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

Metalowy drut o długości 75 centymetrów umieszcza się w piecu w temperaturze 450 stopni Celsjusza. Jeśli długość drutu zmieni się na 75,77 centymetra, a temperatura w pomieszczeniu wynosi 20 stopni Celsjusza, oceń współczynnik rozszerzalności liniowej materiału drutu.
Po schłodzeniu oba końce drutu mocuje się do stojaka i umieszcza wewnątrz pieca w temperaturze 200 stopni Celsjusza. Oceń naprężenie termiczne generowane, jeśli moduł Younga wynosi 7,0 x10 10 paskali i zidentyfikuj materiał drutu.
Współczynnik rozszerzalności liniowej drutu zależy od długości początkowej, gradientu temperatury oraz zmiany długości i jest obliczany jako 2,4 x10-5 na stopnie Celsjusza.
Ponadto generowane naprężenia termiczne można obliczyć za pomocą modułu Younga, gradientu temperatury i współczynnika rozszerzalności liniowej materiału drutu i są obliczane jako 3,02 x102 megapaskale.
Wartości współczynnika rozszerzalności i modułu Younga sugerują, że drut najprawdopodobniej jest wykonany z aluminium.

<ol>
	<li>Protokół OpenStax. (2019). Fizyka uniwersytecka Vol. 2. [Wersja internetowa]. Źródło: <a href="https://openstax.org/details/books/university-physics-volume-2">https://openstax.org/details/books/university-physics-volume-2</a>; str. 15, 18.</li>
</ol>

rozszerzalność cieplna i naprężenie termiczne: rozwiązywanie problemów

Most Golden Gate w San Francisco jest narażony na działanie temperatur w zakresie od -15°C do 40°C. W najzimniejszym miejscu główne przęsło mostu ma długość 1275 m. Zakładając, że most jest wykonany w całości ze stali, jaka jest zmiana jego długości pomiędzy tymi temperaturami?

Aby rozwiązać problem, najpierw zidentyfikuj znane i nieznane wielkości. Początkowa długość (L) mostu wynosi 1275 m, współczynnik rozszerzalności liniowej (L) dla stali wynosi 12 x 10-6/°C, a zmiana temperatury  (ΔT) wynosi 55 °C.

Przypomnijmy, że rozszerzalność cieplna to rozszerzanie się materiału pod wpływem podwyższonej temperatury. Rozszerzalność liniowa to zmiana długości substancji pod wpływem temperatury i jest ona proporcjonalna do długości początkowej i zmiany temperatury. Stała proporcjonalności jest współczynnikiem rozszerzalności liniowej. Używając równania na liniową rozszerzalność cieplną, aby obliczyć zmianę długości, ΔL

<img alt="Równanie1" src="/files/ftp_upload/14164/14164_equation_2v2.svg" style="text-align: center; height: 16px;" />

Podstawiając wszystkie znane wartości do równania, aby obliczyć zmianę długości, ΔL

<img alt="Równanie2" src="/files/ftp_upload/14164/14164_equation_2.svg" style="text-align: center; height: 20px;" />

Stwierdzono, że zmiana długości mostu Golden Gate wynosi 0,84 m. Choć nie jest to duża zmiana w porównaniu z długością mostu, jest ona zauważalna. Zwykle jest on rozłożony na wiele złączy dylatacyjnych, tak że ekspansja na każdym złączu jest niewielka.

Ponadto, jeśli zmienisz temperaturę obiektu, jednocześnie zapobiegając jego rozszerzaniu się lub kurczeniu, obiekt jest poddawany naprężeniom termicznym. Aby obliczyć naprężenie termiczne w obiekcie, którego oba końce są sztywno zamocowane, można przyjąć, że naprężenie rozwija się w dwóch etapach. Po pierwsze, pozwól końcówkom swobodnie się rozszerzać lub kurczyć i znajdź rozszerzanie lub kurczenie się. Po drugie, znajdź naprężenie niezbędne do ściśnięcia lub rozciągnięcia obiektu do jego pierwotnej długości metodami badanymi w równowadze statycznej i sprężystości na podstawie sprężystości w równowadze statycznej. Innymi słowy, ΔL rozszerzalności cieplnej jest równe ΔL odkształcenia sprężystego, z tą różnicą, że znaki są przeciwne.

Rozszerzalność cieplna i naprężenie termiczne: rozwiązywanie problemów

Most Golden Gate w San Francisco jest narażony na działanie temperatur w zakresie od -15 °C do 40 °C. W najzimniejszym momencie główne przęsło mostu znajduje się ...

Education

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Physics

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Unit 1

Jednostka 1

Temperature and Heat

Temperatura i ciepło

KEY TERMS AND CONCEPTS

Kluczowe terminy i pojęcia

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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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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