KEVOS® MAKEOS · Strength
Restrained Thermal Stress
What stress and force build up if this member is prevented from expanding?
Stress and force in a bar or pipe whose thermal expansion is fully or partly restrained, compared with the yield strength.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Elastic modulus | GPa | Elastic modulus from the material data sheet or an approved materials database (steel is typically about 200 GPa). |
| Expansion coefficient | µm/(m·K) | Linear expansion coefficient over the temperature range, from material data. |
| Temperature change | K | Change from the temperature at which the member was fixed (positive for heating). |
| Degree of restraint | % | 100% if the ends cannot move at all; less if supports allow some movement. |
| Cross-section area | mm² | Cross-section area of the member. |
| Yield strength | MPa | Minimum yield strength from the material certificate or specification, not a typical value. |
Method and formulas
- Unrestrained strain ε = α ΔT.
- Stress σ = E α ΔT × restraint (compressive when heated).
- Force on restraints = σ A.
- Example: steel heated 60 K with full restraint reaches 144 MPa and pushes on its anchors with 288 kN.
Limitations
- Uniform temperature through the section; temperature gradients create additional stresses.
- Slender members may buckle before reaching the calculated compressive stress (check with the column buckling tool).
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check rails, pipes and frames fixed at both ends
- Estimate anchor loads from heating
- Decide whether an expansion joint is needed
Who it is for
- Design engineers
- Structural and mechanical engineers
- Engineering students
What you get
- Thermal stress
- Axial force on the restraints
- Unrestrained expansion strain
- Safety factor against yield
Interpreting the result
- If the stress approaches yield or the member is slender, allow movement or add an expansion joint.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 375–376, 578. Topic reference; no source tables or recommended settings are reproduced.
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