Eng-Calculations

Flat face flanges with metal-to-metal contact outside the bolt circle for class 1 flange assembly (identical flange pairs)

Flange dimensions

Flange forces

(a) Integral Illustrated

(b) Integral with Spacer

(c)_Loose-Type_with_Hub — (c) Loose-Type with Hub

Values for calculation

Material of flange

General requirements

G1 - To these stress values a casting quality factor as specified in PG–25 of Section I; UG–24 of Section VIII, Division 1; or TM–190 of Section XII shall be applied.
G2 - These stress values include a joint efficiency factor of 0.60.
G3 - These stress values include a joint efficiency factor of 0.85.
G4 - For Section I applications, these stresses apply when used for boiler, water wall, superheater, and economizer tubes that are enclosed within a setting. A joint efficiency factor of 0.85 is included in values above 450°C.
G5 - Due to the relatively low yield strength of these materials, these higher stress values were established at temperatures where the shorttime tensile properties govern to permit the use of these alloys where slightly greater deformation is acceptable. The stress values in this range exceed 66²/₃% but do not exceed 90% of the yield strength at temperature. Use of these stresses may result in dimensional changes due to permanent strain. These stress values are not recommended for the flanges of gasketed joints or other applications where slight amounts of distortion can cause leakage or malfunction. For Section III applications, Table Y–2 lists multiplying factors that, when applied to the yield strength values shown in Table Y–1, will give allowable stress values that will result in lower levels of permanent strain.
G6 - Creep–fatigue, thermal ratcheting, and environmental effects are increasingly significant failure modes at temperatures in excess of 825°C and shall be considered in the design.
G7 - For Section VIII applications, these stress values are based on expected minimum values of 310 MPa tensile strength and yield strength of 140 MPa resulting from loss of strength due to thermal treatment required for the glass coating operation. UG–85 does not apply.
G8 - These stress values are established from a consideration of strength only and will be satisfactory for average service. For bolted joints where freedom from leakage over a long period of time without retightening is required, lower stress values may be necessary as determined from the flexibility of the flange and bolts and corresponding relaxation properties.
G9 - For Section III applications, the use of these materials shall be limited to materials for tanks covered in Subsections NC and ND, component supports, and for nonpressure–retaining attachments (NC/ND–2190).
G10 - Upon prolonged exposure to temperatures above 425°C, the carbide phase of carbon steel may be converted to graphite. See Nonmandatory Appendix A, A–201 and A–202.
G11 - Upon prolonged exposure to temperatures above 475°C, the carbide phase of carbon–molybdenum steel may be converted to graphite. See Nonmandatory Appendix A, A–201 and A–202.
G12 - At temperatures above 550°C, these stress values apply only when the carbon is 0.04% or higher on heat analysis.
G13 - These stress values at 575°C and above shall be used only when the grain size is ASTM No. 6 or coarser.
G14 - These stress values shall be used when the grain size is not determined or is determined to be finer than ASTM No. 6.
G15 - For Section I applications, use is limited to stays as defined in PG–13 except as permitted by PG–11.
G16 - For Section III Class 3 applications, these S values do not include a casting quality factor. Statically and centrifugally cast products meeting the requirements of NC–2570 shall receive a casting quality factor of 1.00.
G17 - For Section III Class 3 applications, statically and centrifugally cast products meeting the requirements of NC–2571(a) and (b), and cast pipe fittings, pumps, and valves with inlet piping connections of DN 50 and less, shall receive a casting quality factor of 1.00. Other casting quality factors shall be in accordance with the following:
(a) for visual examination, 0.80
(b) for magnetic particle examination, 0.85
(c) for liquid penetrant examination, 0.85
(d) for radiography, 1.00
(e) for ultrasonic examination, 1.00
(f) for magnetic particle or liquid penetrant plus ultrasonic examination or radiography, 1.00
G18 - See Table Y–1 for yield strength values as a function of thickness over this range. Allowable stresses are independent of yield strength in this thickness range.
G19 - This steel may be expected to develop embrittlement after service at moderately elevated temperature. See Nonmandatory Appendix A, A–207 and A–208.
G20 - These stresses are based on weld metal properties.
G21 - For Section I, use is limited to PEB–5.3. See PG–5.5 for cautionary note.
G22 - For Section I applications, use of external pressure charts for material in the form of bar stock is permitted for stiffening rings only.
G23 - For temperatures above the maximum temperature shown on the external pressure chart for this material, Figure CS–2 may be used for the design using this material.
G24 - A factor of 0.85 has been applied in arriving at the maximum allowable stress values in tension for this material. Divide tabulated values by 0.85 for maximum allowable longitudinal tensile stress.
G25 - For Section III applications, for both Class 2 and Class 3, the completed vessel after final heat treatment shall be examined by the ultrasonic method in accordance with NB–2542 except that angle beam examination in both the circumferential and the axial directions may be performed in lieu of the straight beam examination in the axial direction. The tensile strength shall not exceed 860 MPa.
G26 - Material that conforms to Class 10, 11, or 12 is not permitted.
G27 - Material that conforms to Class 11 or 12 is not permitted.
G28 - Supplementary Requirement S15 of SA–781, Alternate Mechanical Test Coupons and Specimen Locations for Castings, is mandatory.
G29 - For Section III applications, impact testing in accordance with the requirements of NC–2300 is required for Class 2 components and in accordance with ND–2300 for Class 3 components.
G30 - These stresses apply to all product forms (C, H, and P) as defined in SA/EN 10028–7.
G31 - The allowable stress value given for 250°C can be used up to the temperature of 260°C.
G32 - The allowable stress value given for 200°C can be used up to the temperature of 204°C.

