12/2013, 6:32 PM 1 2 3 4 5 6 7 8 9
Oreja con conexión para grillete: ASME BTH-1 Descripcion: Atril de Armado de contraejes Fuller 11,023 W [lb] 3.6 Nd
Peso de la carga Design factor
Material: A36 36,000 58,000 29,000,000
Material Fy [psi] Fu [psi] E [psi]
Limite elastico Resistencia a la traccion Modulo de Elesticidad
Dh [in] w [in] t [in] R [in] Leg [in]
Diametro de agujero Ancho de oreja Espesor de oreja Radio Exterior de oreja Altura de filete de soldadura
10 11 12 13 14 15
Dimensiones:
16 17 18 19 20
Esfuerzo de Traccion:
21 22 23 24 25 26
Resistencia al Corte a travez del agujero:
27 28 29 30 31 32
Esfuerzo Cortante en la Soldadura:
2.17 6.10 0.79 3.03 0.24 Ft [psi] = A [in^2] = St [psi] = CheckSt =
Fy/Nd t*(w-Dh) W/A St < Ft
Material Fy [psi] Fu [psi] E [psi]
A36 36,000 58,000
A572 50,000 65,000
A516 16,000 30,000
29,000,000
29,000,000
9,800,000
Esfuerzo de traccion admisible (eq 3-1) Area en tension Esfuerzo de traccion
Av [in^2] = 2*(R-(Dh/2)*cos(radians(45)))*t Area total de dos planos de corte (eq 3-50) Pv [lb] = 0.7*Fu/(1.2*Nd)*Av Doble plano de resistencia al corte (eq 3-49)
E7018/E71T-1
58,000 70,000
psi in^2 psi
10,000 3.10 3,556 Cumple
in^2
3.568
lb
33,536 Cumple
psi psi in^2 lb
58,000 8,056 2.301 18,538 Cumple
in
0.125 Cumple
CheckPv = W < Pv Exx [psi] = Fv [psi] = Aw [in^2] = Fw [lb] = CheckFw =
Fu si Fu
Resistencia a la tracción de la soldadura del metal de aporte Esfuerzo cortante de soldadura admisible(eq 3-53) Área de la soldadura Carga de soldadura admisible
33 Garganta de Soldadura minima: 3-3.4.3 34 garganta_3-3 [in] = IF(K14<=0.25,0.125,IF(K14<=0.5,0.188,(IF(K14<=0.75,0.25,(IF(K14<1.5,0.313)))))) 35 36 check_garganta = Pierna filete*0.707 >=garganta_3-3
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1
Lifting Lug Load Capacity Vs Crack length Calculation Sample Calculation Thickness of Lug (t) Width of Lug (W) Radius of Circular Section (R) Diameter of Hole ( D h )
= = = =
20 200 100 60
Diameter of Pin ( D p )
= Distance from centre of hole to Welding (h)=
mm mm mm mm
57 mm 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) Fracture Toughness ( k 1c )
o
15 C (60 + 0.2 T) Mpa. Sqrt(m) For -140 < T < 150 o 63 C
= = K 1c =
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 Effective width of plate Tensile Load capacity By Fracture Theory K 1c = Fd = Where,
d= d= Fd = =
s =
K 1c = 63 = Load ( P)
=
= = =
345 MPa 200 - 60- 2 x4.5 = 0.9 x 345 x 131 x 20/1000 =
131
F d . s . Sqrt ( p . a ) 0.5 x (3 - d) [ 1 + 1.243 x (1 - d) 3 ] a / (D h / 2 + a) 4.5 / (60/ 2 + 4.5)
=
0.13
0.5 x (3 -0.13) [ 1 + 1.243 x (1 -0.13)^3 ] 2.61 Load (P) Area
=
P / 4000 =
F d . s . Sqrt ( p . a ) 2.61 x 0.00025P x sqrt(3.1416 x 0.0045) 812 kN
0.0003
Temp = 30 Degree Celcius Length of Crack ( a ) (mm) 1 1.5 2 2.5 3 3.5 4 5 5.8 7 8 9 10
Fracture Theory
(D h / 2 + a)
Temperatu re (T) o C
Fracture Toughness ( k 1c )
d = a / (D h / 2 + a)
Fd
Load (P) (kN) Fracture Theory
