Thermal Stress Calculator Formula
Understand the math behind the thermal stress calculator. Each variable explained with a worked example.
Formulas Used
Thermal Stress
thermal_stress = e_mpa * alpha * abs(delta_t)Free Thermal Strain
free_strain = alpha * abs(delta_t)Variables
| Variable | Description | Default |
|---|---|---|
modulus | Elastic Modulus (E)(GPa) | 200 |
alpha | Thermal Expansion Coeff (alpha)(1/deg C) | 0.000012 |
delta_t | Temperature Change (delta T)(deg C) | 80 |
e_mpa | Derived value= modulus * 1000 | calculated |
How It Works
Thermal Stress in Restrained Members
When a material cannot expand or contract freely, temperature changes produce internal stresses.
Formula
sigma_thermal = E alpha delta_T
where E is the elastic modulus, alpha is the coefficient of linear thermal expansion, and delta_T is the temperature change. Heating a restrained member produces compression; cooling produces tension.
Worked Example
A steel rail (E=200 GPa, alpha=12e-6 /deg C) heated by 80 deg C while fully restrained.
modulus = 200alpha = 0.000012delta_t = 80
- 01Free strain = 12e-6 x 80 = 9.6e-4 = 0.000960
- 02Thermal stress = 200,000 MPa x 0.000960 = 192 MPa
- 03This is 77% of steel yield (250 MPa), highlighting why expansion joints are critical.
Ready to run the numbers?
Open Thermal Stress Calculator