27/08/2026
Thermal stresses calculation.!
Thermal stress is an important consideration in pipes, pressure vessels, heat exchangers, boilers, structural members, and other restrained equipment exposed to temperature changes.
When a metal member is heated, it naturally wants to expand. If its expansion is completely or partially restricted by supports, anchors, connected piping, or surrounding equipment, thermal stress develops.
🔹 Free thermal expansion
If the member is free to expand:
δ = α L ΔT
where:
• δ = thermal expansion
• α = coefficient of thermal expansion
• L = original length
• ΔT = temperature change
🔹 Thermal stress in a fully restrained member
For simple axial restraint:
σₜₕ = E α ΔT
where:
• E = Young's modulus
• α = coefficient of thermal expansion
• ΔT = temperature difference
🔹 Thermal force
The resulting axial force can be estimated as:
Pₜₕ = σₜₕ A = E α ΔT A
📐 Example from the infographic
Given:
• Carbon steel
• E = 200 GPa
• α = 12 × 10⁻⁶ /°C
• L = 10 m
• T₁ = 30°C
• T₂ = 180°C
• A = 1.5 × 10⁻³ m²
• Allowable stress = 120 MPa
Temperature difference:
ΔT = 180 − 30 = 150°C
Thermal stress:
σₜₕ = EαΔT
= (200 × 10⁹)(12 × 10⁻⁶)(150)
= 360 MPa
Thermal force:
Pₜₕ = σₜₕA
= (360 × 10⁶)(1.5 × 10⁻³)
= 540 kN
Since 360 MPa > 120 MPa, the calculated thermal stress exceeds the assumed allowable stress.
The corresponding maximum allowable temperature difference is:
ΔTₘₐₓ = Sₐₗₗₒw / (Eα)
= 50°C