Heat treatment requirements

H1 - For temperatures above 550°C, these stress values may be used only if the material is heat treated by heating to the minimum temperature specified in the material specification, but not lower than 1040°C, and quenching in water or rapidly cooling by other means.
H2 - For temperatures above 550°C, these stress values may be used only if the material is heat treated by heating to a minimum temperature of 1095°C, and quenching in water or rapidly cooling by other means.
H3 - Quenched and tempered at 650°C.
H4 - Solution treated and quenched.
H5 - For Section III applications, if heat treatment is performed after forming or fabrication, it shall be performed at 825°C to 1000°C for a period of time not to exceed 10 min at temperature, followed by rapid cooling.
H6 - Material shall be solution annealed at 1100°C to 1170°C, followed by a rapid cooling in water or air.

Size requirements

S1 - For Section I applications, stress values at temperatures of 450°C and above are permissible but, except for tubular products 75 mm O.D. or less enclosed within the boiler setting, use of these materials at these temperatures is not current practice.
S2 - For Section I applications, stress values at temperatures of 475°C and above are permissible but, except for tubular products 75 mm O.D. or less enclosed within the boiler setting, use of these materials at these temperatures is not current practice.
S3 - For Section I applications, stress values at temperatures of 550°C and above are permissible but, except for tubular products 75 mm O.D. or less enclosed within the boiler setting, use of these materials at these temperatures is not current practice.
S4 - For Section I applications, stress values at temperatures of 625°C and above are permissible but, except for tubular products 75 mm O.D. or less enclosed within the boiler setting, use of these materials at these temperatures is not current practice.
S5 - Material that conforms to Class 10, 11, or 12 is not permitted when the nominal thickness of the material exceeds 19 mm.
S6 - Material that conforms to Class 10, 11, or 12 is not permitted when the nominal thickness of the material exceeds 32 mm.
S7 - The maximum thickness of unheat–treated forgings shall not exceed 95 mm. The maximum thickness as–heat–treated may be 100 mm.
S8 - The maximum section thickness shall not exceed 75 mm for double–normalized–and–tempered forgings, or 125 mm for quenched–and–tempered forgings.
S9 - Both DN 200 and larger, and schedule 140 and heavier.
S10 - The maximum pipe size shall be DN 100 and the maximum thickness in any pipe size shall be Schedule 80.
S11 - Either DN 200 and larger and less than schedule 140 wall, or less than DN 200 and all wall thicknesses.

Time–dependent properties

T1 - Allowable stresses for temperatures of 370°C and above are values obtained from time–dependent properties.
T2 - Allowable stresses for temperatures of 400°C and above are values obtained from time–dependent properties.
T3 - Allowable stresses for temperatures of 455°C and above are values obtained from time–dependent properties.
T4 - Allowable stresses for temperatures of 480°C and above are values obtained from time–dependent properties.
T5 - Allowable stresses for temperatures of 510°C and above are values obtained from time–dependent properties.
T6 - Allowable stresses for temperatures of 540°C and above are values obtained from time–dependent properties.
T7 - Allowable stresses for temperatures of 565°C and above are values obtained from time–dependent properties.
T8 - Allowable stresses for temperatures of 595°C and above are values obtained from time–dependent properties.
T9 - Allowable stresses for temperatures of 620°C and above are values obtained from time–dependent properties.
T10 - Allowable stresses for temperatures of 425°C and above are values obtained from time–dependent properties.
T11 - Allowable stresses for temperatures of 350°C and above are values obtained from time–dependent properties.
T12 - Allowable stresses for temperatures of 650°C and above are values obtained from time–dependent properties.

