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.

Ferramenta de Engenharia Gratuita

Calculadora de Tensão Térmica

Calcule a tensão térmica σ = E × α × ΔT para um elemento totalmente restringido submetido a variação de temperatura.

σ = E·α·ΔTElemento Restrito#169

Predefinição de Material

Módulo de Elasticidade E (GPa)

CTE α (×10⁻⁶ /°C)

Variação de Temperatura ΔT (°C)

Predefinições rápidas

Resultados

Tensão Térmica σ

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Deformação Térmica ε

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Tipo de Tensão

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Tensão Térmica em Elementos Restritos

Valores Comuns de CTE

Material	E (GPa)	α (×10⁻⁶/°C)
Aço Carbono	200	12
Aço Inoxidável 304	193	17.3
Alumínio 6061	69	23.6
Cobre	117	16.6
Titânio	114	8.6
Latão	100	19

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