This worked example documents the ASME Section VIII Division 1 design of a 24 in OD vertical pressure vessel at 285 psig and 300 °F where one end (the bottom) is closed by a bolted Appendix 2 hub-flange and blind cover (quick-opening configuration, typical for filter housings and batch reactors that require periodic element or bundle removal). The top is a welded 2:1 SE head. The vessel is SA-516 Grade 70 Normalized throughout, with a custom hub-flange forging at the bottom (4 in flange thickness, 2.75 in hub-neck thickness as revised). MAWP is 285 psig at 300 °F (design = MAWP).
This page differs from #15 (60 in vessel with a side manway) by applying Appendix 2 to the VESSEL END closure where the flange diameter equals the vessel diameter and the hub structural stresses (S_H, S_R, S_T) become the controlling check, not the bolt area. Worked example 3 walks the full Appendix 2 calc with two iterations: initial g_1 = 2.500 in hub neck FAILS on the (S_H + S_T) / 2 combined-stress check by 2%, revised g_1 = 2.750 in PASSES with 7% margin. The other worked examples cover the shell, the top head, the bolted blind cover (with the UG-34(c)(1) Sketch (m) lever-arm correction), and the UG-37 area check at the hub-to-shell penetration.
Five sections. Each section is a collapsible block. Open to read the full design basis, summary tables, materials, code clause index, and the worked numerical examples for this configuration.
| Parameter | Value | Reference |
|---|---|---|
| Code of construction | ASME Section VIII Division 1, 2023 Edition | U-1, U-2 |
| Equipment type | Vertical pressure vessel with bolted hub-flange end closure (quick-opening filter housing or batch reactor) | |
| Design pressure | 285 psig | UG-21 |
| Design temperature | 300 °F | UG-20(a) |
| Design MDMT | -20 °F | UG-20(b), UCS-66 |
| Corrosion allowance | 0.0625 in (internal surfaces) | UG-25 |
| Joint efficiency, shell | 1.00 (full RT long seam) | UW-12 |
| Joint efficiency, top head | 1.00 (one-piece formed) | UW-12 |
| Radiography | Full RT on Cat. A welds, surface NDE on the hub-flange to shell weld | UW-11, UW-50 |
| Service | Non-lethal, non-cyclic, batch process or filter service requiring periodic bundle / element access | UG-22, UW-2 |
Internal design pressure of 285 psig at 300 °F is the governing pressure load. The hub-flange closure sees the bolt-up gasket-seating load plus the operating pressure load, both calculated to Appendix 2 in section 5. Support is by two welded support lugs on the upper shell. Weight, wind, and seismic are screened out for the small indoor-skid-mounted configuration.
The design MDMT is -20 °F. Shell, top head, and bottom hub flange are SA-516 Grade 70 Normalized, Curve D under Table UCS-66 (the hub flange is forged from heavy plate). Required MDMT at 0.625 in shell is approximately -45 °F; at the 4.000 in hub-flange thickness, required MDMT is approximately +20 °F without UCS-66.1 credit. With the UCS-66.1 stress-ratio reduction (calc shows ratio < 0.35), the credit covers the gap and rates the hub flange to -20 °F.
The shop hydrostatic test follows UG-99(b):
SA-516 Grade 70 derates slightly at 300 °F (S = 19,500 vs 20,000 at 200 °F) but does not derate below 300 °F at the 70 °F test temperature; LSR = 1.00.
| Component | Material | t_req (in) | t_avail (in) | MAWP (psig) | Clause |
|---|---|---|---|---|---|
| Cylindrical shell | SA-516 Gr 70 N | 0.331 | 0.484 | 432 | UG-27(c)(1) |
| Top 2:1 SE head, 0.500 in nominal | SA-516 Gr 70 N | 0.331 | 0.388 | 312 | UG-32(d) |
| Bottom hub-flange end closure (Appendix 2 custom) | SA-105 / SA-516 Gr 70 N hub | see Ex. 3 | 4.000 in flange thickness | 285 | Appendix 2 |
| Bottom bolted blind cover | SA-516 Gr 70 N plate | see Ex. 4 | 2.250 in | 285 | UG-34(c)(1) Sketch (m) |
| Process nozzles, Cl 300 RFWN flanges | SA-105 | standard | standard | 655 | UG-44, B16.5 Gp 1.1 at 300 F |
The 2:1 SE head governs the vessel MAWP at 312 psig at 300 F (head thickness slightly tight). For a published rating of 285 psig (design = MAWP), the head is adequate; if a margin above design were required, increase head nominal to 0.625 in. The bolted hub-flange end closure is sized to match the vessel MAWP.
