Thermal Stress Calculator
A fully restrained bar develops σ = EαΔT: steel heated by 50 °C between rigid walls carries 120 MPa.
0 for a fully restrained bar.
For the thermal force; 0 to skip.
120 MPa
- Free expansion αLΔT
- 1.2 mm
- Expansion prevented
- 1.2 mm
Step-by-step solution
- Free expansion δ = αLΔT = 12 × 10⁻⁶ × 2000 mm × 50 = 1.2 mm
- σ = E(δ − gap)/L = 200000 MPa × 1.2 ÷ 2000 = 120 MPa
Thermal Stress Formula
σ = E(αLΔT − gap)/L
σ = EαΔT for a fully restrained bar
Worked Example
A 2 m steel bar (E = 200 GPa, α = 12 × 10⁻⁶ /°C) heated by 50 °C between rigid walls:
- Free expansion δ = αLΔT = 12 × 10⁻⁶ × 2000 mm × 50 = 1.2 mm
- σ = E(δ − gap)/L = 200000 MPa × 1.2 ÷ 2000 = 120 MPa
Expansion prevented: 1.2 mm
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Frequently asked questions
Does thermal stress depend on the bar’s length?
Not for a fully restrained bar: σ = EαΔT. Length matters only when a gap allows part of the expansion.
Is thermal stress tensile or compressive?
Compressive when a restrained bar is heated and tensile when it is cooled.
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Thermal Stress Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/thermal-stress-calculator/
IEEE
Scientific Converters, "Thermal Stress Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/thermal-stress-calculator/