Max Temperature Change for a Stress Limit
The largest temperature change a restrained member can take before its thermal stress reaches the allowable.
Example
You enter
- Allowable stress (psi) 18850
- Modulus E (psi; 29e6 steel, 10e6 alum) 29000000
- Thermal expansion alpha (/F; 6.5e-6 steel) 0.0000065
- Restraint factor (0-1, default 1) 1
You get
- Max temperature change 100.0 F
Details, formula, and sources
dT_max = sigma_allow / (E x alpha x restraint). Fully restrained steel at an 18,850 psi allowable can swing 100 F; aluminum tolerates 145 F for the same stress (lower modulus), and half restraint doubles the swing. Answers 'how big a temperature swing can this take' instead of the stress at one swing. Heating is compression, cooling is tension. A design aid, not the engineer of record.
dT_max = allowable_stress_psi / (E x alpha x restraint); the inverse of sigma = E alpha dT x restraint.
The standard restrained thermal-stress relation (mechanics of materials) solved for the temperature change, by name.
The restrained thermal-stress relation is published free in any mechanics-of-materials reference. The engineer of record governs the design.
Estimate. AHJ and licensed professional govern.
Field names used by the API: allowable_stress_psi, E_psi, alpha, restraint, max_dT_F
- Restrained-stress inverse dT_max = sigma_allow / (E alpha restraint), independent of lengthmechanics of materials
- Sign heating a restrained member -> compression; cooling -> tension; use the governing allowablemechanics of materials
- No buckling check fully restrained is the worst case; buckling under the compression is not checkedscope of this tile