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CALCULATORS / BEAMS, PLATES AND STRUCTURAL SCREENING

Thick-wall cylinder elastic stress calculator

Lame inner-surface hoop stress; outer pressure zero and long elastic cylinder.

structures-thick-wall-pressure.napkin / editable
✓ checks pass

SCENARIO COMPARISON

Compare the numbers.

This source describes an analytical model. Its quantities and checks are the view.

ScenariohoopMPa
26
20.8

All calculated quantities are listed with the inputs. Switch to Source to inspect the equations.

SCENARIOS / CALCULATED VALUESSAME SOURCE

Change an input to see the consequences.

stress budget26.00 MPa✓ passes

BASELINE INPUTS

CALCULATED

hoop26 MPa

Edits change the baseline source.

Calculated from your source · not saved
Baseline · Baseline
stress budget26.00 MPa ✓ passes
alternative · alternative
stress budget20.80 MPa ✓ passes

Illustrative first-order example. Checks are editable requirements, not design standards. The broader topic may require additional equations, data, and validation.

Formula and units

This example uses the following equations. Input names and units match the editable source above.

hoop
hoop = pressure*(outer^2+inner^2)/(outer^2-inner^2) [MPa]

Original worked example

These are the baseline values in the downloadable source. Edits above let you test your own values.

Given

pressure
10 MPa
inner
20 mm
outer
30 mm

Calculated

hoop
26 MPa

Assumptions and limits

Lame inner-surface hoop stress; outer pressure zero and long elastic cylinder.

The requirement checks use the limits written in this example. Passing a check does not establish that the model covers every load, material behavior, or operating condition in a real design.

Download this .napkin example ↓

Take it further with your agent

Napkin keeps the inputs, equations, checks and assumptions together in one study. Your agent sets it up; you change the numbers.

Try with Claude ↗

codex 'Use Napkin (https://napkin.engineering/mcp, or the local Napkin plugin) to build a study: Thick-wall cylinder elastic stress. Inputs: inner and outer radii; pressures; material. Outputs: radial and hoop stress profiles. Model scope: Linear elastic idealizations and stated boundary conditions. Read napkin_capabilities and the current snapshot. Ask me for the values that matter, label assumptions with units, author .napkin source, validate it and apply it with napkin_source using the current revision, then open the study. Add checks for the limits I supply. Keep unsupported analyses explicit.'

Claude needs the Napkin connector; Codex needs the Napkin plugin. Set up your agent ↗

The broader study

The topic brief below describes the broader scope. The worked example above states the particular calculation it implements.

  • Inputs: inner and outer radii, pressures, material
  • Outputs: radial and hoop stress profiles
  • Modes: calculate, compare, sweep
  • Drawing: Deflection and stress diagram

EXECUTABLE WORKED EXAMPLE · FIRST-ORDER MODEL · CHECK THE SCOPE & ASSUMPTIONS

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