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

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Chemistry

CHEM.13

CHEM.13.D

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

Thermal expansion and Thermal stress: Problem Solving

Un filo metallico lungo 75 centimetri viene posto all'interno di una fornace a 450 gradi Celsius. Se la lunghezza del filo cambia a 75,77 centimetri e la temperatura ambiente è di 20 gradi Celsius, valutare il coefficiente di dilatazione lineare del materiale del filo.
Dopo il raffreddamento, entrambe le estremità del filo vengono fissate a un supporto e posizionate all'interno del forno a 200 gradi Celsius. Valutare lo stress termico generato se il modulo di Young è 7,0 x 10 Pascal e identificare il materiale del filo.
Il coefficiente di dilatazione lineare del filo dipende dalla lunghezza iniziale, dal gradiente di temperatura e dalla variazione di lunghezza ed è calcolato come 2,4 x10-5 per gradi Celsius.
Inoltre, lo stress termico generato può essere calcolato utilizzando il modulo di Young, il gradiente di temperatura e il coefficiente di dilatazione lineare del materiale del filo ed è calcolato come 3,02 x102 megapascal.
I valori del coefficiente di dilatazione e del modulo di Young suggeriscono che il filo è molto probabilmente fatto di alluminio.

<ol>
	<li>OpenStax. (2019). Fisica universitaria Vol. 2. [Versione web]. Estratto da <a href="https://openstax.org/details/books/university-physics-volume-2">https://openstax.org/details/books/university-physics-volume-2</a>; pagine 15, 18.</li>
</ol>

espansione termica e stress termico: risolvere i problemi

Il Ponte Golden Gate di San Francisco è esposto a temperature che variano da -15 °C a 40 °C. Al suo punto più freddo, la campata principale del ponte è lunga 1275 m. Supponendo che il ponte sia interamente fatto di acciaio, qual è la variazione della sua lunghezza tra queste temperature?

Per risolvere il problema, identifica prima le grandezze conosciute e sconosciute. La lunghezza iniziale (L) del ponte è di 1275 m, il coefficiente di dilatazione lineare (α) dell'acciaio è 12 x 10-6/C°, e la variazione di temperatura (ΔT) è di 55 °C.

Ricorda che l'espansione termica è l'espansione del materiale con l'aumento della temperatura. L'espansione lineare è il cambiamento nella lunghezza di una sostanza applicando temperatura, ed è proporzionale alla lunghezza iniziale e alla variazione di temperatura. La costante di proporzionalità è il coefficiente di dilatazione lineare. Utilizzando l'equazione per l'espansione termica lineare per calcolare la variazione di lunghezza, ΔL:

<img alt="Equation1" src="/files/ftp_upload/14164/14164_equation_2v2.svg" style="text-align: center; height: 16px;" />

Sostituendo tutti i valori noti nell'equazione per risolvere la variazione di lunghezza, ΔL:

<img alt="Equation2" src="/files/ftp_upload/14164/14164_equation_2.svg" style="text-align: center; height: 20px;" />

La variazione di lunghezza del Ponte Golden Gate risulta essere di 0.84 m. Anche se non è grande rispetto alla lunghezza del ponte, questa variazione di lunghezza è osservabile. Generalmente è distribuita su molte giunture di dilatazione in modo che l'espansione in ciascuna giuntura sia piccola.

Inoltre, se si cambia la temperatura di un oggetto impedendogli di espandersi o contrarsi, l'oggetto è soggetto a stress termico. Per calcolare lo stress termico in un oggetto dove entrambe le estremità sono fissate rigidamente, lo stress può essere considerato come sviluppato in due fasi. In primo luogo, lascia che le estremità siano libere di espandersi o contrarsi e trova l'espansione o la contrazione. In secondo luogo, trova lo stress necessario per comprimere o estendere l'oggetto alla sua lunghezza originale usando i metodi studiati nell'equilibrio statico e nell'elasticità. In altre parole, ΔL dell'espansione termica è uguale a ΔL della distorsione elastica, tranne che i segni sono opposti.

Espansione termica e stress termico: risolvere i problemi

Il Golden Gate Bridge di San Francisco è esposto a temperature che vanno da -15 °C a 40 °C. Nella sua forma più fredda, la campata principale del ponte è ...

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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

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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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mechanisms of heat transfer ii

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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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