Thermal Stress Calculator

What Is Thermal Stress?

Thermal stress appears when a material wants to expand or contract with temperature but is prevented from doing so. Fixed beams, constrained pipes, and bonded layers all build internal stress even without external loads. Engineers use the constrained-expansion model to estimate whether a temperature swing stays within allowable stress limits.

Thermal Stress Formula

When expansion is fully prevented along one direction:

\(E\) is Young's modulus, \(\alpha\) is the linear thermal expansion coefficient, and \(\Delta T\) is the temperature change. Stress grows linearly with each factor. A steel bar with \(E = 200\,\text{GPa}\), \(\alpha = 12 \times 10^{-6}\,\text{/°C}\), and \(\Delta T = 40\,\text{°C}\) develops about 96 MPa of compressive or tensile stress depending on heating or cooling.

When the Formula Applies

The simple relation assumes fully constrained uniaxial expansion. Partial constraint, plastic yielding, and temperature gradients reduce or redistribute stress. Still, it is a fast first check for rails, welded joints, and composite stacks.

Related tools: Thermal Conductivity Calculator, Thermal Expansion Calculator, and Stress Strain Calculator.