Materials expand when heated. If they cannot – rails welded end to end, pipes fixed between walls – the blocked expansion turns into stress. Expansion joints in bridges and pipelines prevent it.
How to use the Thermal Stress Calculator
- Material
- Thermal expansion coefficient α (10⁻⁶/K)
- Young’s modulus E
- Initial temperature T_i
- Final temperature T_f
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose the material (or enter α and E) and the initial and final temperatures. Negative stress is compression (heating), positive is tension (cooling).
Inputs explained
| Field | What to enter |
|---|---|
| Material | Choose one: Aluminium, Brass, Copper, Gold … |
| Thermal expansion coefficient α (10⁻⁶/K) | A number |
| Young’s modulus E | Units: GPa, MPa, Pa, psi, Mpsi |
| Initial temperature T_i | Units: °C, °F, K |
| Final temperature T_f | Units: °C, °F, K |
What each result means
- Thermal stress σ = -[E]×[alpha]×([Final temperature T_f] – [Initial temperature T_i])
- Blocked thermal strain = [alpha]×([Final temperature T_f] – [Initial temperature T_i])
Example values
How the main result changes when Thermal expansion coefficient α changes and everything else stays at the example values above:
| Thermal expansion coefficient α (10⁻⁶/K) | Thermal stress σ (MPa) |
|---|---|
| 6 | -96 |
| 9 | -96 |
| 12 | -96 |
| 15 | -96 |
| 18 | -96 |
| 24 | -96 |
Formula
σ = −E·α·ΔT, ΔT = T_f − T_i
Worked example
Inputs — Material: Structural steel; Initial temperature T_i: 20 °C; Final temperature T_f: 60 °C.
Results — Thermal stress σ = -96 MPa; Blocked thermal strain = 0.00048; Type = Compression.
Key terms
- Coefficient of thermal expansion
- Fractional length change per degree.
Frequently asked questions
Why do railway tracks buckle in heat?
Restrained expansion creates large compressive stress.
How much stress per degree in steel?
About 2.4 MPa per °C.
Does an unrestrained bar have thermal stress?
No – it simply expands freely.
How are thermal stresses avoided?
Expansion joints, loops and sliding supports.