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.

免費工程工具

熱應力計算器

計算受溫度變化影響之完全約束構件的熱應力 σ = E × α × ΔT。

σ = E·α·ΔT約束構件#169

材質預設

彈性模數 E (GPa)

熱膨脹係數 α (×10⁻⁶ /°C)

溫差 ΔT (°C)

快速預設

結果

熱應力 σ

—

熱應變 ε

—

應力類型

—

約束構件中的熱應力

常見熱膨脹係數 (CTE) 數值

材料	E (GPa)	α (×10⁻⁶/°C)
碳鋼	200	12
不鏽鋼 304	193	17.3
鋁 6061	69	23.6
銅	117	16.6
鈦	114	8.6
黃銅	100	19

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