Thermal Stress & Expansion Calculator
Free thermal expansion and locked-in stress for a temperature change.
INPUTS
m
°C
mm²
RESULTS
Free expansion δ = αΔT·L
9.6 mm
Stress if fully restrained σ = EαΔT
96 MPa
Restraint force F = σA
480 kN
Note
Real structures are partially restrained — actual stress lies between 0 and EαΔT
How it works
Materials expand αΔT per unit length. If free, nothing happens structurally; if fully restrained, the blocked strain becomes stress σ = EαΔT — independent of length. This is why bridges have expansion joints and roller bearings: 100 MPa of thermal stress is cheaper to release than to resist.
Worked example
A 20 m steel beam heated +40 °C wants to grow δ = 12e-6·40·20000 = 9.6 mm. Fully restrained instead, it develops σ = EαΔT = 200000·12e-6·40 = 96 MPa — a third of yield from temperature alone.
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