How this calculation works
A free bar changes length with temperature; a perfectly restrained bar instead develops elastic stress that cancels that free thermal strain. This page compares those two quantities for one uniform bar between rigid supports.
Free strain = αΔT; fixed-length mechanical strain = −αΔT; σ = −EαΔT; F = σAA worked example
At E = 200 GPa, coefficient 12 microstrain per degree and a fifty-degree rise, free thermal strain is 0.0006. A one-metre bar would freely grow 0.6 mm. Perfect restraint produces −120 MPa stress and −12000 N force for 100 mm² area.
Good to know
Uniform temperature and linear elastic material with constant properties only. Support compliance, gaps, creep, plasticity and gradients are absent. The compressive result does not check buckling or establish a permissible service temperature.
Reference: MIT — mechanics of materials (opens in a new tab) ↗
What this model answers
A free bar changes length with temperature; a perfectly restrained bar instead develops elastic stress that cancels that free thermal strain.
This page compares those two quantities for one uniform bar between rigid supports.
The Stepped bar series axial extension calculator checks ideal elastic instability. A restrained thermal compression force is not by itself evidence that the bar remains straight.
Keep the input conventions consistent
Temperature change is final minus initial temperature, not the absolute final reading.
Expansion coefficient uses microstrain per degree Celsius. Outputs use tensile-positive stress, so heating with a positive coefficient produces compression and cooling produces tension.
Read the result carefully
In this ideal fully restrained model, length changes the free expansion that would have occurred but does not change the restraint stress.
Area changes axial force at that stress. Real support flexibility or initial slack can substantially change those relationships.
Complete restraint means the net axial length change is prevented, so mechanical strain offsets the free thermal strain. A partially restrained support or compliant joint needs an additional compatibility model. The ideal thermal stress does not become a verified support reaction without knowing the relevant section and actual restraint behavior.
Work through the numbers
At E = 200 GPa, coefficient 12 microstrain per degree and a fifty-degree rise, free thermal strain is 0.0006.
A one-metre bar would freely grow 0.6 mm. Perfect restraint produces −120 MPa stress and −12000 N force for 100 mm² area.
Where the calculation stops
Uniform temperature and linear elastic material with constant properties only.
Support compliance, gaps, creep, plasticity and gradients are absent. The compressive result does not check buckling or establish a permissible service temperature.
A few questions, answered
Why does length not appear in the stress equation?
Both free expansion and elastic axial deformation scale with length, which cancels under perfect fixed-length compatibility.
What should I change in the comparison?
Reverse the temperature change to compare thermal tension and compression.