EN 13445 is the European harmonised standard for unfired pressure vessels — equipment such as heat exchangers, pressure accumulators, separators, and offshore process vessels. Part 3 of the series, EN 13445-3: Design, is the largest and most technically demanding part, providing the rules for calculating required wall thicknesses, verifying component capacities, and demonstrating conformity with the Pressure Equipment Directive (PED).
A defining feature of EN 13445-3 is that it offers two distinct design methodologies: Design by Formula (DBF) and Design by Analysis (DBA). Understanding when to use each — and how the key parameters (nominal design stress f, weld joint factor z, test pressure) behave differently under each route — is essential for engineers working with pressure equipment on offshore or onshore facilities.
1. EN 13445 series structure and Part 3 scope
The EN 13445 series has five active parts:
- Part 1: General — scope, definitions, referenced standards
- Part 2: Materials — material groups, impact requirements, inspection documents
- Part 3: Design — the primary calculation standard
- Part 4: Fabrication — welding, heat treatment, forming
- Part 5: Inspection and testing — NDT, pressure testing, documentation
Part 3 covers vessels operating at pressures above 0.5 bar gauge, made from metallic materials (steels — both ferritic and austenitic, aluminium alloys, nickel alloys, copper alloys). It addresses vessels under internal pressure, external pressure, and combined loading. For offshore pressure equipment — HPU accumulators, subsea umbilical terminations, process separators — Part 3 is the governing design document when EN 13445 is invoked.
2. Design by Formula (DBF): cylindrical shell thickness
The Design by Formula route is the primary route for most standard vessel geometries — cylindrical shells, hemispherical heads, dished heads, cones, and nozzle openings. EN 13445-3 provides explicit formulae for each geometry. For a cylindrical shell under internal pressure, the required thickness e is:
The formula relates the required wall thickness to the calculation pressure P, the mean shell diameter Di (or De, depending on the convention used), the nominal design stress f, and the weld joint factor z. The minimum required thickness is the largest of the value from the pressure formula and any minimum thickness required for corrosion allowance or fabrication.
DBF is the standard route when the vessel geometry matches the scope of the formulae — which covers the vast majority of practical vessel configurations. The key advantage of DBF is speed and verifiability: the calculation is deterministic, traceable, and immediately comparable to previous projects or industry norms.
When DBF is not applicable
DBF has limitations. It does not directly address:
- Vessels with complex geometries (non-standard head shapes, asymmetric nozzle clusters, integral attachments)
- Fatigue assessment beyond the simplified fatigue check
- Vessels subject to significant bending loads in addition to pressure
- Creep at elevated temperatures beyond the range of the design stress tables
In these cases, EN 13445-3 Annex B (Design by Analysis — Direct Route) or Annex C (DBA — Stress Categorisation) is used instead.
3. Nominal design stress f: ferritic vs austenitic steels
The nominal design stress f is the allowable stress used in all DBF calculations. It is a material property that EN 13445-3 derives from the base material's mechanical properties with safety factors applied. The derivation method differs between steel types:
Ferritic steels (including carbon steel and low-alloy steel)
For ferritic steels at temperatures up to the onset of creep (approximately 380–450°C for carbon steel), the nominal design stress f is the minimum of:
- The characteristic yield strength Rp0.2 at temperature divided by a safety factor of 1.5
- The characteristic tensile strength Rm at room temperature divided by a safety factor of 2.4
The governing value is whichever is lower — in practice, for most carbon and low-alloy steels, the tensile strength criterion governs at lower temperatures and the yield criterion governs as temperature increases.
Austenitic steels
Austenitic stainless steels have a higher tensile strength relative to yield strength compared to ferritic steels, and they exhibit more pronounced strain hardening. EN 13445-3 allows two options for austenitic steels:
- Standard route: The same safety factors as ferritic steels apply (1.5 on Rp0.2, 2.4 on Rm)
- Enhanced route: A higher allowable stress based on Rp1.0 (1% proof stress) with a safety factor of 1.5, permitted when enhanced inspection requirements are met. This can give 15–20% higher allowable stress for austenitic grades.
The enhanced route requires that the designer confirm compliance with the additional inspection criteria — which typically means 100% radiographic or ultrasonic testing of all longitudinal and circumferential welds (weld joint factor z = 1.0). Using z = 1.0 combined with the enhanced austenitic allowable stress is a common design choice for high-specification process equipment where weight and size matter.
4. Weld joint factor z
The weld joint factor z (also referred to as the joint efficiency or testing group coefficient) is a reduction factor applied to the nominal design stress f to account for the reduced reliability of welded joints relative to the parent material. A z value of 1.0 implies that the weld is as reliable as the base metal — which requires extensive non-destructive testing to demonstrate.
