Bolted Flange Design

ASME BPVC Section VIII Division 1 Appendix 2

Input

Project Information
Description:Project:
Equipment:Customer:
Report Number:System of Units:
Process Information
Fluid:Internal Design Temperature: °F
Internal Design Pressure: psig
Dimensions
Flange Type:Flange Construction:
Flange Outside Diameter: inFlange Inside Diameter: in
Flange Thickness: inFlange Nozzle Wall Thickness: in
Thickness of Hub at Small End: inThickness of Hub at Back of Flange: in
Hub Length: inFlange Face Inside Diameter: in
Flange Face Outside Diameter: inCorrosion Allowance: in
Use Corrosion Allowance in the Calculation?:NoJoint Efficiency of Pipe:
Use B1 instead of B in the Calculation?:No
Bolting
Bolt Circle Diameter: inBolt Unit Type:
Bolt Size and Class:Bolt Nominal Diameter: in
Bolt Root Area: in^2Number of Bolts:
Material Properties
Flange
Material Name:Material Listing:
Yield Strength at Design Temperature: psigAllowable Stress at Design Temperature: psig
Allowable Stress at Ambient Temperature: psigMaterial Density: lbf/in^3
P-Number Thickness: inExternal Pressure Chart:
UCS-66 Curve:Elastic Modulus at Operating Condition: psig
Elastic Modulus at Seating Condition: psigIs the Material Normalized:No
Bolt
Material Name:Material Listing:
Yield Strength at Design Temperature: psigAllowable Stress at Design Temperature: psig
Allowable Stress at Ambient Temperature: psigMaterial Density: lbf/in^3
P Number Thickness: inExternal Pressure Chart:
UCS 66 Curve:Elastic Modulus at Operating Condition: psig
Elastic Modulus at Seating Condition: psigIs the Material Normalized:No
Gasket
Gasket Thickness: inGasket Outside Diameter: in
Gasket Inside Diameter: inGasket Type:
Gasket Factor:Gasket or Joint-Surface Unit Seating Load: psig
Flange Facing Sketch (Table 2-52):Column from Table 2-52:
Flange Face Width: inSerration Depth: in
Nubbin Width: in

Output

Geometry

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Bolt Spacing (BS)

BS = C * sin(180 / N)

BS = 0 * sin(180 / 0)

BS = NAN in

Maximum Bolt Spacing (BSf)

* ASME Section VIII Div.1 App. 2 - Equation (3)

BSf = 2 * boltOD + (6 * t) / (m + 0.5)

BSf = 2 * 0 + (6 * 0) / (0 + 0.5)

BSf = 0 in

Minimum Circumferential Spacing between Bolts [BSmin]:

BSmin =


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Radial Distance Between Bolt and Hub/Pipe (BSh)

BSh = (C - B) / 2 - g1

BSh = (0 - 0) / 2 - 0

BSh = 0 in

Radial Distance between Hub and Bolts [BShub]:

BShub =

Radial Distance Between Bolt and Flange Edge (BSec)

BSec = (A - C) / 2

BSec = (0 - 0) / 2

BSec = 0 in

Radial Distance between Bolts and the Flange Edge [BSe]:

BSe =

Effective Hub Length (ehl)

ehl = sqrt(B * g0)

ehl = sqrt(0 * 0)

ehl = 0 in

Minimum Hub Length (hmin)

hmin = 1.5 * g0

hmin = 1.5 * 0

hmin = 0 in

Calculated Dimensions

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Hub Small End Required Thickness Due to Internal Pressure (hubt)

hubt = (P * (B / 2)) / (Sfo * E - 0.6 * P)

hubt = (0 * (0 / 2)) / (0 * 1 - 0.6 * 0)

hubt = NAN in

Minimum Pipe Thickness (tnmin)

tnmin = (P * (B - 2 * tn)) / (Sfo * Ep - 0.6 * P)

tnmin = (0 * (0 - 2 * 0)) / (0 * 0 - 0.6 * 0)

tnmin = NAN in

Width Used to Determine the Basic Gasket Seating Width (varN)

* ASME Section VIII Div.1 App. 2 - Table 2-5.2

varN = (GOD - GID) / 2

varN = (0 - 0) / 2

varN = 0 in

Cross-Sectional Area of the Bolts Using Root Diameter of the Thread (Ab)

