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Thermal stress in a fully constrained member under a uniform temperature change: σ_th = E·α·ΔT. Built-in typical Young's modulus E and expansion coefficient α for carbon/alloy steel, aluminum, copper, austenitic stainless and titanium, plus custom values. ΔT in K or °C (same magnitude), result in MPa. Heating (ΔT>0) → compressive stress in the member.
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Tool usage guide
Calculate thermal stress in a fully constrained member using σ_th = E·α·ΔT. Choose a material preset or enter custom Young's modulus and thermal expansion values, then get the stress in MPa with compression or tension identified.
Background
A carbon steel member is fully constrained and experiences a uniform 100 K temperature increase.
Problem
Estimate the compressive thermal stress caused by the prevented expansion.
How to use
Select Carbon steel, enter ΔT as 100, and keep the desired decimal-place setting.
Material: Carbon steel; ΔT: 100 K; E: 210000 MPa; α: 0.000012 1/KOutcome
The calculator returns 252.0000 MPa and identifies the loading as compression.
Background
A fully constrained aluminum member cools uniformly by 50 K.
Problem
Determine the tensile stress produced by the negative temperature change.
How to use
Select Aluminum alloy and enter ΔT as -50.
Material: Aluminum alloy; ΔT: -50 K; E: 70000 MPa; α: 0.000023 1/KIt uses σ_th = E·α·ΔT for a fully constrained member under a uniform temperature change.
Yes. A temperature difference in °C has the same numerical magnitude as in K.
A positive ΔT represents heating and is reported as compressive thermal stress.
A negative ΔT represents cooling and is reported as tensile thermal stress.
Enter E in MPa, α in 1/K, and ΔT in K or °C. The stress result is returned in MPa.
Outcome
The calculator returns -80.5000 MPa and identifies the loading as tension.