Restrained Thermal Stress and Force
The stress a temperature change builds in a member that cannot move.
Example
You enter
- Modulus E (psi; 29e6 steel, 10e6 alum) 29000000
- Thermal expansion alpha (/F; 6.5e-6 steel) 0.0000065
- Temperature change dT (F, + heating) 100
- Cross-section area A (in², for force) 5
- Length L (in, for free expansion) 240
- Restraint factor (0-1, default 1) 1
You get
- Thermal stress 18,850 psi (compression)
- Restraint force 94,250 lb
- Free (blocked) expansion 0.156 in
Checked against published worked examples from: US DOE.
Details, formula, and sources
ScopeA blocked member develops sigma = E alpha dT x restraint (independent of length) and force F = sigma A; the free expansion alpha L dT is what the restraint blocks. Steel +100 F fully restrained -> 18,850 psi; aluminum nets less. Heating = compression, cooling = tension. A design aid, not the engineer of record.
Formula or tablesigma = E alpha dT x restraint; F = sigma A; free_delta = alpha L dT.
Source and editionThe standard restrained thermal-stress relation (mechanics of materials), by name.
Free accessThe restrained thermal-stress relation is published free in any mechanics-of-materials reference. The engineer of record governs the design.
What governsEstimate. AHJ and licensed professional govern.
API field namesE_psi, alpha, dT_F, A_in2, L_in, restraint, sigma_psi, F_lb, free_delta_in
- Restrained stress sigma = E alpha dT x restraint, independent of lengthmechanics of materials
- Sign heating a restrained member -> compression; cooling -> tensionmechanics of materials
- No buckling check fully restrained is the worst case; buckling under the compression is not checkedscope of this tile