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CALCULATORS / BEAMS, PLATES AND STRUCTURAL SCREENING

Beam deflection calculator

Aluminium cantilever · fixed at one end

structures-beam-deflection.napkin / editable
✓ checks pass
Cantilever: 0.72 mm tip deflection, displacement shown at 30 times actual size.CantileverF = 20 Nδ = 0.72 mmL = 300 mm
Current, unloadedDeflected ×30
XZ / DEFLECTION EXAGGERATED ×30FIXED END ALIGNED

Cantilever selected · related inputs are marked.

tip deflection0.72 mm✓ passes

BASELINE INPUTS

CALCULATED

inertia3600 mm^4
deflection0.72464 mm

Edits change the baseline source.

Calculated from your source · not saved
Baseline · 300 mm reach · 12 mm depth
tip deflection0.72 mm ✓ passes
more reach · 500 mm reach · 12 mm depth
tip deflection3.35 mm × fails
deeper section · 500 mm reach · 20 mm depth
tip deflection0.72 mm ✓ 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]
deflection
deflection = load * length^3 / (3 * modulus * inertia) [mm]

Original worked example

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

Given

length
300 mm
width
25 mm
depth
12 mm
load
20 N
modulus
69 GPa

Calculated

inertia
3600 mm^4
deflection
0.724638 mm

Assumptions and limits

Aluminium cantilever · fixed at one end

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: Beam deflection. Inputs: section stiffness; span; supports; load pattern. Outputs: maximum deflection; slope; bending stress. 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: section stiffness, span, supports, load pattern
  • Outputs: maximum deflection, slope, bending stress
  • Modes: calculate, compare, sweep
  • Drawing: Deflection and stress diagram

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

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