Thermal Expansion Calculator
Length change (mm)
1.2
How it works
Materials expand when heated and contract when cooled. Linear thermal expansion: ΔL = α × L₀ × ΔT, where α is the linear thermal expansion coefficient (per °C), L₀ is original length, and ΔT is temperature change. Volumetric expansion ≈ 3 × linear expansion for isotropic materials.
**Coefficients of linear thermal expansion** Steel: 11–13 × 10⁻⁶/°C. Aluminum: 23 × 10⁻⁶/°C (nearly 2× steel). Concrete: 10–12 × 10⁻⁶/°C (close to steel — why rebar works). Invar (FeNi alloy): 1.2 × 10⁻⁶/°C (designed for dimensional stability). Fused silica: 0.55 × 10⁻⁶/°C. PTFE: 112–200 × 10⁻⁶/°C (very high — must be accommodated in PTFE-lined equipment).
**Engineering implications** A 100m steel bridge expands 13mm for each 10°C temperature change. Expansion joints in bridges, pipelines, and railroad tracks accommodate this movement. Bimetallic strips (two metals with different expansion coefficients bonded together) curl when heated — the basis for mechanical thermostats and overheat protection.
**Precision machining and thermal effects** In metrology (precision measurement), parts must be measured at standard temperature (20°C). A 1m steel part measured at 30°C is actually 0.12 mm longer than indicated at 20°C. Gauge blocks and precision instruments are stored at controlled temperature and allowed to stabilize before use.
**Thermal stress in constrained systems** When thermal expansion is restrained, stress builds: σ = E × α × ΔT. For steel at ΔT = 100°C: σ = 200,000 MPa × 12×10⁻⁶ × 100 = 240 MPa. This approaches yield stress. Unconstrained expansion joints, slip-in-sleeve connections, and flexible couplings prevent thermal overstress.
Frequently Asked Questions
- ΔL = α × L₀ × ΔT. Steel α ≈ 12 × 10⁻⁶/°C. A 500 m bridge experiencing 50°C seasonal temperature swing: ΔL = 12×10⁻⁶ × 500 × 50 = 0.30 m = 300 mm. This is 12 inches of movement — significant enough to cause serious damage without expansion joints. US bridges typically have joints every 30–100 m, each accommodating ±15–30 mm. Some long concrete structures use the 'integral abutment' design — flexible approach spans absorb movement without traditional joints, reducing maintenance.
- Concrete and steel have nearly identical thermal expansion coefficients: concrete ≈ 10–12 × 10⁻⁶/°C, steel ≈ 11–13 × 10⁻⁶/°C. This is one of the most fortunate coincidences in structural engineering — it's why reinforced concrete works for temperature variations. If their coefficients differed significantly (as would happen using aluminum rebar), thermal cycling would create shear stresses at the steel-concrete interface, progressively cracking the concrete. This compatibility is a fundamental requirement — most non-steel reinforcements (basalt, GFRP) are chosen partly for similar thermal expansion.
- Piping systems use: expansion loops (U-shaped pipe sections that flex as the pipe expands), expansion joints (bellows that compress/extend), slip joints (one pipe slides inside another), and anchors/guides (controlling where movement occurs). A 100 m steam pipe at 200°C (ΔT = 180°C): ΔL = 12×10⁻⁶ × 100 × 180 = 216 mm. Every design must account for this movement — rigidly constrained pipes at high temperature will develop enormous stresses (σ = E × α × ΔT) and will fail. Pipe stress analysis software calculates thermal stresses in complex piping systems.
- Invar (64% iron, 36% nickel) has α ≈ 1.2 × 10⁻⁶/°C — about 1/10 of steel. This near-zero expansion coefficient (over 0–100°C) makes Invar essential for: precision instruments (scientific balances, clocks, surveying equipment), laser resonator mounts (stability is critical), bimetallic strip bases, and LNG tanker membrane panels. The zero-expansion arises from a quantum-mechanical magnetovolume effect that cancels normal thermal expansion in this specific alloy. Zerodur glass-ceramic achieves α ≈ 0.02 × 10⁻⁶/°C — used for telescope mirrors.