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

K12 Standards

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Chemistry

CHEM.13

CHEM.13.D

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

Thermal expansion and Thermal stress: Problem Solving

Ein 75 Zentimeter langer Metalldraht wird in einen 450 Grad Celsius heißen Ofen gelegt. Wenn sich die Drahtlänge auf 75,77 Zentimeter ändert und die Raumtemperatur 20 Grad Celsius beträgt, bewerten Sie den linearen Ausdehnungskoeffizienten des Drahtmaterials.
Nach dem Abkühlen werden beide Enden des Drahtes an einem Ständer befestigt und bei 200 Grad Celsius in den Ofen gelegt. Bewerten Sie die thermische Spannung, die entsteht, wenn der Elastizitätsmodul 7,0 x 10 Pascal beträgt, und identifizieren Sie das Material des Drahtes.
Der lineare Ausdehnungskoeffizient des Drahtes hängt von der Anfangslänge, dem Temperaturgradienten und der Längenänderung ab und wird mit 2,4 x10-5 pro Grad Celsius berechnet.
Des Weiteren kann die erzeugte thermische Spannung unter Verwendung des Elastizitätsmoduls, des Temperaturgradienten und des linearen Ausdehnungskoeffizienten des Drahtmaterials berechnet werden und wird als 3,02 x102 Megapascal berechnet.
Die Werte des Ausdehnungskoeffizienten und des Elastizitätsmoduls deuten darauf hin, dass der Draht höchstwahrscheinlich aus Aluminium besteht.

<ol>
	<li>OpenStax. (2019). Universitätsphysik Vol. 2. [Webversion]. Abgerufen von <a href="https://openstax.org/details/books/university-physics-volume-2">https://openstax.org/details/books/university-physics-volume-2</a>; S. 15, 18.</li>
</ol>

thermische ausdehnung und thermischer stress: problemlösung

Die Golden Gate Bridge in San Francisco ist Temperaturen von -15 °C bis 40 °C ausgesetzt. Bei niedrigsten Temperaturen ist der Hauptspann der Brücke 1275 m lang. Angenommen, die Brücke besteht vollständig aus Stahl. Wie groß ist die Längenänderung zwischen diesen Temperaturen?

Um das Problem zu lösen, müssen zunächst die bekannten und unbekannten Größen identifiziert werden. Die Anfangslänge (L) der Brücke beträgt 1275 m, der lineare Ausdehnungskoeffizient (α) für Stahl beträgt 12 x 10^-6/°C und die Temperaturänderung (ΔT) beträgt 55 °C.

Es sei daran erinnert, dass die thermische Ausdehnung die Ausdehnung eines Materials mit erhöhter Temperatur ist. Die lineare Expansion ist die Änderung der Länge einer Substanz durch Temperaturanwendung und ist proportional zur Anfangslänge und der Temperaturänderung. Die Proportionalitätskonstante ist der lineare Ausdehnungskoeffizient. Berechnung der Längenänderung anhand der Gleichung für die lineare Wärmeausdehnung, ΔL

<img alt="Equation1" src="/files/ftp_upload/14164/14164_equation_2v2.svg" style="text-align: center; height: 16px;" />

Setzen Sie alle bekannten Werte in die Gleichung ein, um die Längenänderung zu ermitteln, ΔL

<img alt="Equation2" src="/files/ftp_upload/14164/14164_equation_2.svg" style="text-align: center; height: 20px;" />

Die Änderung der Länge der Golden Gate Bridge beträgt 0,84 m. Obwohl die Änderung im Vergleich zur Länge der Brücke nicht groß ist, ist sie beobachtbar. Sie ist im Allgemeinen auf viele Dehnungsfugen verteilt, so dass sich die Ausdehnung an jedem Gelenk geringfügig auswirkt.

Des Weiteren wird bei der Änderung der Temperatur eines Objekts, während seine Ausdehnung oder Kontraktion verhindert wird, das Objekt thermischem Stress ausgesetzt. Um den thermischen Stress in einem Objekt zu berechnen, bei dem beide Enden starr fixiert sind, kann der Stress in zwei Schritten betrachtet werden. Erstens, lassen Sie die Enden sich frei ausdehnen oder zusammenziehen und finden Sie die Ausdehnung oder Kontraktion. Zweitens wird die Spannung ermittelt, die erforderlich ist, um das Objekt auf seine ursprüngliche Länge zu komprimieren oder zu dehnen, und zwar mit den Methoden, die im statischen Gleichgewicht und in der Elastizität der statischen Gleichgewichtselastizität untersucht wurden. Mit anderen Worten: Das ΔL der thermischen Ausdehnung ist gleich dem ΔL der elastischen Verformung, nur dass die Vorzeichen entgegengesetzt sind.

Thermische Ausdehnung und thermischer Stress: Problemlösung

Die Golden Gate Bridge in San Francisco ist Temperaturen von -15 °C bis 40 °C ausgesetzt. Am kältesten ist die Hauptspannweite der Brücke ...

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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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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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