31 31.5 32 32.5 33 33.5 34 35 35.8 37 38 39 40
30 30 30 30 30 30 30 30 30 30 30 30 30
66 66 66 66 66 66 66 66 66 66 66 66 66
0.032 0.048 0.063 0.077 0.091 0.104 0.118 0.143 0.162 0.189 0.211 0.231 0.25
3.157 3.059 2.97 2.89 2.812 2.743 2.67 2.546 2.457 2.337 2.246 2.167 2.096
1492 1257 1121 1031 967 918 882 827 796 762 741 725 711
Temp = 15 Degree Celcius Length of Crack ( a ) (mm) 1 1.5 2 2.5 3 3.5 4 4.5 6 7 8 9 10
(D h / 2 + a)
Temperatu re (T) o C
Fracture Toughness ( k 1c )
d = a / (D h / 2 + a)
Fd
31 31.5 32 32.5 33 33.5 34 34.5 36 37 38 39 40
15 15 15 15 15 15 15 15 15 15 15 15 15
63 63 63 63 63 63 63 63 63 63 63 63 63
0.032 0.048 0.063 0.077 0.091 0.104 0.118 0.13 0.167 0.189 0.211 0.231 0.25
3.157 3.059 2.97 2.89 2.812 2.743 2.67 2.61 2.434 2.337 2.246 2.167 2.096
Temp = Zero Degree Celcius
Fracture Theory Load (P) (kN) Fracture Theory 1424 1200 1070 984 923 876 842 812 754 727 708 692 678
Fracture Theory
Length of Crack ( a ) (mm) 1 1.5 2 2.5 3 3.5 3.7 5 6 7 8 9 10
(D h / 2 + a)
Temperatu re (T) o C
Fracture Toughness ( k 1c )
d = a / (D h / 2 + a)
Fd
Load (P) (kN) Fracture Theory
31 31.5 32 32.5 33 33.5 33.7 35 36 37 38 39 40
0 0 0 0 0 0 0 0 0 0 0 0 0
60 60 60 60 60 60 60 60 60 60 60 60 60
0.032 0.048 0.063 0.077 0.091 0.104 0.11 0.143 0.167 0.189 0.211 0.231 0.25
3.157 3.059 2.97 2.89 2.812 2.743 2.711 2.546 2.434 2.337 2.246 2.167 2.096
1356 1143 1019 937 879 834 821 752 718 693 674 659 646
Temp = -15 Degree Celcius Length of Crack ( a ) (mm) 1 1.5 2 2.5 3 3.1 4 5 6 7 8 9 10
(D h / 2 + a)
Temperatu re (T) o C
Fracture Toughness ( k 1c )
d = a / (D h / 2 + a)
Fd
31 31.5 32 32.5 33 33.1 34 35 36 37 38 39 40
-15 -15 -15 -15 -15 -15 -15 -15 -15 -15 -15 -15 -15
57 57 57 57 57 57 57 57 57 57 57 57 57
0.032 0.048 0.063 0.077 0.091 0.094 0.118 0.143 0.167 0.189 0.211 0.231 0.25
3.157 3.059 2.97 2.89 2.812 2.796 2.67 2.546 2.434 2.337 2.246 2.167 2.096
Temp = -30 Degree Celcius Length of Crack ( a ) (mm)
(D h / 2 + a)
Temperatu re (T) o C
Fracture Toughness ( k 1c )
d = a / (D h / 2 + a)
Fd
Fracture Theory Load (P) (kN) Fracture Theory 1289 1086 968 890 835 826 762 715 682 658 640 626 614
Fracture Theory Load (P) (kN) Fracture Theory
1 1.5 2 2.5 2.6 3.5 4 5 6 7 8 9 10
31 31.5 32 32.5 32.6 33.5 34 35 36 37 38 39 40
-30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30
54 54 54 54 54 54 54 54 54 54 54 54 54
0.032 0.048 0.063 0.077 0.08 0.104 0.118 0.143 0.167 0.189 0.211 0.231 0.25
3.157 3.059 2.97 2.89 2.873 2.743 2.67 2.546 2.434 2.337 2.246 2.167 2.096
Temp = -45 Degree Celcius Length of Crack ( a ) (mm) 1 1.5 2 2.15 3 3.5 4 5 6 7 8 9 10
(D h / 2 + a)
Temperatu re (T) o C
Fracture Toughness ( k 1c )
d = a / (D h / 2 + a)
Fd
31 31.5 32 32.15 33 33.5 34 35 36 37 38 39 40
-45 -45 -45 -45 -45 -45 -45 -45 -45 -45 -45 -45 -45
51 51 51 51 51 51 51 51 51 51 51 51 51
0.032 0.048 0.063 0.067 0.091 0.104 0.118 0.143 0.167 0.189 0.211 0.231 0.25
