EN 13445-3: Shell Thickness, Safety Factors, and Weld Joint Coefficients for Unfired Pressure Vessels

1. Scope and document structure

EN 13445 is the European harmonised standard for unfired pressure vessels — pressure-containing equipment that is not directly heated by combustion. It covers vessels used in process plants, offshore topsides, HVAC systems, cryogenic equipment, and hydraulic accumulators operating under gauge pressure above 0.5 bar.

The standard is published in six parts:

Part 3 (Design) is by far the densest part of the standard. It contains all the thickness formulas, stress analysis methodology, fatigue assessment rules, and special design cases. This article focuses on Part 3, with cross-references to Parts 2 and 5 where relevant.

2. Equipment Directive categories I–IV

The PED classifies pressure equipment into four risk categories (I = lowest risk, IV = highest). The category determines which conformity assessment route is required and the level of third-party involvement in design and production verification.

Category assignment depends on three parameters: fluid group (Group 1 = hazardous fluids including flammable/explosive/toxic; Group 2 = other including steam and compressed air), design pressure PS, and volume V. These parameters are mapped through classification tables in the Directive. The boundaries are roughly:

For offshore applications, the relevant categories are typically III and IV for process vessels containing hydrocarbons or steam. Category determination must be done before choosing a conformity module — the design documentation, weld examination scope, and final test requirements all depend on it.

3. Design by Formula vs Design by Analysis

EN 13445-3 provides two primary design routes:

Design by Formula (DBF) — §5 and §7–§16

DBF uses closed-form analytical expressions for standard geometry (cylindrical shells, spherical shells, hemispherical/ellipsoidal/flat heads, conical sections, nozzles, flanges). The designer selects the applicable formula for the component geometry, inputs material properties and dimensions, and computes the required minimum wall thickness.

DBF is the default route for standard pressure vessel components. It is computationally straightforward, well-auditable, and accepted by all Notified Bodies. The limitations are that it applies only to geometries covered by the standard and does not capture stress concentrations in detail.

Design by Analysis (DBA) — §17–§18

DBA uses numerical stress analysis (typically FEA) or direct stress analysis methods to demonstrate that a vessel design meets the safety objectives where the geometry deviates from standard cases or where the DBF would give overly conservative results. DBA is also the route for vessels in the creep regime or under complex combined loading.

EN 13445-3 §17 (Direct Route DBA) classifies loads and failure modes:

• Gross plastic deformation (GPD) — static failure; controlled by design action effects vs plastic limit load
• Progressive plastic deformation (PD) — ratcheting under cyclic loading
• Instability (I) — buckling under compression or external pressure
• Fatigue (F) — cyclic stress failure
• Static equilibrium (SE) — overturning, sliding

For most offshore process vessels, DBF is used for shell and head design and DBA is reserved for nozzle junction zones, flat heads with irregular penetrations, and saddle support regions where stress concentrations exceed what DBF can address.

4. Nominal design stress f

All DBF thickness formulas in EN 13445-3 are expressed in terms of the nominal design stress f — the material strength property reduced by safety factors appropriate to the design temperature and material type.

Safety factor derivation

For ferritic steels (the most common vessel material) at temperatures below the creep regime, the nominal design stress is:

The safety factors C_r = 2.4 and C_s = 1.5 are defined in EN 13445-3 §6.1. They represent the margin between design stress and material failure — the proof strength factor 1.5 guards against gross yielding at operating conditions; the tensile strength factor 2.4 guards against rupture at ultimate load.

Temperature dependence

At elevated design temperatures, R_p0.2,T decreases. The governing safety factor (C_s / R_p0.2,T) then typically controls, and f decreases accordingly. EN 13445-2 (Materials) provides the minimum elevated-temperature proof strength data for permitted materials — referenced during the f calculation. For austenitic stainless steels (EN 10028-7), an additional factor of 1.2 applies to the proof strength path, reflecting the higher ductility and strain-hardening capacity of austenitic grades.

f vs allowable stress — terminology note

The EN 13445 nominal design stress f is conceptually equivalent to "allowable stress" in ASME VIII Div.1 but is derived differently. ASME uses min(S_y/3, S_u/3.5) for carbon steels at room temperature; EN 13445 uses min(R_p0.2/1.5, R_m/2.4). These produce different absolute values for the same steel. Designs produced under one system cannot simply be re-stamped for the other without recalculation.

