This worked example documents the ASME Section VIII Division 1 design of a 48 in OD vertical pressure vessel under combined internal pressure and full vacuum, 30 psig internal MAWP at 100 °F, with the same vessel rated for 15 psig external pressure (full vacuum) at the same temperature. The shell is SA-516 Grade 70 Normalized at 0.300 in nominal wall, stiffened by one circumferential vacuum ring at midspan. The heads are one F&D torispherical on top and one 2:1 SE on the bottom, both 0.500 in nominal SA-516-70 N. Vacuum is the governing structural load.
The teaching content of the page is the external-pressure design chain: UG-28(c) chart-procedure shell calc with and without the vacuum ring (worked examples 1 and 2), UG-29 vacuum-ring moment-of-inertia calculation (worked example 3), UG-33(e) F&D head external pressure (worked example 4), and UG-33(f) 2:1 SE head external pressure with K_o = 0.9 equivalent sphere radius (worked example 5). The unstiffened shell would carry only 9.8 psi external pressure; with the midspan vacuum ring the shell rating climbs to 33 psig, an 18 psi margin above the 15 psig vacuum requirement. The numbers and the configuration are original to this page; the example demonstrates the external-pressure design chain end to end.
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 under combined internal pressure and full vacuum | |
| Internal design pressure | 30 psig | UG-21 |
| External design pressure | 15 psig (full vacuum) | UG-28 |
| Design temperature | 100 °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, heads | 1.00 (one-piece formed) | UW-12 |
| Radiography | Full RT on Cat. A welds, surface NDE on nozzle attachments and on the vacuum-ring weld | UW-11, UW-50 |
| Service | Non-lethal, non-cyclic, vapor space (typical for absorber column, dryer regen vessel, or flash drum upstream of vacuum service) | UG-22, UW-2 |
The vessel is analyzed for the loadings listed in UG-22. Governing loads for this configuration are:
External pressure under vacuum is the governing structural load. The shell wall is sized to UG-28 with a vacuum-ring at midspan reducing the effective unsupported length from L = 120 in to L_s = 60 in per stiffened span. The vacuum-ring is sized to UG-29.
The Minimum Design Metal Temperature is -20 °F at the full design pressure of 30 psig. The shell and the heads are SA-516 Grade 70 Normalized, Curve D under Table UCS-66. Required MDMT at the shell thickness (0.300 in nominal) is approximately -55 °F at no impact testing.
Two pressure tests are performed after fabrication.
First, the internal hydrostatic test follows UG-99(b). Test pressure is 1.3 times MAWP at design temperature multiplied by the lowest stress ratio across pressure-boundary components, with water at 70 °F in the vertical orientation:
The hydrostatic test is straightforward at this low pressure; the shell and heads have very large margin to their internal-pressure capacity.
Second, a pneumatic vacuum verification follows UG-100. The vessel is held at 15 psia (full vacuum) for not less than 30 minutes, and the vacuum-ring, head transitions, and any nozzle reinforcements are inspected for buckling or unacceptable deflection. The vacuum verification confirms the UG-28 chart-based calculation has been built correctly.
| Component | Material | Internal MAWP (psig) | External P_a (psig) | Clause |
|---|---|---|---|---|
| Cylindrical shell (with one midspan vacuum ring, L_s = 60 in) | SA-516 Gr 70 N | 168 | 33 | UG-27(c)(1), UG-28 |
| Vacuum stiffening ring (0.500 x 3.000 in flat bar, full circumferential weld) | SA-516 Gr 70 N | n/a | I_s = 1.125 in&sup4; supplied vs 0.73 in&sup4; required | UG-29 |
| Top F&D head, 0.500 in nominal | SA-516 Gr 70 N | 171 | 40 | UG-32(c), UG-33(e) |
| Bottom 2:1 SE head, 0.500 in nominal | SA-516 Gr 70 N | 422 | 49 | UG-32(d), UG-33(f) |
| Cl 150 RFWN flanges (3) | SA-105 | 240 | n/a (rating not vacuum-affected) | UG-44, B16.5 Gp 1.1 |
The shell governs the external-pressure capacity at P_a = 33 psig (a margin of 18 psig above the 15 psig vacuum requirement). The shell would not pass the vacuum requirement without the midspan vacuum ring; see worked example 2 for the contrast. The Class 150 flanges govern the internal MAWP at 30 psig (matching the design and the rating for low-vacuum service in the flange's normal range).
