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CTE (α) measures how much a material changes size per degree of temperature change. Units: µm/(m·°C) or equivalently 10⁻⁶/°C.

Example: Steel α ≈ 12 means a 1-meter bar grows 12 µm (0.012 mm) for each 1°C rise. Over 100°C, that's 1.2 mm — significant for precision machinery and piping.

When a member is fully restrained (can't expand freely), the thermal stress is:

σ = E × α × ΔT

For carbon steel at ΔT = 100°C: σ = 200,000 MPa × 12×10⁻⁶ × 100 = 240 MPa. This is close to the yield strength! Always check that constrained thermal stresses don't exceed allowable values.

Linear: Change in one dimension. ΔL = α × L₀ × ΔT

Volumetric: Change in volume. ΔV ≈ 3α × V₀ × ΔT (for isotropic materials).

Volumetric expansion matters for enclosed fluids (tanks, pipes), sealed containers, and precision assemblies.

Guided-cantilever formula: L = √(3 × E × D × Δ / Sₐ) with E in MPa, D and Δ in mm, Sₐ in MPa (L in mm). Rule of thumb for carbon steel (E ≈ 200 GPa, Sₐ ≈ 138 MPa): L ≈ 66 × √(D × Δ) where D = pipe OD (mm) and Δ = expansion (mm).

For DN100 pipe (OD 114 mm) with 6 mm expansion: L ≈ 66 × √(114 × 6) ≈ 1,700 mm ≈ 1.7 m.

Alternatives to loops: bellows expansion joints, sliding supports, changes of direction in routing.

Yes. CTE generally increases with temperature. The values in our database are mean values for the 20–100°C range.

• Cryogenic: CTE is lower (sometimes much lower)
• High-temp (>500°C): CTE increases 10–30% above room-temp values
• Near phase changes: CTE can change dramatically

For critical applications, use specific material data from standards (ASME II-D, EN 13480) for your exact temperature range.