Thermal Expansion Strain Calculator Formula
Understand the math behind the thermal expansion strain calculator. Each variable explained with a worked example.
Formulas Used
Thermal Strain (epsilon)
thermal_strain = alpha_per_c * delta_tLength Change (delta L)
length_change = alpha_per_c * delta_t * lengthThermal Stress if Fully Constrained (E=200 GPa)
thermal_stress = alpha_per_c * delta_t * 200000Variables
| Variable | Description | Default |
|---|---|---|
alpha | Coefficient of Thermal Expansion (alpha)(×10⁻⁶/°C) | 12 |
delta_t | Temperature Change (delta T)(°C) | 100 |
length | Original Length (L)(mm) | 1000 |
alpha_per_c | Derived value= alpha * 1e-6 | calculated |
How It Works
Thermal Expansion and Strain
Materials expand or contract when their temperature changes. The thermal strain is proportional to the temperature change and the coefficient of thermal expansion (CTE).
Formula
epsilon_thermal = alpha × delta_T
delta_L = alpha × delta_T × L
where alpha is the CTE, delta_T is the temperature change, and L is the original length. If the component is constrained from expanding, a thermal stress develops: sigma = E × alpha × delta_T.
Worked Example
A 1000 mm steel bar (alpha = 12 × 10⁻⁶/°C) heated by 100°C.
- 01epsilon = 12 × 10⁻⁶ × 100 = 0.0012 (0.12%)
- 02delta_L = 0.0012 × 1000 = 1.2 mm
- 03If constrained: sigma = 200000 × 0.0012 = 240 MPa
Frequently Asked Questions
What are typical CTE values?
Steel: 11-13 × 10⁻⁶/°C, aluminum: 23 × 10⁻⁶/°C, copper: 17 × 10⁻⁶/°C, concrete: 10-12 × 10⁻⁶/°C, Invar alloy: 1.2 × 10⁻⁶/°C (designed for low expansion).
Why do expansion joints exist on bridges?
Bridges can be hundreds of meters long. Even small thermal strains create centimeters of movement. Expansion joints accommodate this movement; without them, thermal stresses would damage the structure.
Can thermal expansion cause yielding?
Yes. If a component is fully restrained, the thermal stress can exceed yield strength. For steel with yield at 250 MPa and alpha=12e-6, yielding starts at delta_T = 250000/(12×200000) ≈ 104°C.
Learn More
Guide
Thermal Expansion Guide: Calculating Length, Area, and Volume Changes
Understand thermal expansion in engineering materials. Learn to calculate linear, area, and volumetric expansion, handle expansion joints, and avoid thermal stress failures.
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Open Thermal Expansion Strain Calculator