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

75cm 길이의 금속 와이어를 섭씨 450도의 용광로 내부에 넣습니다. 와이어 길이가 75.77cm로 변경되고 실내 온도가 섭씨 20도인 경우 와이어 재료의 선형 팽창 계수를 평가합니다.
냉각 후 와이어의 양쪽 끝을 스탠드에 부착하고 섭씨 200도의 퍼니스 내부에 놓습니다. Young의 계수가 7.0 x 1010 파스칼인 경우 발생하는 열 응력을 평가하고 와이어의 재질을 식별합니다.
와이어의 선형 팽창 계수는 초기 길이, 온도 구배 및 길이 변화에 따라 달라지며 섭씨 2.4 x10-5로 계산됩니다.
또한, 생성된 열 응력은 Young의 계수, 온도 구배 및 와이어 재료의 선형 팽창 계수를 사용하여 계산할 수 있으며 3.02 x102메가파스칼로 계산됩니다.
팽창 계수와 Young의 계수 값은 와이어가 알루미늄으로 만들어졌을 가능성이 가장 높다는 것을 시사합니다.

<ol>
	<li>오픈스택스. (2019). 대학 물리학 Vol. 2. [웹 버전]. 원본 주소 <a href="https://openstax.org/details/books/university-physics-volume-2">https://openstax.org/details/books/university-physics-volume-2</a>; 15, 18쪽.</li>
</ol>

열팽창 및 열응력: 문제 해결

샌프란시스코의 금문교는 -15°C에서 40°C 사이의 온도에 노출되어 있습니다. 가장 추운 날 다리의 주 경간 길이는 1275m입니다. 다리 전체가 강철로 만들어졌다고 가정하면, 두 온도 사이에서 다리 길이의 변화는 얼마입니까?

문제를 해결하려면 먼저 알려진 양과 알려지지 않은 양을 식별하세요. 교량의 초기 길이(L)는 1275m이고 강철의 선팽창 계수(α)는 12 x 10-6 입니다./°C, 온도 변화(ΔT)는 55°C입니다.

열팽창은 온도가 상승함에 따라 재료가 팽창하는 것임을 기억하세요. 선팽창은 온도를 가함으로써 물질의 길이가 변화하는 현상으로, 초기 길이와 온도 변화에 비례합니다. 비례 상수는 선형 팽창 계수입니다. 선형 열팽창 방정식을 사용하여 길이 변화를 계산합니다. ΔL

<img alt="Equation1" src="/files/ftp_upload/14164/14164_equation_2v2.svg" style="text-align: center; height: 16px;" />

알려진 모든 값을 방정식에 대입하여 길이 변화 'L'을 해결합니다.

<img alt="Equation2" src="/files/ftp_upload/14164/14164_equation_2.svg" style="text-align: center; height: 20px;" />

금문교의 길이 변화는 0.84m로 나타났다. 교량의 길이에 비해 크지는 않지만 이러한 길이의 변화를 관찰할 수 있습니다. 일반적으로 여러 개의 신축이음부에 분산되어 각 관절의 팽창이 작습니다.

또한 물체의 팽창이나 수축을 방지하면서 온도를 변화시키면 물체는 열응력을 받게 됩니다. 양쪽 끝이 단단히 고정된 물체의 열응력을 계산하려면 응력이 두 단계로 전개되는 것으로 생각할 수 있습니다. 첫째, 끝이 자유롭게 확장되거나 수축되도록 하여 확장 또는 수축을 찾도록 하십시오. 둘째, 정적 평형 및 정적 평형 탄성에 대한 탄성 연구 방법을 사용하여 물체를 원래 길이로 압축하거나 늘리는 데 필요한 응력을 찾습니다. 즉, 열팽창의 L은 부호가 반대라는 점을 제외하면 탄성 변형의 L과 같습니다.

샌프란시스코의 금문교는 -15°C에서 40°C 사이의 온도에 노출됩니다. 가장 추울 때, 다리의 주요 경간은 ...

Education

교육

JoVE Core

Physics

물리학

Unit 1

제1단원

Temperature and Heat

온도와 열

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 stress is the stress that builds up when an object changes temperature but cannot expand or contract freely. If the object would expand without restraint, the stress is compressive. If it would contract, the stress is tensile. This stress from heating or cooling can become large enough to cause damage. Engineers often reduce it by designing parts so they can move as temperature changes. Highway blocks, for example, are separated by gaps so thermal stress does not build up. When gaps...

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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