Welding requirements

W1 - Not for welded construction.
W2 - Not for welded construction in Section III.
W3 - Welded.
W4 - Nonwelded, or welded if the tensile strength of the Section IX reduced section tension test is not less than 690 MPa.
W5 - Welded, with the tensile strength of the Section IX reduced tension test less than 690 MPa but not less than 655 MPa.
W6 - This material may be welded by the resistance technique.
W7 - In welded construction for temperatures above 450°C, the weld metal shall have a carbon content of greater than 0.05%.
W8 - Welding and oxygen or other thermal cutting processes are not permitted when carbon content exceeds 0.35% by heat analysis.
W9 - For Section I applications, for pressure retaining welds in 21/4Cr–1Mo materials, other than circumferential butt welds less than or equal to 89 mm in outside diameter, when the design metal temperatures exceed 450°C, the weld metal shall have a carbon content greater than 0.05%.
W10 - For Section III applications, material that conforms to Class 10, 13, 20, 23, 30, 33, 40, 43, 50, or 53 is not permitted for Class 2 and Class 3 construction when a weld efficiency factor of 1.00 is used in accordance with Note W12.
W11 - For Section VIII applications, Section IX, QW–250 Variables QW–404.12, QW–406.3, QW–407.2, and QW–409.1 shall also apply to this material. These variables shall be applied in accordance with the rules for welding of Part UF.
W12 - These S values do not include a longitudinal weld efficiency factor. For Section III applications, for materials welded without filler metal, ultrasonic examination, radiographic examination, or eddy current examination, in accordance with NC–2550, shall provide a longitudinal weld efficiency factor of 1.00. Materials welded with filler metal meeting the requirements of NC–2560 shall receive a longitudinal weld efficiency factor of 1.00. Other longitudinal weld efficiency factors shall be in accordance with the following:
(a) for single butt weld, with filler metal, 0.80
(b) for single or double butt weld, without filler metal, 0.85
(c) for double butt weld, with filler metal, 0.90
(d) for single or double butt weld, with radiography, 1.00
W13 - For Section I applications, electric resistance and autogenous welded tubing may be used with these stresses, provided the following additional restrictions and requirements are met:
(a) The tubing shall be used for boiler, waterwall, superheater, and economizer tubes that are enclosed within the setting.
(b) The maximum outside diameter shall be 89 mm.
(c) The weld seam of each tube shall be subjected to an angle beam ultrasonic inspection per SA–450.
(d) A complete volumetric inspection of the entire length of each tube shall be performed in accordance with SA–450.
(e) Material test reports shall be supplied.
W14 - These S values do not include a weld factor. For Section VIII, Division 1, and Section XII applications using welds made without filler metal, the tabulated tensile stress values shall be multiplied by 0.85. For welds made with filler metal, consult UW–12 for Section VIII, Division 1, or TW–130.4 for Section XII, as applicable.
W15 - The Nondestructive Electric Test requirements of SA–53 Type E pipe are required for all sizes. The pipe shall be additionally marked "NDE" and so noted on the material specification.

Material of nozzle neck, vessel or pipe wall

General requirements

Heat treatment requirements

Size requirements

Time–dependent properties

Welding requirements

Material of bolt

General requirements

G1 - Alloy N06625 in the annealed condition is subject to severe loss of impact strength at room temperatures after exposure in the range of 550°C to 750°C.
G2 - Copper–silicon alloys are not always suitable when exposed to certain media and high temperatures, particularly steam above 100°C. The owner, the owner's designated agent, or the user should ensure him/herself that the alloy selected is satisfactory for the service for which it is to be used.
G3 - The maximum operating temperature is arbitrarily set at 250°C because harder temper adversely affects design stress in the creep rupture temperature range.
G4 - This material has reduced toughness at room temperature after exposure for about 5000 h at 325°C and after shorter exposure above 350°C.
G5 - At temperatures above 550°C, these stress values apply only when the carbon is 0.04% or higher on heat analysis.
G6 - For temperatures above 550°C, these stress values may be used only if the material is heat treated by heating it to a minimum temperature of 1040°C.
G7 - The user is cautioned that under certain conditions of temperature and environment or fatigue conditions, stress corrosion of this material shall be considered.
G8 - For all design temperatures, the maximum hardness shall be Rockwell C35 immediately under thread roots. The hardness shall be taken on a flat area at least 3 mm across, prepared by removing threads; no more material than necessary shall be removed to prepare the flat area. Hardness determinations shall be made at the same frequency as the tensile tests.
G9 - For Section VIII, Division 1 applications, use of external pressure charts for material in the form of bar stock is permitted for stiffening rings only.
G10 - For stress relieved tempers, stress values for T3 temper can be used for T351, T3510, and T3511; stress values for T4 temper can be used for T451, T4510, and T4511; and stress values for T6 temper can be used for T651, T6510, and T6511.
G11 - The shipping lot testing method of SA–574, 11.3, is prohibited.
G12 - Since these bolts could be used in flanged joints, the maximum permitted temperature and maximum allowable stress are limited to reduce the potential for bolt relaxation and associated flange leakage.

Heat treatment requirements

H1 - Design stresses for the cold drawn temper based on hot rolled properties until required data on cold drawn is submitted.

