Thermal Stress from Restraint
Thermal Stress from Restraint
A member that cannot expand freely builds up thermal stress instead — the cause of buckled rails and cracked restraints.
For full restraint the thermal stress is σ = E·α·ΔT. where E is Young’s modulus, α the expansion coefficient and ΔT the temperature change.
Inputs
E := 200 GPa=200000 MPa
alpha := 12e-6 K^-1=1.2e-05 1/K
dT := 50 K=50 K
Restrained expansion converts directly into stress.
sigma := E·alpha·dT=120 MPa
Results
Note the stress is independent of length — a 50 K rise in fully restrained steel gives over 100 MPa. This is why rails and pipes need expansion gaps.
Assumptions & limitations
- Full restraint (no expansion allowed).
- Elastic behaviour.
- Uniform temperature change.