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 page is a direct mirror of PVEng's External Pressure Methods sample, with a different configuration and original numbers.
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.