Pressure Vessel Design Theory
ASME Section VIII Division 1
The ASME Boiler and Pressure Vessel Code Section VIII Division 1 provides rules for the design, fabrication, inspection, testing, and certification of pressure vessels operating at pressures exceeding 15 psig (1 bar). It is the most widely used pressure vessel code worldwide.
The code covers materials, design formulas, fabrication requirements, welding procedures, inspection methods, and testing protocols to ensure safe operation under pressure.
Design Pressure and Temperature
Design Pressure: The maximum pressure at the top of the vessel at the coincident design temperature. It should include:
- Static head of liquid
- Pressure surges from pumps or valves
- Safety margin (typically 10% above maximum operating pressure)
Design Temperature: The maximum or minimum metal temperature expected in service. Material allowable stress values vary with temperature and must be obtained from ASME Section II Part D.
Cylindrical Shell Design (UG-27)
For cylindrical shells under internal pressure, the required thickness is calculated using:
t = PR/(SE - 0.6P)
t = minimum required thickness (mm or in)
P = design pressure (MPa or psi)
R = inside radius (mm or in)
S = allowable stress at design temperature (MPa or psi)
E = joint efficiency (dimensionless, 0.7 to 1.0)
This formula is valid when:
- t ≤ 0.5R (thin-wall assumption)
- P ≤ 0.385SE (limits maximum pressure)
Head Design (UG-32)
Pressure vessel heads (closures) come in various shapes, each with specific design formulas:
1. Ellipsoidal Heads (2:1 ratio)
t = PD/(2SE - 0.2P)
Where D = inside diameter. Most common head type, offering good balance between cost and strength. The major axis is equal to the diameter, and the minor axis is half the diameter (2:1 ratio).
2. Torispherical Heads (ASME F&D)
t = 0.885PL/(SE - 0.1P)
Where L = crown radius (typically equal to shell diameter). Also called flanged and dished heads. Most economical to fabricate but requires greater thickness due to stress concentration at the knuckle. Crown radius = D, knuckle radius = 0.06D.
3. Hemispherical Heads
t = PL/(2SE - 0.2P) where L = R
Where L = inside spherical radius = inside cylinder radius. Strongest head design requiring minimum thickness, but most expensive to fabricate. Used for very high pressures or large diameters where weight savings justify cost.
Corrosion Allowance
Corrosion allowance (CA) is additional thickness added to compensate for material loss during the vessel's design life:
tactual = trequired + CA
Typical corrosion allowances:
- 3 mm (1/8 in): Non-corrosive service, stainless steel
- 3-6 mm (1/8 - 1/4 in): Mildly corrosive service
- 6-12 mm (1/4 - 1/2 in): Severely corrosive service
- 0 mm: Only if corrosion-resistant cladding or lining is used
Joint Efficiency (UW-12)
Joint efficiency (E) accounts for the strength reduction at welded joints compared to unwelded plate. It depends on the type of joint and the degree of radiographic examination:
| Examination Type | Joint Efficiency (E) | Description |
|---|---|---|
| Full Radiography | 1.0 | 100% RT of all welds |
| Spot Radiography | 0.85 | Random RT per UW-11 |
| No Radiography | 0.70 | Visual inspection only |
Higher joint efficiency allows thinner walls but requires more thorough examination. For critical services or when weight savings are important, full radiography (E=1.0) is recommended.
Material Selection
Common pressure vessel materials per ASME Section II:
| Material | Max Temp | Typical Use |
|---|---|---|
| SA-516 Grade 70 | 400°C | Most common carbon steel for moderate conditions |
| SA-240 Type 304 | 550°C | Austenitic stainless, corrosive service |
| SA-240 Type 316 | 550°C | Stainless with improved corrosion resistance |
| SA-387 Grade 22 | 600°C | Chromium-molybdenum alloy for high temperature |
Maximum Allowable Working Pressure (MAWP)
After the vessel is built with actual thickness, the MAWP is calculated by rearranging the thickness formula:
MAWP = SE(t - CA)/(R + 0.6(t - CA))
for cylindrical shells
The MAWP is stamped on the vessel's nameplate and represents the highest pressure permitted at the top of the vessel at the designated temperature.
External Pressure Design (UG-28)
Vessels subject to external pressure (vacuum or partial vacuum) must be designed against buckling failure. The procedure in UG-28 uses:
- Length-to-diameter ratio (L/Do)
- Diameter-to-thickness ratio (Do/t)
- Material external pressure charts in Section II Part D
- Stiffening rings if required
External pressure design is significantly different from internal pressure and may control the design for vacuum service or jacketed vessels.
Design Considerations
Nozzle Reinforcement
Openings in the vessel shell require reinforcement per UG-37 to compensate for removed material. Reinforcement area must equal or exceed area removed.
Support Design
Vessel supports (saddles, legs, skirts) must be designed for dead load, operating weight, wind loads, seismic loads, and thermal expansion.
Hydrostatic Testing
All pressure vessels must undergo hydrostatic test at 1.3 times MAWP (or 1.5 times design pressure for lower stress materials) per UG-99.
U-Stamp Certification
Vessels must be fabricated by an ASME-authorized manufacturer and inspected by an Authorized Inspector to receive the U-stamp certification.
Design Workflow
- Establish design conditions (P, T) with appropriate margins
- Select material based on temperature and corrosion requirements
- Determine joint efficiency based on inspection requirements
- Calculate required thickness for shell and heads
- Add corrosion allowance and round up to standard plate thickness
- Verify MAWP meets or exceeds design pressure
- Design nozzle reinforcements, supports, and attachments
- Prepare fabrication drawings with ASME requirements
- Fabricate, inspect, test, and obtain U-stamp
References
- ASME Boiler and Pressure Vessel Code, Section VIII Division 1, "Rules for Construction of Pressure Vessels"
- ASME Section II Part D, "Properties (Customary)", Material allowable stresses
- Megyesy, E.F., "Pressure Vessel Handbook", 17th Edition, Pressure Vessel Publishing (2019)
- Moss, D.R., Basic, M., "Pressure Vessel Design Manual", 4th Edition, Butterworth-Heinemann (2013)
- Bednar, H.H., "Pressure Vessel Design Handbook", Van Nostrand Reinhold (1986)