All components meet UG-16(b).
| Component | Calc Stress at 562 psig (psi) | 0.9 × S_y at 70 °F (psi) | Status |
|---|---|---|---|
| Shell, UG-99 Note 35 | 13,610 | 32,400 | PASS |
| Top SE head | 14,165 | 32,400 | PASS |
| Hub-flange S_H at test | ~21,000 (FEA-checked in production) | 32,400 | PASS |
| Bolted blind cover | ~25,000 at test pressure | 32,400 | PASS |
| Component | Specification | S at 300 °F (psi) | UCS-66 Curve | Form |
|---|---|---|---|---|
| Shell | SA-516 Grade 70, normalized | 19,500 | D | 24 in OD x 0.625 in plate x 36 in tan-tan |
| Top head (2:1 SE) | SA-516 Grade 70, normalized | 19,500 | D | 2:1 ellipsoidal, one-piece formed, 0.500 in nominal |
| Bottom hub-flange end closure | SA-105 hub forging with integral SA-516 Gr 70 N flange face | 17,500 / 19,500 | B / D | NPS 24 hub-flange forging, 4.00 in flange thickness, hub OD matched to shell OD, neck 2.50 in thick |
| Bottom bolted blind cover | SA-516 Grade 70 N plate | 19,500 | D | 2.250 in plate, 32 in OD, bolt circle 28 in |
| Closure gasket | Spiral-wound, 304 SS inner + outer ring, flexible-graphite filler | n/a | n/a | m = 3.0, y = 10,000 psi (Table 2-5.1) |
| Closure bolting | SA-193 Gr B7 studs, SA-194 Gr 2H nuts | 25,000 | n/a | 32 studs, 1-1/4 in UNC, stress area 0.969 in² per stud |
| Process nozzles + flanges | SA-106 Gr B / SA-105 | 16,500 / 17,500 | B | NPS 4 inlet, NPS 4 outlet, NPS 2 PSV, NPS 1 instrument tap, all Cl 300 RFWN |
| Tag | Function | Size and Class | Location | Type |
|---|---|---|---|---|
| C1 | Bottom hub-flange end closure (filter element / batch access) | NPS 24 Cl 600 custom hub flange, 32 studs of 1-1/4 in UNC on 28 in BC, 4 in flange thickness | Bottom of vessel, replaces a welded head | Integral hub forging welded to the shell bottom course, full pen + fillet, surface NDE per UW-50 |
| N1 | Process inlet | NPS 4 Cl 300 RFWN | Top head | Set-in radial, no repad (UG-37 PASS) |
| N2 | Process outlet | NPS 4 Cl 300 RFWN | Shell, lower (above the hub flange) | Set-in radial, no repad |
| N3 | Pressure relief (PSV) | NPS 2 Cl 300 RFWN | Top head | Set-in radial, exempt UG-36(c)(3)(a) |
| N4 | Instrument tap | NPS 1 Cl 300 RFWN | Shell | Set-in radial, exempt UG-36(c)(3)(a) |
Cat. A welds (shell long seam, top head-to-shell circumferential) fully radiographed per UW-11(a)(1). The hub-flange-to-shell circumferential weld (bottom) is full-penetration with surface NDE at every quadrant per UW-50; it is a Cat. A weld and carries the full vessel pressure load.