Ab = BRArea * Nbolt

Ab = 0 * 0

Ab = 0 in^2

Minimum Width According to Dennis Moss Book (Nmin)

Nmin = (Ab * Sba) / (gy * 3.1416 * (GOD + GID))

* Pressure Vessel Design Manual by D. R. Moss and M. M. Basic

Nmin = (0 * 0) / (0 * 3.14 * (0 + 0))

Nmin = NAN in

Basic Gasket Seating Width from Table 2-5.2 (b0)

* ASME Section VIII Div.1 App. 2 - Table 2-5.2

b0 = 0 in

Effective Gasket or Joint-Contact-Surface Seating Width (varb)

varb = b0

varb = 0

varb = 0 in

Diameter at Location of Gasket Load Reaction (G)

varG = GID + varN

varG = 0 + 0

varG = 0 in

Bolt Load

Total Hydrostatic End Force (H)

H = 0.785 * varG^2 * P

H = 0.785 * 0^2 * 0

H = 0 lbf

Total Joint-Contact Surface Compression Load (HP)

HP = 2 * varb * 3.1416 * varG * m * P

HP = 2 * 0 * 3.1416 * 0 * 0 * 0

HP = 0 lbf

Hydrostatic End Force on Area Inside of Flange (HD)

HD = 3.1416 / 4 * B^2 * P

HD = 3.1416 / 4 * 0^2 * 0

HD = 0 lbf

Difference Between H and HD (HT)

HT = H - HD

HT = 0 - 0

HT = 0 lbf

Minimum Required Bolt Load for Operating Conditions (Wm1)

Wm1 = H + HP

Wm1 = 0 + 0

Wm1 = 0 lbf

Minimum Required Bolt Load for Gasket Seating (Wm2)

Wm2 = 3.1416 * varb * varG * gy

Wm2 = 3.1416 * 0 * 0 * 0

Wm2 = 0 lbf


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Total Cross-Sectional Area of Bolts at Root of Thread Required for Operating Conditions (Am1)

Am1 = Wm1 / Sbo

Am1 = 0 / 0

Am1 = NAN in^2

Total Cross-Sectional Area of Bolts at Root of Thread Required for Gasket Seating (Am2)

Am2 = Wm2 / Sba

Am2 = 0 / 0

Am2 = NAN in^2

Total Required Cross-Sectional Area of Bolts (Am)

Am = max(Am1, Am2)

Am = max(NAN, NAN)

Am = NAN in^2

Cross-Sectional Area of the Bolts Using Root Diameter of the Thread (Ab)

Ab = BRArea * Nbolt

Ab = 0 * 0

Ab = 0 in^2

Flange Load

Flange Design Bolt Load for Operating Conditions (Wo)

Wo = Wm1

Wo = 0

Wo = 0 lbf

Flange Design Bolt Load for Gasket Seating (Wg)

Wg = (Am + Ab) * Sba / 2

Wg = (NAN + 0) * 0 / 2

Wg = NAN lbf

Gasket Load (HG)

HG = Wm1 - H

HG = 0 - 0

HG = 0 lbf

Flange Moment Arms

Radial Distance from Bolt Circle to Point of Intersection of Hub and Back Flange (R)

R = (C - B) / 2 - g1

R = (0 - 0) / 2 - 0

R = 0 in

Radial Distance from the Bolt Circle to the Circle on which HD acts (hD)

hD = 0 in

Radial Distance from Gasket Load Reaction to the Bolt Circle (hG)

hG = (C - G) / 2

hG = (0 - 0) / 2

hG = 0 in

Radial Distance from Bolt Circle to the Circle on which HT acts (hT)

hT = 0 in

Flange Moment

Component of Moment due to HD (MD)

MD = HD * hD

MD = 0 * 0

MD = 0 lbf.in

Component of Moment due to HT (MT)

MT = HT * hT

MT = 0 * 0

MT = 0 lbf.in

Component of Moment due to HG (MG)

MG = HG * hG

MG = 0 * 0

MG = 0 lbf.in

Total MOment Acting Upon the Flange - Operating (Mo)

Mo = MD + MT + MG

Mo = 0 + 0 + 0

Mo = 0 lbf.in

Total Moment Acting Upon the Flange - Seating (Ms)

