CALCULATORS / BEAMS, PLATES AND STRUCTURAL SCREENING

Simply supported beam calculator

Simply supported rectangular beam with central point load.

structures-simply-supported.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	inertiamm^4	deflectionmm
	312500	0.333333
	312500	0.170667

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.

deflection budget0.33 mm✓ passes

BASELINE INPUTS

length1 mwidth30 mmdepth50 mmload1000 Nmodulus200 GPa

CALCULATED

inertia312500 mm^4

deflection0.33333 mm

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Simply supported beam
# Scope: Simply supported rectangular beam with central point load.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

length = 1 m
width = 30 mm
depth = 50 mm
load = 1000 N
modulus = 200 GPa

inertia := width*depth^3/12 [mm^4]
deflection := load*length^3/(48*modulus*inertia) [mm]

check deflection budget: deflection <= 2 mm

scenario alternative: length = 0.8 m

Calculated from your source · not saved

Baseline · 1 m reach · 50 mm depth

deflection budget0.33 mm ✓ passes

alternative · 0.8 m reach · 50 mm depth

deflection budget0.17 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/(48*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: 1 m
width: 30 mm
depth: 50 mm
load: 1000 N
modulus: 200 GPa

Calculated

inertia: 312500 mm^4
deflection: 0.333333 mm

Assumptions and limits

Simply supported rectangular beam with central point load.

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: Simply supported beam. Inputs: span; section; load locations; modulus. Outputs: deflection; bending moments. 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: span, section, load locations, modulus
Outputs: deflection, bending moments
Modes: calculate, compare, sweep
Drawing: Deflection and stress diagram

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