3.157 3.059 2.97 2.947 2.812 2.743 2.67 2.546 2.434 2.337 2.246 2.167 2.096
1221 1029 918 843 832 751 722 677 646 623 607 593 581
Fracture Theory Load (P) (kN) Fracture Theory 1153 971 867 842 747 709 682 639 610 589 573 560 549
Kawish Shaikh P.Eng. UofC > Dh/4 ; Hence OK LOAD (P)
> 1.5xDh ; Hence OK mm 2 Both side of Hole 35 mm
Mpa. Sqrt(m)
100 mm
100 mm
Crack Length (a)
60 mm Dia. hole 200 mm
(60 for Steel WT Caterary 4)
> Dh/2 ; Hence OK < 5t ; Hence OK > 2t ; Hence OK
mm 814 kN
P
Crack Lenth (a) Vs Tensile Load (P)
Yeild Theory
Fracture Theory Stress in the Net Section 601 510 458 424 401 383 371 354 344 336 332 330 329
Effective width of Plate (mm) 138 137 136 135 134 133 132 130 128.4 126 124 122 120
573 487 437 405 383 366 354 344 327 321 317 315 314
Fracture Theory
857 851 845 838 832 826 820 807 797 782 770 758 745
345 345 345 345 345 345 345 345 345 345 345 345 345
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 Fracture Net Section will Fracture Net Section will Fracture Net Section will Fracture
Yeild Theory
Fracture Theory Stress in the Net Section
Load (P) (kN) - Yeild Yeild Stress Theory (s)
Effective width of Plate (mm) 138 137 136 135 134 133 132 131 128 126 124 122 120
Load (P) (kN) - Yeild Yeild Stress Theory (s) 857 851 845 838 832 826 820 814 795 782 770 758 745
Yeild Theory
345 345 345 345 345 345 345 345 345 345 345 345 345
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
Stress in the Net Section 546 463 416 386 364 349 344 321 312 305 302 300 299
Effective width of Plate (mm) 138 137 136 135 134 133 132.6 130 128 126 124 122 120
519 440 396 366 346 343 321 305 296 290 287 285 284
Effective width of Plate (mm) 138 137 136 135 134 133.8 132 130 128 126 124 122 120
345 345 345 345 345 345 345 345 345 345 345 345 345
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
Load (P) (kN) - Yeild Yeild Stress Theory (s) 857 851 845 838 832 831 820 807 795 782 770 758 745
345 345 345 345 345 345 345 345 345 345 345 345 345
Yeild Theory
Fracture Theory Stress in the Net Section
857 851 845 838 832 826 823 807 795 782 770 758 745
Yeild Theory
Fracture Theory Stress in the Net Section
Load (P) (kN) - Yeild Yeild Stress Theory (s)
Effective width of Plate (mm)
Load (P) (kN) - Yeild Yeild Stress Theory (s)
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
491 417 375 347 343 314 304 289 281 275 272 270 269
138 137 136 135 134.8 133 132 130 128 126 124 122 120
464 394 354 345 310 296 287 273 265 260 257 255 254
345 345 345 345 345 345 345 345 345 345 345 345 345
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
Yeild Theory
Fracture Theory Stress in the Net Section
857 851 845 838 837 826 820 807 795 782 770 758 745
Effective width of Plate (mm) 138 137 136 135.7 134 133 132 130 128 126 124 122 120
Load (P) (kN) - Yeild Yeild Stress Theory (s) 857 851 845 843 832 826 820 807 795 782 770 758 745
345 345 345 345 345 345 345 345 345 345 345 345 345
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
