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CALCULATORS / BEAMS, PLATES AND STRUCTURAL SCREENING

Column buckling calculator

Euler ideal pin-pin column; no imperfections or material yield

structures-column-buckling.napkin / editable
✓ checks pass

SCENARIO COMPARISON

Compare the numbers.

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

Scenarioinertiamm^4criticalLoadN
32552.164255.2
32552.128557.9

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.

required load64255.24 N✓ passes

BASELINE INPUTS

CALCULATED

inertia32552 mm^4
criticalLoad64255 N

Edits change the baseline source.

Calculated from your source · not saved
Baseline · 1000 mm reach · 25 mm depth
required load64255.24 N ✓ passes
longer · 1500 mm reach · 25 mm depth
required load28557.88 N ✓ 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.

inertia
inertia = width * depth^3 / 12 [mm^4]
critical load
criticalLoad = pi^2 * modulus * inertia / length^2 [N]

Original worked example

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

Given

length
1000 mm
width
25 mm
depth
25 mm
modulus
200 GPa

Calculated

inertia
32552.1 mm^4
critical load
64255.2 N

Assumptions and limits

Euler ideal pin-pin column; no imperfections or material yield

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: Column buckling. Inputs: length; end conditions; section; modulus. Outputs: critical load; slenderness. 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: length, end conditions, section, modulus
  • Outputs: critical load, slenderness
  • Modes: calculate, compare, sweep
  • Drawing: Deflection and stress diagram

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

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