Ms = Wg * (varC - varG) / 2

Ms = NAN * (0 - 0) / 2

Ms = NAN lbf.in

Factors

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Ratio of Outside Diameter of Flange to Inside Diameter (K)

K = A / B

K = 0 / 0

K = NAN

Factor Involving K (Y)

Y = 1 / (K - 1) * (0.66845 + 5.7169 * (K^2 * log10(K) / (K^2 - 1)))

Y = 1 / (NAN - 1) * (0.66845 + 5.7169 * (NAN^2 * log10(NAN) / (NAN^2 - 1)))

Y = NAN

Factor Involving K (U)

U = (K^2 * (1 + 8.55246 * log10(K)) - 1) / (1.36136 * (K^2 - 1) * (K - 1))

U = (NAN^2 * (1 + 8.55246 * log10(NAN)) - 1) / (1.36136 * (NAN^2 - 1) * (NAN - 1))

U = NAN

Factor Involving K (T)

T = (K^2 * (1 + 8.55246 * log10(K)) - 1) / ((1.0472 + 1.9448 * K^2) * (K - 1))

T = (NAN^2 * (1 + 8.55246 * log10(NAN)) - 1) / ((1.0472 + 1.9448 * NAN^2) * (NAN - 1))

T = NAN

Factor Involving K (Z)

Z = (K^2 + 1) / (K^2 - 1)

Z = (NAN^2 + 1) / (NAN^2 - 1)

Z = NAN

Factor (h0)

h0 = sqrt(B * g0)

h0 = sqrt(0 * 0)

h0 = 0 in

Factor Involving g1 and g0 from Table 2.7.1 (A)

factorA = (g1 / g0) - 1

factorA = (0 / 0) - 1

factorA = NAN

Factor from Table 2-7.1 (factorC)

factorC = 43.68 * (h / h0)^4

factorC = 43.68 * (0 / 0)^4

factorC = NAN

Factor from Table 2-7.1 (factorC1)

factorC1 = 1 / 3 + factorA / 12

factorC1 = 1 / 3 + NAN / 12

factorC1 = NAN

Factor from Table 2-7.1 (factorC2)

factorC2 = 5 / 42 + 17 * factorA / 336

factorC2 = 5 / 42 + 17 * NAN / 336

factorC2 = NAN

Factor from Table 2-7.1 (factorC3)

factorC3 = 1 / 210 + factorA / 360

factorC3 = 1 / 210 + NAN / 360

factorC3 = NAN

Factor from Table 2-7.1 (factorC4)

factorC4 = 11 / 360 + (59 * factorA) / 5040 + (1 + 3 * factorA) / factorC

factorC4 = 11 / 360 + (59 * NAN) / 5040 + (1 + 3 * NAN) / NAN

factorC4 = NAN

Factor from Table 2-7.1 (factorC5)

factorC5 = 1 / 90 + (5 * factorA) / 1008 - (1 + factorA)^3 / factorC

factorC5 = 1 / 90 + (5 * NAN) / 1008 - (1. NAN)^3 / NAN

factorC5 = NAN

Factor from Table 2-7.1 (factorC6)

factorC6 = 1 / 120 + (17 * factorA) / 5040 + 1 / factorC

factorC6 = 1 / 120 + (17 * NAN) / 5040 + 1 / NAN

factorC6 = NAN

Factor from Table 2-7.1 (factorC7)

factorC7 = 215 / 2772 + (51 * factorA) / 1232 + (60 / 7 + (225 * factorA) / 14 + (75 * factorA^2) / 7 + (5 * factorA^3) / 2) / factorC

factorC7 = 215 / 2772 + (51 * NAN) / 1232 + (60 / 7 + (225 * NAN) / 14 + (75 * NAN^3) / 7 + (5 * NAN^2) / 2) / NAN

factorC7 = NAN

Factor from Table 2-7.1 (factorC8)

factorC8 = 31 / 6930 + (128 * factorA) / 45045 + (6 / 7 + (15 * factorA) / 7 + (12 * factorA^2) / 7 + (5 * factorA^3) / 11) / factorC

factorC8 = 31 / 6930 + (128 * NAN) / 45045 + (6 / 7 + (15 * NAN) / 7 + (12 * NAN^2) / 7 + (5 * NAN^3) / 11) / NAN

factorC8 = NAN

Factor from Table 2-7.1 (factorC9)