5. Weld joint coefficients z

The weld joint coefficient z (also called weld efficiency) appears in every shell thickness formula in EN 13445-3. It reduces the effective strength of the shell at welded joints to account for the fact that welds may contain defects not detected by examination — with more extensive NDE, a higher z is justified because the probability of undetected defects is lower.

EN 13445-3 Table 5.6-1 defines three z values:

The testing group selection is linked to the PED category. Category III and IV vessels are generally required to use Testing Group 1 (z = 1.0) for longitudinal and circumferential seams. For Category I–II vessels, lower testing groups (and hence lower z) are permitted.

How z affects required thickness

Consider a cylindrical shell under internal pressure with P = 25 bar, D_i = 800 mm, f = 133 MPa, and three z values. The minimum wall thickness (excluding corrosion allowance) varies as follows:

The penalty for not performing volumetric NDE is significant — 43% more material for the same design pressure. For large offshore process vessels where plate weight is a direct cost driver, using z = 1.0 and performing full radiography is typically more economical than the z = 0.7 wall thickness increase, in addition to the PED category obligation.

6. Shell and head thickness formulas

Cylindrical shell under internal pressure (§7.1)

This is the workhorse formula of EN 13445-3. It applies when the wall is thin relative to the radius (e/D_i ≤ 0.16). For thicker walls — pressure vessels with e/D_i > 0.16 — the thick-wall formula in §7.1.4 applies.

Spherical shell under internal pressure (§7.2)

Dished ends — hemispherical (§7.2), ellipsoidal (§7.3.1), torispherical (§7.3.2)

The three common head types have different efficiency factors:

• Hemispherical heads: Same formula as spherical shell — most efficient, thinnest head, highest fabrication cost
• Semi-ellipsoidal heads (2:1 ratio): Required thickness approximately equal to cylindrical shell — standard choice for most vessels
• Torispherical (Klopper-Geerlings) heads: Thickness governed by crown radius and knuckle radius; may require greater thickness than semi-ellipsoidal in some configurations due to knuckle yielding; cheaper to form but heavier

For all dished ends, EN 13445-3 §7.3 also requires checking the knuckle zone for plastic instability (external pressure on the knuckle in suction service, or internal pressure with a thin knuckle relative to the crown radius).

Flat ends (§7.4)

Flat ends are the least efficient head geometry — they resist pressure in bending rather than membrane tension. Required thickness is proportional to diameter squared:

For large flat ends (flanged covers, blind flanges), the required thickness quickly becomes impractical. Most large-diameter pressure-containing closures use dished heads or bolted flanged ends rather than flat plates.

7. Nozzle and opening reinforcement (§9)

Every nozzle (pipe connection, manway, instrument tap) penetrates the shell and locally reduces its load-carrying cross-section. EN 13445-3 §9 requires that the removed material be compensated by reinforcement — either integral (thickened shell or nozzle neck) or pad reinforcement welded around the opening.

Area replacement method

The fundamental check is that the cross-sectional area of reinforcement available within an influence zone around the opening is at least equal to the area of shell removed by the opening:

The influence zone width is typically 2.5 × √(D_i × e_s) on each side of the nozzle centreline. Reinforcement outside this zone does not contribute.

Set-on vs set-through nozzles

Set-in (set-through) nozzles, where the pipe penetrates the shell wall and is welded from both sides, contribute more to reinforcement than set-on nozzles attached to the shell surface only. The weld geometry also affects the required NDE — a full-penetration butt weld is required for nozzles on Category III/IV vessels, with volumetric examination.

Nozzle limitation

EN 13445-3 §9 is limited to isolated openings. When two nozzle influence zones overlap — closely spaced nozzles or clusters — the analysis becomes more complex and often requires DBA rather than the simple area-replacement check.

