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

Un alambre metálico de 75 centímetros de largo se coloca dentro de un horno a 450 grados centígrados. Si la longitud del cable cambia a 75,77 centímetros y la temperatura ambiente es de 20 grados centígrados, evalúe el coeficiente de expansión lineal del material del alambre.
Después de enfriarse, ambos extremos del alambre se unen a un soporte y se colocan dentro del horno a 200 grados centígrados. Evalúe la tensión térmica generada si el módulo de Young es de 7,0 x10 10 pascales e identifique el material del alambre.
El coeficiente de expansión lineal del alambre depende de la longitud inicial, el gradiente de temperatura y el cambio en la longitud y se calcula como 2,4 x10-5 por grados Celsius.
Además, la tensión térmica generada se puede calcular utilizando el módulo de Young, el gradiente de temperatura y el coeficiente de expansión lineal del material del alambre y se calcula como 3,02 x102 megapascales.
Los valores del coeficiente de expansión y el módulo de Young sugieren que lo más probable es que el alambre esté hecho de aluminio.

<ol>
	<li>OpenStax. (2019). Física Universitaria Vol. 2. [Versión web]. Obtenido de <a href="https://openstax.org/details/books/university-physics-volume-2">https://openstax.org/details/books/university-physics-volume-2</a>; págs. 15 y 18.</li>
</ol>

expansión térmica y estrés térmico: resolución de problemas

El Puente Golden Gate de San Francisco está expuesto a temperaturas que varían desde -15 °C hasta 40 °C. En su punto más frío, la longitud del tramo principal del puente es de 1275 m. Suponiendo que el puente está hecho completamente de acero, ¿cuál es el cambio en su longitud entre estas temperaturas? Para resolver el problema, primero identifique las magnitudes conocidas y desconocidas. La longitud inicial (L) del puente es de 1275 m, el coeficiente de expansión lineal (α) para el acero es de 12 x 10-6/°C, y el cambio de temperatura (ΔT) es de 55 °C. Recuerde que la expansión térmica es la expansión en el material con un aumento de temperatura. La expansión lineal es el cambio en la longitud de una sustancia al aplicar temperatura, y es proporcional a la longitud inicial y al cambio de temperatura. La constante de proporcionalidad es el coeficiente de expansión lineal. Usando la ecuación para la expansión térmica lineal para calcular el cambio en la longitud, ΔL. <img alt="Equation1" src="/files/ftp_upload/14164/14164_equation_2v2.svg" style="text-align: center; height: 16px;"> Sustituyendo todos los valores conocidos en la ecuación para resolver el cambio en la longitud, ΔL. <img alt="Equation2" src="/files/ftp_upload/14164/14164_equation_2.svg" style="text-align: center; height: 20px;"> El cambio en la longitud del Puente Golden Gate es de 0.84 m. Aunque no es grande en comparación con la longitud del puente, este cambio en longitud es observable. Generalmente se distribuye en muchas juntas de expansión para que la expansión en cada junta sea pequeña. Además, si se cambia la temperatura de un objeto evitando que se expanda o contraiga, el objeto está sometido a un estrés térmico. Para calcular el estrés térmico en un objeto donde ambos extremos están fijos rígidamente, el estrés puede considerarse como desarrollándose en dos etapas. Primero, dejar que los extremos se expandan o contraigan y encontrar la expansión o contracción. Segundo, encontrar el estrés necesario para comprimir o extender el objeto a su longitud original mediante los métodos estudiados en equilibrio estático y elasticidad en equilibrio estático elasticidad. En otras palabras, ΔL de la expansión térmica es igual a ΔL de la distorsión elástica, excepto que los signos son opuestos.

Expansión térmica y estrés térmico: Resolución de problemas

El puente Golden Gate de San Francisco está expuesto a temperaturas que oscilan entre los -15 °C y los 40 °C. En su punto más frío, el vano principal del puente es ...

Education

Educación

JoVE Core

Physics

Física

Unit 1

Unidad 1

Temperature and Heat

Temperatura y calor

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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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Convection and radiation are two major ways heat moves. In convection, thermal energy is carried by the large-scale flow of matter. Warm air and water rise because they are less dense, so ocean currents and large-scale atmospheric circulation move heat from the tropics toward the poles and move cold air from the poles toward the tropics. Earth’s rotation changes these moving air currents. It interacts with the flow and helps produce the eastward movement of air in the temperate zones.

conduction, convection and radiation: problem solving

conduction-convection-and-radiation-problem-solving

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Heat transfer calculations with conduction and convection use the temperature difference to find the rate of heat flow. Radiation can also be part of the process. The main idea is that heat moves only because one area is hotter than another, and a larger temperature difference leads to faster transfer. To solve a heat transfer problem, first identify the type of transfer involved. It may be conduction, convection, radiation, or a combination of all three. Next, write down the unknown...

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Earth’s energy balance and the greenhouse effect help explain its average temperature. Earth is in radiative contact with both the Sun and dark space. It receives almost all of its energy from solar radiation, and it reflects some of that energy back into outer space. Dark space is very cold, about 3 K, so Earth also radiates energy into it. Heat can move quickly from soil and grasses, and frost can form on clear summer evenings, even in warm latitudes. In a first approximation, Earth’s...

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Radiation heat transfer depends on temperature, surface area, and emissivity. The Stefan-Boltzmann law describes the rate of heat transfer by emitted radiation. In this law, σ is the Stefan-Boltzmann constant, A is the object’s surface area, and T is its temperature in kelvins. The fourth-power dependence on absolute temperature makes radiation highly sensitive to small temperature changes. Even a slight rise in temperature can change the emitted heat a lot. That sensitivity is why radiation...

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

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Golden Gate Bridge Thermal Expansion

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