AD 2000 – Pressure vessel calculations

Chapter 01What this package handbook covers

A pressure vessel is not described by a single equation. Its shell, heads, openings, flanges, supports and, where relevant, cyclic loads require different assessments. This handbook therefore starts with the shared engineering workflow before explaining individual module roles. You will learn to build a calculation, interpret its results and follow changes across project chapters.

The package map covers all 45 identifiers in the inspected AD 2000 module group. The detailed operating guides in this first edition cover B1, B3 and B9. Other modules receive an engineering role and selection guide, not an equivalent individual handbook yet. A project chapter number is not a module identifier: B1 may, for example, occupy chapter 2.

Work in a copy of the supplied demonstration project. Its numbers teach software operation; they are not an approved vessel design. The example intentionally includes only a small selection of assessments and is not a fabrication document.

A useful reading path

1. New users: read the division of tasks, foundations and first steps.
2. Load the example and reproduce the B1/B3/B9 pressure change.
3. Use the three module guides to associate each result with its component and load case.
4. Continue with inverse calculation, variants and the review record.
5. Use the package map for additional tasks and check the applicable code basis.

Chapter 02From vessel to appropriate assessment

Start with a sketch of the physical component: which space is subject to which pressure? Where do geometry, material or thickness change? Where are forces introduced? These boundaries determine the chapters you need. A physical connection between components does not automatically create a software variable link.

The B1 / B3 / B9 learning chain

• B1: a cylindrical shell under internal pressure; the module also provides a spherical construction.
• B3: a dished head; shape, pressure type, knuckle, crown and straight flange affect the conditions being assessed.
• B9: an opening in the parent shell; the locally available load-bearing geometry must match the opening configuration.

These three chapters can share one design pressure. They still answer three different questions. An unremarkable B1 shell check does not establish the adequacy of the head or opening. Likewise, a low B9 utilisation must not be interpreted as the pressure margin of the entire vessel.

When does the project grow?

External pressure requires a stability assessment, for example B6 for a cylindrical shell and an appropriate B3 head configuration. Piping forces on a nozzle may require additional local-load assessments. A horizontal vessel on saddles poses a different support problem from a vertical skirt-supported vessel. Cyclic loading is a separate subject; a static pressure check alone does not settle it.

The module group is an organisational aid, not a guarantee that every member is based exclusively on an AD 2000 sheet. It also contains supporting dimensioning, loading and literature-based methods. Record the specific basis of each method in the calculation documentation.

Chapter 03Package map: all 45 modules

All 45 configured package members are placed here. The group labels in this table are teaching aids, not additional package definitions. “Overview” means source/catalogue review, not an executed example assessment.

Chapter 04Code, edition and program version

AD 2000 addresses more than calculation equations; its scope also includes construction, manufacturing, testing and documentation. The official AD 2000 overview describes that scope. A module handbook replaces neither the required code nor engineering review of applicability.

Distinguish three versions: the basis selected for the project, the implementation in the module and the publisher's latest release. For example, the inspected B5 catalogue source names 2024-01, while the official update service lists B5:2026-07 as its successor. This does not establish that the newer edition is implemented in this installation; conversely, an older catalogue line alone does not prove an unchanged calculation core.

This documentation explains operation and selected relationships from the inspected source. It does not reproduce complete code texts. For a real design, establish the actual agreed and implemented basis. Merely assembling AD modules is not automatic overall approval or conformity assessment.

Chapter 05Establish assumptions before entering numbers

Pressure and temperature belong to a load case

Define the design condition, test condition and any additional conditions separately. The example starts at 1.5 bar design pressure, 2 bar test pressure and 120 °C. Later, only design pressure changes to 3 bar. Test pressure is deliberately not adjusted automatically: this is a propagation test, not a recommendation for an acceptable revised test condition.

The displayed unit is part of an input. A number based on the wrong pressure difference, or a confusion between bar and N/mm², can produce a calculated answer to the wrong problem. Also establish whether pressure at the location being assessed needs to include liquid head. The example does not model that distribution.

A material is more than a name

Material selection, product form, temperature, governing thickness and method basis affect the properties adopted. The example uses existing record 1232, displayed as 1.4571(P). This internal identifier helps reproduce the inspected database; it is not a universally stable material code. In a real project, select through the material dialog and review the displayed properties.