Per UG-16(b), the minimum required thickness is 0.0625 in. All components meet UG-16(b).
| Component | Calc Stress at 39 psig (psi) | 0.9 × S_y at 70 °F (psi) | Status |
|---|---|---|---|
| Shell, UG-99 Note 35 | 4,620 | 32,400 (SA-516-70 N) | PASS |
| Top F&D head | 3,265 | 32,400 | PASS |
| Bottom 2:1 SE head | 1,825 | 32,400 | PASS |
Hydrostatic test stresses are an order of magnitude below the 0.9 × S_y limit of UG-99(b) Note 35. The pneumatic vacuum verification per UG-100 is performed separately on the cleaned, dry vessel and is the controlling test for the vacuum-ring weld and the shell out-of-roundness check.
| Component | Specification | S at 100 °F (psi) | UCS-66 Curve | Form |
|---|---|---|---|---|
| Shell | SA-516 Grade 70, normalized | 20,000 | D | 0.300 in plate, rolled and welded long seam |
| Top head, F&D torispherical | SA-516 Grade 70, normalized | 20,000 | D | 0.500 in plate, one-piece formed, crown radius 48 in, knuckle 3 in |
| Bottom head, 2:1 ellipsoidal | SA-516 Grade 70, normalized | 20,000 | D | 0.500 in plate, one-piece formed |
| Vacuum stiffening ring | SA-516 Grade 70, normalized | 20,000 | D | 0.500 in x 3.000 in flat bar, rolled to fit the shell OD, full circumferential weld |
| Nozzle necks | SA-106 Grade B, seamless | 17,100 | B | NPS 6 / 4 / 1 Schedule 40 pipe |
| Flanges | SA-105 | 20,000 | B | ASME B16.5 RFWN, Class 150, all three process nozzles |
| Bolting | SA-193 Gr B7 studs, SA-194 Gr 2H nuts | 25,000 | n/a | standard B16.5 stud-and-nut sets |
| Tag | Function | Size and Class | Location | Type | Weld |
|---|---|---|---|---|---|
| N1 | Process inlet | NPS 6 Cl 150 RFWN, Sch 40 neck | F&D head, top | Set-in radial, no repad required (vapor service) | Full pen + fillet per UW-16(f) |
| N2 | Vapor outlet | NPS 4 Cl 150 RFWN, Sch 40 neck | SE head, bottom | Set-in radial, exempt under UG-36(c)(3)(a) | Full pen + fillet per UW-16(f) |
| N3 | Vacuum-break / instrument | NPS 1 Cl 150 RFWN, Sch 40 neck | Shell, just above the vacuum ring | Set-in radial, exempt under UG-36(c)(3)(a) | Full pen + fillet per UW-16(f) |
The NPS 6 inlet is the only opening above the UG-36(c)(3)(a) 3.5 in finished-diameter exemption limit. A UG-37 area check on the F&D head shows the opening passes without a repad (A_required < 0.20 in² vs A1 > 0.80 in² in the corroded head wall).
The Category A long seam in the shell and both Category A head-to-shell circumferential welds are examined by full radiography per UW-11(a)(1). The full-circumferential weld attaching the vacuum-stiffening ring to the shell is examined by surface NDE (MT or PT) at every quadrant per UW-50; this is a critical weld because a leak or undersize bead would allow shell ovalization under vacuum.
| Item | Value |
|---|---|
| Shell OD | 48.000 in |
| Shell wall, nominal | 0.300 in |
| Shell wall, mill-min (-12.5%) | 0.263 in |
| Shell wall, corroded (mill-min less CA) | 0.200 in |
| Shell tangent-to-tangent length | 120 in (10 ft) |
| Vacuum-ring location | Midspan, 60 in from each head tangent |
| Vacuum-ring stiffened span L_s (each side) | 60 in |
| Vacuum-ring cross section | 0.500 in (radial) x 3.000 in (axial) |
| Vacuum-ring moment of inertia I_s supplied | 1.125 in&sup4; |
| Top F&D head depth (inside) | ~8.5 in |
| Bottom 2:1 SE head depth (inside) | ~11.7 in |
| Internal volume, new (shell + 2 heads) | 237,500 in³ (1,028 US gal) |
| Empty weight, new (shell + heads + nozzles + ring) | 1,720 lb |
| Empty weight, corroded | 1,520 lb |
| Test weight, water-filled | 10,300 lb |
Every clause applied in the analysis, grouped by topic. The substitutions and results for the most-asked clauses are written out in section 5.
