Materials expand when heated and contract when cooled. This dimensional change affects fits, clearances, and stresses in assemblies. Understanding thermal expansion helps you design for temperature variations and solve fit problems in the shop.
The Thermal Expansion Formula
Linear expansion:
ΔL = α × L × ΔT
Where:
- ΔL = Change in length
- α = Coefficient of linear expansion (CTE)
- L = Original length
- ΔT = Temperature change
Coefficient of Thermal Expansion (CTE)
CTE values in 10⁻⁶ per °F (multiply by 1.8 for per °C):
| Material | CTE (×10⁻⁶/°F) |
|---|---|
| Aluminum | 13.0 |
| Brass | 10.4 |
| Copper | 9.2 |
| Carbon Steel | 6.5 |
| Stainless 304 | 9.6 |
| Cast Iron | 5.9 |
| Invar | 0.7 |
| Titanium | 4.8 |
Calculate Thermal Expansion
Enter material, length, and temperature change to find dimensional change. Includes common material CTE values.
Example Calculation
A 24" aluminum bar heated from 70°F to 200°F:
ΔL = 13.0 × 10⁻⁶ × 24 × (200 - 70)
ΔL = 13.0 × 10⁻⁶ × 24 × 130
ΔL = 0.0406" (about 1mm)
For precision fits, this is significant.
Practical Applications
Shrink Fits
Heat the outer part to expand it, then assemble. As it cools, it contracts onto the inner part creating interference:
ΔT = Interference / (α × Diameter) + Clearance for Assembly
Or cool the inner part (using liquid nitrogen or dry ice) for the same effect.
Expansion Joints
Long runs of pipe or structural members need room to expand:
- Steam lines can grow several inches over long runs
- Railroad tracks have gaps between rails
- Bridges have expansion joints at ends
Bimetallic Effects
When dissimilar materials are joined and heated:
- Steel bolt in aluminum housing loosens when heated
- Aluminum shaft in steel bearing tightens when heated
- Weldments of dissimilar metals distort
Measurement Implications
Precision measurements must account for temperature:
- Standard temperature is 68°F (20°C)
- A 10" steel gage at 90°F reads 0.00015" long
- Precision parts should be measured at ambient equilibrium
- Compare parts and gages at the same temperature
Design Strategies
Accommodate Expansion
- Use slots instead of holes for one fastener position
- Allow clearance for expected growth
- Use flexible connections (bellows, loops)
Minimize Differential
- Use matched materials (same CTE)
- Keep temperature gradients small
- Invar for precision applications where stability is critical
Stress from Restraint
If expansion is restrained, stress develops:
σ = E × α × ΔT
Where E is modulus of elasticity. A steel bar restrained over a 100°F change develops about 19,000 psi stress—significant for design.
Common Mistakes
- Ignoring thermal effects: "It's only a few thousandths"—often matters for fits
- Wrong units: CTE per °F vs. per °C differs by 1.8×
- Average vs. instantaneous: CTE varies with temperature; use appropriate values
- Asymmetric heating: Parts warp if heated unevenly
Thermal expansion is predictable physics. Accounting for it in design and measurement prevents surprises in assembly and operation.