factorC9 = 533 / 30240 + (653 * factorA) / 73920 + (1 / 2 + (33 * factorA) / 14 + (39 * factorA^2) / 28 + (25 * factorA^3) / 84) / factorC

factorC9 = 533 / 30240 + (653 * NAN) / 73920 + (1 / 2 + (33 * NAN) / 14 + (39 * NAN^2) / 28 + (25 * NAN^3) / 84) / NAN

factorC9 = NAN

Factor from Table 2-7.1 (factorC10)

factorC10 = 29 / 3780 + (3 * factorA) / 704 - (1 / 2 + (33 * factorA) / 14 + (81 * factorA^2) / 28 + (13 * factorA^3) / 12) / factor

factorC10 = 29 / 3780 + (3 * NAN) / 704 - (1 / 2 + (33 * NAN) / 14 + (81 * NAN^2) / 28 + (13 * NAN^3) / 12) / NAN

factorC10 = NAN

Factor from Table 2-7.1 (factorC11)

factorC11 = 31 / 6048 + (1763 * factorA) / 665280 + (1 / 2 + (6 * factorA) / 7 + (15 * factorA^2) / 28 + (5 * factorA^3) / 42) / factorC

factorC11 = 31 / 6048 + (1763 * NAN) / 665280 + (1 / 2 + (6 * NAN) / 7 + (15 * NAN^2) / 28 + (5 * NAN^3) / 42) / NAN

factorC11 = NAN

Factor from Table 2-7.1 (factorC12)

factorC12 = 1 / 2925 +(71 * factorA) / 300300 + (8 / 35 + (18 * factorA) / 35 + (156 * factorA^2) / 385 + (6 * factorA^3) / 55) / factorC

factorC12 = 1 / 2925 +(71 * NAN) / 300300 + (8 / 35 + (18 * NAN) / 35 + (156 * NAN2) / 385 + (6 * NAN^3) / 55) / NAN

factorC12 = NAN

Factor from Table 2-7.1 (factorC13)

factorC13 = 761 / 831600 + (937 * factorA) / 1663200 + (1 / 35 + (6 * factorA) / 35 + (11 * factorA^2) / 70 + (3 * factorA^3) / 70) / factorC

factorC13 = 761 / 831600 + (937 * NAN) / 1663200 + (1 / 35 + (6 * NAN) / 35 + (11 * NAN^2) / 70 + (3 * NAN^3) / 70) / NAN

factorC13 = NAN

Factor from Table 2-7.1 (factorC14)

factorC14 = 197 / 415800 + (103 * factorA) / 332640 - (1 / 35 + (6 * factorA) / 35 + (17 * factorA^2) / 70 + factorA^3 / 10) / factorC

factorC14 = 197 / 415800 + (103 * NAN) / 332640 - (1 / 35 + (6 * NAN) / 35 + (17 * NAN^2) / 70. NAN^3 / 10) / NAN

factorC14 = NAN

Factor from Table 2-7.1 (factorC15)

factorC15 = 233 / 831600 + (97 * factorA) / 554400 + (1 / 35 + (3 * factorA) / 35 + factorA^2 / 14 + (2 * factorA^3) / 105) / factorC

factorC15 = 233 / 831600 + (97 * NAN) / 554400 + (1 / 35 + (3 * NAN) / 35. NAN^2 / 14 + (2 * NAN^3) / 105) / NAN

factorC15 = NAN

Factor from Table 2-7.1 (factorC16)

factorC16 = factorC1 * factorC7 * factorC12 + factorC2 * factorC8 * factorC3 + factorC3 * factorC8 * factorC2 - (factorC3^2 * factorC7 + factorC8^2 * factorC1 + factorC2^2 * factorC12)

factorC16 = NAN * NAN * NAN + NAN * NAN * NAN + NAN * NAN * NAN - (NAN^2 * NAN + NAN^2 * NAN + NAN^2 * NAN)

factorC16 = NAN

Factor from Table 2-7.1 (factorC17)

factorC17 = (factor4 * factorC7 * factorC12 + factorC2 * factorC8 * factorC13 + factorC3 * factorC8 * factorC9 - (factorC13 * factorC7 * factorC3 + factorC8^2 * factorC4 + factorC12 * factorC2 * factorC9)) / factorC16