| Clause | Component | Use |
|---|---|---|
| UG-16(b) | All | Minimum required thickness floor of 0.0625 in |
| UG-23 | All | Allowable stress tables, S-values at design temperature |
| UG-25 | All | Corrosion allowance, 0.0625 in on internal surfaces |
| UG-27(c)(1) | Cylindrical shell, nozzle necks | Required thickness for internal pressure, circumferential stress (this vessel is governed by external pressure, not internal) |
| UG-32(c) | Top F&D head | Required thickness for internal pressure on F&D heads (very thin in this case because internal pressure is only 30 psig) |
| UG-32(d) | Bottom 2:1 SE head | Required thickness for internal pressure on 2:1 SE heads |
| Clause | Component | Use |
|---|---|---|
| UG-28(c) | Cylindrical shell | External pressure cylinder rule, Factor A and Factor B chart procedure from ASME II-D Subpart 3 |
| UG-29 | Vacuum stiffening ring | Required moment of inertia for a ring stiffener to act as a line of support, I_s = D_o² L_s (t + A_s/L_s) A / 14 |
| UG-33(d) | Heads | Spherical-head external-pressure rule, basis for UG-33(e) and UG-33(f) |
| UG-33(e) | F&D torispherical head | External pressure on torispherical heads, uses crown radius as R_o in the UG-33(d) sphere formula |
| UG-33(f) | 2:1 SE head | External pressure on 2:1 ellipsoidal heads, uses equivalent sphere radius R_o = 0.9 × D_o (K_o = 0.9) |
| Clause | Use |
|---|---|
| UG-36(c)(3)(a) | Exempts the NPS 4 vapor outlet and NPS 1 instrument from UG-37; the NPS 6 inlet is above the limit and requires UG-37 (passes without repad) |
| UG-37 | Area replacement procedure on the NPS 6 inlet in the F&D head |
| UG-41 | Strength of reinforcement, not invoked because no repad is required |
| UG-44 | Flanges and pipe fittings, ASME B16.5 RFWN Class 150 accepted at the standard rating (240 psig at 200 °F, 285 psig at 70 °F) |
| UG-45 | Nozzle minimum-thickness check on each neck |
| Clause | Use |
|---|---|
| UW-9 | Design of welded joints, Category A long seam and head-to-shell circumferentials, plus the vacuum-ring circumferential weld |
| UW-11(a)(1) | Full radiography on Category A welds |
| Table UW-12 | Joint efficiency E = 1.00 for fully radiographed butt welds and one-piece formed heads |
| UW-15 | Strength of attachment welds, nozzle to shell, and the vacuum-ring to shell fillet |
| UW-16 | Minimum requirements for nozzle attachment welds |
| UW-50 | Final NDE on nozzle attachment welds and on the vacuum-ring weld (MT or PT, full surface) |
| Clause | Use |
|---|---|
| UCS-66 | Required MDMT at the actual component thickness, Fig UCS-66 curves |
| UCS-66.1 | Stress-ratio MDMT reduction (not taken; no-credit rating is colder than the design MDMT) |
| Clause | Use |
|---|---|
| UG-99(b) | Standard hydrostatic test, 1.3 × MAWP × LSR = 39 psig |
| UG-99(b) Note 35 | Stress at test pressure check against 0.9 × S_y |
| UG-100 | Pneumatic vacuum verification at 15 psia for not less than 30 minutes, with inspection of the vacuum-ring weld, head transitions, and shell out-of-roundness |
| Clause | Use |
|---|---|
| UG-116 | Nameplate marking, U stamp, both internal MAWP and external MEAWP marked |
| UG-118 | Nameplate location and attachment |
| UG-120(c) | Manufacturer's Data Report, Form U-1A. External pressure rating recorded. |
Five worked examples. The four external-pressure calculations are the central content of this page. Internal pressure on the shell is a sanity check (the vessel is governed by external pressure, not internal).
First the unstiffened case is computed: if the 0.300 in shell were left unstiffened across the full 120 in tangent-to-tangent length, would it survive 15 psig vacuum? The Factor A and Factor B chart procedure of UG-28(c) is followed using ASME II-D Subpart 3 Figure G (geometry chart) and Figure CS-2 (carbon steel material chart).
| Symbol | Value | Source |
|---|---|---|
| D_o | 48.000 in | Shell outside diameter |
| t | 0.200 in | Shell wall, corroded mill-min |
| D_o / t | 240 | Geometry ratio for chart entry |
| L (unstiffened) | 120 in | Tangent-to-tangent length |
| L / D_o (unstiffened) | 2.50 | Geometry ratio for chart entry |
| A (from Fig G at L/D_o = 2.50, D_o/t = 240) | 0.00012 | Geometry factor |
| B (from Fig CS-2 at A = 0.00012, T = 100 °F) | 1,770 psi | Material factor (elastic region) |
The unstiffened 0.300 in shell would carry only 9.8 psi external pressure. FAIL against the 15 psig vacuum requirement. A vacuum ring is required.
