What is thermal stress?

Thermal stress develops when a material is heated or cooled but cannot freely expand or contract. For a fully constrained member: σ = E × α × ΔT, where E is elastic modulus, α is the coefficient of thermal expansion (CTE), and ΔT is the temperature change.

What is the coefficient of thermal expansion (CTE)?

CTE (α) measures how much a material expands per degree of temperature change. Steel: ~12×10⁻⁶/°C, Aluminum: ~23×10⁻⁶/°C, Copper: ~17×10⁻⁶/°C, Stainless steel: ~17×10⁻⁶/°C.

When does thermal stress occur?

Thermal stress occurs when expansion is constrained: pipes fixed at both ends, rails welded continuously, dissimilar materials bonded together, thick sections with temperature gradients, or any structure restrained from free movement.

How can thermal stress be reduced?

Use expansion joints or loops in piping, allow sliding supports, choose materials with lower CTE, reduce ΔT with insulation, or use flexible connections. In bimetallic systems, match CTE values as closely as possible.

Is thermal stress always compressive when heating?

Yes, for a fully constrained member heated uniformly. The material tries to expand but cannot, so internal compressive stress develops. Cooling causes tensile stress. The sign depends on whether expansion or contraction is restrained.

मुक्त अभियांत्रिकी साधन

उष्णताजन्य ताण गणक

तापमान बदलाला सामोरे जाणाऱ्या पूर्णपणे प्रतिबंधित घटकासाठी उष्णीय ताण σ = E × α × ΔT गणना करा.

σ = E·α·ΔTप्रतिबंधित घटक#169

मटेरियल प्रीसेट

लोचदार मॉड्युलस E (GPa)

CTE α (×10⁻⁶ /°C)

तापमान बदल ΔT (°C)

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उष्णीय ताण σ

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उष्णीय विकृती ε

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ताण प्रकार

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प्रतिबंधित घटकांतील उष्णीय ताण

सामान्य CTE मूल्ये

साहित्य	E (GPa)	α (×10⁻⁶/°C)
कार्बन स्टील	200	12
स्टेनलेस स्टील 304	193	17.3
अॅल्युमिनियम 6061	69	23.6
तांबे	117	16.6
टायटॅनियम	114	8.6
पितळ	100	19

Thermal Stress Calculator | σ = E·α·ΔT | Free Online Tool

Published by Nikolai Shelkovenko on फेब्रुवारी 15, 2026 फेब्रुवारी 15, 2026

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सामान्य CTE मूल्ये

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