Max Temperature Change for a Stress Limit
The inverse of the thermal-stress-restrained tile: the largest temperature change a restrained member can take before its thermal stress reaches the allowable, 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.
Formula and source
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.
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