Crack Length (a) VS Lug Capacity (kN) for 30 oC 1600 1400
Load (kN)
1200 1000
Load (P) (kN) - Fracture Theory
800 Load (P) (kN) -Yeild Theory
600 400 200 0 0
5
10
15
a (mm)
Crack Length (a) VS Lug Capacity (kN) for 15 oC 1600 1400
Load (kN)
1200 1000
Load (P) (kN) - Fracture Theory
800 Load (P) (kN) -Yeild Theory
600 400 200 0 0
5
10 a (mm)
15
Crack Length (a) VS Lug Capacity (kN) for 0 oC 1600 1400
Load (kN)
1200 1000
Load (P) (kN) - Fracture Theory
800 Load (P) (kN) -Yeild Theory
600 400 200 0 0
5
10
15
a (mm)
Crack Length (a) VS Lug Capacity (kN) for -15 oC 1400 1200
Load (kN)
1000 800
Load (P) (kN) - Fracture Theory
600
Load (P) (kN) -Yeild Theory
400 200 0 0
5
10
15
a (mm)
Crack Length (a) VS Lug Capacity (kN) for -30 oC 1400 1200
1200
Load (kN)
1000 800
Load (P) (kN) - Fracture Theory
600
Load (P) (kN) -Yeild Theory
400 200 0 0
5
10
15
a (mm)
Crack Length (a) VS Lug Capacity (kN) for -45 oC 1400 1200
Load (kN)
1000 800
Load (P) (kN) - Fracture Theory
600
Load (P) (kN) -Yeild Theory
400 200 0 0
5
10 a (mm)
15
Load (P) (kN) - Fracture Theory Load (P) (kN) -Yeild Theory
Crack Length (a) VS Lug Capacity (kN) 1600
Load (P) (kN) - Fracture Theory
1400 Load (P) (kN) -Yeild Theory
Load (kN)
1200 1000 800 600 400 200 0 0
2
4
6 a (mm)
8
10
Load (P) (kN) - Fracture Theory Load (P) (kN) -Yeild Theory
Load (P) (kN) - Fracture Theory Load (P) (kN) -Yeild Theory
Load (P) (kN) - Fracture Theory Load (P) (kN) -Yeild Theory
Load (P) (kN) - Fracture Theory Load (P) (kN) -Yeild Theory
apacity (kN) Temp = 30 Degree Celcius Temp = 15 Degree Celcius Temp = Zero Degree Celcius Temp = -15 Degree Celcius Temp = -45 Degree Celcius
10
12
Load (P) (kN) -Yeild Theory
1
Lifting Lug Load Capacity Vs Crack length Calculation Sample Calculation Thickness of Lug (t) Width of Lug (W) Radius of Circular Section (R) Diameter of Hole ( D h )
= = = =
20 200 100 60
Diameter of Pin ( D p )
= Distance from centre of hole to Welding (h)=
mm mm mm mm
57 mm 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) Fracture Toughness ( k 1c )
o
15 C (40 + 0.2 T) Mpa. Sqrt(m) For -140 < T < 150 o 43 C
= = K 1c =
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 Effective width of plate Tensile Load capacity By Fracture Theory K 1c = Fd = Where,
d= d= Fd = =
s =
K 1c = 43 = Load ( P)
=
= = =
345 MPa 200 - 60- 2 x4.5 = 0.9 x 345 x 131 x 20/1000 =
131
F d . s . Sqrt ( p . a ) 0.5 x (3 - d) [ 1 + 1.243 x (1 - d) 3 ] a / (D h / 2 + a) 4.5 / (60/ 2 + 4.5)
=
0.13
0.5 x (3 -0.13) [ 1 + 1.243 x (1 -0.13)^3 ] 2.61 Load (P) Area
=
P / 4000 =
F d . s . Sqrt ( p . a ) 2.61 x 0.00025P x sqrt(3.1416 x 0.0045) 554 kN
0.0003
Temp = 30 Degree Celcius Length of Crack ( a ) (mm) 1 1.5 2 2.5 3 3.5 4 5 5.8 7 8 9 10
Fracture Theory
(D h / 2 + a)
Temperatu re (T) o C
Fracture Toughness ( k 1c )
d = a / (D h / 2 + a)
Fd
Load (P) (kN) Fracture Theory
31 31.5 32 32.5 33 33.5 34 35 35.8 37 38 39 40
30 30 30 30 30 30 30 30 30 30 30 30 30