Time–dependent properties

T1 - Allowable stresses for temperatures of 150°C and above are values obtained from time–dependent properties.
T2 - Allowable stresses for temperatures of 175°C and above are values obtained from time–dependent properties.
T3 - Allowable stresses for temperatures of 230°C and above are values obtained from time–dependent properties.
T4 - Allowable stresses for temperatures of 290°C and above are values obtained from time–dependent properties.
T5 - Allowable stresses for temperatures of 450°C and above are values obtained from time–dependent properties.
T6 - Allowable stresses for temperatures of 480°C and above are values obtained from time–dependent properties.
T7 - Allowable stresses for temperatures of 510°C and above are values obtained from time–dependent properties.
T8 - Allowable stresses for temperatures of 540°C and above are values obtained from time–dependent properties.
T9 - Allowable stresses for temperatures of 565°C and above are values obtained from time–dependent properties.
T10 - Allowable stresses for temperatures of 595°C and above are values obtained from time–dependent properties.
T11 - Allowable stresses for temperatures of 620°C and above are values obtained from time–dependent properties.
T12 - Allowable stresses for temperatures of 650°C and above are values obtained from time–dependent properties.

Welding requirements

W1 - Welding, brazing, and thermal cutting are not permitted.
W2 - If welded, the allowable stress values for the annealed condition shall be used.
W3 - This material may be welded by the resistance technique.
W4 - The stress values given for this material are not applicable when either welding or thermal cutting is employed.
W5 - Except for nonstructural tack welds used as a locking device, welding is prohibited for Section VIII, Division 1 use.

Temperature

$T$ $\mathrm{°C}$

Allowable design stress for material of flange at design temperature (operating condition) or atmospheric temperature (gasket seating)

$S_f$ $\mathrm{MPa}$

Allowable design stress for material of nozzle neck, vessel or pipe wall, at design temperature (operating condition) or atmospheric temperature (gasket seating)

$S_n$ $\mathrm{MPa}$

Allowable bolt stress at design temperature

$S_b$ $\mathrm{MPa}$

Internal design pressure

$P$ $\mathrm{MPa}$

Flange category

Outside diameter of flange

$A$ $\mathrm{mm}$

Inside diameter of flange

$B$ $\mathrm{mm}$

Bolt‐circle diameter

$C$ $\mathrm{mm}$

Number of bolts

$n$

Nominal diameter of bolt

$d_b$ $\mathrm{mm}$

Diameter of bolt hole

$D$ $\mathrm{mm}$

Mean diameter of gasket

$G$ $\mathrm{mm}$

Radial distance from bolt circle to flange‐spacer or flange‐flange bearing circle where tangential contact occurs

$h_C$ $\mathrm{mm}$

Thickness of the flange under consideration

$t$ $\mathrm{mm}$

Thickness of hub at small end

$g_0$ $\mathrm{mm}$

Thickness of hub at back of flange

$g_1$ $\mathrm{mm}$

Hub length

$h$ $\mathrm{mm}$

Cross‐sectional area of the bolts using the root diameter of the thread or least diameter of unthreaded portion, if less

$A_b$ $\mathrm{mm^2}$

Gasket load due to seating pressure, plus axial force generated by self‐sealing of gasket

$H_G$ $\mathrm{N}$

Thickness of spacer

$t_s$ $\mathrm{mm}$

Elasticity factor

$r_E$

Calculation

Factor $ h_0 $

$$h_0=\sqrt{B\cdot g_0}$$

Factor $ A $

$$A=\left(g_1/g_0\right)-1$$

Factor $ C $

$$C=43.68\cdot\left(h/h_0\right)^4$$

Factor $ C_1 $

$$C_1=1/3+A/12$$

Factor $ C_2 $

$$C_2=5/42+17\cdot A/336$$

Factor $ C_3 $

$$C_3=1/210+A/360$$

Factor $ C_4 $

$$C_4=11/360+59\cdot A/5040+\left(1+3\cdot A\right)/C$$

Factor $ C_5 $

$$C_5=1/90+5\cdot A/1008-\left(1+A\right)^3/C$$

Factor $ C_6 $

$$C_6=1/120+17\cdot A/5040 +1/C$$

Factor $ C_7 $

$$C_7=215/2772+51\cdot A/1232+\left(60/7+225\cdot A/14+75\cdot A^2/7+5\cdot A^3/2\right)/C$$

Factor $ C_8 $

$$C_8=31/6930+128\cdot A/45045+\left(6/7+15\cdot A/7+12\cdot A^2/7+5\cdot A^3/11\right)/C$$

Factor $ C_9 $

$$C_9=533/30240+653\cdot A/73920+\left(1/2+33\cdot A/14+39\cdot A^2/28+25\cdot A^3/84\right)/C$$

Factor $ C_{10} $

$$C_{10}=29/3780+3\cdot A/704-\left(1/2+33\cdot A/14+81\cdot A^2/28+13\cdot A^3/12\right)/C$$