8. Worked Example: Offshore Separator Vessel Sizing

The clause-by-clause material above is the toolkit; the value comes when you walk one vessel through the chain. The decisions interlock — PED category constrains the testing group, the testing group sets z, z drives the shell thickness, the thickness governs the nozzle reinforcement area, and the design pressure determines the hydrotest. Walk one offshore production separator end-to-end so the dependencies become concrete.

Vessel: First-stage horizontal production separator on a North Sea platform. Inside diameter D_i = 1500 mm, tan-tan length 6 m, design pressure P_S = 25 bar (2.5 MPa), design temperature 80 °C, fluid: untreated wellstream (oil/gas/water) — Fluid Group 1 (hydrocarbon, flammable). Material: P355NH carbon steel per EN 10028-3.

Step 1 — PED categorisation

Group 1 fluid + P_S = 25 bar + V ≈ 10.6 m³ (cylindrical body only) → P_S × V ≈ 265 bar·m³. Per PED 2014/68/EU classification charts, this lands clearly in Category III. Conformity route: Module B + D (EU type-examination + production QA), Notified Body involvement is mandatory.

Step 2 — Testing group and weld joint coefficient z

Cat III with full volumetric NDE budget on the program → Testing Group 1 per EN 13445-5, which permits z = 1.0 on longitudinal and circumferential butt welds. (Group 2 with z = 0.85 would have been ~17% more material; for a 6 m long, 1500 mm ID shell that is roughly an extra 600 kg of plate — well above the cost of full RT/UT.)

Step 3 — Nominal design stress f

P355NH at 80 °C, R_p0.2 = 345 MPa (after temperature derating, conservatively 340 MPa). Per §6.1 for non-austenitic steels at normal operating: f = min(R_p0.2,t / 1.5, R_m,20 / 2.4). Yield-governed branch: 340 / 1.5 = 226.7 MPa. Take f = 226 MPa.

Step 4 — Cylindrical shell thickness (§7.1)

Add corrosion allowance c = 3 mm (typical for sweet-service production separator with 25-year design life): nominal ordered thickness = 8.34 + 3 = 11.34 mm → specify 12 mm plate (next standard plate thickness up). e/D_i = 0.008 ≪ 0.16 → thin-wall formula valid.

Step 5 — Head selection (§7.3)

Semi-ellipsoidal 2:1 heads chosen — required thickness ≈ cylindrical shell thickness, easier to fabricate than hemispherical, lower height than torispherical (saves topside footprint). Specify 12 mm to match shell, knuckle zone checked per §7.3.1 for plastic instability — not governing at this P/D ratio.

Step 6 — Nozzle reinforcement (§9)

Largest nozzle: 8" Sch 80 inlet (d_i = 193 mm, wall 12.7 mm). Required reinforcement area per area-replacement method:

Influence zone width = 2.5 × √(1500 × 8.34) ≈ 280 mm each side. Available reinforcement = excess shell thickness (12 − 8.34 = 3.66 mm) × 2 × 280 ≈ 2050 mm² + excess in nozzle neck. Total available ≈ 2400 mm² > 1610 mm² → set-through nozzle without pad reinforcement passes. (If d_i were 250 mm or larger — common for 10"+ nozzles — a reinforcement pad would be needed.)

Step 7 — Hydrotest pressure (EN 13445-5)

f at 20 °C (test temp) = 230 MPa, f at 80 °C (design temp) = 226 MPa, ratio f_test/f_design = 1.018. Hydrotest pressure:

Held for 30 minutes minimum at ambient with vessel filled with water, inspected for leaks and visible deformation per EN 13445-5 §10.

9. Common misuses and calculation errors

1. Using z = 1.0 without 100% volumetric examination

The most frequent non-conformity encountered in pressure vessel documentation audits. The designer selects z = 1.0 in the thickness calculation, resulting in a thinner wall; the fabrication specification then requires only spot or visual NDE. This is structurally unsafe — the design assumes full volumetric assurance of weld quality. Confirmation of the testing group used must appear in the fabrication specification and be traceable in the inspection records.

