Name: golden gate bridge thermal expansion
Uploaded: 2023-09-18T17:11:17.000Z
Duration: 1 min 27 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Chemistry

CHEM.13

CHEM.13.D

thermal-expansion-and-thermal-stress-problem-solving

Thermal expansion and Thermal stress: Problem Solving

長さ75センチメートルの金属線を摂氏450度の炉の中に入れます。ワイヤーの長さが75.77センチメートルに変化し、室温が摂氏20度の場合、ワイヤーの材料の線膨張係数を評価します。
冷却後、ワイヤーの両端をスタンドに取り付け、200°Cで炉内に置きます。ヤング率が 7.0 x10 10 パスカルの場合に発生する熱応力を評価し、ワイヤの材料を特定します。
ワイヤの線膨張係数は、初期長さ、温度勾配、および長さの変化に依存し、摂氏1度あたり2.4 x10-5として計算されます。
さらに、発生する熱応力は、ヤング率、温度勾配、およびワイヤの材料の線膨張係数を使用して計算でき、3.02 x102メガパスカルとして計算されます。
膨張係数とヤング率の値から、ワイヤはアルミニウムでできている可能性が最も高いことが示唆されます。

<ol>
	<li>OpenStaxです。(2019). 大学物理学 Vol.2.【Web版】。<a href="https://openstax.org/details/books/university-physics-volume-2">https://openstax.org/details/books/university-physics-volume-2 から取得</a>。15、18ページ。</li>
</ol>

熱膨張と熱応力: 問題解決

サンフランシスコのゴールデンゲートブリッジは、-15 ℃ ～ 40 ℃ の温度にさらされています。 最も寒いときの橋の主径間は 1275 m です。 橋が完全に鋼でできていると仮定すると、これらの温度間で橋の長さはどのように変化しますか?

この問題を解決するには、まず既知の量と未知の量を特定します。 橋の初期の長さ (L) は 1275 m、鋼の線膨張係数 (α) は 12 x 10-6/°C、温度変化 (ΔT) は 55 °C です。

熱膨張とは、温度が上昇したときの材料の膨張であることを思い出してください。 線膨張は、温度を加えることによる物質の長さの変化であり、初期の長さと温度の変化に比例します。 比例定数は線膨張係数です。 線形熱膨張の式を使用して、長さの変化 ΔL

を計算します。

<img alt="Equation1" src="/files/ftp_upload/14164/14164_equation_2v2.svg" style="text-align: center; height: 16px;" />

すべての既知の値を方程式に代入して、長さの変化 ΔL を求めます

<img alt="Equation2" src="/files/ftp_upload/14164/14164_equation_2.svg" style="text-align: center; height: 20px;" />

ゴールデンゲートブリッジの長さの変化は 0.84 m であることがわかります。 橋の長さに比べればそれほど大きくありませんが、この長さの変化は観察できます。 通常、多くの伸縮継手にわたって分散されるため、各継手での拡張は小さくなります。

さらに、物体の膨張や収縮を妨げながら温度を変化させると、物体は熱応力を受けます。 両端が剛に固定されている物体の熱応力を計算するには、応力が 2 段階で進行すると考えることができます。 まず、端を自由に拡張または収縮させて、拡張または収縮を見つけます。 次に、静的平衡と静的平衡弾性に関する弾性で研究された方法によって、物体を元の長さまで圧縮または伸長するのに必要な応力を見つけます。 言い換えれば、符号が反対であることを除けば、熱膨張の ΔL は弾性歪みの ΔL と等しくなります。

サンフランシスコのゴールデンゲートブリッジは、-15°Cから40°Cの範囲の温度にさらされています。最も寒いとき、橋のメインスパンは...

Education

JoVE Core

Physics

物理学

Unit 1

ユニット1

Temperature and Heat

温度と熱

KEY TERMS AND CONCEPTS

主要用語と概念

golden gate bridge thermal expansion

Thermal expansion and thermal stress are shown through the Golden Gate Bridge. The bridge faces temperatures from -15 °C to 40 °C. At its coldest, the main span is 1275 m long. Assuming the bridge is made entirely of steel, the example asks for the change in its length across this temperature range.

To solve the problem, the known values must be identified first. The initial length is 1275 m. The coefficient of linear expansion for steel is 12 x 10 -6 /°C, and the change in temperature is 55 °C. Linear expansion means a material changes length when temperature changes, and the change is proportional to the original length and the temperature change.

The calculation uses the equation for linear thermal expansion to find ΔL. After substituting the given values, the change in length is 0.84 m. That change is small compared with the full span, but it is still observable. In practice, it is spread over many expansion joints so the expansion at each joint stays small.

The same situation also helps explain thermal stress. If an object is heated or cooled while both ends are held rigidly, it cannot expand or contract freely. The stress can be found in two steps. First, let the object expand or contract freely and find ΔL. Then find the stress needed to bring it back to its original length. The thermal expansion ΔL and the elastic distortion ΔL are equal in size, but their signs are opposite.

Golden Gate Bridge Thermal Expansion

temperature and thermal equilibrium

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thermal expansion and thermal stress: problem solving

Thermal expansion and thermal stress are shown through the Golden Gate Bridge. The bridge faces temperatures from -15 °C to 40 °C. At its coldest, the main span is 1275 m long. Assuming the bridge is made entirely of steel, the example asks for the change in its length across this temperature range. To solve the problem, the known values must be identified first. The initial length is 1275 m. The coefficient of linear expansion for steel is 12 x 10 -6 /°C, and the change in temperature is 55...

heat flow and specific heat

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calorimetry

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mechanisms of heat transfer ii

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conduction, convection and radiation: problem solving

conduction-convection-and-radiation-problem-solving

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radiation: applications

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key terms and concepts

Use the Golden Gate Bridge to calculate linear thermal expansion, find the 0.84 m length change, and see how fixed ends create thermal stress.

Golden Gate Bridge Thermal Expansion | JoVE K12

physics

JoVE Core 物理学は、運動学、力学、流体力学、静力学、波動、音響などの基礎的な物理学の理論と応用を、簡潔でわかりやすいアニメーション ビデオで紹介します。さらに、科学者の実際のビデオでは、世界中の今日の研究所で行われている古典的および独自の研究実験における関連概念の適用を示しています。

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Golden Gate Bridge Thermal Expansion

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