Thermal Stress Calculator

How it is calculated

For a bar held rigidly at both ends, the expansion it is prevented from making turns into stress. The tool uses

σ = E × α × ΔT × 10−3

with E = Young's modulus in GPa, α = coefficient of thermal expansion in ppm/°C (the same as µm/m per °C), ΔT = temperature change in °C, and σ in MPa. The factor 10⁻³ only converts GPa × ppm into MPa. The output keeps the sign of ΔT: a temperature rise gives a positive number and a fall gives a negative one. Physically a restrained rise produces compression, so treat the sign as a marker of direction and read the size as the stress magnitude. Modulus must be above zero and α must not be negative; otherwise there is no result.

Common mistakes

• Entering Young's modulus in MPa or Pa instead of GPa. Steel is about 200 GPa; typing 200000 gives 120,000 MPa, a stress no steel could carry.
• Entering α as 0.000012 instead of 12 ppm. The tool expects the value in ppm per °C, so the small decimal form gives a result a million times too small.
• Using the final temperature instead of the temperature change. ΔT is the difference from the temperature at which the member was fitted, not the absolute temperature.
• Assuming the member is fully restrained when it is not. The formula is the upper limit for rigid anchors at both ends; any give in the supports or an expansion joint lowers the real stress.
• Ignoring the sign. A positive output in this tool means heating, which in a rigid member means compression, and compression is what can make a slender member buckle.