In B9, the parent shell, nozzles and reinforcement components may use different materials. Do not copy one strength value indiscriminately into every field. A textual material description alone does not establish that the correct database record was selected.

Actual versus required wall thickness

Required thickness is the result of a specific assessment condition. Actual or final thickness describes your selected geometry. Deductions for tolerance or corrosion can reduce it to a smaller analysis thickness. Record which manufacturing condition the actual thickness represents, particularly for formed heads.

Chapter 06Getting started and operating safely

1. Create a new demonstration project or open the example in the next chapter. Save existing customer work separately first.
2. Search by identifier in the module browser, read the package and construction, and then open it. This example uses a B1 cylinder, a B3 Klöpper head and a B9 single opening.
3. Review the project-standards notification. A suggested standard does not confirm the basis of every chapter.
4. Initially fill the mask from top to bottom: calculation options, conditions, material, geometry and results. This is the intended orientation, although the solver permits other input sequences.
5. Leave an edited field with Tab and wait for processing. Then inspect the value, unit, field status and message panel.

No rigidly predefined inputs and outputs

SOL ALPHA solves relationships between variables. A known quantity may be prescribed, calculated or received from another chapter. What can be determined depends on the remaining constraints and the solution paths implemented by the module. This does not mean every equation is solvable in every direction, or that contradictory extra constraints become acceptable.

An expression such as 100 + 200 can help with numeric entry. Always check the resulting value and unit after submission. The same applies to an entry with a unit, for example 1 bar in a suitable pressure field: the accepted state is what matters. The general tutorials provide short demonstrations of these individual actions.

Colours guide; they do not certify

In the illustrated standard masks, prescribed numeric fields are light and calculated fields are highlighted in turquoise. Linked fields have an additional indication. Theme, focus and warning state may affect presentation. When in doubt, use Variable info and the connection display. A coloured field alone does not mean “safe” or “approved”.

Chapter 07Prepare the worked example

Download the B1/B3/B9 starting project · Download the saved video end state. These files come from the checked tutorial library. The fresh replay on 7 September reopens the starting file, creates the links and changes pressure again.

Use File → Open and the local file picker. Depending on your browser, preserve the suggested .sol download extension. The transport filename also has .txt for static web hosts; its bytes remain an unchanged SOL project. Do not edit it as text.

Check the starting state

The left chapter list must contain B1, B3 and B9. B1 shows a cylinder with 600 mm outside diameter, 8 mm wall thickness, 2000 mm length and a calculated inside diameter of 584 mm. B3 uses a Klöpper head with 600 mm outside diameter and 8 mm final knuckle thickness. B9 uses a cylindrical body, a single plain opening without reinforcement and an opening inside diameter of 80 mm.

All three modules initially use 1.5 bar. Check the material display, not just pressure. B9 also specifies 100 mm available effective shell width; this is not reinforcement-pad width. In B3, the 120 mm value in V4 is the maximum nozzle diameter outside 0.6·Da. Temperature is separate, at V30, and happens to be 120 as well, but in °C.

B1: starting point

123

Chapter 08Link pressure and follow the change

Choose an unambiguous source

1. Activate B1 and locate design pressure V3 at 1.5 bar. Do not select test pressure V16.
2. Open the field context menu and bookmark the variable.
3. Switch to B3. At design pressure V5, choose the connection action from the context menu and select the bookmarked B1 pressure.
4. Switch to B9. Link design pressure V2 to the same B1 variable V3.
5. Check the connection and received value in both destination chapters. Seeing 1.5 alone does not prove a link exists.
6. Return to B1, change design pressure to 3 bar, leave the field and wait for calculation.
7. Revisit B3 and B9. Review pressure, result fields, connection state and messages.

This structure has one source and two recipients; it is not a serial transfer of results: B1:V3 → B3:V5 and B1:V3 → B9:V2. Outside diameter, wall thicknesses, materials and test pressure are not linked in this experiment. A later B1 geometry change must therefore not be treated as an automatically completed B3/B9 update.

