📏 Materials Engineering & Solid Mechanics
Linear & Volumetric Thermal Expansion Calculator
Compute dimensional change ($\Delta L = \alpha L_0 \Delta T$), volumetric growth ($\Delta V \approx 3\alpha V_0 \Delta T$), and constrained thermal stress ($\sigma = E \alpha \Delta T$) in engineering materials.
⚙️ Structural Steel ($12 \times 10^{-6}$)
🔩 Aluminum ($23.1 \times 10^{-6}$)
🥉 Copper ($16.5 \times 10^{-6}$)
🧪 Pyrex Glass ($3.3 \times 10^{-6}$)
💎 Invar Alloy ($1.2 \times 10^{-6}$)
🧱 Concrete ($12.0 \times 10^{-6}$)
Material & Dimensions
1 / °C
°C (or K)
GPa (Steel = 200 GPa)
Length Expansion (ΔL)
+6.00 mm
Strain ($\Delta L / L_0$)
0.0600% (600 με)
Constrained Stress
120.0 MPa
Volumetric Growth
+0.180% (3α)
💡 Engineering Application:
A 10m steel member heated by 50°C expands by 6.00 mm. If clamped between rigid immovable abutments, it develops a massive compressive thermal stress of 120 MPa (requiring bridge expansion joints).
Thermal Expansion Mechanics
Thermal energy increases the average atomic vibrational separation distance in crystal lattices:
- Linear Expansion: $$\Delta L = \alpha \cdot L_0 \cdot \Delta T$$
- Volumetric Expansion (Isotropic Solids): $$\Delta V = \beta \cdot V_0 \cdot \Delta T \approx 3\alpha \cdot V_0 \cdot \Delta T$$
- Constrained Thermal Stress: $$\sigma = E \cdot \varepsilon = E \cdot \alpha \cdot \Delta T$$