Factor $ C_{11} $

$$C_{11}=31/6048+1763\cdot A/665280+\left(1/2+6\cdot A/7+15\cdot A^2/28+5\cdot A^3/42\right)/C$$

Factor $ C_{12} $

$$C_{12}=1/2925+71\cdot A/300300+\left(8/35+18\cdot A/35+156\cdot A^2/385+6\cdot A^3/55\right)/C$$

Factor $ C_{13} $

$$C_{13}=761/831600+937\cdot A/1663200+\left(1/35+6\cdot A/35+11\cdot A^2/70+3\cdot A^3/70\right)/C$$

Factor $ C_{14} $

$$C_{14}=197/415800+103\cdot A/332640-\left(1/35+6\cdot A/35+17\cdot A^2/70+A^3/10\right)/C$$

Factor $ C_{15} $

$$C_{15}=233/831600+97\cdot A/554400+\left(1/35+3\cdot A/35+A^2/14+2\cdot A^3/105\right)/C$$

Factor $ C_{16} $

$$C_{16}=C_1\cdot C_7\cdot C_{12}+C_2\cdot C_8\cdot C_3+C_3\cdot C_8\cdot C_2-\left(C_3^2\cdot C_7+C_8^2\cdot C_1+C_2^2\cdot C_{12}\right)$$

Factor $ C_{17} $

$$C_{17}=\left[C_4\cdot C_7\cdot C_{12}+C_2\cdot C_8\cdot C_{13}+C_3\cdot C_8\cdot C_9-\left(C_{13}\cdot C_7\cdot C_3+C_8^2\cdot C_4+C_{12}\cdot C_2\cdot C_9\right)\right]/C_{16}$$

Factor $ C_{18} $

$$C_{18}=\left[C_5\cdot C_7\cdot C_{12}+C_2\cdot C_8\cdot C_{14}+C_3\cdot C_8\cdot C_{10}-\left(C_{14}\cdot C_7\cdot C_3+C_8^2\cdot C_5+C_{12}\cdot C_2\cdot C_{10}\right)\right]/C_{16}$$

Factor $ C_{19} $

$$C_{19}=\left[C_6\cdot C_7\cdot C_{12}+C_2\cdot C_8\cdot C_{15}+C_3\cdot C_8\cdot C_{11}-\left(C_{15}\cdot C_7\cdot C_3+C_8^2\cdot C_6+C_{12}\cdot C_2\cdot C_{11}\right)\right]/C_{16}$$

Factor $ C_{20} $

$$C_{20}=\left[C_1\cdot C_9\cdot C_{12}+C_4\cdot C_8\cdot C_3+C_3\cdot C_{13}\cdot C_2-\left(C_3^2\cdot C_9+C_{13}\cdot C_8\cdot C_1+C_{12}\cdot C_4\cdot C_2\right)\right]/C_{16}$$

Factor $ C_{21} $

$$C_{21}=\left[C_1\cdot C_{10}\cdot C_{12}+C_5\cdot C_8\cdot C_3+C_3\cdot C_{14}\cdot C_2-\left(C_3^2\cdot C_{10}+C_{14}\cdot C_8\cdot C_1+C_{12}\cdot C_5\cdot C_2\right)\right]/C_{16}$$

Factor $ C_{22} $

$$C_{22}=\left[C_1\cdot C_{11}\cdot C_{12}+C_6\cdot C_8\cdot C_3+C_3\cdot C_{15}\cdot C_2-\left(C_3^2\cdot C_{11}+C_{15}\cdot C_8\cdot C_1+C_{12}\cdot C_6\cdot C_2\right)\right]/C_{16}$$

Factor $ C_{23} $

$$C_{23}=\left[C_1\cdot C_7\cdot C_{13}+C_2\cdot C_9\cdot C_3+C_4\cdot C_8\cdot C_2-\left(C_3\cdot C_7\cdot C_4+C_8\cdot C_9\cdot C_1+C_2^2\cdot C_{13}\right)\right]/C_{16}$$

Factor $ C_{24} $

$$C_{24}=\left[C_1\cdot C_7\cdot C_{14}+C_2\cdot C_{10}\cdot C_3+C_5\cdot C_8\cdot C_2-\left(C_3\cdot C_7\cdot C_5+C_8\cdot C_{10}\cdot C_1+C_2^2\cdot C_{14}\right)\right]/C_{16}$$

Factor $ C_{25} $

$$C_{25}=\left[C_1\cdot C_7\cdot C_{15}+C_2\cdot C_{11}\cdot C_3+C_6\cdot C_8\cdot C_2-\left(C_3\cdot C_7\cdot C_6+C_8\cdot C_{11}\cdot C_1+C_2^2\cdot C_{15}\right)\right]/C_{16}$$