AutoConnect and repeated modules

Automatic connection aids reduce selection effort but do not replace checking the proposed source. With two vessels each containing a B1, “B1” is insufficient: inspect chapter name, instance and the source field's engineering meaning. Two pressure variables with the same unit can describe different spaces or load cases. The teaching case intentionally uses an explicit bookmark link.

If a destination should subsequently become independently prescribed, first establish the intended engineering separation and remove the link. Overwriting a linked field without considering its origin does not create a reliably documented variant.

Watch the complete operating workflow

English interface, bilingual overlays and subtitles. Video requires Internet access; instructions, images and example files are stored locally. Open video directly.

Chapter 09Reference results and what they establish

The table contains saved reference values for the tutorial case. The fresh local run on 7 September 2026 confirmed the starting values and the results after the linked pressure change within the recorded tolerances. Distinguish differences in the last displayed digits from rounded mask values.

B1 required thickness does not rise exactly in proportion to pressure because the evaluated result incorporates additional assumptions and comparison with the test case. B3 crown and knuckle results must be read separately. In B9, geometry remains unchanged during this pressure edit; pressure force and the utilisation considered here rise approximately proportionally.

What was compared?

The reference was established by editing initially unlinked destination chapters individually. Results from the linked change were then compared with that reference. For these quantities, this tests whether linking reaches the same state as an individual edit. It is not an independent formula check, Desktop/Web parity proof or confirmation of a complete design.

The B3 result image also shows a required knuckle thickness of about 1.67632 mm above the “based on the final wall thickness” section. The table explicitly refers to V1/V2/V32 in that latter section, taking the final thickness into account. Do not confuse different result sections simply because their labels resemble one another.

B3: different result bases

123

Chapter 10B1: shell, thickness and allowable pressure

Which question does B1 answer?

For the cylindrical teaching case, B1 assesses a shell under internal pressure. You can compare required thickness against a chosen geometry or obtain an allowable pressure for an existing wall. Another construction branch treats spherical shells. The selector changes the relationships used; renaming a chapter does not change its construction.

Build it step by step

1. Select the cylindrical type. Establish outside diameter and design temperature.
2. Prescribe design and test pressure separately. The example uses 600 mm, 120 °C, 1.5 bar and 2 bar.
3. Select a material through the dialog. Read the operation/test properties and safety factors.
4. Review tolerance c1, corrosion/erosion allowance c2 and joint efficiency v. Adopted values do not validate your manufacturing assumptions.
5. Enter an actual intended thickness, 8 mm in the example. The resulting inside diameter must be understandable.
6. For volumes and weights, also check component length and the associated density/filling assumptions.
7. Read operation and test results separately before assessing the governing result.

Keep four thicknesses distinct

V9 is final wall thickness se. V31 is thickness after the deductions used here: s0 = se − c1 − c2. V18 and V19 are required thicknesses for operation and testing. In the inspected B1 code, V1 takes the larger of those two. “8 mm actual” and “0.918628 mm required” are therefore not competing entries for the same field.

The elementary geometry check is Di = Da − 2·se. With 600 mm and 8 mm, this gives 584 mm. The effective wall portion is 8 − 0.3 − 0 = 7.7 mm. Use these checks as an initial sanity test before investigating more complex results.

Allowable pressure has conditions attached

V36 and V37 give allowable operation and test pressures based on the wall and assumptions in this chapter. The current B1 example shows approximately 37.7872 bar and 64.3818 bar respectively. These are not the allowable operating pressure of the entire project: heads, openings, flanges, other loads and documented applicability limits also need consideration.

Openings, volumes and weights

The B1 opening section provides simplified quantities for unreinforced openings and influence distances. It does not replace arbitrary detailed B9 assessments. In particular, a result capped at the geometric inside diameter is not blanket permission to fabricate an opening of that size.

Distinguish external volume, internal volume and metal volume. Weight quantities may be expressed as forces; the displayed unit governs interpretation. A value in kN must not be passed to a support calculation as kilograms. Likewise, water filling must not silently become the operating contents of a different fluid.

When is B1 insufficient?

For external pressure, different geometry or additional local loads, select the appropriate method. The inspected code includes ratio and thickness conditions, among others, and a limit on joint efficiency. Read the messages: “every field contains a number” does not establish that all conditions are satisfied.