2. Omitting or understating the corrosion allowance c

EN 13445-3 requires the designer to add a corrosion allowance c to the calculated e_s to obtain the nominal ordered thickness. The standard does not prescribe c — it is determined by the designer based on process fluid, expected service life, and material selection. On offshore process equipment in sour service (H₂S-containing), corrosion allowances of 3–6 mm are typical for carbon steel vessels; austenitic stainless (from EN 10028-7) may require zero allowance but must then meet HISC and pitting resistance requirements.

3. Confusing design pressure with maximum allowable working pressure (MAWP)

The design pressure PS used in thickness formulas is the maximum pressure the vessel is designed to contain, including any pressure surge allowances. MAWP is the maximum pressure the as-built vessel can withstand, determined from the actual ordered thickness minus corrosion allowance minus manufacturing tolerance. MAWP is always ≥ PS; if MAWP = PS, the vessel has no thickness margin. For offshore vessels subject to wear or inspection interval constraints, maintaining some MAWP margin is often a project-specific requirement.

4. Applying EN 13445-3 to fired vessels or boilers

EN 13445 explicitly excludes fired pressure vessels (boilers, superheaters, reheaters) — these are covered by EN 12952 and EN 12953. Offshore heat-recovery steam generators (HRSGs), fired heaters, and waste-heat boilers fall outside EN 13445 scope. Applying EN 13445-3 formulas to a fired vessel is a misuse of the standard.

5. Treating EN 13445 and ASME VIII as interchangeable

Safety factors, material allowable stress basis, weld efficiency factors, hydrostatic test pressure multipliers, and NDE scope requirements all differ between EN 13445 and ASME VIII Div.1/Div.2. A vessel designed to ASME VIII cannot be CE-marked as complying with EN 13445 without recalculation and documentation rework — and vice versa.

10. Cross-reference: EN 13445-5 testing requirements

EN 13445-5 (Inspection and Testing) is the operational counterpart to Part 3 — it defines how the vessel design is validated before commissioning. The link between Parts 3 and 5 is bidirectional: Part 5 test requirements depend on the testing group selected in Part 3; and Part 3 allows higher z values precisely because Part 5 specifies more stringent examination for higher testing groups.

Hydrostatic pressure test

The standard hydrostatic test pressure (PT) is:

The hydrostatic test is performed at ambient temperature with the vessel filled with water (or other suitable liquid). The vessel is held at PT for a minimum period (typically 30 minutes) while inspected for leaks and deformation.

Pneumatic test

A pneumatic test with compressed gas at 1.1 × PS is permitted only when a hydrostatic test is impractical — for example, when the vessel cannot be supported under the water load or when residual water would damage the service process. Pneumatic testing carries significantly higher risk due to stored energy, and EN 13445-5 requires additional safety precautions and a lower maximum test pressure (1.1 × PS rather than 1.25 × PS).

NDE scope — Testing Group 1 vs Group 3

For Testing Group 1 vessels (z = 1.0), EN 13445-5 requires:

• 100% volumetric examination (RT or UT) of all longitudinal and circumferential butt welds
• 100% surface examination (MT or PT) of all butt welds and fillet welds of nozzles
• Visual examination of all welds

For Testing Group 3 (z = 0.7), visual examination is the primary requirement for weld quality, with no mandatory volumetric NDE — the thicker wall provides the structural compensation.

11. Using Leide Navigator for EN 13445 queries

All four EN 13445 parts — Part 1, Part 2, Part 3, and Part 5 — are covered by Leide's engineering AI. EN 13445-3 is one of the most extensively supported standards, covering shell and head design, DBA methodology, fatigue assessment, creep analysis, and flanged connections in detail.

Related standards for offshore pressure vessel work also covered include EN 10028-7 (pressure equipment austenitic and duplex steels) and EN 10204 (material inspection certificate types 3.1 and 3.2).