Free Thermal Stress Calculator
Calculate the stress induced in a fully restrained member due to a temperature change.
GPa
1/deg C
deg C
Thermal Stress
192.0 MPa
Free Thermal Strain0.000960 mm/mm
Thermal Stress vs Elastic Modulus (E)
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.
Example Calculation
A steel rail (E=200 GPa, alpha=12e-6 /deg C) heated by 80 deg C while fully restrained.
- 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.
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