factorC17 = (NAN * NAN * NAN + NAN * NAN * NAN + NAN * NAN * NAN - (NAN * NAN * NAN + NAN^2 * NAN + NAN * NAN * NAN)) / NAN

factorC17 = NAN

Factor from Table 2-7.1 (factorC18)

factorC18 = (factorC5 * factorC7 * factorC12 + factorC2 * factorC8 * factorC14 + factorC3 * factorC8 * factorC10 - (factorC14 * factorC7 * factorC3 + factorC8^2 * factorC5 + factorC12 * factorC2 * factorC10)) / factorC16

factorC18 = (NAN * NAN * NAN + NAN * NAN * NAN + NAN * NAN * NAN - (NAN * NAN * NAN + NAN^2 * NAN + NAN * NAN * NAN)) / NAN

factorC18 = NAN

Factor from Table 2-7.1 (factorC19)

factorC19 = (factorC6 * factorC7 * factorC12 + factorC2 * factorC8 * factorC15 + factorC3 * factorC8 * factorC11 - (factorC15 * factorC7 * factorC3 + factor8^2 * factorC6 + factorC12 * factorC2 * factorC11)) / factorC16

factorC19 = (NAN * NAN * NAN + NAN * NAN * NAN + NAN * NAN * NAN - (NAN * NAN * NAN + NAN^2 * NAN + NAN * NAN * NAN)) / NAN

factorC19 = NAN

Factor from Table 2-7.1 (factorC20)

factorC20 = (factorC1 * factorC9 * factorC12 + factorC4 * factorC8 * factorC3 + factorC3 * factorC13 * factorC2 - factorC3^2 * factorC9 + factorC13 * factorC8 * factorC1 + factorC12 * factorC4 * factorC2)) / factorC16

factorC20 = (NAN * NAN * NAN + NAN * NAN * NAN + NAN * NAN * NAN - NAN^2 * NAN + NAN * NAN * NAN + NAN * NAN * NAN)) / NAN

factorC20 = NAN

Factor from Table 2-7.1 (factorC21)

factorC21 = (factorC1 * factorC10 * factorC12 + factorC5 * factorC8 * factorC3 + factorC3 * factorC14 * factorC2 - (factorC3^2 * factorC10 + factorC14 * factorC8 * factorC1 + factorC12 * factorC5 * factorC2)) / factorC16

factorC21 = (NAN * NAN * NAN + NAN * NAN * NAN + NAN * NAN * NAN - (NAN^2 * NAN + NAN * NAN * NAN + NAN * NAN * NAN)) / NAN

factorC21 = NAN

Factor from Table 2-7.1 (factorC22)

factorC22 = (factorC1 * factorC11 * factorC12 + factorC6 * factorC8 * factorC3 + factorC3 * factorC15 * factorC2 - (factorC3^2 * factorC11 + factorC15 * factorC8 * factorC1 + factorC12 * factorC6 * factorC2)) / factorC16

factorC22 = (NAN * NAN * NAN + NAN * NAN * NAN + NAN * NAN * NAN - (NAN^2 * NAN + NAN * NAN * NAN + NAN * NAN * NAN)) / NAN

factorC22 = NAN

Factor from Table 2-7.1 (factorC23)

factorC23 = (factorC1 * factorC7 * factorC13 + factorC2 * factorC9 * factorC3 + factorC4 * factorC8 * factorC2 - (factorC3 * factorC7 * factorC4 + factorC8 * factorC9 * factorC1 + factorC2^2 * factorC13)) / factorC16

factorC23 = (NAN * NAN * NAN + NAN * NAN * NAN + NAN * NAN * NAN - (NAN * NAN * NAN + NAN * NAN * NAN + NAN^2 * NAN)) / NAN

factorC23 = NAN

Factor from Table 2-7.1 (factorC24)

factorC24 = (factorC1 * factorC7 * factorC14 + factorC2 * factorC10 * factorC3 + factorC5 * factorC8 * factorC2 - (factorC3 * factorC7 * factorC5 + factorC8 * factorC10 * factorC1 + factorC2^2 * factorC14)) / factorC16

factorC24 = (NAN * NAN * NAN + NAN * NAN * NAN + NAN * NAN * NAN - (NAN * NAN * NAN + NAN * NAN * NAN + NAN^2 * NAN)) / NAN

factorC24 = NAN

Factor from Table 2-7.1 (factorC25)

