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

يتم وضع سلك معدني بطول 75 سم داخل فرن عند 450 درجة مئوية. إذا تغير طول السلك إلى 75.77 سم ، وكانت درجة حرارة الغرفة 20 درجة مئوية ، فقم بتقييم معامل التمدد الخطي لمادة السلك.
بعد التبريد ، يتم توصيل طرفي السلك بحامل ووضعهما داخل الفرن عند 200 درجة مئوية. قم بتقييم الإجهاد الحراري المتولد إذا كان معامل يونغ 7.0 × 1010 باسكال ، وحدد مادة السلك.
يعتمد معامل التمدد الخطي للسلك على الطول الأولي وتدرج درجة الحرارة والتغير في الطول ويتم حسابه على أنه 2.4 × 10-5 لكل درجة مئوية.
علاوة على ذلك ، يمكن حساب الإجهاد الحراري المتولد باستخدام معامل يونغ ، وتدرج درجة الحرارة ، ومعامل التمدد الخطي لمادة السلك ويتم حسابه على أنه 3.02 × 102 ميجا باسكال.
تشير قيم معامل التمدد ومعامل يونغ إلى أن السلك مصنوع على الأرجح من الألومنيوم.

<ol>
	<li>OpenStax. (2019). جامعة الفيزياء المجلد 2. [نسخة الويب]. تم الاسترجاع من <a href = "https://openstax.org/details/books/university-physics-volume-2" >https://openstax.org/details/books/university-physics-volume-2</a> ؛ ص 15 ، 18.</li>
</ol>

التمدد الحراري والإجهاد الحراري: حل المشكلات

<div style="direction:rtl">يتعرض جسر البوابة الذهبية في سان فرانسيسكو لدرجات حرارة تتراوح بين -15 درجة مئوية إلى 40 درجة مئوية. في أبرد حالاته، يبلغ طول الجسر الرئيسي 1275 مترًا. بافتراض أن الجسر مصنوع بالكامل من الفولاذ، ما التغير في طوله بين درجتي الحرارة؟ لحل المشكلة يجب أولا تحديد الكميات المعروفة وغير المعروفة. الطول الأولي (L) للجسر هو 1275 م، ومعامل التمدد الخطي (α) للصلب هو 12 × 10-6/°C، والتغير في درجة الحرارة (ΔT) هو 55 درجة مئوية. تذكر أن التمدد الحراري هو تمدد المادة مع زيادة درجة حرارتها. التمدد الخطي هو التغير في طول المادة عن طريق تطبيق درجة الحرارة، ويتناسب مع الطول الأولي والتغير في درجة الحرارة. ثابت التناسب هو معامل التمدد الخطي. استخدام معادلة التمدد الحراري الخطي لحساب التغير في الطول ΔL <img alt="Equation1" src="/files/ftp_upload/14164/14164_equation_2v2.svg" style="text-align: center; height: 16px;"> تعويض جميع القيم المعروفة في المعادلة لإيجاد التغير في الطول ΔL <img alt="Equation2" src="/files/ftp_upload/14164/14164_equation_2.svg" style="text-align: center; height: 20px;"> تبين أن التغير في طول جسر البوابة الذهبية يبلغ 0.84 م. وعلى الرغم من أن هذا التغيير في الطول ليس كبيرًا مقارنة بطول الجسر، إلا أنه يمكن ملاحظته. وينتشر بشكل عام على العديد من فواصل التمدد بحيث يكون التمدد عند كل مفصل صغيراً. علاوة على ذلك، إذا تم تغيير درجة حرارة جسم ما مع منعه من التمدد أو الانكماش، فإن الجسم يتعرض للإجهاد الحراري. لحساب الإجهاد الحراري في جسم حيث يتم تثبيت كلا الطرفين بشكل صارم، يمكن اعتبار الإجهاد يتطور في خطوتين. أولاً، دع الأطراف تكون حرة في التمدد أو الانقباض وإيجاد التمدد أو الانكماش. ثانيًا، أوجد الضغط اللازم لضغط الجسم أو تمديده إلى طوله الأصلي من خلال الطرق التي تمت دراستها في التوازن الساكن والمرونة على مرونة التوازن الساكن. بمعنى آخر، ΔL للتمدد الحراري يساوي ΔL للتشوه المرن، باستثناء أن الإشارات متقابلة.</div>

يتعرض جسر البوابة الذهبية في سان فرانسيسكو لدرجات حرارة تتراوح من -15 درجة مئوية إلى 40 درجة مئوية. في أبرد حالاته ، يكون الامتداد الرئيسي للجسر ...

Education

JoVE Core

Physics

الفيزياء

Unit 1

الوحدة الأولى

Temperature and Heat

درجة الحرارة والحرارة

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

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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Heat and temperature are key ideas in thermodynamics and in everyday life. People often connect temperature with hot and cold, but science gives it a more precise meaning. Temperature is the quantity measured with a thermometer. It is also linked to the average translational kinetic energy of particles. Heat is different from temperature. Heat is energy that moves from one place or material to another because there is a difference in temperature. That difference in temperature keeps heat...

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thermal stress

How Temperature Changes Create Stress

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...

heat flow and specific heat

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calorimetry

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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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