Engineering · Stress, Failure & Materials

Thermal Expansion and Restraint Stress Workbench Calculator

Compare free thermal movement, fully restrained uniaxial thermal stress and differential expansion between two explicitly entered materials.

Engineering · Stress, Failure & Materials

Enter the engineering model

Explicit properties, geometry, units and assumptions
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
Try an example
Visual modelSchematic · not to scale
Stress, Failure & Materials: free visual explanationA simplified diagram showing the relationship represented by the selected calculator mode. It is explanatory and not a fabrication, safety or scale drawing.free thermal length changetemperature change → thermal strain αΔT
The diagram explains the selected relationship only. Dimensions, symbols and proportions are illustrative; use the entered values and stated assumptions for the calculation.

Keep every unit basis, sign convention, property source and idealization consistent. Values stay in this browser.

Engineering calculation result

Enter valid values to see the result.

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Understand the model

What this calculator is for

Temperature change first creates a free strain. Stress appears only when movement is restrained, so this workbench deliberately separates movement from the ideal fully restrained case.

1Use the signed temperature change.
2Choose free, restrained or differential behavior.
3Do not treat ideal full restraint as the behavior of an unknown support system.

Visual explanation

Picture a member that can slide freely, then the same member locked between rigid supports. The temperature change is identical; the mechanical response is not.

The governing relationship

Free movement ΔL=αLΔT. Ideal full-restraint stress magnitude is EαΔT. Differential movement is L(α1−α2)ΔT.

Keep the boundary visible

Uniform temperature, constant properties and ideal axial behavior only. Restraint stiffness, creep, yielding, buckling, joints, gradients, cyclic damage and code combinations are excluded.

Quick guide

How to use this calculator

  1. Choose the analysis mode that matches the physical model before entering values.
  2. Enter properties, geometry, loads, states and coefficients from one consistent unit and sign convention.
  3. Use the intermediate outputs to audit the relationship, then retain the stated idealization before applying it.

Calculation method

Transparent engineering model

Free movement ΔL=αLΔT. Ideal full-restraint stress magnitude is EαΔT. Differential movement is L(α1−α2)ΔT.

The calculator evaluates only the declared relationship and preserves visitor-entered assumptions rather than selecting materials, factors, components or standards.

Worked example

Worked example

A 10 m member with α=12×10⁻⁶/°C and ΔT=40°C has 4.8 mm of free thermal movement.

Free movement ΔL=αLΔT. Ideal full-restraint stress magnitude is EαΔT. Differential movement is L(α1−α2)ΔT.

Supported inputs

Precision and limits

Analysis, not approval

Uniform temperature, constant properties and ideal axial behavior only. Restraint stiffness, creep, yielding, buckling, joints, gradients, cyclic damage and code combinations are excluded.

Standards and properties

Material properties, allowable values, load combinations, safety factors, correlations, manufacturer data, codes and jurisdictional requirements are not supplied automatically.

Units and precision

Use one consistent unit basis. Results retain working precision but cannot be more accurate than the entered measurements and properties.

Privacy

Entered engineering values and results stay in this browser and are not sent to analytics or third parties.