With one circumferential vacuum-stiffening ring at midspan, the effective unsupported length drops to L_s = 60 in per stiffened span. The chart procedure is repeated:
| Symbol | Value | Source |
|---|---|---|
| D_o / t | 240 | unchanged |
| L_s | 60 in | Stiffened span (head to ring or ring to head) |
| L_s / D_o | 1.25 | Geometry ratio for chart entry |
| A (from Fig G at L_s/D_o = 1.25, D_o/t = 240) | 0.00040 | Geometry factor, higher than the unstiffened case |
| B (from Fig CS-2 at A = 0.00040, T = 100 °F) | 5,900 psi | Material factor (still elastic, B = A · E / 2 = 0.00040 · 29.5e6 / 2) |
With the vacuum ring at midspan the shell carries 32.8 psi external pressure. PASS against the 15 psig vacuum requirement with a margin of 17.8 psi. The shell at 0.300 in nominal sets the external-pressure rating of the vessel at P_a = 33 psig.
The required moment of inertia of the stiffening ring per UG-29 is computed for the same geometry. The full chart-procedure Factor A is used in the formula.
| Symbol | Value | Source |
|---|---|---|
| D_o | 48.000 in | Shell outside diameter |
| L_s | 120 in | Sum of half-distances to adjacent stiffeners (60 in to each head) |
| t | 0.200 in | Shell wall, corroded |
| A (from Fig G at L_s/D_o = 1.25, D_o/t = 240) | 0.00040 | Same as worked example 2 |
| A_s | 1.500 in² | Cross-section of selected ring (0.500 in x 3.000 in flat bar) |
Required combined I_s' is 1.68 in&sup4;. The supplied ring is a 0.500 in radial x 3.000 in axial flat bar welded full-circumferentially to the shell. Its moment of inertia about the bending axis (radial-axial plane) is:
The supplied combined I_s of 1.975 in&sup4; exceeds the required 1.68 in&sup4; by 18%. PASS. The ring acts as a code line of support per UG-29.
The top F&D head is checked for the 15 psig external pressure per UG-33(e). The clause directs use of the spherical-head external-pressure rule of UG-33(d) with R_o equal to the outside crown radius of the head (R_o = OD for an ASME F&D head, conservatively).
| Symbol | Value | Source |
|---|---|---|
| R_o | 48.000 in | F&D head outside crown radius (= OD for ASME F&D) |
| t | 0.430 in | Head thickness after 10% forming thinning and CA: 0.500 × 0.90 - 0.0625 |
| t / R_o | 0.00896 | Geometry ratio |
| A | 0.125 t / R_o = 0.00112 | UG-33(d) entry into Fig G |
| B (from Fig CS-2 at A = 0.00112, T = 100 °F) | 16,500 psi | Material factor (elastic, B = A · E / 2) |
The F&D head allowable external pressure is 148 psi, ten times the 15 psig vacuum requirement. PASS with very large margin.
The bottom 2:1 SE head is checked for the 15 psig external pressure per UG-33(f). The clause directs use of the spherical-head rule of UG-33(d) with R_o equal to K_o times the head outside diameter, where K_o = 0.9 for a 2:1 ellipsoidal head.
| Symbol | Value | Source |
|---|---|---|
| D_o | 48.000 in | Head outside diameter (matches shell OD) |
| K_o | 0.900 | UG-33(f) for 2:1 SE aspect ratio |
| R_o | 43.200 in | K_o × D_o = equivalent sphere radius |
| t | 0.430 in | Head thickness after 10% forming thinning and CA |
| A | 0.125 t / R_o = 0.00124 | UG-33(d) entry into Fig G |
| B (from Fig CS-2 at A = 0.00124, T = 100 °F) | 18,300 psi | Material factor (elastic) |
The 2:1 SE head allowable external pressure is 182 psi, twelve times the 15 psig vacuum requirement. PASS. The 2:1 SE head outperforms the F&D head under vacuum because the equivalent sphere radius (0.9 D_o) is smaller than the F&D crown radius (1.0 D_o), reducing the effective slenderness.
48 in OD vertical vessels under full vacuum are common in mid-stream gas processing as vacuum towers, dryer regen vessels, and amine flash drums on the suction side of a vacuum-loaded compressor. The teaching value of the example is the cost trade-off between shell thickness and vacuum-stiffening: a 0.300 in shell with one midspan ring is materially cheaper than the 0.5 in shell that would be required to carry the same vacuum without stiffening, and the welded flat-bar ring is straightforward to fabricate. The pneumatic vacuum verification per UG-100 is what catches a misbuilt vacuum ring, since the hydrostatic test at 39 psig does not exercise the buckling failure mode that vacuum can excite.