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

A 75 centimeter long metal wire is placed inside a furnace at 450 degrees Celsius. If the wire length changes to 75.77 centimeters, and the room temperature is 20 degrees Celsius, evaluate the coefficient of linear expansion of the wire&#39;s material.
After cooling, both ends of the wire are attached to a stand and placed inside the furnace at 200 degrees Celsius. Evaluate the thermal stress generated if Young&#39;s modulus is 7.0 x 1010 Pascals, and identify the wire&#39;s material.
The coefficient of linear expansion of the wire depends on the initial length, the temperature gradient, and the change in length and is calculated as 2.4 x10-5 per degrees Celsius.
Further, the thermal stress generated can be calculated using Young&#39;s modulus, the temperature gradient, and the linear expansion coefficient of the wire&#39;s material and is calculated as 3.02 x102 megapascals.
The values of the coefficient of expansion and Young&#39;s modulus suggest that the wire is most likely made of aluminum.

thermal expansion and thermal stress: problem solving

San Francisco's Golden Gate Bridge is exposed to temperatures ranging from -15 °C to 40 °C. At its coldest, the main span of the bridge is 1275 m long. Assuming that the bridge is made entirely of steel, what is the change in its length between these temperatures?
To solve the problem, first, identify the known and unknown quantities. The initial length (L) of the bridge is 1275 m, the coefficient of linear expansion (α) for steel is 12 x 10-6/°C, and the change in temperature (ΔT) is 55 °C.
Recall that thermal expansion is the expansion in material with increased temperature. Linear expansion is the change in the length of a substance by applying temperature, and it is proportional to the initial length and change in temperature. The proportionality constant is the coefficient of linear expansion. Using the equation for linear thermal expansion to calculate the change in length, ΔL
<img alt="Thermal expansion equation ΔL=αLΔT, formula illustrating linear expansion concept." src="/files/ftp_upload/14164/14164_equation_2v2.svg" style="text-align: center; height: 16px;" data-altupdatedat="1761830439000" data-alt="Equation1">
Substituting all the known values into the equation to solve for the change in length, ΔL
<img alt="Thermal expansion equation ΔL=(12×10⁻⁶/°C)(1275 m)(55 °C), formula calculation." src="/files/ftp_upload/14164/14164_equation_2.svg" style="text-align: center; height: 20px;" data-altupdatedat="1761830439000" data-alt="Equation2">
The change in length of the Golden Gate Bridge is found to be 0.84 m. Although not large compared with the length of the bridge, this change in length is observable. It is generally spread over many expansion joints so that the expansion at each joint is small.
Further, if changing the temperature of an object while preventing it from expanding or contracting, the object is subjected to thermal stress. To calculate the thermal stress in an object where both ends are fixed rigidly, the stress can be thought of as developing in two steps. First, let the ends be free to expand or contract and find the expansion or contraction. Second, find the stress necessary to compress or extend the object to its original length by the methods studied in static equilibrium and elasticity on static equilibrium elasticity. In other words, the ΔL of the thermal expansion equals the ΔL of the elastic distortion, except that the signs are opposite.

San Francisco&#39;s Golden Gate Bridge is exposed to temperatures ranging from -15 &#176;C to 40 &#176;C. At its coldest, the main span of the bridge is ...

Education

JoVE Core

Physics

Unit 1

Temperature and Heat

KEY TERMS AND CONCEPTS

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 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 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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conduction, convection and radiation: problem solving

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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