18.6
熱応力
物体の膨張や収縮が妨げられているときにその温度が変化すると、物体は応力を受けます。 拘束がない状態で物体が膨張する場合、応力は圧縮となり、収縮する場合、応力は引張となります。 温度変化によって生じるこの応力は熱応力として知られています。 かなり大きくなり、損傷を引き起こす可能性があります。 このスト…
体は温度変化を受けるとストレスを受けます。このストレスは熱ストレスと呼ばれ、体を永久に変形させることさえあります。
例えば、線路上のロッドの2つのジョイントの間には、ロッドの変形や曲がりを防ぐために意図的にスペースが維持されます。
オブジェクトの熱応力を計算するには、まず熱膨張または熱収縮を決定し、次に応力を計算します。
長さ L0 のロッドを考えてみます。で囲まれています。 熱が加えられると、ロッドの長さはデルタ「L」だけ広がり、ロッドの長さのわずかな変化を評価できます。
これで、同じロッドが両端に固定されています。熱が加えられると、ロッドは膨張できないため、ひずみが発生します。ロッドの元の長さに戻すには、応力を計算できます。
ヤング率の定義を思い出すと、それは応力とひずみの比率です。
したがって、熱応力は、方程式を組み合わせて項を並べ替えることによって決定できます。
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Q1: What is thermal stress and how does it develop in materials?
Thermal stress occurs when an object experiences temperature changes while prevented from expanding or contracting freely. The stress is compressive if the object would expand without constraint, or tensile if it would contract. This stress can be quite large and cause permanent deformation or damage to materials and structures.
Q2: How do engineers prevent thermal stress in infrastructure like railroad tracks?
Engineers design components to expand and contract freely by leaving deliberate gaps or expansion joints. For example, railroad tracks have intentional spaces between joints to prevent rod deformation. When gaps cannot be left, engineers must select compatible materials, such as using steel reinforcing rods in concrete because steel's coefficient of linear expansion nearly equals concrete's.
Q3: How is thermal stress calculated in a constrained object?
To calculate thermal stress, first determine the thermal expansion or contraction the object would undergo. Then calculate the resulting strain. Using Young's modulus, which is the ratio of stress to strain, you can determine thermal stress by combining and rearranging the thermal expansion and strain equations.
Q4: What real-world phenomena result from thermal stress?
Thermal stress explains many observable effects: rock and pavement weathering from ice expansion during freezing, railroad track and roadway buckling on hot days without expansion joints, power line sagging in summer and snapping in cold weather, cracks opening and closing in plaster walls, and glass cookware cracking from rapid or uneven cooling.
Q5: Why does a fixed rod experience strain when heated?
When a rod is fixed at both ends and heated, it cannot expand freely. The thermal expansion that would normally occur is prevented by the fixed constraints, creating internal strain within the material. This constraint-induced strain develops stress that can be calculated using Young's modulus and the material's thermal expansion coefficient.
Q6: What is the difference between compressive and tensile thermal stress?
Thermal stress is compressive when an object is prevented from expanding during heating, creating inward pressure. Thermal stress is tensile when an object is prevented from contracting during cooling, creating outward pulling forces. Both types can cause significant damage if the stress exceeds the material's strength limits.
Q7: Why is material compatibility important in composite structures?
When different materials are bonded together, they must have similar coefficients of linear expansion. If coefficients differ significantly, temperature changes create differential thermal stress at the interface, causing cracking or separation. Steel reinforcing rods in concrete work well because their expansion rates match, preventing stress-induced failure.