factorC25 = (factorC1 * factorC7 * factorC15 + factorC2 * factorC11 * factorC3 + factorC6 * factorC8 * factorC2 - (factorC3 * factorC7 * factorC6 + factorC8 * factorC11 * factorC1 + factorC2^2 * factorC15)) / factorC16

factorC25 = (NAN * NAN * NAN + NAN * NAN * NAN + NAN * NAN * NAN - (NAN * NAN * NAN + NAN * NAN * NAN + NAN^2 * NAN)) / NAN

factorC25 = NAN

Factor from Table 2-7.1 (factorC26)

factorC26 = - (factorC / 4)^(1 / 4)

factorC26 = - (NAN / 4)^(1 / 4)

factorC26 = NAN

Factor from Table 2-7.1 (factorC27

factorC27 = factorC20 - factorC17 - 5 / 12 + factorC17 * factorC26

factorC27 = NAN - NAN - 5 / 12. NAN * NAN

factorC27 = NAN

Factor from Table 2-7.1 (factorC28)

factorC28 = factorC22 - factorC19 - 1 / 12 + factorC19 * factorC26

factorC28 = NAN - NAN - 1 / 12. NAN * NAN

factorC28 = NAN

Factor from Table 2-7.1 (factorC29)

factorC26 = - (factorC / 4)^(1 / 2)

factorC26 = - (NAN / 4)^(1 / 2)

factorC29 = NAN

Factor from Table 2-7.1 (factorC30)

factorC26 = - (factorC / 4)^(3 / 4)

factorC26 = - (NAN / 4)^(3 / 4)

factorC30 = NAN

Factor from Table 2-7.1 (factorC31)

factorC31 = (3 * factorA) / 2 - factorC17 * factorC30

factorC31 = (3 * NAN) / 2 - NAN * NAN

factorC31 = NAN

Factor from Table 2-7.1 (factorC32)

factorC32 = 1 / 2 - factorC19 * factorC30

factorC32 = 1 / 2 - NAN * NAN

factorC32 = NAN

Factor from Table 2-7.1 (factorC33)

factorC33 = 0.5 * factorC26 * factorC32 + factorC28 * factorC31 * factorC29 - (0.5 * factorC30 * factorC28 + factorC32 * factorC27 * factorC29)

factorC33 = 0.5 * NAN * NAN + NAN * NAN * NAN - (0.5 * NAN * NAN + NAN * NAN * NAN

factorC33 = NAN

Factor from Table 2-7.1 (factorC34)

factorC34 = 1 / 12 + factorC18 - factorC21 - factorC18 * factorC26

factorC34 = 1 / 12. NAN - NAN - NAN * NAN

factorC34 = NAN

Factor from Table 2-7.1 (factorC35)

factorC35 = - factorC18 * (factorC / 4)^(3 / 4)

factorC35 = - NAN * (NAN / 4)^(3 / 4)

factorC35 = NAN

Factor from Table 2-7.1 (factorC36)

factorC36 = (factorC28 * factorC35 * factorC29 - factorC32 * factorC34 * factorC29) / factorC33

factorC36 = (NAN * NAN * NAN - NAN * NAN * NAN) / NAN

factorC36 = NAN

Factor from Table 2-7.1 (factorC37)

factorC37 = (0.5 * factorC26 * factorC35 + factorC34 * factorC31 * factorC29 - (0.5 * factorC30 * factorC34 + factorC35 * factorC27 * factorC29)) / factorC33

factorC37 = (0.5 * NAN * NAN + NAN * NAN * NAN - (0.5 * NAN * NAN + NAN * NAN * NAN)) / NAN

factorC37 = NAN

Factor from Table 2-7.1 (factorE1)

factorE1 = factorC17 * factorC36 + factorC18 + factorC19 * factorC3

factorE1 = NAN * NAN + NAN + NAN * NAN

factorE1 = NAN

Factor from Table 2-7.1 (factorE2)

factorE2 = factorC20 * factorC36 + factorC21 + factorC22 * factorC37

factorE2 = NAN * NAN + NAN + NAN * NAN

factorE2 = NAN

Factor from Table 2-7.1 (factorE3)

factorE3 = factorC23 * factorC36 + factorC24 + factorC25 * factorC37

factorE3 = NAN * NAN + NAN + NAN * NAN

factorE3 = NAN

Factor from Table 2-7.1 (factorE4)

