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

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CHEM.13.D

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

Thermal expansion and Thermal stress: Problem Solving

Un fil métallique de 75 centimètres de long est placé à l’intérieur d’un four à 450 degrés Celsius. Si la longueur du fil passe à 75,77 centimètres et que la température ambiante est de 20 degrés Celsius, évaluez le coefficient de dilatation linéaire du matériau du fil.
Après refroidissement, les deux extrémités du fil sont attachées à un support et placées à l’intérieur du four à 200 degrés Celsius. Évaluez la contrainte thermique générée si le module de Young est de 7,0 x10 10 Pascals, et identifiez le matériau du fil.
Le coefficient de dilatation linéaire du fil dépend de la longueur initiale, du gradient de température et du changement de longueur et est calculé comme suit : 2,4 x 10-5 par degrés Celsius.
De plus, la contrainte thermique générée peut être calculée à l'aide du module de Young, du gradient de température et du coefficient de dilatation linéaire du matériau du fil et est calculée comme suit : 3,02 x102 mégapascals.
Les valeurs du coefficient de dilatation et du module de Young suggèrent que le fil est très probablement en aluminium.

<ol>
	<li>OpenStax. (2019). Physique universitaire Vol. 2. [Version Web]. Récupéré de <a href="https://openstax.org/details/books/university-physics-volume-2">https://openstax.org/details/books/university-physics-volume-2</a> ; p. 15 et 18.</li>
</ol>

expansion thermique et contrainte thermique: résolution de problème

Le pont du Golden Gate de San Francisco est exposé à des températures allant de -15 °C à 40 °C. À son niveau le plus froid, la travée principale du pont mesure 1275 m de long. En supposant que le pont est entièrement en acier, quelle est la variation de sa longueur entre ces températures ?

Pour résoudre le problème, commencez par identifier les quantités connues et inconnues. La longueur initiale (L) du pont est de 1275 m, le coefficient de dilatation linéaire (α) pour l'acier est de 12 x 10-6/°C, et la variation de température (ΔT) est de 55 °C.

Rappelez-vous que l'expansion thermique correspond à l'expansion d'un matériau avec une augmentation de température. L'expansion linéaire est le changement de longueur d'une substance en appliquant de la chaleur, et cela est proportionnel à la longueur initiale et à la variation de température. La constante de proportionnalité est le coefficient de dilatation linéaire. Utilisez l'équation de l'expansion thermique linéaire pour calculer la variation de longueur, ΔL.

<img alt="Equation1" src="/files/ftp_upload/14164/14164_equation_2v2.svg" style="text-align: center; height: 16px;" />

Remplacez toutes les valeurs connues dans l'équation pour résoudre la variation de longueur, ΔL.

<img alt="Equation2" src="/files/ftp_upload/14164/14164_equation_2.svg" style="text-align: center; height: 20px;" />

La variation de longueur du pont du Golden Gate est de 0,84 m. Bien que cela ne soit pas considérable par rapport à la longueur du pont, ce changement de longueur est observable. Il est généralement réparti sur de nombreuses articulations d'expansion afin que l'expansion à chaque joint soit faible.

De plus, si l'on change la température d'un objet tout en l'empêchant de se dilater ou de se contracter, l'objet est soumis à une contrainte thermique. Pour calculer la contrainte thermique dans un objet dont les deux extrémités sont fixes de manière rigide, la contrainte peut être considérée comme se développant en deux étapes. Tout d'abord, laissez les extrémités libres de se dilater ou de se contracter et trouvez l'expansion ou la contraction. Deuxièmement, trouvez la contrainte nécessaire pour comprimer ou étendre l'objet à sa longueur d'origine en utilisant les méthodes étudiées en équilibre statique et en élasticité. En d'autres termes, la ΔL de l'expansion thermique est égale à la ΔL de la déformation élastique, sauf que les signes sont opposés.

Expansion thermique et contrainte thermique: Résolution de problème

Le Golden Gate Bridge de San Francisco est exposé à des températures allant de -15 °C à 40 °C. À son point le plus froid, la travée principale du pont est ...

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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...

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conduction-convection-and-radiation-problem-solving

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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

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Golden Gate Bridge Thermal Expansion

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