ASME Boiler and Pressure Vessel Code Section VIII Division 1 paragraphs UG-28 and UG-29 govern the design of cylindrical shells and vacuum stiffeners subject to external pressure. Unlike internal pressure, which is limited by tensile hoop stress, external pressure is governed by structural stability and bifurcation buckling.
1. Geometric Ratios:
Do / t = Outside Diameter / Corroded Wall Thickness
L / Do = Effective Length Between Lines of Support / Outside Diameter
2. Strain Factor A Derivation (ASME Sec II-D Fig G):
For Do/t >= 10:
Factor A = 1.28 / [ (Do / t)^1.5 * (L / Do) ]
(Subject to lower bound L/Do >= 0.05 and upper bound L/Do <= 50.0)
3. Stress Factor B Derivation:
E = Young's Modulus of elasticity at design temperature (psi)
If Factor A falls to the left of the material curve (Elastic Buckling):
Factor B = (Factor A * E) / 2
If Factor A falls on the curve (Inelastic / Yield-Influenced):
Factor B = f_material(A, Temperature)
4. Maximum Allowable External Working Pressure (MAEP, Pa):
Pa = [ 4 * Factor B ] / [ 3 * (Do / t) ]
5. UG-29 Vacuum Stiffener Ring Required Moment of Inertia:
Is = [ Do^2 * L_s * (t + As/Ls) * Factor A_ring ] / 14.0
Where:
L_s = Distance between stiffening rings (in)
As = Cross-sectional area of stiffener ring (in^2)
Is = Required moment of inertia of ring + combined shell band (in^4)
A_ring = Factor A evaluated for stiffener ring buckling
If the calculated allowable pressure $P_a$ is less than the external design pressure $P_{ ext{ext}}$ (typically 15.0 psig for full vacuum), the vessel will experience catastrophic inward wall collapse or lobed buckling. The engineer has two design choices: increase plate thickness $t$, or add intermediate stiffening rings to shorten unsupported length $L$.
5 Fatal Traps & Engineering Pitfalls
1. Designing for Full Vacuum (14.7 psi) Without Adding Liquid Hydrostatic Head
When chemical reactors or refinery fractionation columns are steamed out and blocked in, condensing steam creates a 14.7 psi full vacuum while liquid condensates accumulate at the vessel bottom. If the designer specifies an external design pressure of only 15.0 psi without adding the hydrostatic head of the condensed liquid (often 5 to 15 psi additional), the combined external pressure at the lower courses exceeds the MAEP, crushing the bottom shell plates inward.
2. Overestimating Factor B by Ignoring High-Temperature Modulus Derating
The elastic modulus $E$ of carbon and stainless steels drops substantially at elevated temperatures. For carbon steel SA-516 Gr 70, $E$ drops from 29.5 Mpsi at 70°F down to 24.5 Mpsi at 600°F—a 17% reduction. Because external buckling capacity is directly proportional to $E$ in the elastic regime, designing a hot vacuum vessel using room-temperature modulus values results in an over-predicted MAEP and immediate collapse during high-temperature regeneration cycles.
3. Disregarding Out-of-Roundness Tolerances per UG-80
The theoretical buckling formulas of UG-28 assume a perfectly round cylinder. Paragraph UG-80 sets strict limits on maximum shell out-of-roundness ($D_{max} - D_{min} le 1.0% ext{ of nominal } D$). If plate rolling leaves a flat spot or peak along longitudinal weld seams, the local radius of curvature increases drastically. A 1.5% out-of-roundness imperfection can reduce actual collapse pressure by over 50%, initiating progressive snap-through buckling at normal operating vacuum.
4. Incorrect Unsupported Length (L) Definition Near Formed Heads
Under ASME UG-28, the effective unsupported length $L$ of an unstiffened vessel is NOT merely the tangent-to-tangent straight shell length. For vessels with 2:1 ellipsoidal or torispherical heads, $L$ must include one-third of the depth of each head. For large diameter thin-walled vessels, omitting the head depth contributions underestimates $L$ by several feet, leading to an undersized shell thickness that fails third-party Authorized Inspector (AI) code audits.
5. Intermittent Stiffener Ring Welds Violating UG-29 Attachment Rules
Fabricators frequently attempt to save labor by attaching external vacuum stiffening rings with skip/intermittent fillet welds. Under ASME Section VIII UG-29, intermittent welds are strictly regulated: the total unwelded length between weld segments must not exceed $8t$ for external rings or $12t$ for internal rings, and the gap between ring and shell must not exceed code limits. Inadequate attachment allows the thin shell plate to buckle independently of the stiffener ring.
Frequently Asked Questions
What is the fundamental difference between internal and external pressure vessel design in ASME Section VIII?+
Internal pressure causes membrane tensile stress in the vessel wall, where failure occurs through plastic yielding or ductile bursting with safety margins of 3.5 to 4.0 against tensile strength. External pressure induces compressive hoop stresses, where failure occurs via sudden elastic or plastic buckling (instability) at stresses far below material yield. Because buckling is highly sensitive to geometric imperfections (out-of-roundness, flat spots), ASME UG-28 mandates rigorous chart-based Factor A and Factor B iterative derivations.
What is the design length L for external pressure per UG-28?+
The design length L is the distance between lines of support that resist circumferential buckling. This includes: (1) the distance between lines of support provided by circumferential stiffening rings meeting UG-29; (2) the distance between head tangent lines plus one-third of the depth of each formed head (for torispherical or ellipsoidal heads); or (3) the distance between jacket closure bars in jacketed vessels.
What is the required design pressure for a vessel subject to Full Vacuum (FV)?+
Per ASME Section VIII Div 1 and standard industrial practice, a vessel specified for Full Vacuum must be designed for an external design pressure of at least 15.0 psi (1.034 bar, 103.4 kPa) external. If the vessel contains liquid during steam-out or vacuum conditions, the equivalent hydrostatic head of that liquid must be added to the 15.0 psi external rating at the bottom section of the shell.
How does ASME Section II Part D Factor A and Factor B govern allowable pressure Pa?+
Factor A is a dimensionless strain parameter derived from the shell geometric ratios L/Do and Do/t using Figure G of Section II-D. Factor B is a stress factor (psi) obtained by entering the material external pressure chart (e.g. Figure CS-1, Figure HA-1) at value A and design temperature. If A falls to the left of the material curve (elastic buckling), B = (A * E) / 2. Allowable external pressure is then calculated as Pa = (4 * B) / [3 * (Do / t)].
What is the purpose of UG-29 vacuum stiffening rings?+
Circumferential stiffening rings divide a long vessel into multiple shorter effective lengths (L), dramatically lowering the L/Do ratio. Because allowable external pressure scales inversely with effective length in the elastic buckling regime, adding stiffeners allows thin-walled vessels (e.g. large storage tanks, distillation columns) to withstand full vacuum without requiring heavy, expensive thick plate shells. The stiffener must have a cross-sectional moment of inertia (Is) exceeding the UG-29 threshold.