46 46 46 46 46 46 46 46 46 46 46 46 46
0.032 0.048 0.063 0.077 0.091 0.104 0.118 0.143 0.162 0.189 0.211 0.231 0.25
3.157 3.059 2.97 2.89 2.812 2.743 2.67 2.546 2.457 2.337 2.246 2.167 2.096
1040 876 782 718 674 640 615 577 555 531 517 505 495
Temp = 15 Degree Celcius Length of Crack ( a ) (mm) 1 1.5 2 2.5 3 3.5 4 4.5 6 7 8 9 10
(D h / 2 + a)
Temperatu re (T) o C
Fracture Toughness ( k 1c )
d = a / (D h / 2 + a)
Fd
31 31.5 32 32.5 33 33.5 34 34.5 36 37 38 39 40
15 15 15 15 15 15 15 15 15 15 15 15 15
43 43 43 43 43 43 43 43 43 43 43 43 43
0.032 0.048 0.063 0.077 0.091 0.104 0.118 0.13 0.167 0.189 0.211 0.231 0.25
3.157 3.059 2.97 2.89 2.812 2.743 2.67 2.61 2.434 2.337 2.246 2.167 2.096
Temp = Zero Degree Celcius
Fracture Theory Load (P) (kN) Fracture Theory 972 819 731 672 630 598 575 554 515 496 483 472 463
Fracture Theory
Length of Crack ( a ) (mm) 1 1.5 2 2.5 3 3.5 3.7 5 6 7 8 9 10
(D h / 2 + a)
Temperatu re (T) o C
Fracture Toughness ( k 1c )
d = a / (D h / 2 + a)
Fd
Load (P) (kN) Fracture Theory
31 31.5 32 32.5 33 33.5 33.7 35 36 37 38 39 40
0 0 0 0 0 0 0 0 0 0 0 0 0
40 40 40 40 40 40 40 40 40 40 40 40 40
0.032 0.048 0.063 0.077 0.091 0.104 0.11 0.143 0.167 0.189 0.211 0.231 0.25
3.157 3.059 2.97 2.89 2.812 2.743 2.711 2.546 2.434 2.337 2.246 2.167 2.096
904 762 680 625 586 556 547 501 479 462 449 439 431
Temp = -15 Degree Celcius Length of Crack ( a ) (mm) 1 1.5 2 2.5 3 3.1 4 5 6 7 8 9 10
(D h / 2 + a)
Temperatu re (T) o C
Fracture Toughness ( k 1c )
d = a / (D h / 2 + a)
Fd
31 31.5 32 32.5 33 33.1 34 35 36 37 38 39 40
-15 -15 -15 -15 -15 -15 -15 -15 -15 -15 -15 -15 -15
37 37 37 37 37 37 37 37 37 37 37 37 37
0.032 0.048 0.063 0.077 0.091 0.094 0.118 0.143 0.167 0.189 0.211 0.231 0.25
3.157 3.059 2.97 2.89 2.812 2.796 2.67 2.546 2.434 2.337 2.246 2.167 2.096
Temp = -30 Degree Celcius Length of Crack ( a ) (mm)
(D h / 2 + a)
Temperatu re (T) o C
Fracture Toughness ( k 1c )
d = a / (D h / 2 + a)
Fd
Fracture Theory Load (P) (kN) Fracture Theory 836 705 629 578 542 536 494 464 443 427 416 406 398
Fracture Theory Load (P) (kN) Fracture Theory
1 1.5 2 2.5 2.6 3.5 4 5 6 7 8 9 10
31 31.5 32 32.5 32.6 33.5 34 35 36 37 38 39 40
-30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30 -30
34 34 34 34 34 34 34 34 34 34 34 34 34
0.032 0.048 0.063 0.077 0.08 0.104 0.118 0.143 0.167 0.189 0.211 0.231 0.25
3.157 3.059 2.97 2.89 2.873 2.743 2.67 2.546 2.434 2.337 2.246 2.167 2.096
Temp = -45 Degree Celcius Length of Crack ( a ) (mm) 1 1.5 2 2.15 3 3.5 4 5 6 7 8 9 10
(D h / 2 + a)
Temperatu re (T) o C
Fracture Toughness ( k 1c )
d = a / (D h / 2 + a)
Fd
31 31.5 32 32.15 33 33.5 34 35 36 37 38 39 40
-45 -45 -45 -45 -45 -45 -45 -45 -45 -45 -45 -45 -45
31 31 31 31 31 31 31 31 31 31 31 31 31
0.032 0.048 0.063 0.067 0.091 0.104 0.118 0.143 0.167 0.189 0.211 0.231 0.25
3.157 3.059 2.97 2.947 2.812 2.743 2.67 2.546 2.434 2.337 2.246 2.167 2.096
769 648 578 531 524 473 454 426 407 392 382 373 366