Factor $ C_{26} $

$$C_{26}=-\left(C/4\right)^{1/4}$$

Factor $ C_{27} $

$$C_{27}=C_{20}-C_{17}-5/12+C_{17}\cdot C_{26}$$

Factor $ C_{28} $

$$C_{28}=C_{22}-C_{19}-1/12+C_{19}\cdot C_{26}$$

Factor $ C_{29} $

$$C_{29}=-\left(C/4\right)^{1/2}$$

Factor $ C_{30} $

$$C_{30}=-\left(C/4\right)^{3/4}$$

Factor $ C_{31} $

$$C_{31}=3\cdot A/2-C_{17}\cdot C_{30}$$

Factor $ C_{32} $

$$C_{32}=1/2-C_{19}\cdot C_{30}$$

Factor $ C_{33} $

$$C_{33}=0.5\cdot C_{26}\cdot C_{32}+C_{28}\cdot C_{31}\cdot C_{29}-\left(0.5\cdot C_{30}\cdot C_{28}+C_{32}\cdot C_{27}\cdot C_{29}\right)$$

Factor $ C_{34} $

$$C_{34}=1/12+C_{18}-C_{21}-C_{18}\cdot C_{26}$$

Factor $ C_{35} $

$$C_{35}=-C_{18}\cdot\left(C/4\right)^{3/4}$$

Factor $ C_{36} $

$$C_{36}=\left(C_{28}\cdot C_{35}\cdot C_{29}-C_{32}\cdot C_{34}\cdot C_{29}\right)/C_{33}$$

Factor $ C_{37} $

$$C_{37}=\left[0.5\cdot C_{26}\cdot C_{35}+C_{34}\cdot C_{31}\cdot C_{29}-\left(0.5\cdot C_{30}\cdot C_{34}+C_{35}\cdot C_{27}\cdot C_{29}\right)\right]/C_{33}$$

Factor $ E_1 $

$$E_1=C_{17}\cdot C_{36}+C_{18}+C_{19}\cdot C_{37}$$

Factor $ E_2 $

$$E_2=C_{20}\cdot C_{36}+C_{21}+C_{22}\cdot C_{37}$$

Factor $ E_3 $

$$E_3=C_{23}\cdot C_{36}+C_{24}+C_{25}\cdot C_{37}$$

Factor $ E_4 $

$$E_4=1/4+C_{37}/12+C_{36}/4-E_3/5-3\cdot E_2/2-E_1$$

Factor $ E_5 $

$$E_5=E_1\cdot\left(1/2+A/6\right)+E_2\cdot\left(1/4+11\cdot A/84\right)+E_3\cdot\left(1/70+A/105\right)$$

Factor $ E_6 $

$$E_6=E_5-C_{36}\cdot\left(7/120+A/36+3\cdot A/C\right)-1/40-A/72-C_{37}\cdot\left(1/60+A/120+1/C\right)$$

Factor $ F $ for integral type flanges

$$F=-\cfrac{E_6}{\left(\cfrac{C}{2.73}\right)^{\cfrac{1}{4}}\cdot\cfrac{\left(1+A\right)^3}{C}}$$

Factor $ F_L $ for loose type flanges

$$F_L=-\cfrac{C_{18}\cdot\left(\cfrac{1}{2}+\cfrac{A}{6}\right)+C_{21}\cdot\left(\cfrac{1}{4}+\cfrac{11\cdot A}{84}\right)+C_{24}\cdot\left(\cfrac{1}{70}+\cfrac{A}{105}\right)-\left(\cfrac{1}{40}+\cfrac{A}{72}\right)}{\left(\cfrac{C}{2.73}\right)^{\cfrac{1}{4}}\cdot\cfrac{\left(1+A\right)^3}{C}}$$

Factor $ V $ for integral type flanges

$$V=\cfrac{E_4}{\left(\cfrac{2.73}{C}\right)^{\cfrac{1}{4}}\cdot\left(1+A\right)^3}$$

Factor $ V_L $ for loose type flanges

$$V_L=\cfrac{\cfrac{1}{4}-\cfrac{C_{24}}{5}-\cfrac{3\cdot C_{21}}{2}-C_{18}}{\left(\cfrac{2.73}{C}\right)^{\cfrac{1}{4}}\cdot\left(1+A\right)^3}$$

Factor $ F' $

$\text{if }\ \text{flange }$$\text{category}= \text{Category 1}$

$$F'=g_0^2\cdot\left(h_0+F\cdot t\right)/V$$

$\text{else if }\ \text{flange }$$\text{category}= \text{Category 2}$

$$F'=g_0^2\cdot\left(h_0+F_L\cdot t\right)/V_L$$

$\text{else}$

$$F'=0$$

Factor $ f $

$\text{if }\ \text{flange }$$\text{category}= \text{Category 1}$

$$f=C_{36}/\left(1+A\right)$$

$\text{else}$

$$f=1$$

Diameter $ B_1 $

$\text{if }\ \text{flange }$$\text{category}= \text{Category 3}$

$$B_1=B$$

$\text{else if }\ \text{flange }$$\text{category}= \text{Category 1}\wedge f\geq 1$

