Design by Analysis vs Design by Formula: When DbA Is the Right Choice for PED

Two routes to the same destination

The Pressure Equipment Directive (2014/68/EU) requires that pressure vessels placed on the EU market meet the Essential Safety Requirements (ESRs) of Annex I. In practice, manufacturers demonstrate this by designing to a harmonised standard — most commonly EN 13445 for unfired pressure vessels or ASME VIII for US-origin equipment. Both standards offer two fundamental design approaches: Design by Formula (DbF) and Design by Analysis (DbA).

Both routes lead to the same regulatory destination — a compliant pressure vessel with a valid CE mark under PED. The question is which route is more appropriate for your specific design, and understanding the difference is essential for any engineer working on pressure equipment.

Design by Formula: the standard route

Design by Formula uses closed-form equations derived from simplified shell theory to calculate minimum required wall thicknesses, nozzle reinforcement areas, and flange dimensions. EN 13445-3 provides comprehensive formula sets for cylindrical and spherical shells, dished ends, cones, openings and nozzles, and bolted flanged joints.

DbF is the default route for most standard pressure vessel geometries and is the method most fabricators and their designers use day-to-day. Its main advantages are familiarity, speed, and the fact that it is directly auditable — a Notified Body reviewer can follow each calculation step from input data to compliance demonstration without needing specialist FEA knowledge.

Its limitation is that it is derived from idealised geometries. When the actual vessel deviates significantly from those geometries — complex nozzle arrangements, non-standard head forms, saddle supports, thick-to-thin transitions, or vessels operating under combined pressure and external loads — the formula results become increasingly conservative or, in some cases, inapplicable.

Design by Analysis: the FEA route

Design by Analysis replaces the simplified formulae with a full three-dimensional finite element stress analysis of the actual vessel geometry under all relevant load cases. The stress results are then classified and assessed against allowable limits specified in EN 13445-3 Annex B (Direct Route) or Annex B.9 (Stress Categorisation Route).

DbA is not simply "running FEA on the vessel" — it is a specific, code-defined analysis methodology with strict requirements for model fidelity, load case definition, stress classification, and allowable stress categorisation. A DbA report submitted to a Notified Body must demonstrate compliance with each of those requirements explicitly.

When DbA delivers the most value

Complex geometries beyond the scope of formula methods

Vessel geometries that fall outside the applicability limits of EN 13445-3 formulae — unusual nozzle shapes, large openings exceeding 50% of the shell diameter, non-standard head profiles, or thick shells with d/t ratios outside the formula range — cannot be adequately assessed by DbF alone. DbA is the only rigorous route for these geometries.

Combined loading conditions

EN 13445-3 formula methods are primarily designed for internal pressure loading. When the vessel also experiences significant external loads — wind, seismic, nozzle forces and moments from connected piping, or support reactions — the interaction between pressure and bending stresses requires a combined-load FEA to assess correctly. DbA naturally handles combined loading in a single analysis.

Optimising overly conservative DbF results

Design by Formula is inherently conservative because it assumes idealised stress distributions that are rarely as severe as the formula implies. When a DbF calculation produces a thick wall that is driving significant material cost, DbA often demonstrates that the actual stress distribution at the critical location is substantially lower than the formula predicts — justifying a thinner wall that still has adequate margin. This is the most commercially valuable application of DbA in manufacturing.

Resolving Notified Body technical queries

When a DbF technical file raises queries from a Notified Body — typically around nozzle reinforcement, saddle stresses, or flange rigidity — DbA provides definitive numerical evidence that resolves the query rather than iterating through formula alternatives. This is precisely the scenario described in the CHS Intl case study on the PED compliance page, where DbA resolved 23 NB queries in a single re-submission.

The DbA process under EN 13445-3 Annex B

Stress categorisation route (Annex B.9)

The stress categorisation route requires the analyst to identify stress classification lines (SCLs) through the vessel wall at critical locations, linearise the FEA stress results through the thickness using the standard membrane-bending decomposition, and classify the resulting stress components as primary membrane (Pm), primary bending (Pb), or secondary (Q). Each category has a different allowable stress limit: Pm ≤ f, Pm + Pb ≤ 1.5f, Pm + Pb + Q ≤ 3f, where f is the design stress intensity from EN 13445-3 Table 6-1.

Direct route (Annex B.8)

The direct route uses a limit analysis philosophy — it directly checks against gross plastic deformation, progressive plastic deformation, and fatigue failure modes without the stress categorisation step. This avoids some of the subjectivity inherent in selecting SCL locations and is generally preferred for complex geometries. However, it requires nonlinear FEA (elastic-plastic material models) and is computationally more demanding.

What a DbA report must contain

A DbA technical file submitted to a Notified Body under EN 13445-3 Annex B must include: the FEA model description (geometry, mesh, element types, material models); all load cases with justification; boundary condition definition and sensitivity assessment; stress linearisation results at all critical SCLs (for the categorisation route); a comparison of linearised stresses against code allowables; and a clear compliance statement for each failure mode assessed.

CHS Intl produces DbA reports structured specifically to meet Notified Body review requirements, drawing on experience of accepted submissions across multiple NB organisations in Germany, Belgium, the Netherlands, and the UK.