Fracture Theory Load (P) (kN) Fracture Theory 701 591 527 512 454 431 414 389 371 358 348 340 334
Kawish Shaikh P.Eng. UofC > Dh/4 ; Hence OK LOAD (P)
> 1.5xDh ; Hence OK mm 2 Both side of Hole 35 mm
Mpa. Sqrt(m)
100 mm
100 mm
Crack Length (a)
60 mm Dia. hole 200 mm
(40 for Steel W 350)
> Dh/2 ; Hence OK < 5t ; Hence OK > 2t ; Hence OK
mm 814 kN
P
Crack Lenth (a) Vs Tensile Load (P)
Yeild Theory
Fracture Theory Stress in the Net Section 419 355 319 296 279 267 259 246 240 234 232 230 229
Effective width of Plate (mm) 138 137 136 135 134 133 132 130 128.4 126 124 122 120
391 332 298 276 261 250 242 235 223 219 216 215 214
Fracture Theory
857 851 845 838 832 826 820 807 797 782 770 758 745
345 345 345 345 345 345 345 345 345 345 345 345 345
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 Net Section will Fracture
Yeild Theory
Fracture Theory Stress in the Net Section
Load (P) (kN) - Yeild Yeild Stress Theory (s)
Effective width of Plate (mm) 138 137 136 135 134 133 132 131 128 126 124 122 120
Load (P) (kN) - Yeild Yeild Stress Theory (s) 857 851 845 838 832 826 820 814 795 782 770 758 745
Yeild Theory
345 345 345 345 345 345 345 345 345 345 345 345 345
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
Stress in the Net Section 364 309 278 257 243 232 229 214 208 204 201 200 199
Effective width of Plate (mm) 138 137 136 135 134 133 132.6 130 128 126 124 122 120
337 286 257 238 225 223 208 198 192 188 186 185 184
Effective width of Plate (mm) 138 137 136 135 134 133.8 132 130 128 126 124 122 120
345 345 345 345 345 345 345 345 345 345 345 345 345
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
Load (P) (kN) - Yeild Yeild Stress Theory (s) 857 851 845 838 832 831 820 807 795 782 770 758 745
345 345 345 345 345 345 345 345 345 345 345 345 345
Yeild Theory
Fracture Theory Stress in the Net Section
857 851 845 838 832 826 823 807 795 782 770 758 745
Yeild Theory
Fracture Theory Stress in the Net Section
Load (P) (kN) - Yeild Yeild Stress Theory (s)
Effective width of Plate (mm)
Load (P) (kN) - Yeild Yeild Stress Theory (s)
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
309 263 236 219 216 198 191 182 177 173 171 170 169
138 137 136 135 134.8 133 132 130 128 126 124 122 120
282 239 215 210 188 180 174 166 161 158 156 155 155
345 345 345 345 345 345 345 345 345 345 345 345 345
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
Yeild Theory
Fracture Theory Stress in the Net Section
857 851 845 838 837 826 820 807 795 782 770 758 745
Effective width of Plate (mm) 138 137 136 135.7 134 133 132 130 128 126 124 122 120
Load (P) (kN) - Yeild Yeild Stress Theory (s) 857 851 845 843 832 826 820 807 795 782 770 758 745
345 345 345 345 345 345 345 345 345 345 345 345 345
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
Crack Length (a) VS Lug Capacity (kN) for 30 oC 1200 1000
Load (kN)
800 Load (P) (kN) - Fracture Theory
600 Load (P) (kN) -Yeild Theory