$$B_1=B+g_0$$

$\text{else}$

$$B_1=B+g_1$$

Radial distance from bolt circle to point of intersection of hub and back of flange

$$R=\cfrac{C-B}{2}-g_1$$

Radial distance from the bolt circle, to the circle on which $ H_D $ acts

$\text{if }\ \text{flange }$$\text{category}= \text{Category 1}$

$$h_D=R+0.5\cdot g_1$$

$\text{else}$

$$h_D=\cfrac{C-B}{2}$$

Radial distance from bolt circle to outer edge of flange or spacer

$$h_{Cmax}=\cfrac{A-C}{2}$$

$$h_C< h_{Cmax}$$

Shape factor for full face metal‐to‐metal contact flanges

$$β=\cfrac{C+B_1}{2\cdot B_1}$$

Shape factor

$$a=\cfrac{A+C}{2\cdot B_1}$$

Bolt hole aspect ratio used in calculating bolthole flexibility factor $ r_B $

$$\overline{AR}=\cfrac{n\cdot D}{π\cdot C}$$

Factor $ r_B $

$$r_B=\cfrac{1}{n}\cdot\left(\cfrac{4}{\sqrt{1-\overline{AR}^2}}\cdot\tan^{-1}\left(\sqrt{\cfrac{1+\overline{AR}}{1-\overline{AR}}}\right)-π-2\cdot \overline{AR}\right)$$

Factor $ J_S $

$$J_S=\cfrac{1}{B_1}\cdot\left[\cfrac{2\cdot h_D}{β}+\cfrac{h_C}{a}\right]+π\cdot r_B$$

Factor $ J_P $

$$J_P=\cfrac{1}{B_1}\cdot\left[\cfrac{h_D}{β}+\cfrac{h_C}{a}\right]+π\cdot r_B$$

Radial distance from gasket load reaction to the bolt circle

$$h_G=\cfrac{C-G}{2}$$

Radial distance from the bolt circle, to the circle on which $ H_T $ acts

$\text{if }\ \text{flange }$$\text{category}= \text{Category 1}$

$$h_T=\cfrac{R+g_1+h_G}{2}$$

$\text{else}$

$$h_T=\cfrac{h_D+h_G}{2}$$

Total hydrostatic end force

$$H=\cfrac{π}{4}\cdot G^2\cdot P$$

Hydrostatic end force on area inside of flange

$$H_D=\cfrac{π}{4}\cdot B^2\cdot P$$

Difference between total hydrostatic end force and the hydrostatic end force on area inside of flange

$$H_T=H-H_D$$

Moment due to $ H_D $ , $ H_T $ , $ H_G $

$$M_P=H_D\cdot h_D+H_T\cdot h_T+H_G\cdot h_G$$

Flange Moment Due to Flange‐Hub Interaction

$$M_S=-\cfrac{J_P\cdot F'\cdot M_P}{t^3+J_S\cdot F'}$$

Slope of Flange at Inside Diameter Times $ E $

$$Eθ_B=\cfrac{5.46}{π\cdot t^3}\cdot\left(J_S\cdot M_S+J_P\cdot M_P\right)$$

Contact force between flanges at $ h_C $

$$H_C=\left(M_P+M_S\right)/h_C$$

Bolt load at operating conditions

$$W_{m1}=H+H_G+H_C$$

Operating bolt stress

$$σ_b=W_{m1}/A_b$$

$$σ_b\le S_b$$

Strain length of bolt

$$l=2\cdot t+t_s+1/2\cdot d_b$$

Design prestress in bolts

$$S_i=σ_b-\cfrac{1.159\cdot h_C^2\cdot\left(M_P+M_S\right)}{a\cdot t^3\cdot l\cdot r_E\cdot B_1}$$

Radial flange stress at bolt circle

$$S_R=\cfrac{6\cdot\left(M_P+M_S\right)}{t^2\cdot\left(π\cdot C-n\cdot D\right)}$$

$$S_R\le S_f$$

Radial flange stress at inside diameter

$\text{if }\ \text{flange }$$\text{category}= \text{Category 1}$

$$S_R=-\left(\cfrac{2\cdot F\cdot t}{h_0+F\cdot t}+6\right)\cdot\cfrac{M_S}{π\cdot B_1\cdot t^2}$$

$\text{else if }\ \text{flange }$$\text{category}= \text{Category 2}$

$$S_R=-\left(\cfrac{2\cdot F_L\cdot t}{h_0+F_L\cdot t}+6\right)\cdot\cfrac{M_S}{π\cdot B_1\cdot t^2}$$