EN 13445-3 defines z through a testing group classification (from the fabrication and inspection requirements of EN 13445-4 and 13445-5):
| Testing group | NDE extent (butt welds) | z value | Typical application |
|---|---|---|---|
| 1 | 100% RT or UT of all butt welds | 1.00 | High-hazard vessels, category III/IV PED, critical service |
| 2 | ≥ 25% RT or UT per weld seam | 0.85 | Standard industrial vessels, category II PED |
| 3 | Visual inspection only (spot radiograph or equivalent) | 0.70 | Low-hazard vessels, category I PED, simple geometries |
| 4 | Visual inspection only | 0.70 | Special cases; least common for pressure-critical items |
The practical effect of z is significant: a vessel designed with z = 0.85 requires 18% more wall thickness (or 18% less pressure capacity) than the same vessel designed with z = 1.0 — for the same material and pressure. For weight-critical applications such as offshore separators or compact process modules, the incremental NDE cost to achieve z = 1.0 is often justified by the weight saving.
5. Hydraulic test pressure
After fabrication, all EN 13445 pressure vessels must undergo a hydraulic pressure test before being placed into service. The required test pressure Pt is calculated as a multiple of the design pressure, with the exact multiplier depending on the temperature correction for material properties.
The formula for Pt ensures that the test applies a meaningful proof load relative to the design condition while accounting for the fact that the material yield strength is typically higher at the ambient test temperature than at the elevated design temperature. For most steel vessels designed at moderate temperatures (up to 200–300°C), the test pressure multiplier is typically in the range 1.25–1.43 × PS (maximum allowable pressure), where the exact value depends on the ratio of allowable stress at test temperature to allowable stress at design temperature.
Key points:
- The test is performed at ambient temperature with water (or another liquid) as the test medium
- The pressure is held for a minimum duration (typically 30 minutes for volumes above a threshold)
- The vessel must be visually inspected during and after the test for any signs of leakage or permanent deformation
- For vessels where hydrostatic testing is impractical (very large vessels, vessels that cannot be drained), pneumatic testing with alternative safety measures may be considered — EN 13445-5 covers this in detail
6. Opening reinforcement for nozzles
Every nozzle or opening in a pressure vessel shell removes load-carrying material from the pressure boundary. EN 13445-3 requires that this lost material be compensated either by increased shell thickness in the region of the opening or by the nozzle neck itself, if the nozzle neck has sufficient excess thickness above what the nozzle pressure requires.
The standard uses an area replacement method: the cross-sectional area removed by the opening must be offset by an equivalent cross-sectional area of excess material within a defined compensation zone around the nozzle. The compensation can come from:
- Excess thickness in the shell (shell wall thicker than required by pressure alone)
- Excess thickness in the nozzle neck (nozzle wall thicker than required)
- An added pad or reinforcing ring welded around the nozzle
Two nozzle attachment types are addressed: set-in nozzles (the nozzle penetrates the shell and is fillet/full-penetration welded from the inside) and set-on nozzles (the nozzle sits on the shell surface and is fillet welded externally). Set-in nozzles with full-penetration welds generally provide better compensation efficiency and are preferred for high-pressure or high-temperature service.
The standard also includes limits on the minimum thickness of non-pressure-bearing weld neck flanges and the tilt angle of oblique nozzles — details that appear frequently in third-party vessel design reviews.
7. Design by Analysis (DBA): when formula is not enough
EN 13445-3 Annex B provides a Design by Analysis — Direct Route using plasticity-based limit state verification. Annex C provides a Design by Analysis — Stress Categorisation approach compatible with the traditional stress classification method.
DBA is used when:
- The vessel geometry falls outside the scope of the DBF formulae (e.g., asymmetric nozzle patterns, very large openings, complex transition sections)
- Detailed fatigue assessment is required beyond the EN 13445-3 simplified fatigue check (Annex B.8 or Annex NA)
- The vessel is subject to significant external loads (piping reactions, seismic, vessel support forces) in addition to internal pressure
- The designer wants to take advantage of plastic redistribution to reduce wall thickness below the DBF minimum
DBA requires finite element analysis (FEA) of the vessel and checking against plastic collapse, progressive plastic deformation (ratcheting), and instability (buckling). It is more labour-intensive than DBF but provides more flexibility for non-standard configurations.
The Notified Body's involvement increases for DBA designs — the FEA methodology, material model, and acceptance criteria should be agreed before the analysis is performed, not after.
8. Summary
EN 13445-3 is the most comprehensive European standard for pressure vessel design, and its DBF / DBA framework gives engineers genuine flexibility to choose the appropriate level of analysis for the complexity of the vessel.
For standard cylindrical vessels, DBF with:
- Nominal design stress f derived from yield and tensile strength with appropriate safety factors
- Weld joint factor z selected based on the agreed testing group (1.0 for 100% NDE, 0.85 for 25%)
- Hydraulic test pressure at 1.25–1.43 × PS depending on temperature correction
- Opening reinforcement verified by area replacement method
...is the most common and efficient route. DBA is reserved for geometrically complex vessels or where fatigue life or external loading is a governing concern.
EN 13445-3 is now ingested in the Leide Navigator knowledge base (459 chunks — one of the largest single ingestions). You can query specific formulae, design stress derivation for specific material groups, weld joint factor requirements, or nozzle reinforcement methodology directly.
Query EN 13445-3 in Leide Navigator
EN 13445-3 (Design), EN 13445-2 (Materials), and EN 13445-5 (Inspection) are all ingested. Ask about shell thickness formulae, weld joint factor z, test pressure requirements, or DBF vs DBA selection.