400 200 0 0
5
10
15
a (mm)
Crack Length (a) VS Lug Capacity (kN) for 15 oC 1200 1000
Load (kN)
800 Load (P) (kN) - Fracture Theory
600 Load (P) (kN) -Yeild Theory
400 200 0 0
5
10 a (mm)
15
Crack Length (a) VS Lug Capacity (kN) for 0 oC 1000 900 800 Load (kN)
700 600
Load (P) (kN) - Fracture Theory
500 Load (P) (kN) -Yeild Theory
400 300 200 100 0 0
5
10
15
a (mm)
Crack Length (a) VS Lug Capacity (kN) for -15 oC 900 800 700 Load (kN)
600 Load (P) (kN) - Fracture Theory
500 400
Load (P) (kN) -Yeild Theory
300 200 100 0 0
5
10
15
a (mm)
Crack Length (a) VS Lug Capacity (kN) for -30 oC 900 800
800 700 Load (kN)
600 Load (P) (kN) - Fracture Theory
500 400
Load (P) (kN) -Yeild Theory
300 200 100 0 0
5
10
15
a (mm)
Crack Length (a) VS Lug Capacity (kN) for -45 oC 900 800 700 Load (kN)
600 Load (P) (kN) - Fracture Theory
500 400
Load (P) (kN) -Yeild Theory
300 200 100 0 0
5
10 a (mm)
15
Load (P) (kN) - Fracture Theory Load (P) (kN) -Yeild Theory
Crack Length (a) VS Lug Capacity (kN) 1200
Load (P) (kN) - Fracture Theory
1000 Load (kN)
Load (P) (kN) -Yeild Theory
800 600 400 200 0 0
2
4
6 a (mm)
8
10
Load (P) (kN) - Fracture Theory Load (P) (kN) -Yeild Theory
Load (P) (kN) - Fracture Theory Load (P) (kN) -Yeild Theory
Load (P) (kN) - Fracture Theory Load (P) (kN) -Yeild Theory
Load (P) (kN) - Fracture Theory Load (P) (kN) -Yeild Theory
apacity (kN) Temp = 30 Degree Celcius Temp = 15 Degree Celcius Temp = Zero Degree Celcius Temp = -15 Degree Celcius Temp = -45 Degree Celcius
10
12
Load (P) (kN) -Yeild Theory
Tabla 8.4 Especificaciones para pernos métricos de acero. Clase Intervalo de tamaños (inclusive) (mm) Resistencia límite mínima a la tracción Sp (MPa) Resistencia de fluencia mínima a la tracción Sy (MPa) Resistencia última mínima a la tracción Su (MPa) Característica 4.6 M5-M36 225 240 400 Medio o bajo carbono 4.8 M1.6-M16 310 340 420 Medio o bajo carbono 5.8 M5-M24 380 420 520 Medio o bajo carbono 8.8 M16-M36 600 660 830 Medio o bajo carbono, templado y revenido 9.8 M1.6-M16 650 720 900 Medio o bajo carbono, templado y revenido 10.9 M5-M36 830 940 1040 Martensítico de bajo carbono, templado y revenido 12.9 M1.6-M36 970 1100 1220 De aleación, templado y revenido Tabla 8.3 Especificaciones SAE para pernos UNS de acero. Grado SAE Intervalo de tamaños (inclusive) (in) Resistencia límite mínima a la tracción Sp (ksi) Resistencia de fluencia mínima a la tracción Sy (ksi)
Resistencia última mínima a la tracción Su (ksi) Características del acero 1 ¼ a 1½ 33 36 60 Medio o bajo carbono 2 ¼ a ¾ 55 57 74 Medio o bajo carbono 7/8 a 1½ 33 36 60 4 ¼ a 1½ 65 100 115 Medio carbono estirado en frío 5 ¼ a 1 85 92 120 Medio carbono templado y 1 1/8 a 1½ 74 81 105 revenido 5.2 ¼ a 1 85 92 120 Martensítico de bajo carbono, templado y revenido 7 ¼ a 1½ 105 115 133 Aleado de medio carbono, templado y revenido 8 ¼ a 1½ 120 130 150 Aleado de medio carbono, templado y revenido 8.2 ¼ a 1 120 130 150 Martensítico de bajo carbono, templado y revenido Tabla 8.2 Dimensiones de roscas métricas ISO, series de pasos bastos y finos Diámetro mayor (nominal) d (mm) ROSCA BASTA ROSCA FINA Paso p (mm) Diámetro menor dr (mm) Área de esfuerzo a tracción At (mm2 ) Paso p (mm) Diámetro menor dr (mm) Área de esfuerzo a tracción At (mm2