factorE4 = 1 / 4 + factorC37 / 12 + factorC36 / 4 - factorE3 / 5 - 3 * factorE2 / 2 - factorE1

factorE4 = 1 / 4 + NAN / 12 + NAN / 4 - NAN / 5 - 3 * NAN / 2 - NAN

factorE4 = NAN

Factor from Table 2-7.1 (factorE5)

factorE5 = factorE1 * (1 / 2 + factorA / 6) + factorE2 * (1 / 4 + (11 * factorA) / 84) + factorE3 * (1 / 70 + factorA / 105)

factorE5 = NAN * (1 / 2. NAN / 6). NAN * (1 / 4 + (11 * NAN) / 84). NAN * (1 / 70. NAN / 105)

factorE5 = NAN

Factor from Table 2-7.1 (factorE6)

factorE6 = factorE5 - factorC36 * (7 / 120 + factorA / 36 + (3 * factorA) / factorC) - 1 / 40 - factorA / 72 - factorC37 * (1 / 60 + factorA / 120 + 1 / factorC)

factorE6 = NAN - NAN * (7 / 120. NAN / 36 + (3 * NAN) / NAN) - 1 / 40 - NAN / 72 - NAN * (1 / 60. NAN / 120 + 1 / NAN)

factorE6 = NAN

Factor from Table 2-7.1 for Integral Flange (factorV)

factorV = factorE4 / ((2.73 / factorC)^(1 / 4) * (1 + factorA)^3)

factorV = NAN / ((2.73 / NAN)^(1 / 4) * (1. NAN)^3)

factorV = NAN

Factor from Table 2-7.1 for Loose Hub Flange (factorVL)

factorVL = (1 / 4 - factorC24 / 5 - (3 * factorC21) / 2 - factorC18) / ((2.73 / factorC)^(1 / 4) * (1 + factorA)^3)

factorVL = (1 / 4 - NAN / 5 - (3 * NAN) / 2 - NAN) / ((2.73 / NAN)^(1 / 4) * (1. NAN)^3))

factorVL = NAN

Factor from Table 2-7.1 for Integral Flange (factorF)

factorF = - factorE6 / ((factorC / 2.73)^(1 / 4) * (1 + factorA)^3 / factorC))

factorF = - NAN / ((NAN / 2.73)^(1 / 4) * (1. NAN)^3 / NAN))

factorF = NAN

Factor from Table 2-7.1 for Loose Hub Flange (factorFL)

factorFL = (factorC18 * (1 / 2 + factorA / 6) + factorC21 * (1 / 4 + (11 * factorA) / 84) + factorC24 * (1 / 70 + factorA / 105) - (1 / 40 + factorA / 72)) / ((factorC / 2.73)^(1 / 4) * ((1 + factorA)^3 / factorC))

factorFL = (NAN * (1 / 2. NAN / 6). NAN * (1 / 4 + (11 * NAN) / 84). NAN * (1 / 70. NAN / 105) - (1 / 40. NAN / 72)) / ((NAN / 2.73)^(1 / 4) * ((1. NAN)^3 / NAN))

factorFL = NAN

factorSube = 0 in^-1


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Factor Involving Flange Thickness and Factors e, T and d (factorL)

factorL = (t * factore + 1) / factorT + t^3 / factord

factorL = (0 * 0 + 1) / NAN + 0^3 / 0

factorL = NAN

Flange Stresses

Radial Stress in the Flange for Gasket Seating (SRa)

STa = 0 psig

Tangential Stress in the Flange for Gasket Seating (STa)

STa = 0 psig

Longitudinal Hub Stress in the Flange for Gasket Seating (SHa)

SHa = 0 psig

Average Flange Stress at Seating Condition (Sas)

Sas = (SHa + max(SRa, STa)) / 2

Sas = (0 + max(0, 0)) / 2

Sas = 0 psig

Radial Stress in the Flange for Operating Condition (SRo)

SRo = 0 psig


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Tangential Stress in the Flange for Operating Condition (STo)

STo = (Y * Mo) / (t^2 * B)

STo = (NAN * 0) / (0^2 * 0)

STo = NAN psig

Longitudinal Hub Stress in the Flange for Operating Condition (SHo)