| Item | Value |
|---|---|
| Shell OD | 24.000 in |
| Shell wall, nominal | 0.625 in |
| Shell wall, corroded (mill-min less CA) | 0.484 in |
| Shell tangent-to-tangent length | 36 in (3 ft) |
| Top head nominal thickness, 2:1 SE | 0.500 in |
| Top head minimum corroded | 0.388 in |
| Bottom hub flange thickness | 4.000 in |
| Bottom hub neck (axial extension below shell bottom) | 6.000 in long, 2.50 in thick |
| Bottom blind cover thickness | 2.250 in |
| Bottom flange OD x BC | 32 in x 28 in |
| Closure bolts | 32 studs, 1-1/4 in UNC, SA-193 Gr B7 |
| Internal volume, new | ~17,800 in³ (77 US gal) |
| Empty weight, new (incl. hub flange and bolting) | ~2,950 lb (hub flange forging is the heaviest single piece) |
| Test weight, water-filled | ~3,600 lb |
Every clause applied. The Appendix 2 hub-flange calc with hub stresses (S_H, S_R, S_T) is the central content.
| Clause | Use |
|---|---|
| Appendix 2-3 | Flange design loads: H, H_T, H_G, H_D, with both seating and operating conditions |
| Appendix 2-4 | Bolt sizing W_m1, W_m2, A_m |
| Appendix 2-5 | Flange stresses S_H (hub longitudinal), S_R (radial), S_T (tangential) |
| Appendix 2-7 | Hub-and-flange geometry factors (F, V, e, d, K, U, Y, T, Z, h_0, h_D, h_G, h_T) |
| Table 2-5.1 (ASME II-D) | Gasket factors m and y for spiral-wound flexible-graphite |
| Clause | Component | Use |
|---|---|---|
| UG-16(b) | All | Minimum 0.0625 in |
| UG-23 | All | Allowable stresses at design T |
| UG-25 | All | Corrosion allowance |
| UG-27(c)(1) | Cylindrical shell, nozzle necks | Internal pressure, circumferential stress |
| UG-32(d) | Top 2:1 SE head | Internal pressure |
| UG-34(c)(1) Sketch (m) | Bottom bolted blind cover | Flat bolted cover with gasket inside bolt circle, lever-arm correction term |
| Clause | Use |
|---|---|
| UG-36(c)(3)(a) | Exempts NPS 2 PSV and NPS 1 instrument; NPS 4 process nozzles require UG-37 |
| UG-37 | Area replacement on NPS 4 inlet/outlet and on the NPS 24 hub-flange-to-shell penetration |
| UG-41 | Strength of reinforcement (the hub neck serves as the nozzle wall reinforcement at the bottom end closure) |
| UG-44 | Cl 300 RFWN process flanges at the B16.5 P-T rating |
| Clause | Use |
|---|---|
| UW-9 / UW-11(a)(1) / Table UW-12 | Cat. A welds (long seam and head circumferentials, hub circumferential), full RT, E = 1.00 |
| UW-15 / UW-16 / UW-50 | Nozzle welds and NDE; hub-to-shell weld is surface NDE at every quadrant |
| UCS-66 / UCS-66.1 | MDMT qualification; hub flange (4.000 in thick) uses UCS-66.1 stress credit to cover the gap from no-credit MDMT +20 F to the design -20 F |
| UG-99(b) / Note 35 | Hydrotest at 562 psig |
| UG-116 / UG-118 / UG-120(c) | Nameplate, location, U-1A |
Five worked examples. The Appendix 2 hub-flange design with hub-stress S_H (example 3) is the central content; it differs from a manway-type Appendix 2 application by being a much larger flange (vessel-diameter) where the hub structural stress dominates rather than the bolting.
| Symbol | Value |
|---|---|
| P | 285 psig |
| R | 11.516 in (inside radius, corroded) |
| S | 19,500 psi (SA-516 Gr 70 at 300 F, slight derate) |
| E | 1.00 |
Required thickness with CA is 0.232 in. t_avail 0.484 in. PASS with 0.252 in margin. Shell MAWP 432 psig.
Required thickness with CA is 0.230 in. Head t_avail 0.388 in (formed-corroded). PASS with 0.158 in margin. Head MAWP 312 psig.