$\text{else}$

$$S_R=0$$

$$S_R\le S_f$$

Ratio of outside diameter of flange to inside diameter of flange

$$K=A/B$$

Factor $ Z $

$$Z=\cfrac{K^2+1}{K^2-1}$$

Tangential flange stress at inside diameter

$\text{if }\ \text{flange }$$\text{category}= \text{Category 1}$

$$S_T=\cfrac{t\cdot Eθ_B}{B_1}+\left(\cfrac{2\cdot F\cdot t\cdot Z}{h_0+F\cdot t}-1.8\right)\cdot\cfrac{M_S}{π\cdot B_1\cdot t^2}$$

$\text{else if }\ \text{flange }$$\text{category}= \text{Category 2}$

$$S_T=\cfrac{t\cdot Eθ_B}{B_1}+\left(\cfrac{2\cdot F_L\cdot t\cdot Z}{h_0+F_L\cdot t}-1.8\right)\cdot\cfrac{M_S}{π\cdot B_1\cdot t^2}$$

$\text{else}$

$$S_T=\cfrac{t\cdot Eθ_B}{B_1}$$

$$S_T\le S_f$$

Longitudinal hub stress

$\text{if }\ \text{flange }$$\text{category}= \text{Category 1}$

$$S_H=\cfrac{h_0\cdot Eθ_B\cdot f}{0.91\cdot\left(g_1/g_0\right)^2\cdot B_1\cdot V}$$

$\text{else if }\ \text{flange }$$\text{category}= \text{Category 2}$

$$S_H=\cfrac{h_0\cdot Eθ_B}{0.91\cdot\left(g_1/g_0\right)^2\cdot B_1\cdot V_L}$$

$\text{else}$

$$S_H=0$$

$\text{if }\ \text{product }$$\text{form }$$\text{flange}= \text{Castings}$

$$S_H\le S_f$$

$\text{else}$

$$S_H\le 1.5\cdot S_f$$

$\text{if }\ \text{product }$$\text{form }$$\text{nozzle }$$\text{neck }$$\text{vessel }$$\text{or }$$\text{pipe }$$\text{wall}= \text{Castings}$

$$S_H\le S_n$$

$\text{else}$

$$S_H\le 1.5\cdot S_n$$

Requirements

$$\left(S_H+S_R\right)/2 \le S_f$$$$\left(S_H+S_T\right)/2 \le S_f$$

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Flat face flanges with metal-to-metal contact outside the bolt circle for class 1 flange assembly (identical flange pairs)

Values for calculation

Calculation

Factor $ h_0 $

Factor $ A $

Factor $ C $

Factor $ C_1 $

Factor $ C_2 $

Factor $ C_3 $

Factor $ C_4 $

Factor $ C_5 $

Factor $ C_6 $

Factor $ C_7 $

Factor $ C_8 $

Factor $ C_9 $

Factor $ C_{10} $

Factor $ C_{11} $

Factor $ C_{12} $

Factor $ C_{13} $

Factor $ C_{14} $

Factor $ C_{15} $

Factor $ C_{16} $

Factor $ C_{17} $

Factor $ C_{18} $

Factor $ C_{19} $

Factor $ C_{20} $

Factor $ C_{21} $

Factor $ C_{22} $

Factor $ C_{23} $

Factor $ C_{24} $

Factor $ C_{25} $

Factor $ C_{26} $

Factor $ C_{27} $

Factor $ C_{28} $

Factor $ C_{29} $

Factor $ C_{30} $

Factor $ C_{31} $

Factor $ C_{32} $

Factor $ C_{33} $

Factor $ C_{34} $

Factor $ C_{35} $

Factor $ C_{36} $

Factor $ C_{37} $

Factor $ E_1 $

Factor $ E_2 $

Factor $ E_3 $

Factor $ E_4 $

Factor $ E_5 $

Factor $ E_6 $

Factor $ F $ for integral type flanges

Factor $ F_L $ for loose type flanges

Factor $ V $ for integral type flanges

Factor $ V_L $ for loose type flanges

Factor $ F' $

Factor $ f $

Diameter $ B_1 $

Radial distance from bolt circle to point of intersection of hub and back of flange

Radial distance from the bolt circle, to the circle on which $ H_D $ acts

Radial distance from bolt circle to outer edge of flange or spacer

Shape factor for full face metal‐to‐metal contact flanges

Shape factor

Bolt hole aspect ratio used in calculating bolthole flexibility factor $ r_B $

Factor $ r_B $

Factor $ J_S $

Factor $ J_P $

Radial distance from gasket load reaction to the bolt circle

Radial distance from the bolt circle, to the circle on which $ H_T $ acts

Total hydrostatic end force

Hydrostatic end force on area inside of flange

Difference between total hydrostatic end force and the hydrostatic end force on area inside of flange

Moment due to $ H_D $ , $ H_T $ , $ H_G $

Flange Moment Due to Flange‐Hub Interaction

Slope of Flange at Inside Diameter Times $ E $

Contact force between flanges at $ h_C $

Bolt load at operating conditions

Operating bolt stress

Strain length of bolt

Design prestress in bolts

Radial flange stress at bolt circle