) 3.0 0.50 2.39 5.03 3.5 0.60 2.76 6.78 4.0 0.70 3.14 8.78 5.0 0.80 4.02 14.18 6.0 1.00 4.77 20.12 7.0 1.00 5.77 28.86 8.0 1.25 6.47 36.61 1.00 6.77 39.17 10.0 1.50 8.16 57.99 1.25 8.47 61.20 12.0 1.75 9.85 84.27 1.25 10.47 92.07 14.0 2.00 11.55 115.4 1.50 12.16 124.55 16.0 2.00 13.55 156.7 1.50 14.16 167.25 18.0 2.50 14.93 192.5 1.50 16.16 216.23 20.0 2.50 16.93 244.8 1.50 18.16 271.50 22.0 2.50 18.93 303.4 1.50 20.16 333.50 24.0 3.00 20.32 352.5 2.00 21.55 384.42 27.0 3.00 23.32 459.4 2.00 24.55 495.74 30.0 3.50 25.71 560.6 2.00 27.55 621.20 33.0 3.50 28.71 693.6 2.00 30.55 760.80 36.0 4.00 31.09 816.7 3.00 32.32 864.94 39.0 4.00 34.09 975.8 3.00 35.32 1028.4 Tabla 8.1 Dimensiones de roscas unificadas (UNS), serie de roscas bastas (UNC) y finas (UNF). Tamaño Diámetro mayor (nominal) d (in) ROSCA BASTA (UNC) ROSCA FINA (UNF) Ancho aproximado entre caras AT (in) Número de hilos por pulgada Diámetro menor dr (in) Área de esfuerzo a tracción At (in2 ) Número de hilos por pulgada Diámetro menor
dr (in) Área de esfuerzo a tracción At (in2 ) Cabeza Tuerc 0 0.0600 - - - 80 0.0438 0.0018 1 0.0730 64 0.0527 0.0026 72 0.0550 0.0028 2 0.0860 56 0.0628 0.0037 64 0.0657 0.0039 3 0.0990 48 0.0719 0.0049 56 0.0758 0.0052 4 0.1120 40 0.0795 0.0060 48 0.0849 0.0066 5 0.1250 40 0.0925 0.0080 44 0.0955 0.0083 6 0.1380 32 0.0974 0.0091 40 0.1055 0.0101 8 0.1640 32 0.1234 0.0140 36 0.1279 0.0147 10 0.1900 24 0.1359 0.0175 32 0.1494 0.0200 12 0.2160 24 0.1619 0.0242 28 0.1696 0.0258 ¼ 0.2500 20 0.1850 0.0318 28 0.2036 0.0364 7/16 7/16 5/16 0.3125 18 0.2403 0.0524 24 0.2584 0.0581 ½ ½ 3/8 0.3750 16 0.2938 0.0775 24 0.3209 0.0878 9/16 9/16 7/16 0.4375 14 0.3447 0.1063 20 0.3725 0.1187 5/8 11/16 ½ 0.5000 13 0.4001 0.1419 20 0.4350 0.1600 ¾ ¾ 9/16 0.5625 12 0.4542 0.1819 18 0.4903 0.2030 13/16 7/8 5/8 0.6250 11 0.5069 0.2260 18 0.5528 0.2560 15/16 15/16 ¾ 0.7500 10 0.6201 0.3345 16 0.6688 0.3730 1 1/8 1 1/8 7/8 0.8750 9 0.7307 0.4617 14 0.7822 0.5095 1 5/16 1 5/16 1 1.0000 8 0.8376 0.6057 12 0.8917 0.6630 1 ½ 1 ½ 1 1/8 1.1250 7 0.9394 0.7633 12 1.0167 0.8557 1 11/16 1 11/16 1 ¼ 1.2500 7 1.0644 0.9691 12 1.1417 1.0729 1 7/8 1 7/8 1 3/8 1.3750 6 1.1585 1.1549 12 1.2667 1.3147 2 1/16 2 1/16 1 ½ 1.5000 6 1.2835 1.4053 12 1.3917 1.5810 2 ¼ 2 ¼ 1 ¾ 1.7500 5 1.4902 1.8995 2 5/8 2 5/8 2 2.0000 4.5 1.7113 2.4982 3 3 2 ¼ 2.2500 4.5 1.9613 3.2477 3 3/8 3 3/8 2 ½ 2.5000 4 2.1752 3.9988 3 ¾ 3 ¾ 2 ¾ 2.7500 4 2.4252 4.9340 4 1/8 4 1/8 3 3.0000 4 2.6752 5.9674 4 ½ 4 ½ 3 ¼ 3.2500 4 2.9252 7.0989 4 7/8 3 ½ 3.5000 4 3.1752 8.3286 5 ¼ 3 ¾ 3.7500 4 3.4252 9.6565 5 5/8 4 4.0000 4 3.6752 11.083 6