SHo = 0 psig

Average Flange Stress at Operating Condition (Sao)

Sao = (SHo + max(SRo, STo)) / 2

Sao = (0 + max(0, NAN)) / 2

Sao = NAN psig

Average Flange Stress at Seating Condition (Sas)

Sas = (SHa + max(SRa, STa)) / 2

Sas = (0 + max(0, 0)) / 2

Sas = 0 psig

Average Flange Stress at Operating Condition (Sao)

Sao = (SHo + max(SRo, STo)) / 2

Sao = (0 + max(0, NAN)) / 2

Sao = NAN psig

Equation Used to Calculate MAWP (beta)

beta = (3.1416 / 4) * (B^2 * hD + 2 * varb * varG * m * hG + varG^2 * hT - B^2 * hT)

beta = (3.1416 / 4) * (0^2 * 0 + 2 * 0 * 0 * 0 * 0 + 0^2 * 0 - 0^2 * 0)

beta = 0 in^3

Equation Used to Calculate MAWP (alpha_sh)

alpha_sh = 0

Equation Used to Calculate MAWP (alpha_sr)

alpha_sr = 0

Equation Used to Calculate MAWP (alpha_st)

alpha_st = 0

Maximum Allowable Working Pressure for Operating using SH and SR (mawp_hro)


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Maximum Allowable Working Pressure for Operating using SH and SR (mawp_hto)

mawp_hto = (2 * Sfo) / (alpha_sh + alpha_st)

mawp_hto = (2 * 0) / (0 + 0)

mawp_hto = NAN psig

Maximum Allowed Working Pressure for Operating (mawp_hto)

mawp_hto = max(mawp_hro, mawp_hto)

mawp_hto = max(0, NAN)

mawp_hto = NAN psig

Maximum Allowable Working Pressure for Gasket Seating using SH and SR (mawp_hra)


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Maximum Allowable Working Pressure for Gasket Seating using SH and SR (mawp_hta)

mawp_hta = (2 * Sfa) / (alpha_sh + alpha_st)

mawp_hta = (2 * 0) / (0 + 0)

mawp_hta = NAN psig

Maximum Allowed Working Pressure for Gasket Seating (mawp_hta)

mawp_hta = max(mawp_hra, mawp_hta)

mawp_hta = max(0, NAN)

mawp_hta = NAN psig

Flange Thickness and Weight

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Minimum Required Flange Thickness (tmin)

tmin = 300 in

Finished Flange Weight (fw)

fw = density * 10^9 * 3.1416 * (t * ((A / 2)^2 - (B / 2)^2 - N * (boltOD / 2)^2) + h * (((B + 2 * g1) / 2)^2 + ((B + 2 * g0) / 2)^2))

fw = 0 * 10^9 * 3.1416 * (0 * ((0 / 2)^2 - (0 / 2)^2 - 0 * (0 / 2)^2) + 0 * (((0 + 2 * 0) / 2)^2 + ((0 + 2 * 0) / 2)^2))

fw = 0 lb

Bolt Stresses

Bolt Stress in Gasket Seating Condtion (BSa)

BSa = Wm2 / Ab

BSa = 0 / 0

BSa = NAN psig

Bolt Stress in Gasket Operating Condition (BSo)

BSo = Wm1 / Ab

BSo = 0 / 0

BSo = NAN psig

Flange Rigidity Index

Rigidity Index for Gasket Seating (JSeating)

JSeating = (109.4 * Ms) / (Efs * t^3 * 0.2 * LN10(K))

JSeating = (109.4 * NAN) / (0 * 0^3 * 0.2 * LN10(NAN))

JSeating = NAN

Rigidity Index for Operating Condition (JOperating)

JOperating = (109.4 * Mo) / (Efo * t^3 * 0.2 * LN10(K))

JOperating = (109.4 * 0) / (0 * 0^3 * 0.2 * LN10(NAN))

JOperating = NAN

Summary of Results
Operating [psig]Gasket Seating [psig]
ActualAllowedActualAllowed
Longitudinal Hub00
Radial Flange00
Tangential Flange0NAN
Maximum Average0NAN
BoltingNANNAN
Minimum Required Flange Thickness + CA:300in
Maximum Allowed Working Pressure (Operating):NANpsig
Maximum Allowed Working Pressure (Gasket Seating):NANpsig
Finished Weight of Flange:0lb