Engineering task and calculation objective
Flat face flanges with metal-to-metal contact outside the bolt circle behave fundamentally differently from conventional flange joints with an inside gasket: the contact ring outside the bolts acts as a lever fulcrum, so the bolt load in the operating condition rises beyond the pure hydrostatic end force (prying effect). This module calculates such joints to ASME BPVC Section VIII Division 1, Mandatory Appendix Y — the only part of the code that explicitly captures this contact behavior.
The Appendix Y procedure takes the geometry (bolt circle diameter, number of bolts, bolt root and hole diameters, hub dimensions, flange thicknesses t or tI/tII), the gasket data (seating pressure, self-sealing force, basic gasket seating width per Table 2-5.1/2) and the loading, and determines the actual operating bolt stress as well as the longitudinal hub stress and the radial and tangential flange stresses. The method distinguishes identical and non-identical flange pairs as well as Classes 1 to 3 (integral flange, loose flange with/without hub, combinations).
In practice, you typically need to calculate a flange to Appendix Y for joints with O-ring or self-energizing gaskets where the flange faces bear on each other outside the bolt circle — for example high-pressure covers, compact flanges or equipment covers where an Appendix 2 calculation would underestimate the real additional bolt load.
Standard and calculation basis: ASME Appendix Y, 2023 Edition
Calculation workflow
- Define geometry and flange category: First the flange type and category are selected: integral flange with tapered hub (Fig. 2-4 sketch 6, 6a, 6b), integral flange where the pipe constitutes the hub, or loose flange, and identical or non-identical flange pair (Class 1 to 3). This is complemented by the inside diameter including allowances, the hub thicknesses on the pipe side and flange side, the axial hub length and the flange thicknesses t or tI and tII.
- Enter bolt and gasket data: Bolt circle diameter, number of bolts, root diameter and root area Ab, together with the bolt hole diameter, determine the available bolt capacity. For the gasket, the outside and inside diameters, the basic gasket seating width per Table 2-5.1/2, the seating pressure y and the self-sealing force are entered; an inserted spacer ring enters the deformation analysis with its thickness.
- Elastic interaction analysis per Appendix Y: Appendix Y solves the compatibility condition between flange rotation, bolt elongation and the contact force at the metal-to-metal contact outside the bolt circle. This yields the contact force HC at the lever fulcrum and the actual bolt load in the operating condition — which, because of the prying effect, exceeds the pure pressure end force.
- Calculate stresses: From the forces and moments, the longitudinal hub stress, the radial flange stress (also at the bolt circle, deducting the bolt holes) and the tangential flange stress are determined, together with the operating bolt stress and the required prestress for the gasket seating condition.
- Check against the allowable values: The stresses are checked against the allowable values Sf or Sfa = 1.5·Sf (for a different hub/pipe material), and the bolt stresses against Sb or Sa. Reduced limits apply to cast iron. All checks must be satisfied in both the gasket seating and the operating condition.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| 3 | 3=BII < C/2) Class (1-3) | - |
| 3=Loose-type flange without hub) | Ca (1-3) | - |
| Load case (1=Operation, 2=Test, ≥3 exceptional) | lc | – |
| Flange (I) material *) | I | – |
| Temperature | T | °C |
| Calculation pressure | p0 | MPa |
| Thickness | 2,3 | mm |
| Strength | Prüftemperatur | MPa |
| Strength | Betrieb | MPa |
| Safety fac. | Prüfung | - |
| Safety fac. | Betrieb | - |
| Allow. c1 | (I) | mm |
| Corr.all.c2 | (I) | mm |
| Outside diam. | Flansch-Außendurchmesser | mm |
| Inside diameter of flange + allowances | B+ | mm |
| Basic gasket seating width acc. Table 2-5.1&2 | b0 | mm |
| Bolt circle diameter | C | mm |
| Bolt hole diameter | D | mm |
| Outside diam. | Schrauben-Nenndurchmesser | mm |
| Modulus of elasticity | I | MPa |
| Modulus of elasticity | II | MPa |
| Axial hub length (Category 1-2) | h | mm |
| Flansch-Kontakt | (0 ≤ hC ≤ hCmax = ) hC | mm |
| Max. distance of contact force and bolt circle | hCmax | mm |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Root area of all bolts | Ab | mm² |
| Bolt hole aspect ratio = n*D/(Pi*C) | AR | - |
| Shape factor = (A+C)/2B1 | a | - |
| Mean hub diameter (corrected) | B1 | mm |
| Effective gasket seating width = 2.5*√b0 | b | mm |
| C1 | C1 C2 C3 | - |
| C2 | C1 C2 C3 | Nmm |
| C3 | C1 C2 C3 | - |
| C4 | C4 X | Nmm |
| d | d e L | mm³ |
| Faktor | EI* = EI*tI3 EII* = EII*tII3 | Nmm |
| Faktor | EI* = EI*tI3 EII* = EII*tII3 | Nmm |
| FL/h0=Faktor | d e L | 1/mm |
| 2-7.2 | F V FL VL | - |
| 2-7.4 | F V FL VL | - |
| Factor F' for class 1 eq.(5) or FI' class 3 eq.(6) | F' | mm³ |
| Ansatzspannung | g1/g0 h/h0 f Max[1; ] | - |
| Diameter of Gasket force acc. App.2 Table 2-5.2 | G | mm |
| Shell side hub thickness (thin end, without allowances) | g0 | mm |
| Flange side hub thickness (thick end, without all.) | g1 | mm |
| Hydrost. forces | H HD HT | N |
| Contact force between flanges at hC | HC | N |
| Hydrost. forces | H HD HT | N |
| Gasket seating + self-sealing force = Pi*b*G*Pgs + Fss | HG | N |
Frequently asked questions
How does Appendix Y differ from the classical flange calculation per Appendix 2?
Appendix 2 assumes that the flange faces transmit force only through the gasket and are free to rotate. With metal-to-metal contact outside the bolt circle, however, an additional bearing point arises: the flange rests on its outer rim, and the bolt must carry the lever force (prying) in addition to the pressure end force. Appendix Y models this elastic interaction; an Appendix 2 calculation would not be conservative for such joints with respect to the bolt loading.
For which gaskets does the method apply?
Appendix Y is intended for joints in which the gasket does not prevent contact of the flange faces — typically O-rings, metal O-rings or other self-energizing gaskets in a groove inside the bolt circle. The gasket self-sealing force and the seating pressure enter as separate inputs. A flat soft gasket covering the full face width does not fall under Appendix Y but, depending on the design, under Appendix 2.
What do Classes 1 to 3 mean in Appendix Y?
Class 1 denotes a pair of identical flanges, Classes 2 and 3 combinations of non-identical flanges or a flange against a flat plate/cover. Since the rotational stiffnesses differ for non-identical pairings, contact force and moment are shared differently; the module therefore performs the interaction analysis for both partners jointly.
Why does the bolt load in operation rise above the preload?
With contact outside the bolt circle, the contact ring acts as the fulcrum of a lever: the internal pressure pushes the flange center open, the flange tilts about the contact ring, and the bolt sits between load and fulcrum. The resulting additional force (prying force) adds to the hydrostatic end force. This is exactly why the operating bolt stress and the prestress must be verified separately under Appendix Y.