B1: results after changing pressure

123

Chapter 11B1 inverse calculation: target or persistent constraint?

Suppose your shell geometry is fully determined by Da = 600 mm and se = 8 mm. The solver gives Di = 584 mm. An installation requirement now calls for Di = 580 mm. Outside diameter, inside diameter and thickness cannot all be chosen independently: one previous constraint must be adjusted or released.

Route A: seek a target value

1. Locate calculated inside diameter V27 and enter 580.
2. When the target/release selection appears, choose the quantity that may actually change. The recorded example selects wall thickness.
3. Confirm and inspect: outside diameter stays at 600 mm, thickness becomes approximately 10 mm, and inside diameter becomes 580 mm.
4. Then check the field roles. In the evidenced target-seeking workflow, the adjusted thickness remains an input; Di remains calculated.

This distinction matters: target seeking found a suitable input; it did not necessarily exchange the future input/output roles. Di may therefore change again after a later edit.

Route B: prescribe inside diameter persistently

1. In a copy of the initial state, release the existing wall-thickness constraint using the release action.
2. Then prescribe Di = 580 mm independently while retaining Da = 600 mm.
3. Verify that Di is now an input and se is calculated. The geometry again gives approximately 10 mm.
4. Review the other assessments and messages after changing thickness. Material properties or allowances may depend on thickness.

The associated B1 inverse-calculation video and saved field-role comparison date from 6 September. The fresh run for this handbook checks the pressure chain, not that entire inverse workflow again. Values around 9.999998 mm in the saved example are numerical approximations to 10 mm, not a meaningful manufacturing tolerance.

Watch the complete operating workflow

English interface, bilingual overlays and subtitles. Video requires Internet access; instructions, images and example files are stored locally. Open video directly.

Chapter 12B3: head shape, knuckle, crown and straight flange

Choose the construction first

B3 includes Klöpper, Korbbogen and hemispherical heads and different pressure types. Shape and pressure type are separate selectors. The image's general chapter title retains a broader English description; for the illustrated case, the actual “Torispherical head (Kloepper type)” selection governs. Read the selected configuration, not only the heading.

A knuckle joins the crown to the cylindrical edge region. Loading is not uniform across those regions. B3 therefore provides thicknesses and conditions for different parts of the head. One crown result does not automatically settle the knuckle or straight-flange assessment.

Reproduce the teaching case

1. Select a Klöpper head under internal pressure. Check the manufacturing option: the example treats knuckle and crown as having equal thickness.
2. Check Da = 600 mm, p = 1.5 bar and p′ = 2 bar. V4 = 120 mm belongs to the opening topic, not temperature.
3. In the material section, check T = 120 °C and the actual selected material record.
4. Check 8 mm final knuckle thickness and the crown thickness resulting from this manufacturing option.
5. Read allowances, safety factors and joint efficiency. B3:c1 = 0 mm is part of the demonstration state, not a general recommendation.
6. Open results: distinguish the calculation basis, operation/testing and the additional conditions.

Associate results correctly

In the checked case, V1 gives required knuckle thickness and V2 gives required crown thickness in the assessed branch. V32 summarises the thickness requirement there. After changing pressure they are approximately 1.06875 mm, 0.627199 mm and 1.06875 mm. The mask can show another preliminary thickness result above them. The “based on the final wall thickness” heading explains why similarly named fields need not be identical.

Actual straight-flange thickness, required straight-flange thickness and influence length are also separate quantities. The visible strength condition is a result. It is not satisfied by attempting to activate a checkbox. With incomplete inputs, a condition may remain unknown; that is not a confirmed pass.

External pressure and openings

External pressure changes the governing conditions. The inspected source contains quantities for elastic modulus, buckling safety and plastic instability, among others. Do not copy internal-pressure results into an external-pressure case. This first edition does not include a freshly checked complete external-pressure example.

Opening diameters, location zones and, where applicable, neighbouring openings affect specific conditions. The example's maximum nozzle diameter does not establish adequacy for arbitrary position and loading. A real nozzle's location, shape, reinforcement and possible additional loads must match the chosen assessment method.

