Beam support reactions calculator

Simply supported beam with one point load within the span.

statics-support-reactions.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	rightReactionN	leftReactionN
	40	60
	32	48

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.

load inside supports0.40 m✓ passes

BASELINE INPUTS

load100 Nspan1 mposition0.4 m

CALCULATED

rightReaction40 N

leftReaction60 N

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Beam support reactions
# Scope: Simply supported beam with one point load within the span.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

load = 100 N
span = 1 m
position = 0.4 m

rightReaction := load*position/span [N]
leftReaction := load-rightReaction [N]

check load inside supports: position <= span

scenario alternative: load = 80 N

Calculated from your source · not saved

Baseline · Baseline

load inside supports0.40 m ✓ passes

alternative · alternative

load inside supports0.40 m ✓ 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.

right reaction: rightReaction = load*position/span [N]
left reaction: leftReaction = load-rightReaction [N]

Original worked example

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

Given

load: 100 N
span: 1 m
position: 0.4 m

Calculated

right reaction: 40 N
left reaction: 60 N

Assumptions and limits

Simply supported beam with one point load within the span.

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 support reactions. Inputs: loads; load positions; supports. Outputs: support forces and moments. Model scope: Rigid-body, quasistatic equilibrium. 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: loads, load positions, supports
Outputs: support forces and moments
Modes: calculate, compare, sweep
Drawing: Free-body diagram

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