CALCULATORS / SHAFTS, COUPLINGS AND ROTATING ASSEMBLIES

Combined shaft bending and torsion calculator

Solid circular shaft bending and torsion; von Mises screen.

shafts-combined-load.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	bendingMPa	shearMPa	equivalentMPa
	30.1805	7.54512	32.8884
	24.1444	7.54512	27.4543

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.

equivalent stress budget32.89 MPa✓ passes

BASELINE INPUTS

moment10 N*mtorque5 N*mdiameter15 mm

CALCULATED

bending30.18 MPa

shear7.5451 MPa

equivalent32.888 MPa

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Combined shaft bending and torsion
# Scope: Solid circular shaft bending and torsion; von Mises screen.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

moment = 10 N*m
torque = 5 N*m
diameter = 15 mm

bending := 32*moment/(pi*diameter^3) [MPa]
shear := 16*torque/(pi*diameter^3) [MPa]
equivalent := sqrt(bending^2+3*shear^2) [MPa]

check equivalent stress budget: equivalent <= 100 MPa

scenario alternative: moment = 8 N*m

Calculated from your source · not saved

Baseline · Baseline

equivalent stress budget32.89 MPa ✓ passes

alternative · alternative

equivalent stress budget27.45 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.

bending: bending = 32*moment/(pi*diameter^3) [MPa]
shear: shear = 16*torque/(pi*diameter^3) [MPa]
equivalent: equivalent = sqrt(bending^2+3*shear^2) [MPa]

Original worked example

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

Given

moment: 10 N*m
torque: 5 N*m
diameter: 15 mm

Calculated

bending: 30.1805 MPa
shear: 7.54512 MPa
equivalent: 32.8884 MPa

Assumptions and limits

Solid circular shaft bending and torsion; von Mises screen.

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: Combined shaft bending and torsion. Inputs: bending moment; torque; geometry. Outputs: combined stress; diameter screening. Model scope: Elastic shaft models and specified supports. 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: bending moment, torque, geometry
Outputs: combined stress, diameter screening
Modes: calculate, compare, sweep
Drawing: Shaft load diagram

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