B3: the selection defines the task

123

Chapter 13B9: openings and contributing regions

Shell and opening type define the scope

The inspected B9 catalogue provides single and adjacent opening configurations. The mask also distinguishes parent-shell shape, load condition, opening type and reinforcement. The teaching case is explicitly a single plain opening without reinforcement in a cylindrical shell. It is not a complete reinforced welded-nozzle example.

The displayed assessment broadly compares pressure loading with the contributing cross-sectional area and associated strength assumptions in the relevant section. It does not count all metal present anywhere around the opening. Geometric limits determine which widths and regions may contribute.

Sequence for the teaching case

1. Select a cylindrical body, single opening and operation as the assessed condition.
2. For opening 1, verify “Opening” and reinforcement “No”. Do not accidentally enable a nozzle or reinforcement branch.
3. Check 120 °C and initially 1.5 bar; pressure will later be received from B1.
4. Check parent-shell material and its strength/safety assumptions.
5. Check Da = 600 mm, final shell thickness 8 mm, c1 = 0.3 mm and c2 = 0 mm.
6. Check opening inside diameter 80 mm and available effective shell width 100 mm.
7. Read analysis thickness, diameter definitions, contributing area and utilisation; do not skip messages or geometric conditions.

Three easily confused quantities

Diameter: V61 is the example's final inside diameter, 584 mm. V9 uses an analysis/corroded definition and gives 584.6 mm. Different values are not automatically a transfer error here.

Thickness: V13 is the final shell thickness, 8 mm. V247 is analysis thickness, 7.7 mm. V1 describes analysis thickness at the opening edge and shows 8 mm in this state. Field names and references matter more than expecting the same number everywhere.

Width: V493 limits the available effective shell width. The result image shows an actually contributing width of about 67.533 mm. Entering 100 mm does not force the method to credit all 100 mm. It does not describe a welded reinforcement pad either.

Multiple sections make multiple statements

V476 to V482 refer to different assessment directions, openings and interactions. Which are applicable and visible depends on the configuration. A second opening requires consideration of spacing, direction, geometry and possibly different materials. The single checked section cannot establish the adequacy of adjacent openings.

Materials and additional loads

Where the construction requires them, the source supplies the parent shell, nozzle 1, reinforcement 1, nozzle 2 and reinforcement 2 separately. Only active, physically present components may be interpreted as contributing. This pressure experiment does not assess additional piping forces and moments; a suitable additional-load assessment may be needed.

B9 is not B9N

The inspected catalogue lists B9 with a B9:2023-03 basis and B9N with an older B9 basis. B9N is a separate execution token with different configurations. Do not blindly transfer variable numbers or saved expectations between them. For archive comparisons, always record the actual identifier, construction and source version.

B9: single plain opening

123

B9: utilisation and contributing width

12

Chapter 14Build meaningful variants and parameter studies

A variant changes a justified design assumption; it is not merely another column of numbers. First state what must remain fixed, what may change and which results matter. For example, external geometry may be fixed while available thicknesses are explored. In another case, thickness is fixed by available pipe and allowable pressure is the desired output.

A controlled learning exercise

1. Save the starting project under a new name.
2. Change only the common B1 pressure and verify reception in B3/B9.
3. For each state, record pressure, thickness results and relevant utilisation together with warnings.
4. Return to 1.5 bar and check whether the same starting results are recovered.
5. Only then investigate a second influence. Do not change material, construction, geometry and pressure simultaneously when trying to understand a difference.

The tutorials also demonstrate starting a parameter study through a supported entry sequence such as 1,2...3. Inspect the actual generated study points and units before interpreting results. This handbook does not claim a freshly verified B1/B3/B9 series using that syntax; the checked connection experiment uses two individual pressure states.

A curve point is meaningful only when its assumptions fit the model and the associated assessment is evaluable. Do not interpret hidden, unknown or aborted points as zeros. Save a complete project for interesting variants, not merely a screenshot.

Chapter 15Save, reopen and investigate differences

A reproducible state needs more than final numbers

Save a short note with the project: identifiers and constructions, program/data version, material selection, changed constraints, connections and outstanding messages. For inverse calculation, record which variable was released. Two projects with identical visible numbers can contain different constraints and react differently to the next edit.