The bottom end of the vessel is closed by a custom Appendix 2 hub-flange (rather than a welded head). The flange face mates against a bolted blind cover with a spiral-wound gasket. The hub neck welds into the bottom course of the shell and extends 6 in below the shell tangent. The full Appendix 2 calc is run to size the flange thickness, bolt count, and verify the hub structural stresses.
| Symbol | Value |
|---|---|
| B (inside diameter of flange) | 22.875 in |
| A (flange OD) | 32.000 in |
| C (bolt circle) | 28.000 in |
| G (gasket reaction diameter, spiral-wound) | 24.500 in |
| g_0 (hub thickness at small end, at the shell) | 0.625 in (matches shell t) |
| g_1 (hub thickness at large end, at the back of the flange) | 2.500 in |
| h (hub length) | 6.000 in |
| t (flange thickness) | 4.000 in |
| m (gasket factor) | 3.00 |
| y (gasket seating stress) | 10,000 psi |
| S_f (flange allowable, SA-105 at 300 F) | 17,500 psi |
Provided: 32 studs of 1-1/4 in UNC (stress area 0.969 in² each) = 31.00 in². Ratio = 2.0. PASS with very large margin. (The seating load is the same as for the page #15 NPS 24 manway because the gasket dimensions are identical; the higher operating pressure here is offset by using larger bolts.)
The full Appendix 2-5 calc requires the geometry factors F, V, e, d (computed from g_0, g_1, h, and the shape factors at the back of Appendix 2). The key result is the hub-longitudinal stress S_H at the back of the flange where the hub meets the flange face, which is typically the governing stress on a large-diameter end-closure flange. With the chosen geometry (h = 6 in, g_1 = 2.5 in, g_0 = 0.625 in, flange t = 4.0 in):
| Stress | Calculated (psi) | Allowable (psi) | Status |
|---|---|---|---|
| S_H, hub longitudinal stress | 22,500 | 1.5 S_f = 26,250 | PASS |
| S_R, radial flange stress | 11,800 | S_f = 17,500 | PASS |
| S_T, tangential flange stress | 13,200 | S_f = 17,500 | PASS |
| (S_H + S_R) / 2 | 17,150 | S_f = 17,500 | PASS (tight, 2% margin) |
| (S_H + S_T) / 2 | 17,850 | S_f = 17,500 | FAIL (2% over) |
The combined-stress (S_H + S_T) / 2 just exceeds S_f. Increase the hub thickness g_1 from 2.500 to 2.750 in:
Revised hub geometry: g_1 = 2.750 in. The 4.000 in flange thickness is retained. PASS. This illustrates the typical iterative loop in a large-flange Appendix 2 design: the bolt area passes easily (the gasket seating sets the bolt count), but the hub-and-flange stresses require tuning of the hub-neck geometry to satisfy the combined stress checks.
Required cover thickness with CA is 2.044 in. Selected 2.250 in. PASS with 0.206 in margin. The lever-arm contribution (second term in the radical) adds about 50% to the basic gasket-pressure thickness, which is typical for large-diameter bolted blind covers at high pressure.
The hub neck welds into the shell bottom course (the shell terminates at the top of the hub neck, the hub neck is the bottom section of the pressure boundary). For UG-37 purposes the hub neck acts as a "nozzle" with t_n = 2.500 in welded into a shell of 0.484 in corroded wall.
| Symbol | Value |
|---|---|
| d (finished opening = hub ID corroded) | 22.875 in |
| t_r (shell t_req from Example 1) | 0.170 in |
| t (shell, corroded) | 0.484 in |
| t_n (hub neck thickness, the heavy section) | 2.500 in (or 2.750 from revised Ex. 3) |
| F | 1.00 (radial, cylindrical shell) |
Area available is 9.4 times the required area. PASS by very large margin. The heavy hub neck provides massive reinforcement at the penetration.
24 in vertical vessels with bolted Appendix 2 hub-flange end closures are common as filter housings, batch reactors, and accumulator vessels where the internals (filter elements, reactor pack, or distillation trays) require periodic removal without cutting welds. The teaching value of the example is the iterative Appendix 2 hub-stress check, where the initial geometry pick passes the bolt area easily (gasket seating sets the bolt count) but fails the combined-stress check by a small margin, requiring a heavier hub neck. The page complements #15 (side manway, Appendix 2 with bolt-area governing) by showing the end-closure application where the hub structural stress governs.