1. Save the edited state under a new filename.
2. Reopen it in a separate demo environment without replacing unsaved work.
3. Check source/destination values and input/calculated roles.
4. Check links at the destination variables; matching initial numbers are insufficient.
5. Repeat a known edit and verify the reference results.

The supplied end file is the saved state from the existing video. The fresh pressure-chain run reopened the starting file, created links and checked results; it does not establish a new independent save/reopen roundtrip. The evidence keeps these scopes separate.

When a value differs

Start with the first differing input or intermediate quantity, not the final percentage. Check construction, unit, material state, allowances, actual geometry, field role, connection origin and load case in turn. Compare displayed rounding with internally recorded precision. An old archive can itself contain an incompletely resolved state.

A useful defect report includes the smallest reproducible project copy, initial state, exact action, expected/observed result, identifier and variable number. Review confidential data before sharing; the supplied files here are dedicated tutorial cases.

Chapter 16Review results and hand over the work

Review record for a connected project

1. Task: Are component, spaces, loads and design boundaries clearly described?
2. Basis: Are actual modules, constructions and implemented method versions recorded?
3. Inputs: Are units, materials, temperatures, pressures and manufacturing assumptions correct?
4. Geometry: Are shared dimensions consistent? Are different allowances justified?
5. Connections: Does each common quantity have an unambiguous source? Are independent load cases kept separate?
6. Results: Have operation/testing, required/actual quantities and all relevant sections been reviewed?
7. Completeness: Are there unknown conditions, warnings or additional assessments outside the three teaching modules?
8. Change check: Do affected chapters reach the expected state after a source edit?
9. Handover: Are project file, report, open issues and responsible review stored together?

The software supports the work but cannot infer every unknown condition in your plant. A pressure vessel can remain inadequately assessed despite substantial static thickness margin if a load case is omitted or a method is applied outside its scope.

A report, not a heap of numbers

Organise output by component and load case. Give chapters meaningful names, such as “Shell A”, “Upper head A” and “Opening N1 in shell A”. Explain the common pressure source and document intentional differences. Keep outstanding assessments visible; a clearly stated open issue is more useful than an unsupported green overall verdict.

Chapter 1720 practical questions

Chapter 18Terms and field roles

Chapter 19B1 / B3 / B9 field reference

Selected operating and result fields. Numbers are meaningful only together with the identifier. Units and example values, where present, come from the freshly loaded starting case; “—” means not presented here as a numeric example. This does not claim complete documentation of all internal, conditional or hidden fields.

B1

B3

B9

Chapter 20Sources, evidence and limits of this edition

Documentation basis

Web source: main13.0 / 38cc72859ed8a9cd0d1c88dcd3d05a85aab78e44. Desktop/module source: fix-iteration/v10 / 40606b705b2df95e550ffef5e98ab733ccc66229. The review covered package registration, module descriptions and selected mask/calculation areas of B1, B3 and B9. The source snapshot records paths and SHA-256 hashes of the files used. Not every equation in every one of the 45 package modules was individually verified as an engineering method.

Fresh local replay

On 7 September 2026, a separate browser demo project was created, the saved starting case reopened, both pressure connections established and the change to 3 bar checked. Seven result quantities across three modules matched the recorded targets. The exact version of the already running plugin binaries was not independently identified. The source commits above are therefore not presented as proven runtime versions.

Runtime evidence · Image provenance · File and scope manifest. The six screenshots come from this owned run. Demo-licence notices and message areas have not been retouched. Highlights are separate HTML elements; the original images remain accessible.

Historical supporting material

The pressure-chain video, saved video end state and inverse-calculation video date from 6 September 2026. The pressure reference compares linked and individually edited chapters in the same calculation environment. The documentation makes no claim of independent Desktop parity or comprehensive code verification.

Not yet covered by a complete detailed guide

Other AD modules, B3 external pressure, B9 adjacent/reinforced openings, additional loads and complete load-case combinations require their own checked examples and individual guides. Placement in the package map does not complete those tasks. For other calculation bases, see EN 13445 – Pressure vessel calculations and ASME – Pressure vessel calculations. The existing WTS handbook remains available as a separate thermal-design learning path.